EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-PBC-REPORT-2018-007

Physics Beyond Colliders at CERN

Beyond the Standard Model Working Group Report

J. Beacham1, C. Burrage2,∗, D. Curtin3, A. De Roeck4, J. Evans5, J. L. Feng6,
C. Gatto7, S. Gninenko8, A. Hartin9, I. Irastorza10, J. Jaeckel11, K.
Jungmann12,∗, K. Kirch13,∗, F. Kling6, S. Knapen14, M. Lamont4, G.
Lanfranchi4,15,∗,∗∗, C. Lazzeroni16, A. Lindner17, F. Martinez-Vidal18, M.
Moulson15, N. Neri19, M. Papucci4,20, I. Pedraza21, K. Petridis22, M.
Pospelov23,∗, A. Rozanov24,∗, G. Ruoso25,∗, P. Schuster26, Y. Semertzidis27,
T. Spadaro15, C. Vallée24, and G. Wilkinson28.

Abstract: The Physics Beyond Colliders initiative is an exploratory study
aimed at exploiting the full scientific potential of the CERN’s accelerator
complex and scientific infrastructures through projects complementary to the
LHC and other possible future colliders. These projects will target
fundamental physics questions in modern particle physics. This document
presents the status of the proposals presented in the framework of the Beyond
Standard Model physics working group, and explore their physics reach and the
impact that CERN could have in the next 10-20 years on the international
landscape.

∗ PBC-BSM Coordinators and Editors of this Report
∗∗ Corresponding Author<EMAIL_ADDRESS>

1 Ohio State University, Columbus OH, United States of America
2 University of Nottingham, Nottingham, United Kingdom
3 Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7
Canada
4 European Organization for Nuclear Research (CERN), Geneva, Switzerland
5 Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA
6 Department of Physics and Astronomy, University of California, Irvine, CA
92697-4575, USA
7 Sezione di Napoli, INFN, Napoli (Italy) and Northern Illinois University
(US)
8 Institute for Nuclear Research of the Russian Academy of Sciences, 117312
Moscow, Russia
9 University College London, Gower Street, London WC1E 6BT, UK
10 Grupo de Física Nuclear y Altas Energías, Universidad de Zaragoza,
Zaragoza, Spain
11 Theory Institute of University of Heidelberg, Heidelberg, Germany
12 VSI (Van Swinderen Institute), University of Groningen, Groningen, the
Netherlands
13 ETH Zurich and Paul Scherrer Institute, Villigen, Switzerland
14 Institute for Advanced Study, Princeton, NJ, USA
15 Laboratori Nazionali di Frascati, INFN, Frascati (Rome), Italy
16 University of Birmingham, Birmingham, United Kingdom
17 DESY, Hamburg, Germany
18 IFIC/University of Valencia-CSIC, Valencia, Spain
19 NFN Sezione di Milano and Università di Milano, Milano, Italy
20 Lawrence Berkeley National Laboratory and UC Berkeley, Berkeley, CA
21 Benemerita Universidad Autonoma de Puebla, Mexico
22 University of Bristol, Bristol, United Kingdom
23 Perimeter Institute, Waterloo and University of Victoria, Victoria, Canada
24 CPPM, CNRS-IN2P3 and Aix-Marseille University, Marseille, France
25 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
26 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
27 KAIST/IBS, Daejeon, Korea
28 University of Oxford, Oxford, UK

###### Contents

  1. 1 Introduction
  2. 2 Physics Motivations
    1. 2.1 Hidden Sector portals
      1. 2.1.1 Vector portal models
      2. 2.1.2 Scalar portal models
      3. 2.1.3 Neutrino portal models
      4. 2.1.4 Axion portal models
  3. 3 Experiments proposed in the PBC context
  4. 4 Proposals sensitive to New Physics in the sub-eV mass range
    1. 4.1 Solar axions helioscopes: IAXO
    2. 4.2 Laboratory experiments: JURA
  5. 5 Proposals sensitive to New Physics in the MeV-GeV mass range
    1. 5.1 Proposals at the PS beam lines
      1. 5.1.1 REDTOP
    2. 5.2 Proposals at the SPS beam lines
      1. 5.2.1 NA64++
      2. 5.2.2 NA62++
      3. 5.2.3 LDMX @ eSPS
      4. 5.2.4 AWAKE
      5. 5.2.5 KLEVER
      6. 5.2.6 SHiP @ BDF
    3. 5.3 Proposals at the LHC interaction points
      1. 5.3.1 FASER
      2. 5.3.2 MATHUSLA
      3. 5.3.3 CODEX-b
  6. 6 Proposals sensitive to New Physics in the multi-TeV mass range
    1. 6.1 KLEVER
    2. 6.2 TauFV
    3. 6.3 CPEDM and LHC-FT
  7. 7 Physics reach of PBC projects
  8. 8 Physics reach of PBC projects in the sub-eV mass range
    1. 8.1 Axion portal with photon dominance (BC9)
  9. 9 Physics reach of PBC projects in the MeV-GeV mass range
    1. 9.1 Vector Portal
      1. 9.1.1 Minimal Dark Photon model (BC1)
      2. 9.1.2 Dark Photon decaying to invisible final states (BC2)
      3. 9.1.3 Milli-charged particles (BC3)
    2. 9.2 Scalar Portal
      1. 9.2.1 Dark scalar mixing with the Higgs (BC4 and BC5)
    3. 9.3 Neutrino Portal
      1. 9.3.1 Neutrino portal with electron-flavor dominance (BC6)
      2. 9.3.2 Neutrino portal with muon-flavor dominance (BC7)
      3. 9.3.3 Neutrino portal with tau-flavor dominance (BC8)
    4. 9.4 Axion Portal
      1. 9.4.1 Axion portal with photon-coupling (BC9)
      2. 9.4.2 Axion portal with fermion-coupling (BC10)
      3. 9.4.3 Axion portal with gluon-coupling (BC11)
  10. 10 Physics reach of PBC projects in the multi-TeV mass range
    1. 10.1 Measurement of EDMs as probe of NP in the multi TeV scale
    2. 10.2 Experiments sensitive to Flavour Violation
    3. 10.3 $B$ physics anomalies and $BR(K\to\pi\nu\bar{\nu})$
  11. 11 Conclusions and Outlook
  12. A ALPS: prescription for treating the FCNC processes
  13. B ALPs: production via $\pi^{0},\eta,\eta^{\prime}$ mixing

Executive Summary

The main goal of this document follows very closely the mandate of the Physics
Beyond Colliders (PBC) study group, and is “an exploratory study aimed at
exploiting the full scientific potential of CERN’s accelerator complex and its
scientific infrastructure through projects complementary to the LHC, HL-LHC
and other possible future colliders. These projects would target fundamental
physics questions that are similar in spirit to those addressed by high-energy
colliders, but that require different types of beams and experiments111See
https://pbc.web.cern.ch ”.

Fundamental questions in modern particle physics as the origin of the neutrino
masses and oscillations, the nature of Dark Matter and the explanation of the
mechanism that drives the baryogenesis are still open today and do require an
answer.

So far an unambiguous signal of New Physics (NP) from direct searches at the
Large Hadron Collider (LHC), indirect searches in flavour physics and direct
detection Dark Matter experiments is absent. Moreover, theory provides no
clear guidance on the NP scale. This imposes today, more than ever, a
broadening of the experimental effort in the quest for NP. We need to explore
different ranges of interaction strengths and masses with respect to what is
already covered by existing or planned initiatives.

Low-mass and very-weakly coupled particles represent an attractive
possibility, theoretically and phenomenologically well motivated, but
currently poorly explored: a systematic investigation should be pursued in the
next decades both at accelerator-based experiments and with proposals aiming
at detecting axions and axion-like particles with terrestrial experiments.

Very high energy scales ($\sim 100$ TeV) will never be directly reachable with
colliders that exist now or in any foreseeable future and can be explored only
using extremely rare or forbidden decays as probe to the NP in the multi-TeV
range. Electric dipole moments are simultaneously probes of NP in the
extremely low ($<10^{-15}$ eV) and in the very large ($>100$ TeV) mass scale
range.

The CERN laboratory could offer an unprecendented variety of high-intensity,
high-energy beams and scientific infrastructures that could be exploited to
this endevour. This effort would nicely complement and further broaden the
already rich physics programme ongoing at the LHC and HL-LHC.

This document presents the status of the proposals presented in the framework
of the PBC Beyond the Standard Model (BSM) physics working group, and explore
their physics reach and the consequent impact that CERN could have in the next
10-20 years on the international landscape.

##  1 Introduction

The Physics Beyond Colliders BSM study group has considered about 15 different
proposals aiming at exploiting the CERN accelerator complex and scientific
infrastructure. These proposals will be sensitive to New Physics in a range of
masses and couplings unaccessible to other existing or planned initiatives in
the world, as the experiments at the Large Hadron Collider (LHC) or at a
Future Circular Collider (FCC), Dark Matter (DM) direct detection experiments
and flavor physics initiatives.

This document focusses on the searches for Physics Beyond the Standard Model
(BSM) also known as NP. It introduces the physics motivations and the
complementarity of the proposals presented within the PBC-BSM activity with
respect to the LHC and other initiatives in the world in the quest for NP. NP
is required to answer open questions in modern particle physics, as the origin
of the neutrinos masses and oscillations, the baryogenesis and the nature of
Dark Matter. A viable possibility is so called hidden sector physics, that
comprises new particles with masses below the electro-weak (EW) scale that
couple very weakly to the Standard Model (SM) world via portals. Another
viable possibility is that NP is well above the EW scale (and therefore well
beyond the direct reach of the LHC and any other future high-energy collider),
and can be only probed via indirect effects in extremely rare or forbidden
processes in the SM or by testing the presence of electric dipole moments
(EDMs) either in elementary particles (such as proton and deuteron) or in more
complex systems.

Three main categories of experiments have been identified, following the NP
mass range they are sensitive to:

  * -

experiments sensitive to NP with mass in the sub-eV range and very weakly
coupled to SM particles: these are mostly experiments searching for axions and
axion-like particles using a large variety of experimental techniques;

  * -

experiments sensitive to NP with mass in the MeV-GeV range and very weakly
coupled to SM particles: these are accelerator-based experiments that could
exploit the large variety of high-intensity high-energy beams currently
available or proposed at CERN;

  * -

experiments sensitive to NP with mass in the multi-TeV range and strongly
coupled to SM particles: these are experiments searching for extremely rare or
forbidden processes, that could be produced via high-intensity beams.

The document is organized as follows. Section 2 presents a brief summary of
the main physics motivations. In particular in Section 2.1 it discusses in
detail portals to a hidden sector along with a set of benchmark cases that
have been identified as theoretically and phenomenologically motivated target
areas to explore the physics reach of the PBC proposals and put them in the
world wide landscape. The proposals presented in the framework of the PBC-BSM
study group are briefly described in Section 3 and classified in terms of
their sensitivity to a given mass range and to a set of benchmark cases. A
more detailed description is then given in Sections 4-6 ordered along the
identified main mass ranges. The physics reach of the PBC-BSM proposals is
shown in Sections 7-10 along with the current status of these searches at
ongoing and/or planned initiatives in the world that are or will be important
players on the same timescale of the PBC proposals. Brief conclusions are
drawn in Section 11.

##  2 Physics Motivations

With the discovery at the LHC of the Higgs boson Aad:2012tfa ;
Chatrchyan:2012xdj , the last missing piece for the experimental validation of
the SM is now in place. An additional LHC result of great importance is that a
large new territory has been explored and no unambiguous signal of NP has been
found so far. These results, together with several constraints from flavor
phenomenology and the absence of any charged lepton flavour violation process,
indicate that there might be no NP with a direct and sizeable coupling to SM
particles up to energies $\sim 10^{5}$ TeV unless specific flavour
structures/symmetries are postulated.

The possibility that the SM holds well beyond the electroweak (EW) scale must
now seriously considered. The SM theory is renormalizable and predictive and
the measured masses of the Higgs boson and the top quark fall into a narrow
region of parameters where consistency of the SM does not require new
particles up to a very high energy scale, possibly all the way up to the
Planck scale Degrassi:2012ry ; Buttazzo:2013uya ; Bezrukov:2012sa . However
some yet unknown particles or interactions are required to explain a number of
observed phenomena in particle physics, astrophysics, and cosmology as the
neutrino masses and oscillations, the baryon asymmetry of the universe, the
Dark Matter (DM) and the cosmological inflation.

  * -

Neutrino oscillations
Propagating neutrinos have been seen to oscillate between different flavours.
This implies the existence of a neutrino mass matrix which differentiates the
flavour eigenstates from the mass eigenstates. This is absent in the SM. It
is, additionally, challenging to explain why the observed neutrino masses are
so much smaller than the masses of other leptons. One common mechanism to
generate such a mass matrix is the, so called, seesaw mechanism, which
introduces one or more heavy sterile neutrinos. This heavy mass scale,
combined with the SM scales, allows for the generation of very light mass
eigenstates for the electroweak neutrinos. Estimates for the mass of these
additional neutrinos range from $10^{-9}-10^{15}\leavevmode\nobreak\ \mbox{
GeV}$.

  * -

Abundance of matter, absence of anti-matter
All of the structure that we see in the universe is made of matter, and there
is very little indication of the presence of significant amounts of anti-
matter.

The dominance of matter over not anti-matter can be explained by processes in
the early universe violating $B$-number conservation, as well as $C$ and $CP$
symmetries, and occuring out of equilibrium. These Sakharov conditions
Sakharov:1967dj  are necessary to generate the baryon asymmetry when assuming
symmetric initial conditions and $CPT$ conservation. Neither the
$CP$-violation nor the out-of-equilibrium condition can be accomodated without
extending the SM in some way. In particular our new understanding of the Higgs
mechanism means that we now know that the electroweak phase transition is not
a strong first order transition, and so cannot be the explanation for the
asymmetry between matter and antimatter that we see in the present universe
222An alternative model assumes $CPT$ and $B$-number violation. It could
create a matter anti-matter asymmetry in thermal equilibrium Coleman:1998ti ;
Jackiw:1999yp . An active field with a multitude of experimental searches for
$CPT$ violating processes exists worldwide, among which leading activities are
located at the CERN AD facility. They have yielded many tight bounds already
on Lorentz and $CPT$ violation Kostelecky:2008ts ..

  * -

Dark Matter
Evidence that the particles of the SM are not abundant enough to account for
all of the matter in the universe comes from a multitude of galactic and
cosmological observations. Two key observations are galactic dynamics and the
Cosmic Microwave Background (CMB). The stability of spiral galaxies, and their
observed rotation curves require an additional (cold) matter component to be
clustered on galactic scale. This additional component contains a significant
fraction of the total mass of the galaxy and has a greater spatial extent than
the visible galactic matter. Observations of the CMB tell us about the average
properties of the universe that these microwave photons have passed through
since the epoch of decoupling. Again this tells us that, on average, SM matter
can only account for approximately 5% of the universe that we see, and that
there is an additional $25\%$ of our current universe which appears to be cold
and dark non-relativistic matter.

There are many proposed models of DM which would be compatible with these
observations, ranging from ultra-light scalars with masses
$10^{-31}\mbox{GeV}$ to a distribution of black holes with masses up to 10
$M_{\rm sun}$, being $M_{\rm sun}$ the mass of the sun.

  * -

Cosmological inflation and dark energy
Additionally, observations of the CMB indicate that our universe began with a
period of exponential inflation, and is currently undergoing a second period
of accelerated expansion. No explanation for either of these periods of the
universe’s evolution exists within the SM.

In addition to the evidence described above there are a number of other hints
that physics beyond the SM is required. These are typically unusually large
fine tunings of parameters which are challenging to explain within the SM
framework. These should not be taken to have the same status, regarding
motivating NP, as the observational evidence described above, but rather as
possible sign posts to parts of the model which are not yet fully understood.

  * -

Higgs mass fine tuning
The Higgs boson is the only scalar field present in the SM. In contrast to the
other particles we observe, it is not understood how to protect the mass of
the scalar Higgs field from quantum corrections driving it to a much higher
scale without a high degree of fine tuning. Possible solutions to this problem
include low-scale supersymmetry, the existence of extra spatial dimensions,
and dynamical relaxation mechanisms.

  * -

Strong CP problem
There is no reason to expect that the strong sector of the SM would respect
$CP$ symmetry. Without a large degree of fine tuning, this level of $CP$
violation would produce an electric dipole moment for the neutron at an
observable level. Unlike the other fine tuning problems we discuss here, it is
not even possible to make an anthropic argument for why the degree of $CP$
violation in the strong sector should be unobservably small.

The most common explanation for this degree of fine tuning, is the
introduction of a pseudo scalar field, the axion, which dynamically relaxes
the degree of $CP$ violation to small values. With an appropriately chosen
mass the axion may also make up all or part of the DM in our universe.

  * -

Cosmological constant and dark energy
As mentioned above, the CMB combined with other cosmological observations, in
particular of Type 1a supernovae, indicates that approximately $70\%$ of the
energy density in our current universe is due to a cosmological constant, or
something that behaves very similarly. A cosmological constant term in the
Einstein equations is naturally generated by quantum fluctuations of the
vacuum, but unfortunately this is many orders of magnitude too large to be
compatible with cosmological observations. Explaining why such a large
cosmological constant is not seen typically requires a significant amount of
fine tuning.

There is a vast landscape of theoretical models to address some, or all, of
the above mentioned motivations for NP. This often involves introducing new
particles which can be bosons or fermions, heavy or light, depending on the
theory and the problems it addresses. There are theories that aim to make the
most minimal modification possible to the SM, whilst still addressing all of
the motivations for new physics that we have described here, as well as model
independent approaches, which try to parametrize all of the possible ways
certain types of new physics could extend the SM. Here we will outline the
most popular classes of current theoretical ideas for BSM physics.

  * -

New physics at the TeV scale and beyond
If there is an intermediate scale between the EW and the Planck scale, it is
necessary to introduce a mechanism to protect the Higgs mass from receiving
large quantum corrections. The most commonly studied possibility, by far, is
the introduction of supersymmetry. No compelling hints for supersymmetry have
yet been seen at the LHC, which suggests that, if this symmetry is realized in
nature, it may only be restored at an energy scale much higher than can
currently be reached with collider experiments. We will see that precision
measurements, such as Kaon physics, $B$ physics, and EDM measurements, can
indirectly search for NP at a much higher scale than can be directly probed
with the LHC or any future high-energy collider.

  * -

Right handed neutrinos
The introduction of right handed is motivated by explanations of neutrino
masses, in particular their smallness via the see-saw mechanism. However, it
can also be a useful ingredient for generating baryon asymmetry via
leptogenesis. If the new neutrino masses are at the GeV scale, they could also
generate this asymmetry directly through baryogenesis. The introduction of
such right handed neutrinos can generate $CP$ violation, but as yet the scale
at which this happens is not constrained, if it lies near the electroweak
scale it could lead to observable EDMs. The masses of the neutrinos can lie
anywhere from the GUT scale down to $\sim$100 MeV.

A viable example including right-handed neutrinos is the Neutrino Minimal
Standard Model ($\nu$MSM) Asaka:2005an ; Asaka:2005pn  which accounts for
neutrino masses and oscillations, for the evidence of DM and for the baryon
asymmetry of the Universe. This model adds to the SM only three right-handed
singlet sterile neutrinos or Heavy Neutral Leptons (HNLs), one with a mass in
the keV range that acts as DM candidate and the other two with a mass in the
GeV range and Yukawa couplings in the range $10^{-11}-10^{-6}$.

  * -

WIMP dark matter models
The idea that the DM is a thermal relic from the hot early universe motivates
non-gravitational interactions between dark and ordinary matter. The canonical
example involves a heavy particle with mass between 100-1000 GeV interacting
through the weak force (WIMPs), but so far no WIMP has been observed. However
a thermal origin is equally compelling even if DM is not a WIMP: DM with any
mass from a MeV to tens of TeV can achieve the correct relic abundance by
annihilating directly into SM matter. Thermal DM in the MeV-GeV range with SM
interactions is overproduced in the early Universe so viable scenarios require
additional SM neutral mediators to deplete the overabundance Lee:1977ua ;
Boehm:2002yz ; Boehm:2003hm ; Pospelov:2007mp ; Feng:2008ya ; Feng:2008mu ;
Pospelov:2008zw ; ArkaniHamed:2008qn ; Pospelov:2008jd . The sub-GeV range for
the dark matter mediators can additionally provide a solution to some
outstanding cosmological puzzles including an explanation of why the mass
distribution at the center of a galaxy is smoother than expected.

  * -

Axion dark matter models
Axions are another well motivated DM candidate, that may simultaneously solve
the $CP$ problems of QCD. Axion DM particles are sufficiently light that they
must be produced non-thermally through a gravitational, or misalignment
production mechanism. Alternatively axions may be heavy and thermally produced
in the early universe. The minimal axion model relates the mass and coupling
constant of the axion. If this condition is relaxed the theory can be
generalized to one of axion-like-particles (ALPs) and such a generalization
may also be motivated from string theory. The search for axions and ALPs in
the sub-eV mass range comprises a plethora of different experimental
techniques and experiments as haloscopes, solar helioscopes and pure
laboratory experiments among which, for example, regeneration or light-
shining-through a wall (LSW) experiments. ALPs with masses in the MeV-GeV
range can be produced, and possibly detected, at accelerator-based
experiments.

So far the experimental efforts have been concentrated on the discovery of new
particles with masses at or above the EW scale with sizeable couplings with SM
particles. Another viable possibility, largely unexplored, is that particles
responsible of the still unexplained phenomena beyond the SM are below the EW
scale and have not been detected because they interact very feebly with the SM
particles. Such particles are thought to be linked to the so called hidden
sector. Given the exceptionally low-couplings, a high intensity source is
necessary to produce them at a detectable rate: this can be astrophysical
sources, or powerful lasers, or high-intensity accelerator beams. The search
for NP in the low-mass and very low coupling regime at accelerator beams is
what is currently called the intensity frontier.

Hidden Sector particles and mediators to the SM can be light and long-lived.
They interact very weakly with SM fields that do not carry electromagnetic
charge, like the Higgs and the $Z^{0}$ bosons, the photon and the neutrinos.
They are singlet states under the SM gauge interactions and the couplings
between the SM and hidden-sector particles arise via mixing of the hidden-
sector field with a SM “portal” operator. In the following Section we will
present the generic framework for hidden sector portals along with a set of
specific benchmark cases that will be used in this document to compare the
physics reach of a large fraction of proposals presented within this study.

###  2.1 Hidden Sector portals

The main framework for the BSM models, the so-called portal framework, is
given by the following generic setup (see e.g. Refs. Patt:2006fw ;
Batell:2009di ; Alekhin:2015byh ). Let $O_{\rm SM}$ be an operator composed
from the SM fields, and $O_{\rm DS}$ is a corresponding counterpart composed
from the dark sector fields. Then the portal framework combines them into an
interaction Lagrangian,

${\cal L}_{\rm portal}=\sum O_{\rm SM}\times O_{\rm DS}.$ (1)

The sum goes over a variety of possible operators and of different composition
and dimension. The lowest dimensional renormalisable portals in the SM can be
classified into the following types:

Portal | Coupling
---|---
Dark Photon, $A_{\mu}$ | $-\tfrac{\epsilon}{2\cos\theta_{W}}F^{\prime}_{\mu\nu}B^{\mu\nu}$
Dark Higgs, $S$ | $(\mu S+\lambda S^{2})H^{\dagger}H$
Axion, $a$ |  $\tfrac{a}{f_{a}}F_{\mu\nu}\tilde{F}^{\mu\nu}$, $\tfrac{a}{f_{a}}G_{i,\mu\nu}\tilde{G}^{\mu\nu}_{i}$, ${\partial_{\mu}a\over f_{a}}\overline{\psi}\gamma^{\mu}\gamma^{5}\psi$
Sterile Neutrino, $N$ | $y_{N}LHN$

Here, $F^{\prime}_{\mu\nu}$ is the field strength for the dark photon, which
couples to the hypercharge field, $B^{\mu\nu}$; $S$ is a new scalar singlet
that couples to the Higgs doublet, $H$, with dimensionless and dimensional
couplings, $\lambda$ and $\mu$; $a$ is a pseudoscalar axion that couples to a
dimension-4 diphoton, di-fermion or digluon operator; and $N$ is a new neutral
fermion that couples to one of the left-handed doublets of the SM and the
Higgs field with a Yukawa coupling $y_{N}$.

According to the general logic of quantum field theory, the lowest canonical
dimension operators are the most important. All of the portal operators
respect all of the SM gauge symmetries. Even the global symmetries are kept in
tact with the only exception being the (accidental) lepton number conservation
if the HNL is Majorana. The kinetic mixing and $S^{2}H^{\dagger}H$ operators
are generically generated at loop level unless targeted symmetries are
introduced to forbid them333E.g. a $Z_{2}$ symmetry for the hidden photon
field..

The PBC-BSM working group has identified the main benchmark physics cases,
presented the corresponding Lagrangians, and defined the parameter space to be
examined in connection with experimental sensitivities. In the subsequent
Sections, we formulate the benchmark models in some detail.

####  2.1.1 Vector portal models

A large class of BSM models includes interactions with light new vector
particles. Such particles could result from extra gauge symmetries of BSM
physics. New vector states can mediate interactions both with the SM fields,
and extra fields in the dark sector that e.g. may represent the DM states.

The most minimal vector portal interaction can be written as

${\cal L}_{\rm vector}={\cal L}_{\rm SM}+{\cal L}_{\rm
DS}-\frac{\epsilon}{2\cos\theta_{W}}F^{\prime}_{\mu\nu}B_{\mu\nu},$ (2)

where ${\cal L}_{\rm SM}$ is the SM Lagrangian, $B_{\mu\nu}$ and
$F^{\prime}_{\mu\nu}$ are the field stengths of hypercharge and new
$U(1)^{\prime}$ gauge groups, $\epsilon$ is the so-called kinetic mixing
parameter Holdom:1985ag , and ${\cal L}_{\rm DS}$ stands for the dark sector
Lagrangian that may include new matter fields $\chi$ charged under
$U^{\prime}(1)$,

${\cal L}_{\rm
DS}=-\frac{1}{4}(F^{\prime}_{\mu\nu})^{2}+\frac{1}{2}m_{A^{\prime}}^{2}(A^{\prime}_{\mu})^{2}+|(\partial_{\mu}+ig_{D}A^{\prime}_{\mu})\chi|^{2}+...$
(3)

If $\chi$ is stable or long-lived it may constitute a fraction of entirety of
dark matter. At low energy this theory contains a new massive vector particle,
a dark photon state, coupled to the electromagnetic current with
$\epsilon$-proportional strength, $A^{\prime}_{\mu}\times\epsilon
J^{\mu}_{EM}$.

We define the following important benchmark cases (BC1-BC3) for the vector
portal models.

  * •

BC1, Minimal dark photon model: in this case the SM is augmented by a single
new state $A^{\prime}$. DM is assumed to be either heavy or contained in a
different sector. In that case, once produced, the dark photon decays back to
the SM states. The parameter space of this model is then
$\\{m_{A^{\prime}},\epsilon\\}$.

  * •

BC2, Light dark matter coupled to dark photon: this is the model where
minimally coupled viable WIMP dark matter model can be constructed
Boehm:2003hm ; Pospelov:2007mp . The preferred values of dark coupling
$\alpha_{D}=g_{D}^{2}/(4\pi)$ are such that the decay of $A^{\prime}$ occurs
predominantly into $\chi\chi^{*}$ states. These states can further rescatter
on electrons and nuclei due to $\epsilon$-proportional interaction between SM
and DS states mediated by the mixed $AA^{\prime}$ propagator Batell:2009di ;
Izaguirre:2014dua .

The parameter space for this model is
$\\{m_{A^{\prime}},\epsilon,m_{\chi},\alpha_{D}\\}$ with further model-
dependence associated with properties of $\chi$ (boson or fermion). The
suggested choices for the PBC evaluation are 1\. $\epsilon$ vs
$m_{A^{\prime}}$ with $\alpha_{D}\gg\epsilon^{2}\alpha$ and
$2m_{\chi}<m_{A^{\prime}}$, 2. $y$ vs. $m_{\chi}$ plot where the yield
variable $y$, $y=\alpha_{D}\epsilon^{2}(m_{\chi}/m_{A^{\prime}})^{4}$, is
argued Izaguirre:2015yja  to contain a combination of parameters relevant for
the freeze-out and DM-SM particles scattering cross section. One possible
choice is $\alpha_{D}=0.1$ and $m_{A^{\prime}}/m_{\chi}=3$.

  * •

BC3, Millicharged particles: this is the limit of $m_{A^{\prime}}\to 0$, in
which case $\chi$ of $\bar{\chi}$ have an effective electric charge of
$|Q_{\chi}|=|\epsilon g_{D}e|$ Holdom:1985ag ; Jaeckel:2010ni . The suggested
choice of parameter space is $\\{m_{\chi},Q_{\chi}/e\\}$, and $\chi$ can be
taken to be a fermion.

The kinetic mixing coupling of $A^{\prime}$ to matter is the simplest and most
generic, but not the only possible vector portal. Other cases considered in
the literature include gauged $B-L$ and $L_{\mu}-L_{\tau}$ models, and
somewhat less motivated leptophylic and leptophobic cases, when $A^{\prime}$
is assumed to be coupled to either total lepton current, or total baryon
current with a small coupling $g^{\prime}$.

Such other exotic vector mesons however, generically mix with the SM photon at
one loop, which is often enhanced by the number of flavors and/or colors of
the quarks/leptons running in the loop. This means that the kinetically mixed
dark photon benchmarks outlined above also cover these scenarios, to some
extent.

####  2.1.2 Scalar portal models

The 2012 discovery of the BEH mechanism, and the Higgs boson $h$, prompts to
investigate the so called scalar or Higgs portal, that couples the dark sector
to the Higgs boson via the bilinear $H^{\dagger}H$ operator of the SM. The
minimal scalar portal model operates with one extra singlet field $S$ and two
types of couplings, $\mu$ and $\lambda$ OConnell:2006rsp ,

${\cal L}_{\rm scalar}={\cal L}_{\rm SM}+{\cal L}_{\rm DS}-(\mu S+\lambda
S^{2})H^{\dagger}H.$ (4)

The dark sector Lagrangian may include the interaction with dark matter
$\chi$, ${\cal L}_{\rm DS}=S\bar{\chi}\chi+...$. Most viable dark matter
models in the sub-EW scale range imply $2\cdot m_{\chi}>m_{S}$ Krnjaic:2015mbs
.

At low energy, the Higgs field can be substituted for $H=(v+h)/\sqrt{2}$,
where $v=246$ GeV is the the EW vacuum expectation value, and $h$ is the field
corresponding to the physical 125 GeV Higgs boson. The non-zero $\mu$ leads to
the mixing of $h$ and $S$ states. In the limit of small mixing it can be
written as

$\theta=\frac{\mu v}{m_{h}^{2}-m_{S}^{2}}.$ (5)

Therefore the linear coupling of $S$ to SM particles can be written as
$\theta_{S}\times\sum_{\rm SM}O_{h}$, where $O_{h}$ is a SM operator to which
Higgs boson is coupled and the the sum goes over all type of SM operators
coupled to the Higgs field.

The coupling constant $\lambda$ leads to the coupling of $h$ to a pair of $S$
particles, $\lambda S^{2}$. It can lead to pair-production of $S$ but cannot
induce its decay. An important property of the scalar portal is that at loop
level it can induce flavour-changing transitions, and in particular lead to
decays $K\to\pi S$, $B\to K^{(*)}S$ etc OConnell:2006rsp ; Batell:2009jf ;
Bezrukov:2009yw  and similarly for the $hS^{2}$ coupling Bird:2004ts . We
define the following benchmark cases for the scalar portal models:

  * •

BC4, Higgs-mixed scalar:  in this model we assume $\lambda=0$, and all
production and decay are controlled by the same parameter $\theta$. Therefore,
the parameter space for this model is $\\{\theta,m_{S}\\}$.

  * •

BC5, Higgs-mixed scalar with large pair-production channel:  in this model the
parameter space is $\\{\lambda,\theta,m_{S}\\}$, and $\lambda$ is assumed to
dominate the production via e.g. $h\to SS$, $B\to K^{(*)}SS$, $B^{0}\to SS$
etc. In the sensitivity plots shown in Section 9.2 a value of the branching
fraction $BR({h\to SS})$ close to $10^{-2}$ is assumed in order to be
complementary to the LHC searches for the Higgs to invisible channels.

We also note that while the 125 GeV Higgs-like resonance has properties of the
SM Higgs boson within errors, the structure of the Higgs sector can be more
complicated and include e.g. several scalar doublets. In the two-Higgs doublet
model the number of possible couplings grows by a factor of three, as $S$ can
couple to 3 combinations of Higgs field bilinears, $H_{1}^{\dagger}H_{1}$,
$H_{2}^{\dagger}H_{2}$ and $H_{1}H_{2}$. Therefore, the experiments could
investigate their sensitivity to a more complicated set of the Higgs portal
couplings that are anyhow beyond the present document.

####  2.1.3 Neutrino portal models

The neutrino portal extension of the SM is very motivated by the fact that it
can be tightly related with the neutrino mass generation mechanism. The
neutrino portal operates with one or several dark fermions $N$, that can be
also called heavy neutral leptons or HNLs. The general form of the neutrino
portal can be written as

${\cal L}_{\rm vector}={\cal L}_{\rm SM}+{\cal L}_{\rm DS}+\sum F_{\alpha
I}(\bar{L}_{\alpha}H)N_{I}$ (6)

where the summation goes over the flavour of lepton doublets $L_{\alpha}$, and
the number of available HNLs, $N_{I}$. The $F_{\alpha I}$ are the
corresponding Yukawa couplings. The dark sector Lagrangian should include the
mass terms for HNLs, that can be both Majorana or Dirac type. For a more
extended review, see Ref. Gorbunov:2007ak ; Alekhin:2015byh . Setting the
Higgs field to its v.e.v., and diagonalizing mass terms for neutral fermions,
one arrives at $\nu_{i}-N_{J}$ mixing, that is usually parametrized by a
matrix called $U$. Therefore, in order to obtain interactions of HNLs, inside
the SM interaction terms, one can replace $\nu_{\alpha}\to\sum_{I}U_{\alpha
I}N_{I}$. In the minimal HNL models, both the production and decay of an HNL
are controlled by the elements of matrix $U$.

PBC has defined the following benchmark cases:

  * •

BC6, Single HNL, electron dominance: Assuming one Majorana HNL state $N$, and
the predominant mixing with electron neutrinos, all production and decay can
be determined as function of parameter space $(m_{N},|U_{e}|^{2})$.

  * •

BC7, Single HNL, muon dominance: Assuming one Majorana HNL state $N$, and the
predominant mixing with muon neutrinos, all production and decay can be
determined as function of parameter space $(m_{N},|U_{\mu}|^{2})$.

  * •

BC8, Single HNL, tau dominance: One Majorana HNL state with predominant mixing
to tau neutrinos. Parameter space is $(m_{N},|U_{\tau}|^{2})$.

These are representative cases which do not exhaust all possibilities.
Multiple HNL states, and presence of comparable couplings to different
flavours can be even more motivated than the above choices. The current choice
of benchmark cases is motivated by simplicity.

####  2.1.4 Axion portal models

QCD axions are an important idea in particle physics Peccei:1977hh ;
Weinberg:1977ma ; Wilczek:1977pj  that allows for a natural solution to the
strong CP problem, or apparent lack of CP violation in strong interactions.
Current QCD axion models are restricted to the sub-eV range of axions.
However, a generalization of the minimal model to axion-like particles (ALPs)
can be made Jaeckel:2010ni . Taking a single pseudoscalar field $a$ one can
write a set of its couplings to photons, quarks, leptons and other fields of
the SM. In principle, the set of possible couplings is very large and in this
study we consider only the flavour-diagonal subset,

${\cal L}_{\rm axion}={\cal L}_{\rm SM}+{\cal L}_{\rm
DS}+\frac{a}{4f_{\gamma}}F_{\mu\nu}\tilde{F}_{\mu\nu}+\frac{a}{4f_{G}}{\rm
Tr}G_{\mu\nu}\tilde{G}_{\mu\nu}+\frac{\partial_{\mu}a}{f_{l}}\sum_{\alpha}\bar{l}_{\alpha}\gamma_{\mu}\gamma_{5}l_{\alpha}+\frac{\partial_{\mu}a}{f_{q}}\sum_{\beta}\bar{q}_{\beta}\gamma_{\mu}\gamma_{5}q_{\beta}$
(7)

The DS Lagrangian may contain new states that provide UV completion to this
model (for the case of the QCD axion they are called the PQ sector). All of
these interactions do not lead to large additive renormalization of $m_{a}$,
making this model technically natural. Note, however, that the coupling to
gluons does lead to the non-perturbative contribution to $m_{a}$.

The PBC proposals have considered the following benchmark cases:

  * •

BC9, photon dominance: assuming a single ALP state $a$, and the predominant
coupling to photons, all phenomenology (production, decay, oscillation in the
magnetic field) can be determined as functions on
$\\{m_{a},g_{a\gamma\gamma}\\}$ parameter space, where
$g_{a\gamma\gamma}=f^{-1}_{\gamma}$ notation is used.

  * •

BC10, fermion dominance: assuming a single ALP state $a$, and the predominant
coupling to fermions, all phenomenology (production and decay) can be
determined as functions on $\\{m_{a},f^{-1}_{l},f^{-1}_{q}\\}$. Furthermore,
for the sake of simplicity, we take $f_{q}=f_{l}$.

  * •

BC11, gluon dominance:  this case assumes an ALP coupled to gluons. The
parameter space is $\\{m_{a},f^{-1}_{G}\\}$. Notice that in this case the
limit of $m_{a}<m_{a,QCD}|_{f_{a}=f_{G}}$ is unnatural as it requires fine
tuning and therefore is less motivated.

The ALP portals, $BC9-BC11$, are effective interactions, and would typically
require UV completion at or below $f_{i}$ scales. This is fundamentally
different from vector, scalar and neutrino portals that do not require
external UV completion. Moreover, the renormalization group (RG) evolution is
capable of inducing new couplings. All the sensitivity plots shown in Section
7 assume a cut-off scale of $\Lambda=1$ TeV. Details about approximations and
assumptions assumed in computing sensitivities for the BC10 and BC11 cases are
reported in Appendices A and B.

##  3 Experiments proposed in the PBC context

The PBC-BSM working group has considered about 15 different initiatives which
aim at exploiting the CERN accelerator complex and scientific infrastructure
with a new, broad and compelling physics programme that complement the quest
of NP at the TeV scale performed at the LHC or other initiatives in the world.
The proposals have been classified in terms of their sensitivity to NP in a
given mass range, as reported below.

  1. 1.

Sub-eV mass range
Axions and ALPs with gluon- and photon-coupling can have masses ranging from
$10^{-22}$ eV to $10^{9}$ eV. Axions and ALPs with gluon-coupling in the sub-
eV mass range can generate a non-zero oscillating electric dipole moment
(oEDM) in protons. The PBC proposal related to the study of oEDMs in protons
is CP-EDM.

The search for axions and ALPs with photon-coupling and mass in the sub-eV
range comprises a plethora of different experimental techniques and
experiments as haloscopes, solar helioscopes and pure laboratory experiments
among which, for example, regeneration or light-shining-through a wall (LSW)
experiments. Two experiments have been proposed in the framework of the PBC-
BSM study: the International AXion Observatory (IAXO) aims at searching
axions/ALPs coming from the sun by using the axion-photon coupling, and the
JURA experiment, considered as an upgrade of the ALPS II experiment, currently
under construction at DESY, and exploiting the LSW technique.

  2. 2.

MeV-GeV mass range
Heavy neutral leptons, ALPs, Light Dark Matter (LDM) and corresponding light
mediators (Dark Photons, Dark Scalars, etc.) could have masses in the MeV-GeV
range and can be searched for using the interactions of proton, electron and
muon beams available (or proposed) at the PS and SPS accelerator complex and
at the LHC interaction points. Ten proposals discussed in the PBC-BSM working
group are aiming to search for hidden sector physics in the MeV-GeV range and
are classified in terms of the accelerator complex they want to exploit:

     * -

PS extracted beam lines: REDTOP.

     * -

SPS extracted beam lines: NA62++ or NA62 in dump mode at the K12 line
currently used by the NA62 experiment; NA64${}^{++}(e)$ and NA64${}^{++}(\mu)$
proposed at the existing H4 and M2 lines of the CERN SPS; LDMX at a proposed
slow-extracted primary electrons line at the SPS; SHiP at the proposed Beam
Dump Facility (BDF) at the SPS, and AWAKE at the IP4 site of the SPS.

     * -

LHC interaction points: MATHUSLA, FASER, MilliQan, and CODEX-b at the
ATLAS/CMS, ATLAS, CMS and LHCb interaction points of the LHC, respectively.
These experiments probe New Physics from below the MeV to the TeV scale, but
their physics case is beyond the scope of this document. We focus on comparing
their reach to NP in the MeV-GeV range to the other proposals at the PS and
SPS lines.

  3. 3.

$>>$TeV mass range
The search for new particles at a very high mass scale is traditionally
performed by studying clean and very rare flavor processes, as for example
$K^{+}\to\pi^{+}\nu\overline{\nu}$ and $K_{\rm L}\to\pi^{0}\nu\overline{\nu}$
rare decays or lepton-flavor-violating (LFV) processes as $\tau\to 3\mu$. The
KLEVER project aims at measuring the branching fraction of the very rare and
clean decay $K_{L}\to\pi^{0}\nu\overline{\nu}$ using an upgraded P42/K12 line
at the SPS; TauFV is a fixed-target experiment proposed at the BDF to search
for the LFV decay $\tau\to 3\mu$ and other lepton-flavour-violating (LFV)
$\tau$ decays produced in the interactions of a primary high-energy proton
beam with an active target. Proposals searching for permanent EDMs in protons,
deuterons or charmed hadrons, can be also probe NP at the ${\mathcal{O}}$(100)
TeV scale, if the EDMs is originated by new sources of CP violation. PBC
proposals aiming at studying permanent EDM in proton and deuteron, and
EDMs/MDMs in charmed and strange hadrons are CPEDM and LHC-FT, respectively.

Table 1 summarizes the projects presented in the PBC-BSM study group framework
divided on the basis of their sensitivity of NP at a given mass scale, along
with their main physics cases and the characteristics of the required beam,
whenever is applicable.

The physics reach of the PBC BSM projects is schematically shown in Figure 1
in a generic plane of coupling versus mass, along with the parameter space
currently explored at the LHC: the PBC-BSM projects will be able to explore a
large variety of ranges of NP couplings and masses using very different
experimental techniques and are fully complementary to the exploration
currently performed at the high energy frontier and at Dark Matter direct
detection experiments.

Figure 1:  Schematic overview of the BSM landscape, based on a selection of
specific models, with a rough outline of the areas targeted by the PBC
experiments. The $x-$axis corresponds to the mass $m_{X}$ of the lightest BSM
state, and the $y-$axis to the scale of the effective new interaction
$f=M_{\rm Mediator}/g$, where $M_{\rm Mediator}$ is the mass of a heavy
mediator and $g$ its (dimensionless) coupling constant to the Standard Model.
The grey shaded area outlines the currently excluded regions for a class of
models corresponding to the benchmarks BC9 and BC11 (see Refs Abel:2017rtm ;
Jaeckel:2010ni ; Irastorza:2018dyq ).

Table 1: Projects considered in the PBC-BSM working group categorized in terms of their sensitivity to a set of benchmark models in a given mass range. The characteristics of the required beam lines, whenever applicable, are also displaied. Proposal | Main Physics Cases | Beam Line | Beam Type | Beam Yield
---|---|---|---|---
sub-eV mass range: |  |  |  |
IAXO | axions/ALPs (photon coupling) | – | axions from sun | –
JURA | axions/ALPs (photon coupling) | laboratory | eV photons | –
CPEDM |  $p,d$ oEDMs | EDM ring | $p,d$ | –
| axions/ALPs (gluon coupling) |  | $p,d$ | –
LHC-FT | charmed hadrons oEDMs | LHCb IP | 7 TeV $p$ | –
MeV-GeV mass range: |  |  |  |
SHiP | ALPs, Dark Photons, Dark Scalars | BDF, SPS | 400 GeV $p$ |  $2\cdot 10^{20}$/5 years
| LDM, HNLs, lepto-phobic DM, .. |  |  |
NA62++ | ALPs, Dark Photons, | K12, SPS | 400 GeV $p$ | up to $3\cdot 10^{18}$/year
| Dark Scalars, HNLs |  |  |
NA64++ | ALPs, Dark Photons, | H4, SPS | 100 GeV $e^{-}$ |  $5\cdot 10^{12}$ eot/year
| Dark Scalars, LDM |  |  |
| \+ $L_{\mu}-L_{\tau}$ | M2, SPS | 160 GeV $\mu$ |  $10^{12}-10^{13}$ mot/year
| \+ CP, CPT, leptophobic DM | H2-H8, T9 |  $\sim$ 40 GeV $\pi,K,p$ |  $5\cdot 10^{12}$/year
LDMX | Dark Photon, LDM, ALPs,… | eSPS | 8 (SLAC) -16 (eSPS) GeV $e^{-}$ |  $10^{16}-10^{18}$ eot/year
AWAKE/NA64 | Dark Photon | AWAKE beam | 30-50 GeV $e^{-}$ |  $10^{16}$ eot/year
RedTop | Dark Photon, Dark scalar, ALPs | CERN PS | 1.8 or 3.5 GeV |  $10^{17}$ pot
MATHUSLA200 | weak-scale LLPs, Dark Scalar, | ATLAS or CMS IP | 14 TeV $p$ | 3000 fb-1
| Dark Photon, ALPs, HNLs |  |  |
FASER | Dark Photon, Dark Scalar, ALPs, | ATLAS IP | 14 TeV $p$ | 3000 fb-1
| HNLs, $B-L$ gauge bosons |  |  |
MilliQan | milli charge | CMS IP | 14 TeV $p$ | 300-3000 fb-1
CODEX-b | Dark Scalar, HNLs, ALPs, | LHCb IP | 14 TeV $p$ | 300 fb-1
| LDM, Higgs decays |  |  |
$>>$ TeV mass range: |  |  |  |
KLEVER | $K_{\rm L}\to\pi^{0}\nu\overline{\nu}$ | P42/K12 | 400 GeV $p$ |  $5\cdot 10^{19}$ pot /5 years
TauFV | LFV $\tau$ decays | BDF | 400 GeV $p$ |  ${\mathcal{O}}(2\%)$ of the BDF proton yield
CPEDM |  $p,d$ EDMs | EDM ring | $p,d$ | –
| axions/ALPs (gluon coupling) |  | $p,d$ | –
LHC-FT | charmed hadrons MDMs, EDMs | LHCb IP | 7 TeV $p$ | –

##  4 Proposals sensitive to New Physics in the sub-eV mass range

Axions and ALPs have been searched for in dedicated experiments since their
proposal, however to date no detection has been reported and only a fraction
of the available parameter space has been probed. Indeed, nowadays there are
experiments or proposals that studies masses starting from the lightest
possible value of $10^{-22}$ eV up to several GeV. The apparata employed in
such a search are highly complementary in the mass reach and use detection
techniques that are not common, taking advantage for example of solid state
physics, optical and microwave spectroscopy, resonant microwave cavities,
precision force measuring system, highly sensitive optical polarimetry. A
relevant point which characterizes the detector is the choice of the axion
source: in fact, due to the extremely weak coupling with ordinary matter,
axion production in a laboratory will be suffering from extremely small fluxes
compared with possible natural sources like the Sun or the Big Bang.

Different experiments can probe different couplings, but the majority of the
running or proposed experiment are actually exploiting the coupling of the
axion to two photons through the Primakoff effect. The following categories
can then be identified:

\- Dark matter haloscopes
Taking advantage of the large occupation number for the axion in the local
dark matter halo, an axion haloscope searches for the reconversion of dark
matter axions into visible photons inside a magnetic field region. A typical
detector is a resonant microwave cavity placed inside a strong magnetic field
PhysRevLett.51.1415 . The signal would be a power excess in the cavity output
when the cavity resonant frequency matches the axion mass. Current research is
limited in range to a few $\mu$eV masses, but several new proposals are on the
way.

\- Solar helioscopes
Axion and ALPS can be efficiently produced in the solar interior with
different reactions: Primakoff conversion of plasma photons in the
electrostatic field of a charged particles, thus exploiting the axion to
photon coupling; Axio-recombination, Bremsstrahlung and Compton are other
possible channels based on the axion electron coupling. Solar axions escape
from the sun and can be detected in earth laboratory by their reconversion
into photons (X-rays) in a strong electromagnetic field.

\- Pure laboratory experiment
Laboratory searches for axions can be essentially divided into three
categories: polarization experiments MAIANI1986359 , regeneration experiments
(light-shining-through wall - LSW) PhysRevLett.59.759  and long range forces
experiments PhysRevD.30.130 . The key advantage for this apparata is the model
independency of the detection scheme, however fluxes are so low that only ALPs
coupling can be probed. Among others, the LSW type apparatus feature an axion
source, for example a powerful laser traversing a dipolar magnetic field, and
an axion reconverter placed after a barrier, again based on a static e.m.
field. Reconverted photons can the be detected with ultra low background
detectors.

Table 2 compares the physics reach, the model dependency, the mass range of a
possible axion or ALP particle, the intensity of the expected flux and the
wavelength of the detected photons for three categories of experiments
sensitive to axions/ALPs with photon-coupling.

Table 2: Comparison between the main techniques employed in the search for axion like particles in the sub eV range. Category | Haloscopes | Helioscopes | Lab experiments
---|---|---|---
Physics reach | ALPs & QCD axion | ALPs & QCD axion | ALPs
Model dependency | Strong | Weak | Absent
Ranges | Resonance detector | Wide band | Wide band
Flux | Very high | high | low
Typical photon | Microwave | X-rays | Optical

###  4.1 Solar axions helioscopes: IAXO

Brief presentation, unique features

The International Axion Observatory (IAXO) is a new generation axion
helioscope Armengaud:2014gea , aiming at the detection of solar axions with
sensitivities to the axion-photon coupling $g_{a\gamma}$ down to a few 10-12
GeV-1, a factor of 20 better than the current best limit from CAST (a factor
of more than 104 in signal-to-noise ratio). Its physics reach is highly
complementary to all other initiatives in the field, with unparalleled
sensitivity to highly motivated parts of the axion parameter space that no
other experimental technique can probe. The proposed baseline configuration of
IAXO includes a large-scale superconducting multi-bore magnet, specifically
built for axion physics, together with the extensive use of X-ray focusing
based on cost-effective slumped glass optics and ultra-low background X-ray
detectors. The unique physics potential of IAXO can be summarized by the
following statements:

  * -

IAXO follows the only proposed technique able to probe a large fraction of QCD
axion models in the meV to eV mass band. This region is the only one in which
astrophysical, cosmological (DM) and theoretical (strong CP problem)
motivations overlap.

  * -

IAXO will fully probe the ALP region invoked to solve the transparency
anomaly, and will largely probe the axion region invoked to solve observed
stellar cooling anomalies.

  * -

IAXO will partially explore viable QCD axion DM models, and largely explore a
subset of predictive ALP models (dubbed ALP miracle) recently studied to
simultaneously solve both DM and inflation.

  * -

The above sensitivity goals do not depend on the hypothesis of axion being the
DM, i.e. in case of non-detection, IAXO will robustly exclude the
corresponding range of parameters for the axion/ALP.

  * -

IAXO relies on detection concepts that have been tested in the CAST experiment
at CERN. Risks associated with the scaling up of the different subsystems will
be mitigated by the realization of small scale prototype BabyIAXO.

  * -

IAXO will also constitute a generic infrastructure for axion/ALP physics with
potential for additional search strategies (e.g. the option of implementing RF
cavities to search for DM axions).

Key requirements

The main element of IAXO is a new dedicated large-scale magnet, designed to
maximize the helioscope figure of merit. The IAXO magnet will be a
superconducting magnet following a large multi-bore toroidal configuration, to
efficiently produce an intense magnetic field over a large volume. The design
is inspired by the ATLAS barrel and end-cap toroids, the largest
superconducting toroids ever built and presently in operation at CERN. Indeed
the experience of CERN in the design, construction and operation of large
superconducting magnets is crucial for the project. IAXO will also make
extensive use of novel detection concepts pioneered at a small scale in CAST,
like X-ray focusing and low background detectors. The former relies on the
fact that, at grazing incident angles, it is possible to realize X-ray mirrors
with high reflectivity. IAXO envisions newly-built optics similar to those
used onboard NASA’s NuSTAR satellite mission, but optimized for the energies
of the solar axion spectrum. Each of the eight $\sim$60 cm diameter magnet
bores will be equipped with such optics. For BabyIAXO, using existing optics
from the ESA’s XMM mission is being considered. At the focal plane of each of
the optics, IAXO will have low-background X-ray detectors. Several
technologies are under consideration, but the most developed one are small
gaseous chambers read by pixelised microbulk Micromegas planes. They involve
low-background techniques typically developed in underground laboratories,
like the use of radiopure detector components, appropriate shielding, and the
use of offline discrimination algorithms. Alternative or additional X-ray
detection technologies are also considered for IAXO, like GridPix detectors,
Magnetic Metallic Calorimeters, Transition Edge Sensors, or Silicon Drift
Detectors. All of them show promising prospects to outperform the baseline
Micromegas detectors in aspects like energy threshold or resolution, which are
of interest, for example, to search for solar axions via the axion-electron
coupling, a process featuring both lower energies that the standard Primakoff
ones, and monochromatic peaks in the spectrum.

Open questions, feasibility studies

As a first step the collaboration pursues the construction of BabyIAXO, an
intermediate scale experimental infrastructure. BabyIAXO will test magnet,
optics and detectors at a technically representative scale for the full IAXO,
and, at the same time, it will be operated and will take data as a fully-
fledged helioscope experiment, with sensitivity beyond CAST and potential for
discovery.

Status, plans and collaboration

After a few years of preparatory phase, project socialization and interaction
with funding bodies, the IAXO collaboration was eventually formalized in July
2017. A collaboration agreement document (bylaws) was signed by 17
institutions from Croatia, France, Germany, Italy, Russia, Spain, South
Africa, USA, as well as CERN. They include about 75 physicists at the moment.
It is likely that this list will increase with new members in the near future.
A collaboration management is already defined and actively implementing steps
towards the BabyIAXO design and construction. The experiment will likely be
sited at DESY, and it is expected to be built in 2-3 years, entering into data
taking in 3-4 years.

The collaboration already nicely encompasses all the know-how to cover
BabyIAXO needs, and therefore a distribution of responsibilities in the
construction of the experiment exists already. The magnet of (Baby)IAXO is of
a size and field strength comparable to that of large detector magnets
typically built in high energy physics. For this IAXO relies on the unique
expertise of CERN in large superconducting magnets. The CERN magnet detector
group has already led all magnet design work so far in the IAXO CDR. The
technical design of the BabyIAXO magnet, for which CERN has allocated one
Applied Fellow, has started in January 2018. Further CERN participation is
expected in terms of, at the least, allocation of expert personnel to oversee
the construction of the magnet, as well as the use of existing CERN
infrastructure. Other groups with magnet expertise in the collaboration are
CEA-Irfu and INR. The groups of LLNL, MIT and INAF are experts in the
development and construction of X-ray optics, in particular in the technology
chosen for the IAXO optics. Detector expertise exists in many of the
collaboration groups, encompassing the technologies mentioned above.
Experience in general engineering, large infrastructure operation and
management is present in several groups and in particular in centers like CERN
or DESY. Many of the groups have experience in axion phenomenology and the
connection with experiment, and more specifically experience with running the
CAST experiment. Following these guidelines the collaboration board is in the
process of defining a collaboration agreement (MoU) to organize the
distribution of efforts and commitments among the collaborating institutes.

IAXO has also submitted a separate document to be considered in the update of
the ESPP.

###  4.2 Laboratory experiments: JURA

Brief presentation, unique features

The pioneer LSW experiment was conducted in Brookhaven by the BFRT
collaboration Cameron:1993mr , and the two most recent results are those of
the experiments ALPS Ehret:2010mh  and OSQAR PhysRevD.92.092002 . ALPS is DESY
based and used a decommissioned HERA magnet. ALPS is currently performing a
major improvement to phase II, where a set of 10 + 10 HERA magnets will be
coupled to two 100 m long Fabry Perot cavities. ALPS II 1748-0221-8-09-T09001
will in fact take advantage of a resonant regeneration apparatus, thus
expecting a major improvement of the current limit on LSW experiment given by
OSQAR. ALPS II will represent the current state of the art LSW experiment, and
for this reason its activities are monitored with interest by the PBC since
they will give key elements to judge the proposal JURA (Joint Undertaking on
the Research for Axion-like particles).

ALPS II aims to improve the sensitivity on ALP-photon couplings by three
orders of magnitude compared to existing exclusion limits from laboratory
experiments in the sub-meV mass region. ALPS II will inject a 30 W laser field
into the 100 m long production cavity (PC) which is immersed in a 5.3 T
magnetic field. The circulating power inside the PC is expected to reach 150
kW. The 100 m long regeneration cavity (RC) on the other side of the wall will
have a finesse of 120,000. The RC is also placed inside a similar 5.3 T
magnetic field. The employed two different photon detection concepts are
expected to be able to measure fields with a photon rate as low as $\sim
10^{-4}$ photons per second. A next generation experiment for a LSW techniques
will mainly rely on improved magnetic field structure, since from the optical
part only limited improvements seems to be feasible. The project JURA
basically combines the optics and detector development at ALPS II with dipole
magnets for future accelerators under development at CERN.

The sensitivity of ALPS II in the search for axion-like particles is mainly
limited by the magnetic field strength and the aperture (which limits the
length of the cavities) of the HERA dipole magnets. JURA assumes the usage of
magnets under development for an energy upgrade of LHC or a future FCC.

Key requirements

Several options of these future magnets are of interest to the JURA
initiative. In one of them the inner high temperature superconductor part
would be omitted, so that magnets with a field of about 13 T and 100 mm
aperture would be available (the modified HERA dipoles provide 5.3 T and 50
mm). In Table 3 experimental parameters of ALPS II and this option of JURA are
compared. They follow from assuming the installation of optical cavities
inside the magnet bore in a (nearly) confocal configuration.

Table 3: Comparison of experimental parameters of ALPS II at DESY and the JURA proposal Parameter | Sensitivity | ALPS II | JURA | Rel. sensitivity
---|---|---|---|---
|  |  |  | JURA / ALPS II
Magnet aperture |  | 50 mm | 100 mm |
Magnetic field amplitude B | $g_{a\gamma}\propto B^{-1}$ | 5.3 T | 13 T | 2.5
Magnetic field length L | $g_{a\gamma}\propto L^{-1}$ | 189 m | 960 m | 5.1
Effective laser power P | $g_{a\gamma}\propto P^{-1/4}$ | 0.15 MW | 2.5 MW | 2.0
Regeneration build up |  |  |  |
(finesse F) | $g_{a\gamma}\propto F^{-1/4}$ | 40 k | 100 k | 1.3
Detector noise rate R | $g_{a\gamma}\propto R^{1/8}$ |  $10^{-4}$ Hz |  $10^{-6}$ Hz | 1.8
Total gain |  |  |  | 56

Open questions, feasibility studies

The project JURA is a long term development, for which the experiment ALPS II
can be considered as a feasibility study, especially for the resonant
regeneration scheme. There are in fact some open questions: for example, the
possibility of running cavities of very high finesses for distances of the
order of several hundreds meters is still open. The linewidth of such cavities
is in fact of the order of a few Hz, about one order of magnitude better than
current state of the art. Another issue is the detector noise, however recent
development using coherent detection schemes seems to be very promising. Of
course, the development of new magnets at CERN is not related to JURA, and
thus this project will just rely on other projects’ results.

JURA in the abovementioned configuration would surpass IAXO by about a factor
of 2 in the photon-ALP coupling. It would allow to determine the photon-
coupling of a lightweight ALP discovered by IAXO unambiguously and in a model-
independent fashion or probe a large fraction of the IAXO parameter space
model independently in case IAXO does not see anything new.

Status, plans and collaboration

ALPS II is currently being constructed at DESY in the HERA tunnels. The
tunnels and hall are currently being cleared and magnet installation will
begin early 2019. The optics installation will begin at the end of 2019 and
first data run is scheduled for 2020. About two years of operation is then
expected. The time schedule for JURA is foreseen to be for a 2024-2026
starting time by using a LHC dipole magnet in its first phase. At the moment
there is no real collaboration and JURA might be considered an idea to for a
possible experiment which should grow within the years to come.

##  5 Proposals sensitive to New Physics in the MeV-GeV mass range

Feebly-interacting particles with masses in the MeV-GeV region can be produced
in the decay of beauty, charm and strange hadrons and by photons produced in
the interactions of a proton, electron or muon beam with a dump or an active
target. Their couplings to SM particles are very suppressed leading to
exceptionally low expected production rates, and therefore high-intensity
beams are required to improve over the current results.

Accelerator experiments represent a unique tool to test models with light dark
matter (LDM) in the MeV-GeV range, under the hypothesis that DM annihilates
directly to SM particles via new forces/new dark sector mediators. The
advantage of accelerator experiments is that the DM is produced in a
relativistic regime, and therefore its abundance depends very weakly on the
assumptions about its specific nature, while the rates can be predicted from
thermal freeze-out.

In addition, accelerator based experiments can probe the existence of Heavy
Neutral Leptons (HNLs) with masses between 100 MeV and $\sim$10 GeV in a range
of couplings phenomenologically motivated and challenge the see-saw mechanism
in the freeze-in regime.

Hidden sector physics in the MeV-GeV mass range can be studied at fixed-
target, dump and colliders experiments. The focus of this document is on
initiatives that want to exploit the CERN accelerator complex beyond the LHC,
as eg extracted beam lines at the PS and SPS injectors, however proposals
designed to be operated at or near the LHC interaction points have been
included in the study to provide a complete landscape scenario of the physics
reach at CERN achievable in the next 10-20 years. Several experimental
approaches can be pursued to search for HNLs, ALPs, LDM and corresponding
light mediators, depending on the characteristics of the available beam line
and the proposed experiment. These can be classified as follows:

  * -

Detection of visible decays:
HNLs, ALPs and LDM mediators are very weakly coupled to the SM particles and
can therefore decay to visible final states with a probability that depends on
the model and scenario. The detection of visible final state is a technique
mostly used in beam-dump experiments and in collider experiments (Belle,
ATLAS, CMS and LHCb), where typical signatures are expected to show up as
narrow resonances over an irreducible background. This approach is of
particular importance when the light mediator has a mass which is less than
$2m_{\chi}$, being $m_{\chi}$ the mass of the LDM, in which case the mediator
can decay only to visible final states.

  * -

Direct detection of LDM scattering in the detector material:
LDM produced in reactions of electrons and/or protons with a dump can travel
across the dump and be detected via the scattering with electrons and/or
protons of a heavy material. This technique has the advantage of probing
directly the DM production processes but requires a large proton/electron
yield to compensate the small scattering probability. Moreover the signature
is very similar to that produced by neutrino interactions. This is a limiting
factor unless it is possible to use a bunched beam and time-of-flight
techniques.

  * -

Missing momentum/energy techniques:
Invisible particles (as LDM or HNLs, ALPs, and light mediators with very long
lifetimes) can be detected in fixed-target reactions as, for example,
$e^{-}Z\to e^{-}ZA^{\prime}$ with $A^{\prime}\to\chi\overline{\chi}$ by
measuring the missing momentum or missing energy carried away from the
escaping invisible particle(s). Main challenge of this approach is the very
high background rejection that must be achieved, that relies heavily on the
detector hermeticity and, in some cases, on the exact knowledge of the initial
and final state kinematics. This technique guarantees an intrinsic better
sensitivity for the same luminosity than the technique based on the detection
of HNLs, ALPs and light mediator going to visible decays or based on the
direct detection of LDM scattering in the detector, as it is independent of
the probability of decays or scattering. However it is much more model-
dependent and more challenging as far as the background is concerned.
Moreover, if the mediator decays promptly or with a short lifetime to detected
SM particles, these techniques have no sensitivity.

  * -

Missing mass technique:
This technique is mostly used to detect invisible particles (as DM candidates)
in reactions with a well-known initial state, as for example
$e^{+}e^{-}\to\gamma A^{\prime}$ with $A^{\prime}\to\chi\overline{\chi}$. This
technique requires detectors with very good hermeticity that allow to detect
all the other particles in the final state. Characteristic signature of this
reaction is the presence of a narrow resonance emerging over a smooth
background in the distribution of the missing mass. Main limitation of this
technique is the knowledge of the background arising from processes in which
particles in the final state escape the apparatus without being detected.

The timescale of the PBC-BSM projects that will explore the MeV-GeV mass range
is shown in Figure 2 and compared with other similar initiatives in the world.
A concise description of each proposal along with beam request, key
requirements for the detectors, open questions and feasibility studies, is
shown in the following Sections.

Figure 2: Tentative timescale for PBC projects exploring the MeV-GeV mass
range compared to other similar initiatives in the world that could compete on
the same physics cases.

###  5.1 Proposals at the PS beam lines

####  5.1.1 REDTOP

Brief presentation, unique features
REDTOP is a fixed target experiment searching for physics BSM primarily in
ultra-rare decays of the $\eta$ and $\eta^{\prime}$ mesons produced in the
interactions of the high-intensity, low-energy (few GeV) proton beam with a
target. REDTOP was originally proposed at FNAL 444http://redtop.fnal.gov/wp-
content/uploads/2016/02/REDTOP_EOI_v10.pdf. but recently expressed interest to
be hosted at CERN. The experiment requires to collect approximately $10^{13}$
$\eta$ ad $10^{11}$ $\eta^{\prime}$ mesons produced in the interactions of
1017 protons with energy in the range 1.7-1.9 GeV (for $\eta$ production) and
about the same number of protons with an energy of about 3.5 GeV (for
$\eta^{\prime}$ production). A fast detector, blind to most hadrons and
baryons produced from the inelastic scattering of the beam, surronds the
target systems and covers about 98% of the solid angle.

The $\eta$ and $\eta^{\prime}$ mesons are quite unique in nature. The additive
quantum numbers for these particles are all zero, the same as for the vacuum
and the Higgs, with the exception of their negative parity, leading to the
suppression of SM decays. An attractive feature of the $\eta$ and
$\eta^{\prime}$ mesons is that they are flavor-neutral, so its SM _C_ \- and
_CP_ -violating interactions are known to be very small.

Thus, rare $\eta$ /$\eta^{\prime}$ decays are a promising place to look for
BSM effects. They complement analogous searches performed with $K$ and $B$
mesons with the unique feature that their decays are flavor-conserving. Such
decays, therefore, can provide distinct insights into the limits of
conservation laws, and open unique doors to new BSM models at branching
fraction sensitivity levels typically below 10-9. Notably, however, current
experimental upper limits for $\eta$ decays are many orders of magnitude
larger, so $\eta$ decays have not been competitive with rare decays of
flavored mesons.

Rare $\eta/\eta^{\prime}$ decays can be also exploited to search for dark
photons as, eg, in the process $\eta\to\gamma
A^{\prime},A^{\prime}\to\mu^{+}\mu^{-}$. ALPs and Dark Photons could be
radiated from the beam trough multiple processes Dobrich:2015jyk  (Primakoff
effect, Drell-Yan, proton bremsstrahlung, etc). Such models indicate that the
production cross section of the ALPS increases at low beam energy, making such
searches more advantageous Dobrich:2015jyk .

Beam, beam time
In order to generate 1013 $\eta$ mesons on the 10-foils target systems of the
experiment, approximately 1017 protons with energy in the range 1.7-1.9 GeV
are required. The same number of protons with an energy of about 3.5 GeV would
generate appriximately 1011 $\eta^{\prime}$ mesons. These yields give enough
sensitivity for exploring physics BSM as they correspond to sample of mesons a
factor about 104 larger than the existing world sample. A near-CW beam is
necessary in order to limit the pile-up of events and to suppress the
combinatorial background. Only about 0.5% of the beam interacts inelastically
with the target systems. Consequently, the power dissipatated in the latter
corresponds to only 15 mW total (1.5 mW/target foil) for a 1.8 GeV proton beam
and 24 mW total (2.4 mW/target foil) for a 3.5 GeV proton beam. The remaining
(99.5% ) of the beam is unaffected and it could be deviated toward other
experimental apparatuses downstream of REDTOP.

The collaboration aims to integrate about $10^{17}$ pot at 1.8 GeV ($\eta-
factory)$ and $10^{17}$ pot at 3.5 GeV ($\eta^{\prime}-factory)$ . These
yields could be provided in one or multiple years, depending on the
availaility of such beam at CERN.

Key requirements for detector
The REDTOP detector is being designed to sustain a maximum inelastic
interaction rate of about 5$\times$108 evt/sec. These capabilities exceed the
event rate expected at CERN by about one order of magnitude and could portend
to running the detector at future, high-intensity proton facility (for
example, PIP-II at Fermilab). In order to sustain such an event rate, the
detector must be: a) very fast; b) blind to the baryons. The latter are
produced within the target with a multiplicity of about 5/event and could
easily pile-up if detected. On the other hand, since BSM physics is being
searched for mostly in channels with charged leptons in the final state, the
detector must have good efficiency to electrons and muons and excellent PID
capabilities. The above requirements are fullfilled by adopting an Optical-TPC
Oberla:2015oha  for the tracking systems and a high-granularity, dual-readout
ADRIANO calorimeter Gatto:2015gna .

A fiber tracker, with identical features as that under construction for the
LHCb experiment Kirn:2014cza , has been recently included in the detector
layout.

The schematic layout of the detector is shown in Figure 3.

Figure 3: Schematic layout of REDTOP detector.

Open questions, feasibility studies
Few open questions exist, at this stage, for REDTOP. The largest unknown is
related to the available accelerator complex and the experimental hall where
the experiment could be operated. Both LEAR and Booster were considered as
options for REDTOP and rejected. A possibility could be to use the 24 GeV, T8
proton beam line that currently serves CHARM and IRRAD facilities with a
maximum intensity of $6.5\times 10^{11}$ ppp over 0.4 s. REDTOP would require
lower kinetic energy (2-3 GeV) and a much longer flat-top. No showstoppers
have been identified but machine studies would be required and, in any case,
the impact on the rest of the CERN physics program would be significant.

The second unknown is related to the Detector R&D still necessary to complete
the design of the apparatus. In fact, while a multi-year R&D has been in place
for ADRIANO and for the fiber tracker, very little has been done for the
moment toward the development of an Optical-TPC prototype. The latter is
conditional to the availability of R&D funding which, at present, is still not
in place. The Collaboration is considering, meanwhile, to launch a simulation
campaign to understand if alternative, more conventional solutions could be
found that are compatible with the event rate expected at REDTOP.

Timeline
The Collaboration has estimated that about two years of detector R&D are
necessary (dominated by the R&D on the Optical-TPC) and about 1 year for the
construction and installation of the detector. The solenoid and the lead-glass
required for the Cerenkov component of ADRIANO are readily available from INFN
while the fibers for Tracker and for the Scintillating component of ADRIANO
are commercially available with short lead times. The low cost, large area
photo-detectors required for the O-TPC are becoming commercially available at
Incom and the production of about 100 units for REDTOP seems not to represent
a problem for the company.

Under the assumption that the funding for the Optical-TPC is available
starting in 2020, REDTOP would be ready to install in 2022 and run in 2023,
one year before LS3. The proposed schedule is very agressive but considered
feasible by the Collaboration. However, the PBC coordinators decided to have a
conservative approach and consider REDTOP a proposal for Run 4. A full
proposal will be presented to the SPSC immediately after the conclusion of the
ESPP process (mid-2020). A coincise document will also be submitted by
December 18th for the next update of the ESPP.

Status of the collaboration
REDTOP Collaboration counts, presently, 23 Institutions and 67 Collaborators,
as reported here: http://redtop.fnal.gov/collaboration/.

###  5.2 Proposals at the SPS beam lines

####  5.2.1 NA64++

Brief presentation, unique features
The NA64 is a hermetic general purpose detector to search for dark sector
particles in missing energy events from high-energy ($\sim$ 100 GeV)
electrons, muons, and hadrons scattering off nuclei in an active dump. A high
energy electron beam, for example, can be used to produce a vector mediator,
e.g. dark photon $A^{\prime}$, via the reaction $e^{-}Z\to
e^{-}ZA^{\prime};\;A^{\prime}\to\chi\overline{\chi}$ where $A^{\prime}$ is
produced via kinetic mixing with bremsstrahalung photons and then decay
promptly and invisibly into light (sub-GeV) DM particles Gninenko:2013rka ;
Andreas:2013lya  in a hermetic detector Gninenko:2016kpg ; Gninenko:2017yus .
The signature of possible $A^{\prime}$ would appear as a single isolated
electromagnetic shower in the active dump with detectable energy accompanied
by missing energy in the rest of the detector.

The advantage of this technique compared to traditional beam dump experiments
is that the sensitivity to $A^{\prime}$ scales as $\epsilon^{2}$ instead of
$\epsilon^{4}$, $\epsilon$ being the kinetic mixing strength, as the
$A^{\prime}$ is required to be produced but not detected in the far apparatus.
Another advantage of the NA64 approach is the high energy of the incident
beam, that boosts the centre-of-mass system relative to the laboratory system:
this results in an enhanced hermeticity of the detector which provides a
nearly full solid angle coverage.

The missing energy technique can be used also with high energy muon and hadron
beams. The reaction of muon scattering off nuclei
$\mu+Z\to\mu+Z+Z^{\prime}_{\mu}$ is sensitive to dark sector particles
predominantly coupled to muons Gninenko:2014pea ; Gninenko:2018num , and, as
such, is fully complementary to the dark photon searches. This search is quite
appealing and very timely in particular in connection to the $g_{\mu}-2$
anomaly Gninenko:2018tlp , and will be competing with other proposal at
Fermilab Kahn:2018cqs  and elsewhere (see, e.g. Ref. Chen:2018vkr  for a
review). A $Z_{\mu}$ model gauging the $L_{\mu}-L_{\tau}$ lepton number could
also explain the hints of LFU violations in $R_{K}$ and $R_{K^{*}}$ ratios
observed by LHCb Aaij:2014ora ; Aaij:2017vbb . The sensitivity to a $Z_{\mu}$
particle compatible with the observed $B$-anomalies and other constraints is
currently under study by the Collaboration.

High energy hadron beams can be used to search for dark sector particles in
the decays $K_{L},K_{S},\pi^{0},\eta,\eta^{\prime}\to$ invisible, where the
neutral mesons $M^{0}$ are produced via the charge-exchange reactions
$\pi(K)p\to M^{0}n+E_{\rm miss}$ Gninenko:2015mea ; Gninenko:2014sxa ;
Barducci:2018rlx . This type of search with neutral kaons is also quite
complementary, see eg. Refs Barducci:2018rlx ; Abada:2016plb  to the current
CERN and the proposed PBC program in the kaon sector.

Key requirements for detector, beam, beam time, timeline
NA64 is currenly taking data at the H4 beam line of the SPS Banerjee:2016tad ;
Banerjee:2017hhz ; Banerjee:2018vgk . The beam line is a 100 GeV electron beam
with a maximum intensity of $\sim 10^{7}\leavevmode\nobreak\ e^{-}$ per SPS
spill. Beam intensity and transverse size have been optimized to guarantee an
efficient detection of the synchrotron radiation during NA64 operation. The
detection of synchrotron radiation is necessary to reach the electron beam
required purity.

NA64 has collected about $3\times 10^{11}$ eot before LS2, and aims at
reaching $5\times 10^{12}$ eot during Run 3.

The NA64 detector is a spectrometer with a low material budget tracker, micro-
MEGA, GEM and straw-tubes based, followed by an active target, which is a
hodoscopic electromagnetic calorimeter (ECAL), Shashlik-type, for the
measurement of the energy of the recoil electrons. A high-efficient veto
counter and a massive, hermetic hadronic calorimeter are positioned just after
ECAL to efficiently detect muons or hadronic secondaries produced in the
$e^{-}A$ interactions in the active target.

The key feature of the NA64 apparatus is the detection of the synchrotron
radiation from 100 GeV electrons in the magnetic field to significantly
enhance electron identification and suppress background from the hadron
contamination in the beam. The addition of a compact tungsten calorimeter
after the syncrotron radiation detector as a active target for the production
of energetic $A^{\prime}$ or $X$-boson explaining the ${}^{*}Be$ anomaly
Feng:2016jff ; Feng:2016ysn , enables the search of $A^{\prime}\to e^{+}e^{-}$
visible decays. The first results obtained in 2016-2017 for the both
$A^{\prime}\to\chi\overline{\chi}$ and $A^{\prime}\to e^{+}e^{-}$ decay modes
Banerjee:2016tad ; Banerjee:2017hhz ; Banerjee:2018vgk  confirm the validity
and sensitivity of the NA64 technique for searching for dark sector physics.

The NA64++ experiment proposed in the PBC context aims at using high-energy
electron, muon and hadron beams extracted at the SPS and currently available
at the CERN North Area, starting in Run 3.

  * -

NA64${}^{++}(e)$:
NA64 plans to continue the data taking after LS2 with the main goal to
integrate up to $5\times 10^{12}$ eot at the H4 line in about $(6-8)$ months.
The preparation of an area able to host a quasi-permanent installation of NA64
began in 2018.

An upgrade of the detector is also needed in order to cope with a high
intensity beam: this includes the replacement of the electro-magnetic
calorimeter electronics, the addition of a zero-degree hadron calorimeter, and
the upgrade of the data acquisition system.

  * -

NA64${}^{++}(\mu)$:
A new detector served by the M2 beam line and located in the EHN2 experimental
hall in the CERN North Area is proposed to be built after LS2 to investigate
dark sector predominantly coupled to the second and third generation and
Lepton-Flavor-Violating (LFV) $\mu-\tau$ conversion with a high energy muon
beam. The M2 line, currently serving the COMPASS experiment, is able to
provide muons with momentum of $\simeq(100-160)$ GeV/c, and intensity up to
$\sim 10^{8}$ $\mu$/spill.

The detector setup follows closely the one currently operating with $e^{-}$
beam: an active (muon) target followed by a large hadron calorimeter located
in a magnetic field, which is used both to measure the outgoing muon momentum
and to veto events with associated hadrons. The signal consists of a muon with
outgoing momentum significantly lower than the incoming one and no energy
deposition in the rest of the detector.

A key issue is the purity of the incoming muon beam: a background study
performed in 2017 shows that the level of the hadron contamination in the muon
beam can be reduced down to the negligible level $\leq 10^{-6}$ by using nine
$Be$ absorbers. Another key issue is the precise measurement of the momentum
of the outgoing muon and its identification with high purity.

Some modification of the M2 upstream part are also foreseen, as described in
the PBC Conventional Beams WG Report Pbc:002 . Assuming a muon beam intensity
of $\sim 3\times 10^{7}$ $\mu$/spill, with $\sim 4\times 10^{3}$ spills per
day, about 1.5 years are necessary to accumulate $\sim 5\times 10^{13}$ mot.
NA64 has submitted in October the addendum for the SPSC555CERN-
SPSC-2018-024/SPSC-P-348-ADD-3. for the Phase 1 of NA64${}^{++}(\mu)$, which
requires $10^{6}$ muons/s at 100 GeV.

  * -

NA64${}^{++}(h)$:

the NA64 studies with hadron beams are less advanced and will continue during
the coming years. Integrated luminosities of $10^{13}$ pions-on-target,
$10^{12}$ kaons-on-target, and $10^{12}$ protons-on-target could investigate
dark sector models complementary to the dark photon one. These searches would
require $(20-50)$ GeV hadron beams that could be provided by the H4 line
without modification. The Collaboration aims to start data taking with hadron
beams after LS3.

Open questions, planned feasibility studies
The main open question for NA64${}^{++}(e)$ is the detector ability to cope
with the higher beam intensity, which is already available, and hence
increased pile-up: this has already been positively answered based on the
preliminary analysis of the data sample collected during the 2018 run where an
intensity close to $\sim 10^{7}e$/spill has been reached. With such an
intensity and 4000/spills/day, about four months will be required to collect
$4\times 10^{12}$ eot. Upgrades of the detector and data acquisition system
are planned during LS2. As for NA64${}^{++}(e)$, key issues for
NA64${}^{++}(\mu)$ are the beam purity and beam momentum measurement, and
detector hermeticity. In both cases, the time sharing in the two (highly
demanded) beam lines (H4 and M2) with other potential users (eg. COMPASS,
MUonE, etc.) is an issue and will require a careful planning and
prioritization of the operations.

Status of the Collaboration
The collaboration currently consists of $\simeq 50$ participants representing
14 Institutions from Chile, Germany, Greece, Russia, Switzerland, and USA. An
updated list of authors and institutions can be found at:
https://na64.web.cern.ch. The NA64 Collaboration has also submitted a separate
document for the next update of the ESPP.

####  5.2.2 NA62++

Brief presentation, unique features
NA62 Gonnella:2017hsz  is a fixed target experiment at the CERN SPS with the
main goal of measuring the BR of the ultra-rare decay
$K^{+}\to\pi^{+}\nu\overline{\nu}$ with 10% precision. It is currently taking
data at the K12 beam line at the CERN SPS. The NA62 long decay volume,
hermetic coverage, low material budget, full PID capability and excellent
tracking performance, make NA62 a suitable detector for the search for hidden
particles. The possibility of dedicating part of Run 3 to this physics case is
timely, since the projected sensitivity surpasses that of competitive
experiments in the same time range. NA62 proposes to integrate $\sim 10^{18}$
pot operating the detector in dump mode for few months during Run 3.

Location, beam requirements, beam time, timeline
NA62 is currently operating at the K12 beam line in the North Area. At full
intensity, a beam of $3\times 10^{12}$ protons-per-pulse (ppp), 400 GeV
momentum, in 3.5 s long effective spills from the SPS hit a beryllium target
to produce a 75 GeV momentum-selected 750-MHz intense secondary beam of
positive particles, 6% of which are charged kaons. The beryllium target used
by NA62 is followed by two 1.6 m long, water-cooled, beam-defining copper
collimators (TAX) which can act also as a dump of $\sim 10.7$ nuclear
interaction lengths each. In the standard NA62 operation, roughly 50% of the
beam protons punch through the beryllium target and are absorbed by the TAX
collimators.

At the NA62 nominal beam intensity, $10^{18}$ pot can be acquired in
${\mathcal{O}}(3)$ months of data taking. The dump-mode operation can be
obtained by lifting the NA62 Beryllium target away from the beam line and by
closing the first TAX collimator, placed $\sim$ 22 m downstream of the target.
The muon halo emerging from the dump is partially swept away by the existing
muon clearing system. The switching from the standard beam mode to the beam-
dump mode takes a few minutes and it is already done regularly. About $3\times
10^{16}$ pot in dump mode have already been collected and are being analysed
for background studies.

The NA62 Collaboration is preparing a thorough plan for running after the end
of LS2 with a fraction of the beam time in dump mode during Run 3 (2021-2023).
A possible sharing could be two years in beam mode to complete the measurement
of the branching fraction (BR) of the $K^{+}\to\pi^{+}\nu\overline{\nu}$ mode
and ${\mathcal{O}}(1)$ year in beam dump mode. The proposal will take into
account the results obtained on the measurement of the
$BR(K^{+}\to\pi^{+}\nu\overline{\nu})$ based on the analysis of data taken in
current (2016-2018) run.

Detector description, key requirements for detector
A schematic layout of the NA62 detector is shown in Figure 4.

Figure 4: Layout of the NA62 experiment.

The secondary positively charged hadron beam of 75 GeV/c momentum reaches the
120 m long, 2 m diameter, in-vacuum decay volume, placed 100 m downstream of
the target. A Cherenkov counter (KTAG) filled with $N_{2}$ along the beam line
identifies and timestamps kaons, which are about 6% of the hadron beam. Three
silicon pixel stations (Gigatracker, GTK) measure the momentum and the time of
all the particles in the beam at a rate of 750 MHz. A guard ring detector
(CHANTI) tags hadronic interactions in the last GTK station at the entrance of
the decay volume. Large angle electromagnetic calorimeters (LAV) made of lead
glass blocks surround the decay vessel can be used to veto particles up to 50
mrad. A magnetic spectrometer made of straw tubes in vacuum measures the
momentum of the charged particles.

A 17 m long RICH counter filled with Neon separates $\pi$, $\mu$ and $e$ up to
40 GeV/c. The time of charged particles is measured both by the RICH and by
scintillator hodoscopes (CHOD and NA48-CHOD) placed downstream to the RICH.
The electromagnetic calorimeter filled with liquid krypton (LKr) covers the
forward region and complements the RICH for the particle identification. A
shashlik small-angle calorimeter (IRC) in front of LKr detects $\gamma$
directed on the inner edges of the LKr hole around the beam axis. The hadronic
calorimeter made of two modules of iron-scintillator sandwiches (MUV1 and
MUV2) provides further $\pi-\mu$ separation based on hadronic energy. A fast
scintillator array (MUV3) identifies muons with sub-nanosecond time
resolution. A shashlik calorimeter (SAC) placed on the beam axis downstream of
a dipole magnet bending off-axis the beam at the end of the NA62 detector,
detects $\gamma$ down to zero angle. A multi-level trigger architecture is
used when operated in beam mode. The hardware-based level-0 trigger uses
timing information from CHOD, RICH and MUV3, and calorimetric variables from
electromagnetic and hadronic calorimeters. Higher-level software-based trigger
requirements are based on variables from KTAG, LAV and magnetic spectrometer.

Such a setup is perfectly suited to perform a comprehensive search for hidden
particles in a large variety of visible final states.

Open questions, feasibility studies
The operation of NA62 in dump mode does not pose particular problems and no
show-stopper have been identified. The analysis of ${\mathcal{O}}(10^{16})$
pot collected in dump mode shows that the background can be kept under control
for hidden particles decaying to final states that are then fully
reconstructed. The addition of an Upstream Veto at the front of the fiducial
volume is currently being studied: this detector should be able to further
reduce the combinatorial di-muon background coming from random combinations of
halo muons and to open the possibility of detecting also partially
reconstructed final states. In normal operation mode half of the protons do
not interact with the Be target and impinge upon the TAXes: these data are
used for some specific background studies, namely for the di-muon background.

Minor modifications to the beam line are possible, too, aimed at reducing the
upstream-produced background (mainly again halo muons). A full GEANT4-based
simulation of the beam line has been implemented and is being used to study
optimized settings of the existing magnetic elements of the line and possibly
an optimized new layout for the beam-dump operation. Preliminary studies show
that the component of the muon flux above 20 GeV can be reduced by two orders
of magnitude with an appropriate setting of the magnetic elements of the beam
line. The maximum intensity achievable is under study, as well, with some
prospects of increase beyond the present nominal one. These aspects are under
study within the PBC Conventional Beams working group.

Status of the collaboration
The NA62 collaboration is made of 213 authors from 31 Institutions. An updated
list of authors and institutions can be found at: https://na62.web.cern.ch.

####  5.2.3 LDMX @ eSPS

Brief presentation, unique features
The Light Dark Matter eXperiment (LDMX) aims to probe Dark Matter (DM)
parameter space far below expectations from the thermal freeze-out mechanism
by exploiting the missing-energy missing-momentum technique in a fixed-target
experiment with a primary electron beam of modest GeV-range energy, low
current and high duty-cycle. LDMX is the only experiment exploiting this
technique among those presented in the PBC framework, and it has a unique
physics reach. Apart from its unparalleled sensitivity to sub-GeV DM scenarios
over a wide mass range, it will have sensitivity to a variety of other BSM
phenomena Akesson:2018vlm .

A high-intensity primary electron beam can be provided via an X-band 70 m long
linac based on CLIC technologies that could accelerate electrons to 3.5 GeV
and fill the SPS in 1-2 sec. The beam could be further accelerated up to 16
GeV by the SPS and then slowly extracted to a Meyrin site. The eSPS
collaboration has recently submitted an expression of interest to the SPSC
Akesson:2018yrp .

The design of the experiment is driven by two main goals: to measure the
distinguishing properties of DM production and to efficiently reject potential
backgrounds, in particular photo-nuclear reactions of bremsstrahlung photons.
The signal signature has three main features: (i) a reconstructed recoiling
electron with energy substantially less than the beam energy but also (ii)
detectable, with measurable transverse momentum, and (iii) the absence of any
other activity in the final state. A constraint on the DM particle production
rate can be transferred into robust bounds on the interaction strength which
in turn can be compared to direct freeze-out rates that would yield the
observed cosmic DM abundance.

The missing-momentum approach has distinct advantages compared to other
techniques such as missing mass (requires the reconstruction of all final
state particles and allows only much lower luminosity), beam-dump experiments
(have to pay the penalty of needing an additional interaction of the DM in the
detector), or missing-energy only (suffers from higher backgrounds due to
fewer kinematic handles and lack of discrimination between electrons and
photons).

Key requirements for detector, beam, beam time, timeline
Reaching the full potential of the missing-momentum technique places demanding
constraints on the experiment and the beamline supporting it. A high
repetition rate of electrons is required (as much as $\sim 10^{9}$ electrons-
on-target (eot) per second) in order to reach the envisaged integrated
luminosities of $10^{14}-10^{16}$ eot, while keeping an extremely low electron
density per bunch ($1-5e^{-}$/bunch).

This requires a fast detector that can individually resolve the energies and
angles of incident electrons, while simultaneously rejecting a variety of
potential background processes that vary in rate over many orders of
magnitude. The LDMX design makes use of a low-mass, silicon-based tracking
system in a 1.5 T dipole magnet to measure the momentum of the incoming
electrons, and to cleanly reconstruct electron recoils, thereby providing a
measure of missing momentum. A high-speed, high-granularity $Si-W$ calorimeter
with MIP sensitivity is used to reject potential high rate bremsstrahlung
background at trigger level, and to work in tandem with a scintillator-based
hadron calorimeter to veto rare photo-nuclear reactions. The design leverages
new and existing calorimeter technology under development for the HL-LHC, as
well as existing tracking technology and experience from the HPS experiment
Adrian:2015hst . The experiment is fairly small-scale for HEP standards. Thus
it could be built, commissioned and run over the course of a few years. A
rendering of the proposed experimental design is shown in Figure 5.

Figure 5: The LDMX experiment layout.

The scenario for a CERN SPS beam outlined below envisages a beam energy
between 3.5 and 16 GeV Akesson:2018yrp . Further requirements for the beam are
a low current and large beam-spot to ease the identification of individual
electrons, paired with a high duty factor for large integrated luminosity.

All of this can be provided at CERN in three basic steps: a new LINAC
providing electrons with 3.5 GeV, injecting into the SPS where the electrons
are accelerated to up to 16 GeV, followed by a slow extraction of electrons to
be delivered to the experiment. The bunch spacing can be any multiple of 5 ns
up to 40 ns, the average number of electrons per bunch can range from $<$1 up
to anything that can be tolerated by the experiment, and there is a high
flexibility in the beam size, such that for example a beam spot of 2
cm$\times$ 30 cm is perfectly feasible. To achieve $10^{16}$ eot in one year
would require approximately one third of the time the SPS is not used as a
proton accelerator.

The Collaboration considers that the beamline could be available
conservatively in 2025 (or even a few years earlier depending on CERN
priorities) and that this would accommodate comfortably the time needed for
the final design and construction of the detector. Hence, data taking could
start in 2025 (or earlier), and be completed within a few years, as little as
1-2 years for the most optimistic luminosity scenarios. In addition to the
LDMX experiment itself, the main construction needs are the electron linac as
injector to the SPS, a 50 m tunnel for last path of the extracted beam, and a
small experimental hall. The potential of such a primary electron beam
facility goes beyond LDMX: (i) It also opens for a beam-dump search for
visibly decaying dark photons, (ii) gives a Jefferson laboratory type facility
with extended energy range for Nuclear Physics, and (iii) would be a
significant Accelerator Physics R&D-asset at CERN.

Open questions, planned feasibility studies
The design studies up to now Akesson:2018vlm  have been based on the
assumption of a 4 GeV beam with on average one electron at a rate of 46 MHz.
They have demonstrated the experiment’s ability to reach close to 0 background
for $4\times 10^{14}$ eot. Within this scenario, in-depth studies of the
simulation of photo-nuclear backgrounds are progressing, in order to refine
the hadron calorimeter design. This will be followed by detector prototyping
in 2019/20.

The sensitivities for the other BSM phenomena outlined in Ref. Akesson:2018vlm
will be studied in the near future. Other plans for the near future include
further studies of multi-electron events (starting now with 2e/bunch) as well
as 16 GeV beam energy; how many electrons/bunch can be tolerated in terms of
triggering, reconstruction and identification, how high a granularity is
needed and feasible, and how short a bunch spacing can be handled. This will
feed into the determination of the exact run conditions in terms of the beam
parameters described above, in order to achieve a luminosity of $10^{16}$ EOT,
which will allow to probe all thermal targets below a few hundred MeV. A
further handle on the effective luminosity especially for the study of high-
mass signals (where degradation in momentum resolution is tolerable) is the
target material and thickness, that can be modified from the default 10%
$X_{0}$ W. The exploration of these parameters has only just begun.

Status of the Collaboration
LDMX@eSPS is currently being proposed by 78 physicists from 23 Institutions as
listed in the Letter of Intent submitted to the SPSC666CERN-
SPSC-2018-023/SPSC-EOI-018. in September 2018. A condensed version of the LOI
will be submitted for the next update of ESPP.

####  5.2.4 AWAKE

Brief presentation, unique features

The AWAKE experiment is placed underground at point 4 of the SPS, at the
former site of the CNGS target complex. The AWAKE phase-I consisted of a 10 m
long plasma cell impinged by 400 GeV proton bunches extracted from the SPS. A
laser pulse, co-propagating with a proton bunch, creates a plasma in a column
of rubidium vapour and seeds the modulation of the bunch into microbunches.
Recently electrons have been accelerated in the wakefield of the proton
microbunches. Based on the success of AWAKE phase-I, the collaboration is
currently investigating the possibility of accelerating an electron beam to
5-10 GeV in a 10-20 m plasma cell. A possible implementation of this phase is
an electron beam dump experiment where electrons are accelerated to
${\mathcal{O}}(50)$ GeV using SPS bunches with $3.5\times 10^{11}$ ppp every 5
sec.

Electron bunches of $5\times 10^{9}$ electrons/bunch can be impinged upon a
tungsten target where a Dark Photon could be produced and detected by an
NA64-like experiment downstream. The experiment aims to detect visible dark
photon decays to $e^{+}e^{-}$ initially, with the possibility of extending to
$\mu^{+}\mu^{-}$ and $\pi^{+}\pi^{-}$ final states.

Key requirements for detector, beam, beam time, timeline

The dark photons decay in a decay volume of order 10 m long, and the decay
products are detected in three micromegas trackers MM1, MM2, MM3 as well as a
tungsten plastik shashlik calorimeter, ECAL and the further possible addition
of a HCAL. A downstream magnet separates decay products and allows the
momentum reconstruction. A schematic layout of the experiment is shown in
Figure 6.

Figure 6: The AWAKE/NA64 conceptual layout.

The advantage of this experimental setup is the luminosity gain provided by
deploying bunches of electrons. This enables a larger eot in a shorter time
frame and results in an extended coverage of the sensitivity parameter space.
Taking into account the LIU-SPS with upgraded extraction kickers and a 12 week
experimental run with a 70% SPS duty cycle, AWAKE/NA64 expects to integrate
$10^{16}$ eot in one year of operation. This is more than three orders of
magnitude larger than the expected integrated eot by NA64 in Run 3.

The proposed experiment requires a location accessible to SPS protons that
drive the AWAKE accelerator and tunnel length long enough to accommodate a
50-100 meters long plasma cell as well as 20 metres of dump, drift volume and
detectors.

A possible location is in the former CNGS target hall and decay tunnel. This
project relies on the successful implementation of the AWAKE acceleration
concept and could be installed at earliest during LS3.

Open questions, planned feasibility studies
Ongoing feasibility studies will include full reconstruction of the dark
photon mass, as well as GEANT studies which incorporate realistic AWAKE
electron bunches at different average beam energies.

The simulation of a NA64-like experiment on a possible AWAKE-based beam line
is still in a very early stage: the evaluation of the background rates and
experimental efficiencies is still to be done and therefore is not contained
in the sensitivity curves shown in Section 9.

Status of the Collaboration
The AWAKE/NA64 team consists of the following: E. Gschwendtner, A. Caldwell,
M. Wing, A. Hartin, J. Chappell, A. Petrenko, P. Mugli and A. Pardons for
AWAKE. S. Gninenko, P. Crivelli and E. Depero for NA64.

The AWAKE collaboration has also submitted a separate document for the next
update of the ESPP.

####  5.2.5 KLEVER

The main goal of the KLEVER experiment is look for New Physics in the multi-
TeV mass range via a measurement of the rare decay
$K_{L}\to\pi^{0}\nu\overline{\nu}$ and is discussed in Section 6. However, the
experiment may also be sensitive to specific signatures of hidden sector
physics at the MeV-GeV scale, as discussed in Section 9.

####  5.2.6 SHiP @ BDF

Brief presentation, unique features
The Search for Hidden Particles (SHiP) experiment has been proposed to study a
wide variety of models containing light long-lived particles with masses below
${\mathcal{O}}(10)$ GeV with unprecedented sensitivity.

This will be achieved through two main points. Firstly, using the copious
amounts of charm, beauty, $\tau$ leptons and photons produced in an
interaction of the intense beam designed to be operated at the Beam Dump
Facility (BDF) Pbc:001  at the SPS, which in turn can produce hidden sector
particles such as a Heavy Neutral Leptons, Dark Scalars, Dark Photons, Axion
Like Particles, Light Dark Matter, R-parity violating neutralinos etc.. The
BDF will be able to provide $4\times 10^{13}$ 400 GeV protons per 1-sec long
spill, corresponding to an integrated yield of $2\times 10^{20}$ pot in 5
years of operation. Secondly, by reducing the background to zero over the
experiment lifetime through the combination of a magnetic muon shield to sweep
away muons from reaching the detector acceptance, decay volume under vacuum,
veto systems surrounding the detector, timing coincidence through a dedicated
fast timing detector, and a magnetic spectrometer within the decay volume.

Detector description, key requirements for detector
The main experimental challenge concerns the requirement of highly efficient
reduction of beam-induced backgrounds to below 0.1 events in the projected
sample of $2\times 10^{20}$ protons on target. To this end, the experimental
configuration includes a long target made of heavy material to stop pions and
kaons before their decay, a decay volume in vacuum, a muon shield based on
magnetic deflection able to reduce the flux of muons emerging from the target
by six orders of magnitude in the detector acceptance, and a hermetic veto
system surrounding the whole decay volume.

The SHiP experiment incorporates two complementary apparatuses. The first
detector immediately downstream of the muon shield consists of an emulsion
based spectrometer optimised for recoil signatures of hidden sector particles
and $\tau$ neutrino physics. The second detector system aims at measuring the
decays of Hidden Sector particles to fully reconstructible final states as
well as partially reconstructible final states that involve neutrinos. The
spectrometer is designed to accurately reconstruct the decay vertex, the mass,
and the impact parameter of the hidden particle trajectory at the proton
target. A set of calorimeters and muon stations provide particle
identification. A dedicated timing detector with $\sim$100 ps resolution
provides a measure of coincidence in order to reject combinatorial
backgrounds. The decay volume is surrounded by background taggers to tag
neutrino and muon interactions in the vacuum vessel walls and in the
surrounding infrastructure.

A schematic of the detector layout is shown in Figure 7.

Figure 7: Layout of the SHiP detector.

Beam requirements, beam time, timeline
The BDF facility is described in a separate report 777Beam Dump Facility
Report in preparation for the ESPP. It consists of a 400 GeV momentum primary
proton beam line slowly extracted from the SPS in spills 1 sec long. It is
able to provide up to $4.0\times 10^{13}$ protons per cycle, 7.2 sec long. The
SHiP operational scenario is based on a similar fraction of beam time as the
past CERN Neutrinos to Gran Sasso (CNGS) program. In the baseline scenario,
the beam sharing delivers an annual yield of $4\times 10^{19}$ protons to the
SHiP experimental facility and a total of $10^{19}$ to the other physics
programs at the CERN North Area, while respecting the beam delivery required
by the LHC and HL-LHC. The physics sensitivities are based on acquiring a
total of $2\times 10^{20}$ protons on target, which may thus be achieved in
five years of nominal operation.

CERN’s North Area has a large space next to the SPS beam transfer lines which
is largely free of structures and underground galleries, and is entirely
located on the current CERN territory. The proposed implementation is based on
minimal modification to the SPS complex and maximum use of the existing beam
lines. The design foresees space for future extensions. SHiP profits from the
unique feature in the SPS of slow extraction of a de-bunched beam over a
timescale of around a second. It allows tight control of combinatorial
background, and allows diluting the large beam power deposited on the proton
target both spatially and temporally. Should an observation require
consolidation, a second mode of operation with slow extraction of bunched beam
is also foreseen in order to further increase the discrimination between the
signature of a Light Dark Matter object, by measuring their different times of
flight, and background induced by neutrino interactions.

The schedule for the SHiP experiment and the experimental facility is largely
driven by the CERN long-term accelerator schedule. Accordingly, the schedule
aims at profiting as much as possible from data taking during Run 4 (currently
2027-2029). Most of the experimental facility can be constructed in parallel
to operating the North Area beam facilities. The connection to the SPS has
been linked to Long Shutdown 3 (i.e. for LHC 2024-2026) but requires that the
stop of the North Area is extended by one year (2025-2026). The schedule
requires preparation of final prototypes and the TDRs for both the detector
and the facility by beginning 2022, and construction and installation between
2023 and beginning 2027.

Background and feasibility studies
An extensive simulation campaign was performed to optimise the design of the
muon shield, detector setup as well as develop a selection that reduces all
possible sources of background to $<0.1$ events over the experiment lifetime.
The backgrounds considered were: neutrinos produced through the initial
collision that undergo deep inelastic scattering anywhere in the SHiP facility
producing $V^{0}$s; muons deflected by the shield that undergo deep inelastic
scattering in the experimental hall or anywhere within the decay volume
producing $V^{0}$s; muons in coincidence from the same spill (combinatorial
muons) escaping the shield; cosmic muons interacting anywhere in the decay
volume or with experimental hall.

The rate and momentum spectrum of the muon halo obtained with the full
simulation is being calibrated using data from a dedicated 1-month long run
performed in July 2018 where a smaller replica of the SHiP target was exposed
to ${\mathcal{O}}(5\times 10^{11})$ 400 GeV protons. Results are expected by
the Comprehensive Design Report, due by the end of 2019.

All samples rely on GEANT4 to simulate the entire SHiP target, muon shield,
detector, and experimental hall (walls, ceiling, floor). In addition, neutrino
interactions were simulated through GENIE.

A highly efficient selection is devised to reject all types of backgrounds and
is detailed in the SHiP Technical Proposal. This selection requires two good
quality tracks reconstructed in the SHiP spectrometer. Additional criteria are
placed on the vertex quality, distance of closest approach, and impact
parameter of the two-track system. In addition, candidates are rejected if the
veto systems either at the front or around the decay vessel are compatible
with an interaction within them. Tracks are also required to be in coincidence
within a 300 ps timing window ($\sim 3\sigma$).

A neutrino sample equivalent to ten years of SHiP operation resulted in
exactly zero events surviving a basic selection. In order to ensure this
background source is negligible, a sample corresponding to fifty years of
operation is being simulated. The combinatorial, deep inelastic and cosmic
muon backgrounds are expected to produce $\leq 10^{-3}$ events over the
experiment lifetime. Further studies will be conducted with even larger
samples to further optimise the selection. In addition, backgrounds to Light
Dark Matter signatures are currently under evaluation.

In addition to simulation studies, a thorough R&D campaign on all sub-
detectors has been carried out in the last three years with the aim to have
realistic estimate of detector performance obtained with suitable
technological choices.

Open questions:
The main challenges concern the beam losses and activation during the slow
extraction process, the design of the large muon shield, and the exact
knowledge of the spectrum of the muon halo.

  * -

Significant progress has been made in the studies of techniques to reduce the
beam losses and activation. Studies in 2017 confirmed the intensity reach to
within a factor of two. Deployment of crystal channeling in conjunction with
modified optics to reduce the beam density at the end of 2018, both in MD and
in operation, now shows that the baseline proton yield is realistically within
reach.

  * -

The design and performance of the muon shield poses certain technological
challenges. These include how to best assemble sheets of Grain Oriented (GO)
steel without disrupting the magnetic circuit, how to cut the GO sheets into
desired configurations, and how to best connect the GO sheets to achieve the
desired stacking factor. In order to address these questions a prototyping
campaign is underway.

  * -

The design of the muon shield and the residual rate of muons depends on the
momentum distribution of the muons produced in the initial proton collision.
The latest shield optimisation and rate estimates were performed using PYTHIA
simulations. In order to validate these simulations a test beam campaign was
performed in July to measure the muon flux using a replica of SHiP’s target.
Further details can be found in Ref. [SHiP-EOI-016]. The data are currently
being analysed. Depending on the outcome of this test beam campaign, a further
optimisation of the shield configuration will be performed.

Status of the collaboration
The SHiP Expression of Interest was submitted to SPSC in October 2013. This
was followed by the Technical Proposal submitted to the SPSC in April 2015.
The SHiP Technical Proposal was successfully reviewed by the SPSC and the CERN
RB up to March 2016, with a recommendation to prepare a Comprehensive Design
Study report by 2019.

SHiP is currently a collaboration of 295 members from 54 institutes (out of
which 4 are associate Institutes) representing 18 countries, CERN and JINR.
The status of the collaboration is kept up-to-date in the CERN greybook888 See
https://greybook.cern.ch/greybook/experiment/detail?id=SHiP.. In addition to
the experimental groups, about 40 people from the CERN Accelerator Division
are currently working on the design and R&D of the Beam Dump Facility.

The formal organisation of SHiP consists of a Country Representative Board
(CRB), Interim Spokesperson, Technical Coordinator and Physics Coordinator,
and the group of project conveners as elected and ratified by the CRB. The
organisation has been adopted for the Comprehensive Design Study phase. A
report which summarizes the simulation studies and R&D activities is in
preparation for the SPSC999SHiP Collaboration, Status of the SHiP experiment,
CERN CDS, will be submitted to the SPSC in January 2019.

A contribution which summarizes the status of the experiment will be submitted
to the ESPP update 101010SHiP Collaboration, The Search for Hidden Particles
experiment at the CERN SPS accelerator, has been submitted to ESPP update..

###  5.3 Proposals at the LHC interaction points

####  5.3.1 FASER

Brief presentation, unique features
FASER (ForwArd SEarch expeRiment at the LHC) is a proposed small and
inexpensive experiment designed to search for light, weakly-interacting
particles at the LHC. Such particles are dominantly produced along the beam
collision axis and are typically long-lived particles (LLPs), traveling
hundreds of meters before decaying. To exploit both of these properties, FASER
is to be located along the beam collision axis, 480 m downstream from the
ATLAS interaction point (IP). At this location, FASER and a larger successor,
FASER 2, will enhance the LHC’s discovery potential by providing sensitivity
to dark photons, dark Higgs bosons, heavy neutral leptons, axion-like
particles, and many other proposed new particles.

The FASER signal is LLPs that are produced at or close to the IP, travel along
the beam collision axis, and decay visibly in FASER:

$pp\to\text{LLP}+X,\quad\text{LLP travels}\ \sim 480\leavevmode\nobreak\
\text{m},\quad\text{LLP}\to\text{charged tracks}+X\text{ (or
$\gamma\gamma+X$)}\ .$ (8)

These signals are striking: two oppositely charged tracks (or two photons)
with very high energy ($\sim\text{TeV}$) that emanate from a common vertex
inside the detector and which have a combined momentum that points back
through 100 m of rock and concrete to the IP.

The sensitivity reach of FASER has been investigated for a large number of new
physics scenarios Feng:2017uoz ; Feng:2017vli ; Batell:2017kty ; Kling:2018wct
; Helo:2018qej ; Bauer:2018onh ; Cheng:2018vaj ; Feng:2018noy ;
Hochberg:2018rjs ; Berlin:2018jbm ; Dercks:2018eua ; Ariga:2018uku . FASER
will have the potential to discover a broad array of new particles, including
dark photons, other light gauge bosons, heavy neutral leptons with dominantly
$\tau$ couplings, and axion-like particles. FASER 2 will extend FASER’s
physics reach in these models to larger masses and also probe currently
uncharted territory for dark Higgs bosons, other types of heavy neutral
leptons, and many other possibilities.

Location, beam requirements, beam time, timeline
FASER will be located 480 m downstream from the ATLAS IP in service tunnel
TI12 as shown in Figure 8. TI18 is also a possibility. Both TI12 and TI18 were
formerly used to connect the SPS to the LEP tunnel, but they are currently
empty and unused.

Figure 8:  View of FASER in tunnel TI12. The trench lowers the floor by 45 cm
at the front of FASER to allow FASER to be centered on the beam collision
axis. Credit: CERN Site Management and Buildings Department.

The proposed timeline is for FASER to be installed in TI12 during Long
Shutdown 2 (LS2), in time to collect data during Run 3 of the 14 TeV LHC from
2021-23. FASER’s cylindrical active decay volume has a radius
$R=10\leavevmode\nobreak\ \text{cm}$ and length $L=1.5\leavevmode\nobreak\
\text{m}$, and the detector’s total length is under 5 m. To allow FASER to
maximally intersect the beam collision axis, the floor of TI12 should be
lowered by 45 cm. This will not disrupt essential services, and no other
excavation is required. FASER will run concurrently with the LHC and require
no beam modifications. Its interactions with existing experiments are limited
only to requiring bunch crossing timing and luminosity information from ATLAS.

If FASER is successful, a larger version, FASER 2, with an active decay volume
with $R=1\leavevmode\nobreak\ \text{m}$ and $L=5\leavevmode\nobreak\
\text{m}$, could be installed during LS3 and take data in the 14 TeV HL-LHC
era. FASER 2 would require extending TI 12 or TI18 or widening the staging
area UJ18 adjacent to TI18.

Detector description, key requirements for detector
The layout of the FASER detector is illustrated in Figure 9. At the entrance
to the detector on the left is a double layer of scintillators (gray) to veto
charged particles coming through the cavern wall from the IP, primarily high-
energy muons. The veto layer is followed by a $1.5\leavevmode\nobreak\
\text{m}$ long, 0.6 T permanent dipole magnet (red) with a
$20\leavevmode\nobreak\ \text{cm}$ aperture. This serves as the decay volume
for LLPs decaying into a pair of charged particles, with the magnet separating
these to a detectable distance. Next is a spectrometer consisting of two
$1\leavevmode\nobreak\ \text{m}$ long, 0.6 T dipole magnets with three
tracking stations (blue), each composed of layers of precision silicon strip
detectors located at either end and in between the magnets. Scintillator
planes (gray) for triggering and precision time measurements are located at
the entrance and exit of the spectrometer. The final component is an
electromagnetic calorimeter (purple) to identify high energy electrons and
photons and measure the total electromagnetic energy.

Figure 9: Layout of the FASER detector. See text for description of the
detector components.

Open questions, feasibility studies
The FASER signals are two extremely energetic ($\sim\text{TeV}$) coincident
tracks or photons that start at a common vertex and point back to the ATLAS
IP. Muons and neutrinos are the only known particles that can transport such
energies through 100 m of rock and concrete between the IP and FASER.
Preliminary estimates show that muon-associated radiative processes and
neutrino-induced backgrounds may be reduced to negligible levels.

Recently a FLUKA study Ferrari:2005zk ; Bohlen:2014buj ; FLUKAstudy  from the
CERN Sources, Targets and Interactions group has been carried out to assess
possible backgrounds and the radiation level in the FASER location. The study
shows that no high energy ($>100$ GeV) particles are expected to enter FASER
from proton showers in the dispersion suppressor or from beam-gas
interactions. In addition, the radiation level expected at the FASER location
is very low due to the dispersion function in the LHC cell closest to FASER.

Emulsion detectors and battery-operated radiation monitors were installed in
TI12 and TI18 during Technical Stops in 2018. The results from these in situ
measurements have validated the FLUKA estimates, confirming that the high-
energy particle background is highly suppressed and radiation levels are also
very low and not expected to be problematic for detector electronics.
Additional work is ongoing to refine background estimates, evaluate signal
efficiencies, and optimize the detector.

Status of the collaboration
FASER submitted a Letter of Intent (CERN-LHCC-2018-030/LHCC-1-032
Ariga:2018zuc ) to the LHCC in July 2018. At its September meeting, the LHCC
reviewed the LoI favorably and encouraged the FASER Collaboration to submit a
Technical Proposal. This was submitted to the LHCC in November 2018, and based
on a positive review, the LHCC has recommended approving the FASER proposal. A
working group has also been created within the PBC activities to study the
interplay between the detector, the civil engineering, the backgrounds and
radiation levels at the FASER installation point. Two private foundations have
expressed their intent to support FASER’s construction and operation costs.

The FASER group currently (December 2018) consists of 27 collaborators (22
experimentalists and 5 theorists) from 16 institutions in China, Germany,
Israel, Japan, Poland, Switzerland, the United Kingdom, and the United States.
The list of collaborators is the following:

– Tsinghua University, China: G. Zhang;
– University of Mainz, Germany: M. Schott;
– Technion, Israel: E. Kajomovitz;
– Weizmann Institute, Israel: L. Levinson;
– KEK, Japan: Y. Takubo;
– Kyushu University, Japan: T. Ariga (Kyushu/Bern), H. Otono;
– Nagoya University, Japan: O. Sato;
– National Centre for Nuclear Research, Warsaw, Poland: S. Trojanowski
(Sheffield/Warsaw);
– University of Bern, Switzerland: A. Ariga and T. Ariga (Kyushu/Bern);
– CERN, Switzerland: J. Boyd (contact with PBC accelerator group), S. Kuehn,
and B. Petersen;
– University of Geneva, Switzerland: F. Cadoux, Y. Favre, D. Ferrere, S.
Gonzalez-Sevilla, P. Iacobucci, and A. Sfyrla;
– University of Sheffield, United Kingdom: S. Trojanowski (Sheffield/Warsaw);
– Rutgers University, United States: I. Galon;
– University of California, Irvine, United States: D. Casper, J. L. Feng
(contact with the PBC BSM group), F. Kling, J. Smolinsky, A. Soffa;
– University of Oregon, United States: E. Torrence;
– University of Washington, United States: Shih-Chieh Hsu.

The updated status of the collaboration and experiment are available at:
https://twiki.cern.ch/twiki/bin/viewauth/FASER/WebHome. FASER has submited
also a separate document for the next ESPP update.

####  5.3.2 MATHUSLA

Brief presentation, unique features
The basic motivation for the MATHUSLA detector (MAssive Timing Hodoscope for
Ultra-Stable neutraL pArticles) Chou:2016lxi  is the search for LLPs produced
in $\sqrt{s}=14$ TeV HL-LHC collisions, with lifetimes much greater than the
size of the main detectors and up to the BBN constraint of $\sim 0.1$ sec,
with the peak sensitivity near $\beta c\tau\sim$ 100 m. MATHUSLA also has a
secondary physics case as a cosmic ray telescope.

This proposal has been the subject of several studies Co:2016fln ; Dev:2016vle
; Dev:2017dui ; Caputo:2017pit ; Curtin:2017izq ; Evans:2017kti ; Helo:2018qej
; DAgnolo:2018wcn ; Berlin:2018pwi ; Deppisch:2018eth ; Jana:2018rdf ;
Dev:2018sel , and the physics motivation from both a bottom-up and top-down
point of view, including connections to naturalness, dark matter, baryogenesis
and neutrino masses, has been explored in a comprehensive white paper
Curtin:2018mvb . The MATHUSLA collaboration has also recently presented its
Letter of Intent Alpigiani:2018fgd  to the LHCC. Given that some overlap
exists between the MATHUSLA physics case and the PBC framework, the LHC
Committee recommended MATHUSLA to be discussed within the PBC framework as
well.

Location, beam requirements, beam time, timeline
The size of the detector and the corresponding location is not yet finalized.
All sensitivity estimates in this document assume the MATHUSLA200 benchmark
geometry from the Letter of Intent Alpigiani:2018fgd , which was also the
original layout proposed in Chou:2016lxi ; Curtin:2018mvb . This geometry
assumes a very large detector, $200\times 200$ m2 area detector built on the
surface, situated 100 m horizontally and vertically away from a LHC
interaction point IP (either ATLAS or CMS IP), and a decay volume height of 20
m above the ground.

It is very unlikely that a detector with these large dimensions can be
implemented at CERN, hence the sensitivity plots shown in this document should
be properly rescaled once the final geometry will be finalized and the exact
distance from the ATLAS/CMS IP points determined. An integrated luminosity of
3 ab-1 corresponding to the full HL-LHC period is assumed, with a hypothetical
start of the data taking during Run 4. The timeline for the construction of
the detector is under study.

Detector description, key requirements for detector