*

Final

August 29, 2024

Neutrinos from Stored Muons (nuSTORM)
Submitted to the Snowmass 2021 DPF Community Planning Exercise

L. Alvarez Ruso1, T. Alves2, S. Boyd3, A. Bross4, P.R. Hobson5, P. Kyberd6,
J.B. Lagrange7, K. Long2,7, X.-G. Lu3, J. Pasternak2,7, M. Pfaff2,8, C.
Rogers7 on behalf of the nuSTORM collaboration222 The nuSTORM collaboration is
presented in the addendum.

1 Instituto de Fisica Corpuscular (IFIC), Centro Mixto CSIC-UVEG, Edificio
Institutos Investigación, Paterna, Apartado 22085, 46071 Valencia, Spain
2 Physics Department, Blackett Laboratory, Imperial College London, Exhibition
Road, London, SW7 2AZ, UK
3 Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
4 Fermilab, P.O. Box 500, Batavia, IL 60510-5011, USA
5 Department of Physics and Astronomy, Queen Mary University of London,
London, E1 4NS, UK
6 College of Engineering, Design and Physical Sciences, Brunel University,
Uxbridge, Middlesex, UB8 3PH, UK
7 STFC, Rutherford Appleton Laboratory, Harwell Campus, Didcot, OX11 0QX
8 Department of Physics, Technical University Munich (TUM), James-Franck-Str.
1, D-85748 Garching, Germany

## Executive summary

The 2020 Update of the European Strategy for Particle Physics (ESPP) [1]
recommended that muon beam R&D should be considered a high-priority future
initiative and that a programme of experimentation be developed to determine
the neutrino cross-sections required to extract the most physics from the DUNE
and Hyper-K long-baseline experiments. The ENUBET [2, 3, 4] and nuSTORM [5, 6]
collaborations have begun to work within and alongside the CERN Physics Beyond
Colliders study group [7] and the international Muon Collider collaboration
[8] to carry out a joint, five-year R&D programme to deliver a detailed plan
for the implementation of an infrastructure in which:

  * •

ENUBET and nuSTORM deliver the neutrino cross-section measurement programme
identified in the ESPP and allow sensitive searches for physics beyond the
Standard Model to be carried out; and in which

  * •

A 6D muon ionisation cooling experiment is delivered as part of the technology
development programme defined by the international Muon Collider
collaboration.

This document summarises the status of development of the nuSTORM and 6D
cooling experiments and identifies opportunities for collaboration in the
development of the initiative outlined above.

### Elements of the proposed initiative:

ENUBET
The ENUBET (Enhanced NeUtrino BEams from kaon Tagging; NP06) collaboration
proposes a dedicated facility to measure $\nu_{\mu}$ and $\nu_{e}$ cross-
sections precisely using a combination of monitored, narrow-band neutrino
beams at the GeV energy scale and by instrumenting the meson-decay tunnel with
a segmented calorimeter. The ENUBET approach is based on monitoring the
production of large-angle positrons from $K^{+}\rightarrow\pi^{0}e^{+}\nu_{e}$
(Ke3) decays in the decay tunnel. In addition, ENUBET will monitor muons
produced in kaon and pion decays, thus providing a precise measurement of the
$\nu_{\mu}$ flux. Due to the optimisation of the focusing-and-transport system
of the momentum-selected narrow-band beam of the parent mesons, the Ke3 decay
represents the main source of electron neutrinos. Furthermore, the positron
rate may be used to measure the $\nu_{e}$ flux directly. Consequently, the
monitored $\nu_{e}$ beam will lower the uncertainties on the neutrino flux and
flavour for a conventional beam from the current level of O(7%-10%) to $\sim
1\%$. Similar precision is expected for the $\nu_{\mu}$ flux, with the bonus
that the neutrino energy will be determined with a precision of $\sim 10$% at
the single neutrino level by the “narrow-band off-axis technique”, i.e. using
only the position of the $\nu_{\mu}$ interaction vertex.

nuSTORM
The Neutrinos from Stored Muons, nuSTORM, facility has been designed to
deliver a definitive neutrino-nucleus scattering programme using beams of
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from the decay of muons confined within a storage ring. The facility is
unique, it will be capable of storing $\mu^{\pm}$ beams with momentum of
between 1 GeV/c and 6 GeV/c and a momentum spread of $\pm 16$%. The neutrino
beams generated will span neutrino energies from approximately 300 MeV to 5.5
GeV. This will allow neutrino-scattering measurements to be made over the
kinematic range of interest to the DUNE and Hyper-K collaborations. At
nuSTORM, the flavour composition of the beam and the neutrino-energy spectrum
are both precisely known. The storage-ring instrumentation will allow the
neutrino flux to be determined to a precision of 1% or better. By exploiting
sophisticated neutrino-detector techniques such as those being developed for
the near detectors of DUNE and Hyper-K, the nuSTORM facility will:

  * •

Serve the future long- and short-baseline neutrino-oscillation programmes by
providing definitive measurements of
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scattering cross-sections with percent-level precision;

  * •

Provide a probe that is 100% polarised and sensitive to isospin to allow
incisive studies of nuclear dynamics and collective effects in nuclei;

  * •

Deliver the capability to extend the search for light sterile neutrinos beyond
the sensitivities that will be provided by the FNAL Short Baseline Neutrino
(SBN) programme; and

  * •

Create an essential test facility for the development of muon accelerators to
serve as the basis of a multi-TeV lepton-antilepton collider and a Neutrino
Factory.

To maximise its impact, nuSTORM should be implemented such that data-taking
begins by $\approx 2030$ when the DUNE and Hyper-K collaborations will each be
accumulating data sets capable of determining oscillation probabilities with
percent-level precision.

Muon Collider demonstrator
Muon beams of high brightness have been proposed as the source of neutrinos at
a Neutrino Factory and as the means to deliver multi-TeV lepton-antilepton
collisions at a Muon Collider. In most of these proposals the muon beam is
derived from pion decay as is proposed here for nuSTORM. nuSTORM, which will
have beams with the highest ever stored-muon beam power, will allow many of
the challenges associated with the muon storage ring in such facilities to be
addressed, including:

  * •

The complete implementation of a muon storage ring of large acceptance
including the injection and extraction sections; and

  * •

The design and implementation of instrumentation by which to determine the
muon-beam energy and flux to 1% or better. A novel polarimeter system will be
required in order to determine the stored-muon energy and the energy spread.

The opportunity nuSTORM provides for the study of ionisation cooling is
particularly important. The Muon Ionisation Cooling Experiment (MICE) [9] has
demonstrated ionisation cooling in the 4-dimensional transverse phase space
[10]. To prove the feasibility of a Muon Collider therefore requires a follow-
on demonstration of ionisation cooling in the full six-dimensional (6D) phase
space. The facility we propose to develop will be capable of delivering the
required demonstration of 6D ionisation cooling.

### Opportunity:

With their existing proton-beam infrastructure, CERN and Fermilab are both
uniquely well-placed to implement ENUBET, nuSTORM, and the 6D-cooling
experiment as part of the required Muon Collider demonstrator. The design of
ENUBET, carried out within the framework of a European Research Council funded
design study, includes the precise layout of the kaon/pion focusing beamline,
photon veto and timing system as well as the development and test of a
positron tagger together with the required electronics and readout. The
feasibility of implementing nuSTORM at CERN has been studied by the CERN
Physics Beyond Colliders study group while a proposal to site nuSTORM at FNAL
was developed for the last Snowmass study in 2013. The FNAL study focused on
the optimisation of the muon storage ring to provide exquisite sensitivity in
the search for sterile neutrinos. In the Physics Beyond Colliders study, the
muon storage ring was optimised to carry out a definitive neutrino-nucleus
scattering programme using stored muon beams with momentum in the range 1
GeV/c to 6 GeV/c while maintaining its sensitivity to physics beyond the
Standard Model.

The study of nuSTORM is now being taken forward in the context of the
demonstrator facility required by the international Muon Collider
collaboration that includes the 6D muon ionisation cooling experiment. The
muon-beam development activity is being carried out in close partnership with
the ENUBET collaboration and the Physics Beyond Colliders Study Group. In
consequence we now have the outstanding opportunity to forge an
internationally collaborative activity to deliver a concrete proposal on a
five-year timescale for the implementation of an infrastructure in which:

  * •

ENUBET and nuSTORM deliver the neutrino cross-section measurement programme
identified in the ESPP and allow sensitive searches for physics beyond the
Standard Model to be carried out; and

  * •

A 6D muon ionisation cooling experiment is delivered as part of the technology
development programme defined by the international Muon Collider
collaboration.

##  1 Introduction

nuSTORM, the ‘Neutrinos from Stored Muons’ facility, has been designed to
provide intense neutrino beams with well-defined flavour composition and
energy spectrum. By using neutrinos from the decay of muons confined within a
storage ring, a beam composed of equal fluxes of electron- and muon-neutrinos
can be created for which the energy spectrum can be calculated precisely.
According to current design considerations, it will be possible to store muon
beams with momentum from 1 GeV/c to 6 GeV/c and a momentum acceptance of $\pm
16$%. Through its unique characteristics, the nuSTORM facility will have the
capability to:

  * •

Serve a definitive neutrino-nucleus scattering programme with uniquely well-
characterised
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  * •

Allow searches for physics beyond the Standard Model and light sterile
neutrinos with the exquisite sensitivity necessary to go beyond the reach of
the FNAL Short Baseline Neutrino programme; and

  * •

Provide the technology test-bed required for the development of muon beams
capable of serving in a multi-TeV lepton-antilepton (muon) collider.

nuSTORM is based on a low-energy muon decay ring (see figure 1). Pions,
produced in the bombardment of a target, are captured in a magnetic channel.
The magnetic channel is designed to deliver a pion beam with momentum
$p_{\pi}$ and momentum spread $\sim\pm 10\%\,p_{\pi}$ to the muon decay ring.
The pion beam is injected into the production straight of the decay ring.
Roughly half of the pions decay as the beam passes through the production
straight. At the end of the straight, the return arc selects a muon beam of
momentum $p_{\mu}<p_{\pi}$ and momentum spread $\sim\pm 16\%\,p_{\mu}$ that
then circulates. Undecayed pions and muons outside the momentum acceptance of
the ring are directed to a beam dump. Pions from the target can also be
directed to a decay channel in which low-energy muons are collected and
transported to a 6D ionisation cooling experiment. ENUBET can be served with
pion and kaon beams in the same complex through the addition of a third
transfer line from the target complex.

Target6D cooling demonstrator$\mu$$\mu$$\mu$Storage ring$\pi$OCS$\nu_{\mu}$,
$\nu_{e}$, Detector Figure 1:  Schematic of the nuSTORM muon and neutrino-beam
facility. The proton beam extracted from the FNAL Main Injector or the CERN
SPS or PS strikes a target. Pions are collected using a horn and directed into
conventional transfer lines that transport pions either to nuSTORM or a 6D
muon ionisation cooling demonstration experiment. ENUBET, which requires pion
and kaon beams, can be served using a third transfer line (not shown).

A detector placed on the axis of the nuSTORM production straight will receive
a bright flash of muon neutrinos from pion decay followed by a series of
pulses of muon and electron neutrinos from subsequent turns of the muon beam.
Appropriate instrumentation in the decay ring and production straight will be
capable of determining the integrated neutrino flux with a precision of
$\mbox{\raisebox{-1.72218pt}{$\;\stackrel{{\scriptstyle<}}{{\scriptstyle\sim}}\;$}}1$%.
The flavour composition of the neutrino beam from muon decay is known and the
neutrino-energy spectrum can be calculated precisely using the Michel
parameters and the optics of the muon decay ring. The pion and muon momenta
($p_{\pi}$ and $p_{\mu}$) can be optimised to measure
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interactions with per-cent-level precision over the neutrino-energy range
$0.3\mbox{\raisebox{-1.72218pt}{$\;\stackrel{{\scriptstyle<}}{{\scriptstyle\sim}}\;$}}E_{\nu}\mbox{\raisebox{-1.72218pt}{$\;\stackrel{{\scriptstyle<}}{{\scriptstyle\sim}}\;$}}5.5$
GeV and to search for light sterile neutrinos with excellent sensitivity.

##  2 Motivation

The case for the nuSTORM facility rests on three themes:

  1. 1.

The uniquely well-defined neutrino beam generated in muon decay can be
exploited to make detailed studies of neutrino-nucleus scattering over the
neutrino-energy range of interest to present and future long- and short-
baseline neutrino oscillation experiments. The high-flux beams illuminating
the detectors of future long-baseline experiments will allow the accumulation
of very large data sets. Projections of the rate at which data will be
collected in long-baseline experiments indicate that the statistical error
will be reduced to the percent level by 2028–30. To optimise the discovery
potential of such facilities requires that the systematic uncertainties be
reduced to the percent level on a comparable timescale. This can be achieved
by dedicated cross-section measurements by which to break the correlation
between the cross-section and flux uncertainties and to reduce the overall
systematic uncertainty to a level commensurate with the statistical and other
systematic uncertainties in experiments such as Hyper-Kamiokande and DUNE.

The nuSTORM
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programme is no less important for the next generation of short-baseline
experiments for which uncertainties in the magnitude and shape of backgrounds
to the sterile-neutrino searches will become critically important. At nuSTORM,
the flavour composition of the neutrino beam is known and its energy spectrum
may be determined precisely using the storage-ring instrumentation. The
precise knowledge of the neutrino flux combined with advanced detector
techniques that are currently being developed will allow nuSTORM to provide
the measurements necessary to maximise the sensitivity of the next generation
of long- and short-baseline experiments.

  2. 2.

The nuSTORM neutrino beam instrumented with state-of-the art and magnetised
near and far detectors, will allow searches for physics Beyond the Standard
Model of unprecedented sensitivity to be carried out. The signal to background
ratio for this combination is of order ten and is much larger than for other
accelerator-based projects.

  3. 3.

The storage ring itself, and the muon beam it contains, can be used to carry
out the R&D programme required to implement the next step in the incremental
development of muon accelerators for particle physics. Muon accelerators have
been proposed as sources of intense, high-energy electron- and muon-neutrino
beams at the Neutrino Factory [11, 12] and as the basis for multi-TeV
$l^{+}l^{-}$ collisions at the Muon Collider [13, 14]. An incremental approach
to the development of the facility has been outlined in [15], which has the
potential for the elucidation of the physics of flavour at the Neutrino
Factory and to provide multi-TeV $l^{+}l^{-}$ collisions at the Muon Collider.
nuSTORM would be the first neutrino-beam facility to be based on a stored muon
beam and will provide a test-bed for the development of the technologies
required for a multi-TeV Muon Collider and/or a Neutrino Factory.

Just as the three legs of a tripod make it a uniquely stable platform, the
three individually-compelling themes that make up the case for nuSTORM
constitute a uniquely robust case for a facility that will be at once
immensely productive scientifically and seminal in the creation of a new
technique for particle physics.

###  2.1 Neutrino-nucleus scattering

nuSTORM will allow unprecedentedly precise studies of both elementary
processes and neutrino-nucleus scattering to be performed. These prospects are
not only interesting by themselves as a source of information about the axial
structure of nucleons and nuclei, but also crucial to achieve the high-
precision goals of neutrino oscillation experiments [16, 17]. Indeed, near
detectors help to reduce systematic uncertainties but do not turn oscillation
analysis into a mere rescaling because near and far detectors are not
identical, have different efficiencies and are illuminated by different
neutrino fluxes. In addition, oscillation probabilities depend on the neutrino
energy which is not known on an event-by-event basis but has to be
reconstructed. To minimise any bias in neutrino-energy reconstruction a
realistic simulation of the interaction process is necessary.

####  2.1.1 Elementary processes

In this context, by elementary processes one understands neutrino-nucleon
interactions, whose relevance is often underestimated. The available
information about them is scarce and comes mostly from old bubble chamber
experiments. These cross-sections could be measured directly using hydrogen or
deuterium targets or indirectly with the help of hydrogen-enriched targets and
subtraction techniques. Examples of these are the solid hydrogen concept [18],
where the (anti)neutrino proton interactions are obtained from the subtraction
of events in plastic (CH2) and graphite (C) targets and a high pressure TPC
with hydrogen-rich gases (such as CH4), where the cross-section on hydrogen
would be extracted using transverse kinematic imbalance [19, 20]. nuSTORM is
the ideal place for such experiments because of the precision that can be
achieved. The input for event generators would be highly valuable.
Furthermore, the availability of both muon and electron flavours of neutrinos
under similar experimental conditions would allow the investigation of flavor-
dependent features such as radiative corrections and non-standard (BSM)
interactions.

The simplest elementary process is charged-current quasielastic scattering
($\nu_{l}\,n\rightarrow l^{-}\,p$ and $\bar{\nu}_{l}\,p\rightarrow l^{+}\,n$).
Even for such a basic process, which could serve as a standard candle to
constrain neutrino fluxes, the dependence of the axial form factor ($F_{A}$)
on the four-momentum transferred to the nucleon squared ($Q^{2}$) is not
precisely measured. Moreover, it has been noticed recently that lattice-QCD
determinations of $F_{A}(Q^{2})$ are in fairly good agreement among themselves
but in tension with empirical determinations [21] (see Fig. 2, left, taken
from this review). These lattice-QCD results would imply a 20% increase of the
quasielastic cross-section, as shown in the right panel of Fig. 2, also from
[21].

Figure 2: Left: $F_{A}$ obtained in recent lattice-QCD studies compared to its
determination from bubble chamber experiments using the z-expansion. Right: QE
integrated cross-section from various parametrizations of the form factors.
Details can be found in reference [21] from where these plots are taken.

Neutrinos also scatter inelastically on nucleons, predominantly leading to
single pion ($\pi N$) but also to $\gamma N$, $\pi\pi N$, $\eta N$, $\rho N$,
$KN$, $\pi\Sigma$, $\bar{K}N$, $KY$, $\ldots$ final states. For inelastic
processes, the cross-section arises from the interplay of resonant and non-
resonant amplitudes, which become highly non-trivial at higher invariant mass
hadronic final states, with several overlapping resonances and coupled
channels. This is the shallow inelastic scattering region, where a large
fraction of events at DUNE will be found. The dynamics have been investigated
in detail in partial wave analyses of large data sets available for photon,
electron and pion-nucleon interactions. This information is valuable to
constrain weak inelastic processes and has been used in their modelling as
reviews, for instance, in reference [22]. However, the properties of the axial
current at finite $Q^{2}$ remain experimentally unconstrained. The transition
from the resonant to the deep-inelastic scattering regime is also highly
uncertain. Quark-hadron duality on one hand and QCD (higher-twist and target
mass) corrections on the other are valuable tools to describe it (see
reference [23] for a recent review), but progress in their development is
hindered by the lack of experimental nuclear-effect-free information from
elementary targets. With muon momenta in the range $1\leq p_{\mu}\leq 6$
GeV$/c$, the resulting neutrino spectrum goes up to $\sim 5.5$ GeV and would
make the detailed study of this region possible.

####  2.1.2 Neutrino-nucleus interactions

There is considerable interest in the study of neutrino scattering on the
heavy targets used in oscillation experiments. nuSTORM will have a strong
impact by characterising the flavour differences which are particularly
important at low energy and momentum transfers (in the laboratory frame).
These differences can arise from a subtle interplay between lepton kinematic
factors and response functions [24]. The search for CP-invariance violation in
present and planned long-baseline neutrino-oscillation experiments is based on
the measurement of the rate of $\nu_{e}$ appearance in $\nu_{\mu}$ beams.
nuSTORM has the potential to perform high-statistics measurements of the
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301\relax$}\cr\vskip-1.29167pt\cr$\scriptscriptstyle\nu$\cr}}}_{e}$ cross-
sections and, in particular, the $\sigma(\nu_{e})/\sigma(\nu_{\mu})$ cross-
section ratio, which is among the largest systematic uncertainties at DUNE
[25]. With the help of nuSTORM, the required sensitivity to CP violation can
be reached with a smaller exposure.

Measurements of quasielastic-like scattering at nuSTORM can also lead to a
better description of initial state nucleon-nucleon correlations and meson-
exchange currents, which are known to provide a sizeable contribution to the
semi-inclusive electron scattering cross-section and have been found important
at MiniBooNE and T2K: comparisons of different theoretical results to data can
be found, for example, in Figures 8-9 of reference [26] (MiniBooNE) and in
Figures 7-9 of reference [27] (T2K). The comparisons of the SUSA model to
these data have been recently summarised in reference [28]. Discrepancies with
theory (or, at least with its generator implementation) have been found at the
higher energy and momentum transfers probed at MINERvA and NOvA as can be
appreciated in references [29, 30]. With unprecedented understanding of the
beam flux (see section 3.3) and sophisticated detector designs (see section
3.2), nuSTORM can play an important role in understanding these differences.

The characterisation of nuclear corrections to parton distribution functions
will also benefit from precise measurements of the inclusive neutrino-nucleus
cross-section, to unravel the differences in nuclear effects observed in weak
and electromagnetic processes and to resolve the tensions that have been
observed by nCTEQ. It was suggested that $\nu A$ and $l^{\pm}A$ data could
only be reconciled if the correlations in $\nu A$ were not taken into account.
However, a more recent comprehensive nCTEQ analysis indicates that neglecting
correlations does not relieve the tension between $\nu A$ and $l^{\pm}A$ data.
More precise data on a wider variety of nuclear targets would be most welcome.

With a suitable detector set, nuSTORM can also study exclusive channels in
neutrino-nucleus scattering (see section 3.4). These include one and two-
nucleon knockout but also single and multiple meson production. These
reactions are largely influenced by strong final state interactions between
the produced particles and the nuclear environment. Pions, in particular, can
scatter, change charge or be absorbed on their way out of the nucleus [31].
Pion production will play an important role in the future neutrino oscillation
programme. Pioneering measurements of pion production by MINERvA (cf. review
article [32] and references therein) have shown tensions with model
predictions (see, for example, figure 3). Accurate modelling of these
interactions are crucial to reduce biases in calorimetric neutrino energy
determination.

Figure 3:  Flux-averaged differential cross-section in the emulated nucleon
momentum, $p_{\textrm{n}}$, measured by MINERvA with the Low-Energy NuMI beam
flux peaking at 3 GeV on a scintillator (CH) target. The peak region of the
$p_{\textrm{n}}$ distribution directly reflects the Fermi motion of the struck
neutron in the charged-current $\pi^{0}$ production [33, 34, 35]. Comparisons
with NuWro [36] and GiBUU [37, 38, 39] predictions are made. Figures from
reference [40].

###  2.2 Searches for physics beyond the Standard Model

####  2.2.1 Rare scattering processes

If the precision of the nuSTORM concept is combined with high statistics, the
study of rare processes with small cross-sections becomes feasible. Processes
in this category include neutrino-electron scattering, coherent meson
production, weak and electromagnetic production of single photons and
dileptons. In addition to elementary quasielastic scattering, neutrino-
electron scattering or even coherent meson production could be precisely
measured and used as standard candles for flux determination in other
experiments. Furthermore, weak couplings and $\sin^{2}{\theta_{W}}$ can be
extracted, providing a precision test of the Standard Model (SM). Unlike DUNE,
nuSTORM has access to both $\nu_{\mu}-$ and $\nu_{e}-$electron scattering.

While these exotic processes are allowed in the SM, precision measurements can
disclose physics beyond the Standard Model (BSM). This is the case in neutrino
tridents in which neutrino scattering off the Coulomb field of a heavy nucleus
generates a pair of charged leptons. The existence of light $Z^{\prime}$ or
other particles in the dark sector can modify the trident cross-section [41].

Single photon emission in neutral current interactions is another rare process
that has received attention as a background in $\nu_{e}$ appearance
measurements in Cherenkov detectors. Its cross-section has never been measured
and, so far, only upper limits from NOMAD, T2K and, more recently, MicroBooNE
are available. Besides, some of the proposed explanations of the MiniBooNE
anomaly involve the production of a heavy (1–100 MeV) neutrino via
electromagnetic ($\gamma$ mediator), weak ($Z$) or BSM ($Z^{\prime}$)
interactions, leading to a signal in the single photon or $e^{+}e^{-}$
channels (see reference [42] for a recent review). While recent MicroBooNE
results disfavour some explanations of the MiniBooNE anomaly, the full range
of possible solutions is still unexplored [43].

####  2.2.2 Short-baseline flavour transitions and sterile neutrino searches

The unique neutrino beam composition at nuSTORM allows to use
$\mu^{+}\rightarrow e^{+}\,\nu_{e}\bar{\nu}_{\mu}$ decay to search for short-
baseline oscillations using muon final states. In particular, for the first
time, nuSTORM would allow to search for $\nu_{\mu}$ appearance from
$\nu_{e}\rightarrow\nu_{\mu}$ oscillations, which is not subject to photon-
like and intrinsic $\nu_{e}$ contamination as in other accelerator
experiments. This appearance measurement relies on a good charge
identification to discriminate the $\mu^{-}$ signal from the intrinsic
$\mu^{+}$ background from the muon-decay $\bar{\nu}_{\mu}$ component. The
latter can also be used to search for
$\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{\mu}$ disappearance. The low flux
systematics allow to reach greater levels of precision in the total
normalisation of the event rate, and one can expect this measurement to be
limited by the cross-section uncertainties. Nevertheless, greater sensitivity
can be achieved by identifying spectral distortions of the $\mu^{+}$ spectrum
in the detector; this would require accurate momentum measurement.

In Ref. [44], a detailed study of the sensitivity of the previous Fermilab
design of nuSTORM to sterile neutrinos was performed. This was based on a far
detector located at $2$ km from the muon storage ring and a total of $10^{21}$
POT, corresponding to approximately $2\times 10^{18}$ useful muon decays. The
detector was a $1.3$ kt magnetised iron-scintillator detector with excellent
muon charge discrimination. The final sensitivity was found to be greater than
$5\sigma$ throughout the entire region of oscillation parameter space
preferred by the MiniBooNE and LSND results. Ref. [6] expanded the scope of
the oscillation search to show that nuSTORM can also provide very stringent
tests of the unitarity of the neutrino mixing matrix, non-standard
interactions, as well as Lorentz and CPT symmetries.

In summary, nuSTORM would be capable of addressing open questions concerning
the non-unitarity of the neutrino mixing matrix, non-standard interactions,
Lorentz invariance (and CPT violation) and provide a definitive test of light
sterile neutrinos [44, 6].

###  2.3 Technology test-bed

A Muon Collider has the potential to deliver lepton-anti-lepton collisions at
centre-of-mass energies up to 10 TeV at a cost and on a timescale advantageous
when compared to electron-positron or next-generation hadron colliders [45].
The international Muon Collider collaboration is developing conceptual designs
for facilities capable of operation at centre-of-mass energies of 3 TeV and 10
TeV [8].

nuSTORM will have the world’s highest power stored muon beam. Such a beam will
provide the opportunity to develop and test technologies that will be critical
to the delivery of muon beams with the brightness necessary for the Muon
Collider to deliver the specified luminosity of $\sim 10\times 10^{34}\,{\rm
cm}^{-2}\,{\rm s}^{-1}$. In particular, a low-energy muon beam may be produced
through the capture of an appropriate pion-beam phase space at the nuSTORM
target. The muon beam derived from pion decay could be directed towards a muon
ionisation cooling system designed to demonstrate the feasibility of reducing
the muon-beam phase space in all six phase-space dimensions.

The principle of ionisation cooling was demonstrated by the MICE collaboration
[10]. The MICE experiment determined the change in the transverse emittance of
a muon beam as it passed through a single liquid-hydrogen or lithium-hydride
absorber. The muon beams used by MICE had momentum in the range 140 MeV/c to
240 MeV/c and emittance in the range 3 mm to 10 mm. For the Muon Collider to
achieve its design luminosity requires transverse and longitudinal emittances
of $25\,\mu$m and 7.5 MeV m respectively. An experiment based on the lessons
learnt at MICE, can be used to develop the techniques to compress the 6D
phase-space volume of a muon beam to the values required to achieve the
luminosity specification of the Muon Collider.

####  2.3.1 Muon ionisation cooling

Ionisation cooling is effected by passing a muon beam through a material (the
absorber), in which it loses energy, and subsequently accelerating the beam to
restore the energy lost in the absorber. The ionisation cooling process occurs
on a short timescale and is therefore able to cool the beam efficiently with
modest decay losses. The net effect of the energy-loss/re-acceleration process
is to reduce the transverse beam size, i.e. to reduce the _transverse
emittance_.

Multiple Coulomb scattering is detrimental to the cooling performance. Energy
absorbers made from materials having low atomic number, such as lithium or
hydrogen, are preferred as the ratio of ionisation energy loss to multiple
Coulomb scattering is favourable. If the beam is tightly focused the effect of
multiple Coulomb scattering relative to the intrinsic beam divergence is
reduced. Therefore ionisation cooling lattices must be designed to maintain
very tight focusing.

Random fluctuations in energy loss, known as energy straggling, tend to result
in an increase in the beam-energy spread and hence longitudinal emittance. It
is possible to reduce the longitudinal emittance of the beam by introducing a
dipole and wedge-shaped absorber onto the beamline. The dipole bends lower
momentum particles more strongly, introducing a correlation between energy and
position. By aligning the thicker part of the wedge with high energy particles
and the thinner part of the wedge with low energy particles, the energy spread
is removed and replaced with an increased spread in position. This is an
emittance exchange process; the energy spread of the beam is decreased at the
expense of an increased transverse emittance. Transverse emittance, in turn,
is reduced by the ionisation cooling process. Overall the size of the beam in
the 6D phase space $(x,p_{x},y,p_{y},t,E)$ is reduced.

####  2.3.2 6D cooling system design

The baseline design for the Muon Collider ionisation cooling system is of
order 1 km long. The main part comprises the rectilinear cooling system
described in [46]. In this system, focusing is achieved by means of solenoids
having fields up to around 12 T. A weak dipole field is introduced that
creates a position-energy correlation and wedge-shaped absorbers are used to
deliver 6D cooling. Early parts of the system, where the beam has large
emittance, are optimised for large acceptance, while later parts of the system
are optimised for cooling to low emittance.

The proposed demonstrator facility would comprise around 50 m of cooling
equipment, as shown in figure 4. Low momentum pions are diverted from the
target region by means of a dipole switchyard. Off-momentum pions are rejected
and the resultant beam is collimated while the pions decay to muons.
Collimation is necessary in order to deliver a low emittance beam suitable for
demonstration of later stages of the cooling system. A short, high voltage
section of RF then accelerates or decelerates particles that are out of phase
with the RF cavities yielding a bunched beam. Finally, a short focusing system
is used to ensure parameters such as muon-beam divergence and position spread
are matched to the cooling channel focusing system.

Figure 4:  Schematic of a possible implementation of the Muon Collider
demonstrator for 6D cooling.

For beam cooling, a tightly packed lattice of RF cavities, absorbers and
solenoids is envisaged. The later stages of the rectilinear cooling system
operate in the second stability region, where each cell of the magnet lattice
has two foci; one at the absorber and a weaker focus in the centre of the RF
cavities. This can be achieved with solenoids having fields up to about 10 T.
Sufficient dispersion can be achieved by appropriate choice of dipole polarity
and field, so that low angle wedges can be used while yielding a satisfactory
longitudinal cooling performance.

Instrumentation is required upstream and downstream of the cooling system to
measure the beam emittance and a dedicated section of beamline is foreseen to
support this. Additional instrumentation is required in each module to support
operations such as beam alignment and RF phasing. Beam intersecting devices or
instrumentation of the absorbers may be an effective means of monitoring the
muon beam, less readily achievable in a more conventional beamline.

##  3 nuSTORM facility; overview

The following sections give a brief description of the development of the
nuSTORM concept since it was presented in [6]. The authors are actively
developing the accelerator design, the detector concept, and the analysis
framework. Therefore the summary presented below should be considered a
snapshot in the development of the nuSTORM facility.

###  3.1 Accelerator facility

####  3.1.1 Target and pion transport

The feasibility of implementing nuSTORM at the SPS at CERN was presented in
[6]. The proton beam extracted from the SPS at 100 GeV is focused on a solid
(low-$Z$) target placed inside a focusing horn. In the simulations presented
below, the proton beam impinges on an inconel target. Other materials for the
target, such as graphite, may be considered. Particles emerging from the
target are focused by the horn and collected in a short transfer line with a
large momentum acceptance of $\sim\pm 10\%$. The transfer line is composed of
dipoles, collimators and quadrupoles. It is proposed that the target, horn and
the initial part of the transfer line are contained in an inert helium
atmosphere to reduce activation and corrosion of beam-line equipment by
limiting the presence of ozone and nitrogen oxides. The target-and-collection
system will be installed underground in a cavern, with a shaft giving access
to a surface building. The shaft and surface buildings will be offset with
respect to the incoming proton beam direction, the target, and the outgoing
pion beam.

The design of the pion transfer line is based on the initial FNAL design. The
design was modified to accommodate the projected radiation hazards and an
improved injection scheme. A modular construction scheme, allowing for a
greater degree of flexibility during the design phase and using simple
quadrupole FODO cells and achromatic dipole bends, was adopted. An initial
capture section will be present inside the initial containment vessel, which
will be followed by the proton absorber. A series of collimators will be used
in addition to the bending sections to reduce the radiation load on the
downstream beam lines.

The first achromatic bending section is used to divert particles within the
desired momentum range away from the proton absorber towards the ring. This is
key to reduce the radiation dose to downstream elements and provide a momentum
selection for the transmitted pion beam. A quadrupole FODO lattice is used to
transport the beam to a second achromatic bending section followed by beta-
function matching and injection into the ring. The length of this section was
chosen to ensure the radiation contamination within the arc sections of the
ring is minimised, whilst being short enough to ensure that pions of low
momentum can be successfully transported. Building on [6], the beta-function
and dispersion matching section has been defined and the first integration of
the transfer line with the ring injection system has been performed.

Pion production in the target was simulated using MARS [47] and FLUKA [48,
49]. The particle-distribution was used as input for beam-dynamics studies of
the transfer line using BDSIM code [50]. The beam dynamics simulations
confirmed the large momentum acceptance of the transfer line. The layout of
the transfer line simulated in BDSIM is shown in figure 5. The optical
functions of the transfer line, shown in figure 6, were reproduced using beam
dynamics simulations in BDSIM. The values of the optical functions obtained
with BDSIM agree well with the design values and provide the correct beam
conditions at the injection to the ring.

Figure 5:  Schematic drawing of the pion transfer line generated in BDSIM
code.  Figure 6:  The $\beta$ functions ($\beta_{x}$\- blue, $\beta_{y}$\-
green) and dispersion ($D_{x}$\- red) in the pion transfer line downstream
from the horn until the end of the injection septum generated using beam
dynamics simulations in BDSIM code.

####  3.1.2 Storage ring design

The nuSTORM decay ring, shown schematically in figure 7, is a compact
racetrack storage ring with a circumference of $\sim 616$ m that incorporates
large aperture magnets. In order to include the orbit combination section
(OCS), used for the stochastic injection of the pion beam into the ring, a
dispersion suppressor is needed between the arc and the production straight.
Strong bending magnets are also needed in the arcs to minimise the arc length,
in order to maximise the number of useful muon decays.

Figure 7:  Schematic drawing of the revision of the muon storage ring. The
beam circulates in an clockwise direction. The production straight (at $x\sim
30$ m) is composed of large aperture quadrupoles that produce the large values
of the betatron function required to minimise the divergence of the neutrino
beam produced in muon decay. The lattices of the arcs and return straight are
based on the Fixed Field Alternating gradient (FFA) concept and allow a large
dynamic aperture to be maintained.

Several designs for the nuSTORM storage ring have already been proposed based
either on a separated function magnet or Fixed Field Alternating gradient
(FFA) approach [51, 52, 53]. To serve the neutrino-scattering programme, the
ring was redesigned to store muon beams with a momentum of between 1 GeV/c and
6 GeV/c with a momentum acceptance of up to $\pm 16$%, thereby increasing the
neutrino flux. To keep the momentum acceptance and transverse dynamic
acceptance large, and simultaneously to maximise the muon accumulation
efficiency, a hybrid concept was developed (figure 7). Conventional FODO
optics, used in the production straight, are combined with FFA cells, for
which the chromaticity is zero, in the arcs and in the return straight. This
allows the revised lattice to achieve:

  * •

Zero dispersion in the quadrupole injection/production straight;

  * •

Zero chromaticity in the arcs and in the return straight, thereby limiting the
overall chromaticity of the ring; and thus

  * •

Large overall transverse and momentum acceptance.

The arcs exploit superconducting combined-function magnets with magnetic
fields of up to $\sim 2.6$ T. The return straight is based on combined-
function room-temperature magnets. The production straight uses large-aperture
room temperature quadrupoles. The vertical magnetic field around the ring for
the maximum momentum ($\sim 6$ GeV/c) muon closed orbit in the racetrack FFA
ring is shown in figure 8. The mean betatron functions in both the production
and return straights are kept large enough to minimise the contribution of
betatron oscillations to the angular spread of the neutrino beam, such that
both can be used to serve a neutrino-physics programme.

The arc cells have a high magnet-packing factor to minimise the arc length and
are connected with the injection and return straights using specific matching
sections. The matching section serving the injection straight matches
dispersion to zero and allows a long straight for injection to be
accommodated. Additional matching sections are between the arcs and the cells
of the return straight. The Twiss parameters around the ring are shown in
figure 9. Selected parameters of the hybrid design for the racetrack ring are
summarised in table 1. The reference tunes of the machine ($8.203$, $5.159$)
are chosen such that they are not close to the dangerous resonances. The off-
momentum tunes have been chosen to avoid integer and half-integer resonances
(see figure 10). Further reduction of the chromaticity of the ring is possible
by altering the nonlinear magnetic field distribution in the regular arc
cells.

Total circumference | 616 m
---|---
Length of one straight section | 180 m
One straight section/circumference ratio | 29%
Operational momentum range | 1–6 GeV/c
Reference momentum | 5.2 GeV/c
Reference tunes ($Q_{h}$, $Q_{V}$) | ($8.203$, $5.159$)
Momentum acceptance | $\pm 16\%$
Number of cells in the ring: |
Straight quad cells | 6
Arc first matching cells | 4
Arc cells | 12
Arc second matching cells | 4
Straight matching FFA cells | 1 (+1 mirror)
Straight FFA cells | 8
Table 1: Selected parameters of the hybrid FFA storage ring. Figure 8:  The
vertical magnetic field for the maximum momentum ($\sim 6$ GeV/c) muon closed
orbit in the racetrack FFA ring.  Figure 9:  The betatron functions
(horizontal-blue and vertical-purple) and dispersion (green) for reference
momentum ($5.2$ GeV/c) muon closed orbit in the racetrack FFA ring.  Figure
10:  The machine tunes for the muon beam stored in the nuSTORM ring at the
reference momentum of 5.2 GeV/c with the momentum spread of $\pm 16$%.

The performance of the hybrid FFA design for the storage ring was verified in
tracking studies. In order to incorporate tracking through the combined-
function magnets, taking into account the fringe fields and large amplitude
effects, a code used for the full FFA machine developed previously was used
[53]. It is a stepwise tracking code based on Runge-Kutta integration, using
Enge-type fringe fields. The results of the multi-turn tracking show that the
dynamical acceptance of the machine is about $1\,\pi$ mm rad in both
transverse planes, which is required for the needs of the experimental
programme, as shown in figure 11. The studies to cross-check the results with
the PyZgoubi code, as performed successfully before [53], are underway.

Figure 11:  The horizontal (left-hand plot) and the vertical (right-hand plot)
dynamical acceptance studies in the hybrid nuSTORM ring at the reference
momentum of 5.2 GeV/c. Particles are tracked over 100 turns with different
amplitudes in the plane of study including a small off-set from the closed
orbit in the other plane. The black ellipse represents the acceptance of
$1\,\pi$ mm rad.

###  3.2 Detector considerations

As has been described, the detector at the nuSTORM facility will deliver a
rich programme of neutrino-interaction physics that can be explored with
unprecedented precision and an unprecedented reach in searches for new
phenomena. In order to take full advantage of these opportunities, the
detector requirements extend far beyond that needed for a 3-flavor oscillation
search. Options for the detectors are discussed below, but we list some of the
overarching performance requirements here:

  * •

Highly segmented detectors capable of operation at high event rate. Detectors
with precise 3D tracking (or very precise timing) capability over 4$\pi$ are
required.

  * •

Detectors with excellent muon and electron ID capability.

  * •

Detectors with excellent energy resolution.

  * •

A magnetised detector so that the charge of the muon and electron in the final
state can be determined. In addition reconstruction via spectrometry can be
applied to event reconstruction as opposed to being done via calorimetry. This
is particularly important for higher energy nuSTORM tunes neutrino
interactions where the outgoing muon’s momentum must be measured via
spectrometry.

  * •

Detectors with excellent hadronic particle ID, i.e. p/$\pi$/K separation at
momenta from a few hundred MeV/c to a few GeV/c.

  * •

Detectors with neutron detection capability (with energy determination).

  * •

A detector that presents a variety of nuclear targets to measure cross-
sections as a function of the nuclear target mass number A.

Many of the detector concepts now incorporated in the upgraded T2K near
detector [54] and those being developed for DUNE [55] are appropriate for
detectors at nuSTORM. These concepts include:

  1. 1.

Highly-segmented tracking scintillator detector (SuperFGD);

  2. 2.

Pixelated LAr detector;

  3. 3.

Magnetised high-pressure gaseous Ar TPC (HPgTPC);

  4. 4.

Straw-Tube trackers (STT) with thin targets.

Magnetisation of all these detectors is under consideration. The SuperFGD for
T2K is a magnetised detector as will be the STT for DUNE. The HPgTPC is by
design a magnetised detector. Although magnetisation concepts for a pixelated
LAr have been developed, the high cost for the magnet system presents
obstacles to its use, although R&D on high-temperature superconductor and
cable may make this option affordable.

Although the concept of magnetisation in neutrino detectors is not new, the
application of a collider-detector design for neutrino physics is. One such
example is the high-pressure gas TPC (HPgTPC) detector concept (called ND-GAr)
for the DUNE near detector complex [56]. An overview of the detector is shown
in Figure 12.

Figure 12:  Schematic of the ND-GAr concept. From inside out, Yellow: HPgTPC,
Blue: ECAL, Grey: Superconducting solenoid in its cryostat and Red: Return
Iron.

ND-GAr is a large detector with a magnetic volume that is approximately 7 m in
diameter and 7.5 m long (both the HPgTPC and the ECAL are in the magnetic
volume). The solenoid magnet and the return iron provide pressure containment.
This detector offers many advantages including: capability to vary the target
nucleus (main gas component) from He to Xe, operation at pressures from 1 Bar
to 10 Bar, 4$\pi$ tracking with track thresholds down to 5 MeV, excellent
particle ID which allows for very precise determination of exclusive final
states and the addition of a magnetic field allows for energy measurement via
spectrometry as well as calorimetry (from the ECAL). In DUNE, ND-GAr functions
as muon catcher for the pixelated LAr detector which is just upstream. The
return iron has a window which allows muons that exit the LAr to be accurately
momentum analysed in the HPgTPC.

###  3.3 Neutrino fluxes

We consider the neutrino energy spectrum at the front face of a detector of
area 5 m by 5 m placed 50 m beyond the end of the nuSTORM production straight.
We present the results for two pion energies, 3 GeV and 5 GeV and three
neutrino signals: $\nu_{\mu}$ from pion decay in the production straight,
referred to as pion flash; $\nu_{\mu}$ and $\nu_{e}$ from muon decays in time
with the pion decays in the production straight; $\nu_{\mu}$ and $\nu_{e}$
from muons which decay in the production straight of the nuSTORM ring after
the end of the pion flash. These numbers for the 5 GeV pion beam are
normalised to the number of protons on target; for the 3 GeV beam there are
still unexplained losses in the FLUKA simulation and so we show results
normalised to the number of pions accepted by the transfer line. The number of
pions produced when modelling the production target with MARS and FLUKA are
sufficiently different that attempting to normalise rates to protons on target
would be misleading.The results are presented assuming a 100 GeV proton beam
on the production target; we have not considered in detail the effect of using
the 26 GeV beam from the CERN PS. The distributions are similar in pion angle
and energy, but the 100 GeV beam produces about a factor of 5 more pions at
all energies. At present we are agnostic on the choice of primary beam energy,
merely noting that a lower energy requires more intensity or longer running
for the same sensitivity.

Neutrinos from muons which decay before they reach the end of the production
straight and are captured by the ring, overlap in time with the pion decays in
the production straight and constitute a background to the pion flash signal
of around 1%. While neutrinos from muons which are captured by the nuSTORM
ring and decay during subsequent rotations round the ring, are essentially
background free. A number of other sources of backgrounds are considered and
where it can be shown that the contamination will be well below 1%, no attempt
is made to simulate them in detail. A description of the simulation and
background estimation can be found in Appendix A and B.

####  3.3.1 Pion flash neutrinos at $E_{\pi}$=5 GeV and 3 GeV

The biggest source of neutrinos are those from the pion flash. Figure 13 shows
the energy spectrum of those pions. The plot on the left is for a central
$E_{\pi}$ of 5 GeV and right a central $E_{\pi}$ of 3 GeV, in each case with a
$\pm 10\%$ momentum bite, corresponding to the design parameters of the
machine. The background from in-time muon decays is shown scaled up by a
factor 40.

Figure 13:  Left: Pion flash energy spectrum for $E_{\pi}$=5 GeV and
associated muon backgrounds. Right: Pion flash energy spectrum for $E_{\pi}$=3
GeV and associated muon backgrounds.

####  3.3.2 Muon signal neutrinos $E_{\pi}$=5 GeV and 3 GeV

The number of $\nu_{\mu}$’s and $\nu_{e}$’s, which reach the front face of the
detector is similar; their energy spectrum is similar with the $\nu_{\mu}$’s
being slightly harder. We simulated three times as many events at 3 GeV in
order to give us a comparable number of events at 3 GeV and 5 GeV. Dropping
the central pion energy to 2 GeV looses another factor of 2. This energy
dependence is largely due to the way the angular distribution of the neutrinos
broadens as the $Q$ value of the decay becomes a larger fraction of the beam’s
kinetic energy. The distance of the detector front face from the end of the
production straight has not been optimised, but when we start detailed design
of the hall and accelerator layout, it will be important to keep this distance
as short as possible.

Figure 14:  Signal neutrinos from muon decay. Left: $\nu_{\mu}$ (Red) and
$\nu_{e}$ (Blue) at $E_{\pi}$=5 GeV normalised to protons on target. Right:
$\nu_{\mu}$ (Red) and $\nu_{e}$ (Blue) at $E_{\pi}$=3 GeV normalised to pions
entering the transfer line.

###  3.4 Event composition and kinematic distributions

Measurements of neutrino interaction cross-sections on various target nuclei
has been a significant experimental focus in the last 10-15 years of neutrino
physics as their importance to the systematics budget of the long baseline
neutrino oscillation experiments became clear. In recent years the T2K
experiment has produced data on $\nu_{\mu}$ and $\nu_{e}$ interactions on
scintillator at an average neutrino energy of 600 MeV[57, 58, 59], and the
$\mbox{MINER}{\nu}\mbox{A}$[32, 40, 60, 61] experiment has produced similar
data but at average neutrino energies of 3 GeV and on a variety of target
nuclei. The results of both experiments show that, although the primary lepton
kinematics are reasonably well predicted by our models, the hadronic
multiplicities, identities and kinematics are still poorly described. A
detector for nuSTORM meeting the overarching requirements described above will
address these issues.

In order to quantify the detector requirements, GENIE v3.06[62] was used to
simulate neutrino interactions on a carbon nuclear target. As input to this
simulation, the $\nu_{\mu}$ flux for an initial pion energy of 5 GeV and 3 GeV
discussed above were implemented. As the fluxes are not, presently, absolutely
normalised, only the relative event category composition can be studied. The
shapes of the kinematic distributions of final state particles which might be
visible in a detector can, however, be used to inform the detector design.

The relative event rate composition for interactions of neutrinos from muon
decay in the production straight is shown in table 2 for the 5 GeV and 3 GeV
pion beams.

$\nu_{\mu}$ Channel |  $E_{\pi}=3$ GeV |  $E_{\pi}=5$ GeV
---|---|---
CC Quasi-elastic | 0.41 | 0.32
2p2h | 0.12 | 0.12
Resonance Production | 0.43 | 0.49
Deep Inelastic | 0.03 | 0.09
Coherent Pion | 0.005 | 0.005
Table 2:  Relative event category composition of $\nu_{\mu}$ interactions in a
Carbon target. Shown are the relative event rates using $\nu_{\mu}$ from muon
decay in the production straights, for two energies of initial pions from the
target.

For either pion energy, the event sample is dominated by the quasi-elastic and
resonance interaction channels. The transition from quasi-elastic to resonant
meson production is known as the dual region and is poorly understood. A large
sample of neutrino interaction in this region would be crucial to
understanding the physics. In addition, there is a smaller component of the
Deep Inelastic Scattering (DIS) interaction channel. This is, however, in a
low $Q^{2}$ and $W^{2}$ region, known as the Shallow Inelastic region. This
region, which represents the transition from resonant meson production to the
DIS region, is not well-understood, neither experimentally nor theoretically.

Figures 15, 16 and 17 show distributions from simulated muon neutrino
interactions on carbon nuclei. The neutrinos were generated from muon decay in
the production straight and are shown for initial pion energies of 5 GeV and 3
GeV. Figure 15 shows the energy of the primary muon and angle of the primary
muon to the neutrino beam direction. The final state visible hadron
multiplicity is shown in Figure 16, and the kinematics of protons produced in
these interactions are shown in Figure 17.

Figure 15:  (Left) Momentum of the primary muon from $\nu_{\mu}$ interactions
on carbon. The neutrinos are generated from muon decay in the nuSTORM
production straight and are generated with two different energies for the
pions at the target. (Right) Angle of the primary muon from $\nu_{\mu}$
interactions on carbon with respect to the beam direction.  Figure 16:
Charged hadron multiplicity in the detector.

Figure 17:  (Left) Momentum of protons in the hadronic final state of
$\nu_{\mu}$ interactions on carbon. The neutrinos are generated from muon
decay in the nuSTORM production straight and are generated with two different
energies for the pions at the target. (Right) Angle of protons in the hadronic
final state from $\nu_{\mu}$ interactions on carbon with respect to the beam
direction.

##  4 Opportunity

nuSTORM will be the first neutrino-beam facility to be based on a stored muon
beam and will provide a test-bed for the development of the technologies
required for a multi-TeV Muon Collider and/or a Neutrino Factory. It will also
serve the nuclear physics community by providing a unique probe of flavour-
dependent collective effects in nuclei and a new tool to study the origin of
nucleon spin. Both CERN and FNAL are ideally suited to the implementation of
nuSTORM as the proton infrastructure at each laboratory is well-matched to the
nuSTORM requirements and the scientific and technology-development outcomes of
nuSTORM are an excellent match to both CERN’s and FNAL’s missions. It is
conceivable that the implementation of nuSTORM will drive a step-change in
capability comparable to that produced by Van der Meer’s focusing horn and
create a new technique for the study of the nature of matter and the forces
that bind it.

The ENUBET [2, 3, 4] and nuSTORM [5, 6] collaborations have begun to work
within and alongside the CERN Physics Beyond Colliders study group [7] and the
international Muon Collider collaboration [8] to carry out a joint, five-year
design study and R&D programme to deliver a concrete proposal for the
implementation of an infrastructure in which:

  * •

ENUBET and nuSTORM deliver the neutrino cross-section measurement programme
identified in the recent update of the European Strategy for Particle Physics
and allow sensitive searches for physics beyond the Standard Model to be
carried out; and in which

  * •

A 6D muon ionisation cooling experiment is delivered as part of the technology
development programme defined by the international Muon Collider
collaboration.

This document summarises the status of the nuSTORM and 6D-cooling experiments
and identifies opportunities for collaboration in the development of the
initiative.

Strong synergies have been identified in the proton, target, meson-capture,
and radiation-safety facility required to serve ENUBET (Enhanced NeUtrino
BEams from kaon Tagging; NP06) [2, 3, 4], nuSTORM [5, 6], and the 6D muon
ionisation cooling experiment. In the European context the study of a facility
capable of serving ENUBET, nuSTORM and the 6D ionisation cooling demonstration
experiment is mandated in the 2020 Update of the European Strategy for
Particle Physics (ESPP) [1], which recommended that muon beam R&D should be
considered a high-priority future initiative and that a programme of
experimentation be developed to determine the neutrino cross-sections required
to extract the most physics from the DUNE and Hyper-K long-baseline
experiments. An initial concept for such a facility in which the target
station is served by the PS proton beam is shown in figure 18 [45].

Figure 18:  Schematic of a facility capable of serving ENUBET, nuSTORM and a
6D ionisation cooling facility on the CERN PS. The proton beam, entering from
the bottom edge of the figure, impinges on the meson-production target placed
in the neck of a horn which focuses accepted beam into a chicane in which the
desired momentum bite is accepted. A magnetic switchyard and transfer lines
then transport the resulting pion and kaon beams to the three experimental
facilities [45].

The study of nuSTORM is now being taken forward in the context of the
demonstrator facility required by the international Muon Collider
collaboration that includes the 6D muon ionisation cooling experiment. The
muon-beam development activity is being carried out in close partnership with
the ENUBET collaboration and the Physics Beyond Colliders Study Group. The
opportunity, therefore, is to forge an international collaboration to deliver
on a five-year timescale a concrete proposal for the implementation of an
infrastructure in which:

  * •

ENUBET and nuSTORM deliver the neutrino cross-section measurement programme
identified in the ESPP and allow sensitive searches for physics beyond the
Standard Model to be carried out; and

  * •

A 6D muon ionisation cooling experiment is delivered as part of the technology
development programme defined by the international Muon Collider
collaboration.

## Appendix

##  Appendix A Simulation

The studies are based on preliminary simulations to estimate the fluxes of
neutrinos which might be expected at the front face of a detector of volume 5
m x 5 m x 5 m placed 50 m downstream of the end of the nuSTORM production
straight. This is purpose written code which tracks charged particles from the
production target, down the transfer line into the production straight and for
multiple turns round the nuSTORM ring. These particles are assumed to
propagate down the optical axis of the machine and with uniform bending fields
and without fringe fields. The pions decay with the correct distribution of
lifetimes and produce muons and neutrinos with the correct kinematic
distributions. The muons are likewise allowed to decay with the correct
lifetime and the decay products are given the correct kinematic distributions.
The resulting neutrinos are tracked and the position and momentum of those
which cross the plane of the front face of the detector and are within 10 m of
the detector centre are recorded. Those within $\pm 2.5\,\text{m}$ in the
vertical and horizontal plane are counted as the flux crossing the front face
of the detector.

In order to improve the accuracy of the simulation, the distributions are
smeared using the results of two other programmes. The momentum distribution
and emittance of the pion beam which leaves the production region are modelled
using FLUKA and these distributions define the starting conditions of the
beam. The magnetic lattice of the transfer line and production straight are
modelled using BDSIM. These numbers are used to model the emittance of the
beam as it travels through the transfer line, down the production straight and
is finally captured by the ring. The acceptance of the nuSTORM ring to muons
is modelled using the results from [63]. This is used to smear the position
and momentum of the decay products from both the pion decay and the subsequent
muon decay.

##  Appendix B Background estimates

We have modelled the number of neutrinos we expect from the pion flash in the
production straight and the background from muons which decay before they
reach the first bend. We have also modelled the number of neutrinos produced
by muons which are captured in the nuSTORM ring and subsequently decay. There
are possible additional backgrounds to these two sources; we have investigated
those and have ignored any background which is less than 1% of the signal. A
summary of the calculations and reasoning is given below.

###  B.1 Decays in the transfer line at $E_{\pi}$=5 GeV

Neutrinos from pion decay in the transfer line which reach the detector will
overlap in time from the decays in the production straight. Figure 19 shows
the x and y distributions of neutrinos from pion decay in the transfer line at
the plane of the detector front face. If we look at the y position (vertical)
of the neutrinos which reach the plane, we see that the distribution is
symmetrical and strongly peaked around zero. The x position has a similar
shape, but the transfer line is at an angle to the production straight and so
only the tail of the distribution passes through the detector front face. Only
11 neutrinos from 500k pions at the target arrive at the detector, compared
with the pion flash in the production straight where 7138 neutrinos reach the
detector from 50k pions; a contamination of less than 0.01%. The mean energy
of these neutrinos is 0.06 GeV; in order to be thrown wide enough by the Q
value from the decay to reach the detector, the neutrino must have a low
energy in the nuSTORM rest frame. This source can therefore be ignored. Of the
81835 muons produced by pion decay 195 decay before the end of the transfer
line and even if all the neutrinos produced by the muon decay reach the
detector, then this represents only 0.27% of the flash signal. Although some
of the muons will make it from the transfer line into the production straight,
most of them will be absorbed by the material surrounding the beam tunnel, or
by the material inside the tunnel. They will be brought to rest by about 15 m
of soil. These muons will decay at rest and the resulting neutrinos will be
distributed isotropically. The acceptance of a detector with a
$25\leavevmode\nobreak\ \text{m}^{2}$ front face at a distance of around 250 m
means results in only 8 of these neutrinos being visible in the detector, and
those at very low energy. We conclude that neutrinos from muon decay in the
transfer line can also be ignored.

###  B.2 Decays in the transfer line at $E_{\pi}$=3 GeV

At 3 GeV the distribution is wider, as can be seen in Figure 20. The peak at
zero is lower in the y position but the tail is higher in the x position. The
combined effect of these is that 34 neutrinos arrive at the detector and their
mean energy is slightly higher (0.10 GeV), because the forward beaming from
the pion momentum is smaller and thus the Q value can push the resulting
neutrinos out to wider angles. The contribution at less than 0.03% is still
negligible. The muon decays in the production straight are still at a low
level and even if the transfer line was directed straight at the detector they
would still only produce a rate of around 0.2%.

The same argument on the muons which are bought to rest by the surrounding
material, but in a shorter distance, applies for the 3 GeV sample.

Hence, decays in the transfer line for both pions and muons at pion energies
of 3 and 5 GeV are at a level we ignore in this study.

Figure 19: Neutrinos from pion decay in the transfer line at the plane defined
by the front face of the detector. Y distribution (left), X distribution
(right)

Figure 20: Neutrinos from pion decay in the transfer line at the plane defined
by the front face of the detector. Y distribution (left), X distribution
(right)

###  B.3 Decays at the start of the first bend

We don’t have a design which accurately models what happens to the pions as
they enter the first bend at the end of the production straight. However we
know from modelling of the transfer line that by the time the beam has been
bent by 8 degrees neutrinos produced by the beam have only a small chance of
reaching the detector. If we look at the number of pions which decay in the
the arc as the beam turns through 8 degrees and assume that the acceptance for
these neutrinos is the average of that for a beam at zero degrees and a beam
at 8 degrees, then the background is about 1%. And since most pions will
actually hit an absorber and at worst decay at rest, the actual background
will be smaller and at much lower energies.

###  B.4 Kaons in the transfer line

We have not modelled Kaon kinematics, but the number produced at the target is
significantly lower than the number of pions. Even if all of those decay, the
number of Kaon decays is less than the number of pion decays and there is no
reason to believe the acceptance for their neutrinos will be any greater than
those from pion decays. We conclude the number of kaon neutrinos is much less
than our 1% cutoff for modelling.

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## The nuSTORM collaboration

Canada

S. Bhadra, S. Menary
Department of Physics and Astronomy, York University, 4700 Keele Street,
Toronto, Ontario, M3J 1P3, Canada

M. Hartz†
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
† Also at Kavli Institute for the Physics and Mathematics of the Universe, The
University of Tokyo Kashiwa Campus, 5-1-5 Kashiwanoha, Kashiwa, Chiba
277-8583, Japan

China

J. Tang
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China

Germany

U. Mosel
Justus Liebig Universität,m, Ludwigstraße 23, 35390 Gießen, Germany

M.V. Garzelli
II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee
149, 22761 Hamburg, Germany

W. Winter
Deutsches Elektronen-Synchrotron (DESY), Platanenallee 6, 15738 Zeuthen,
Germany

India

S. Goswami, K. Chakraborty
Physical Research Laboratory, Ahmedabad 380009, India

S.K. Agarwalla
Institute of Physics, Sachivalaya Marg, Sainik School Post, Bhubaneswar
751005, Orissa, India

Italy

E. Santopinto
INFN Sezione di Genova, Via Dodecaneso, 33-16146, Genova, Italy

M. Bonesini
Sezione INFN Milano Bicocca, Dipartimento di Fisica G. Occhialini, Milano,
Italy

L. Stanco
INFN, Sezione di Padova, 35131 Padova, Italy

D. Orestano, L. Tortora
INFN Sezione di Roma Tre and Dipartimento di Matematica e Fisica, Università
Roma Tre, Roma, Italy

Japan

Y. Mori
Kyoto University Institute for Integrated Radiation and Nuclear Science
(KURNS), 2, Asashiro-Nishi, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan

Y. Kuno, A. Sato
Osaka University, Graduate School, School of Science, 1-1 Machikaneyama-cho,
Toyonaka, Osaka 560-0043, Japan

South Korea

M. Chung
UNIST, Ulsan, Korea

The Netherlands

F. Filthaut†
Nikhef, Amsterdam, The Netherlands
† Also at Radboud University, Nijmegen, The Netherlands

Poland

J.T. Sobczyk
Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna
9,50-204, Wroclaw, Poland

Spain

J.J. Gomez-Cadenas
Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4,
20018 Donostia-San Sebastián, Gipuzkoa, Spain

J.A. Hernando Morata
Universidade de Santiago de Compostela (USC), Departamento de Fisica de
Particulas, E-15706 Santiago de Compostela, Spain

L. Alvarez Ruso, A. Cervera, A. Donini, P. Hernandez, J. Lopez Pavon†, J.
Martín-Albo, O. Mena, P. Novella, M. Sorel
Instituto de Fisica Corpuscular (IFIC), Centro Mixto CSIC-UVEG, Edificio
Institutos Investigación, Paterna, Apartado 22085, 46071 Valencia, Spain
† Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland

Sweden

R. Ruber
Department of Physics and Astronomy, Uppsala University, Ångströmlaboratoriet,
Lägerhyddsvägen 1, Box 516, 751 20 Uppsala, Sweden

Switzerland

C.C. Ahdida, W. Bartmann, J. Bauche, M. Calviani, N. Charitonidis, J. Gall, B.
Goddard, C. Hessler, J. Kopp†, M. Lamont, J.A. Osborne, E. Radicioni, A. de
Roeck, F.M. Velotti
CERN,CH-1211, Geneva 23, Switzerland
† Also at PRISMA Cluster of Excellence, Johannes Gutenberg University, Mainz,
Germany

A. Blondel, E.N. Messomo, F. Sanchez Nieto
University de Geneve, 24, Quai Ernest-Ansermet, 1211 Geneva 4, Suisse

United Kingdom

M.A. Uchida
Cavendish Laboratory (HEP), JJ Thomson Avenue, Cambridge, CB3 0HE, UK

S. Easo, R.E. Edgecock, J.B. Lagrange, W. Murray, C. Rogers
STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX,
UK

J.J. Back, G. Barker, S.B. Boyd, P.F. Harrison
Department of Physics, University of Warwick, Coventry, CV4 7AL, UK

S. Pascoli
Institute for Particle Physics Phenomenology, Department of Physics,
University of Durham, Science Laboratories, South Rd, Durham, DH1 3LE, UK

S.-P. Hallsjö, F.J.P. Soler
School of Physics and Astronomy, Kelvin Building, University of Glasgow,
Glasgow G12 8QQ, Scotland, UK

H.M. O’Keeffe, L. Kormos, J. Nowak, P. Ratoff
Physics Department, Lancaster University, Lancaster, LA1 4YB, UK

C. Andreopoulos†, N. McCauley, C. Touramanis
Department of Physics, Oliver Lodge Laboratory, University of Liverpool,
Liverpool, L69 7ZE, UK
† Also at STFC, Rutherford Appleton Laboratory, Harwell Campus, Chilton,
Didcot, OX11 0QX, UK

T. Alves, D. Colling, P. Dornan, P. Dunne, P. Franchini, P.M. Jonsson, P.B.
Jurj, A. Kurup, P. Litchfield, K. Long†, T. Nonnenmacher, M. Pfaff∗, J.
Pasternak†, M. Scott, J.K. Sedgbeer, W. Shorrock, M.O. Wascko
Physics Department, Blackett Laboratory, Imperial College London, Exhibition
Road, London, SW7 2AZ, UK
† Also at STFC, Rutherford Appleton Laboratory, Harwell Campus, Chilton,
Didcot, OX11 0QX, UK
∗ Also at Technical University of Munich (TUM), Arcisstrasse 21 D-80333
Munich, Germany

F. di Lodovico, T. Katori
King’s College London, Strand, London WC2R 2LS, UK

A. Bevan, L. Cremonesi, P. Hobson
Queen Mary University of London, Mile End Road, London E1 4NS, UK

R. Nichol
Department of Physics and Astronomy, University College London, Gower Street,
London, WC1E 6BT, UK

R. Appleby, S. Tygier
The University of Manchester, 7.09, Schuster Laboratory, Manchester, M13 9PL,
UK and the Cockcroft Institute, Daresbury Laboratory, WA4 4AD, UK

X. Lu, D. Wark, A. Weber†
Particle Physics Department, The Denys Wilkinson Building, Keble Road, Oxford,
OX1 3RH, UK
† Also at STFC, Rutherford Appleton Laboratory, Harwell Campus, Chilton,
Didcot, OX11 0QX, UK

P.J. Smith
University of Sheffield, Dept. of Physics and Astronomy, Hicks Bldg.,
Sheffield S3 7RH, UK

P. Kyberd, D.R. Smith
College of Engineering, Design and Physical Sciences, Brunel University
London, Uxbridge, Middlesex, UB8 3PH, UK

United States of America

S.J. Brice, A.D. Bross, S. Chattopadhay†, S. Feher, L. Fields, P. Hanlet, N.
Mokhov, J.G. Morfín, D. Neuffer, J. Paley, S. Parke, Z. Pavlovic, M. Popovic,
P. Rubinov, V. Shiltzev
Fermilab, P.O. Box 500, Batavia, IL 60510-5011, USA
† Northern Illinois University, 1425 W. Lincoln Hwy., DeKalb, IL 60115-2828,
USA

P. Huber, C. Mariani, J.M. Link
Virginia Polytechnic Inst. and State Univ., Physics Dept., Blacksburg, VA
24061-0435

B. Freemire, A. Liu
Euclid Techlabs, LLC, 365 Remington Blvd, Bolingbrook, IL, 60440, USA

D.M. Kaplan, P. Snopok
Illinois Institute of Technology, Chicago, IL, USA

S.R. Mishra
Department of Physics and Astronomy, University of South Carolina, Columbia SC
29208, USA

K. Mahn
High Energy Physics, Biomedical-Physical Sciences Bldg., Michigan State
University, 220 Trowbridge Rd, East Lansing, MI 48824, USA

A. de Gouvêa
Northwestern University, Dept. of Physics and Astronomy, 2145 Sheridan Road,
Evanston, Illinois 60208-3112 USA

V. Pandey
Department of Physics, University of Florida, Gainesville, FL 32611, USA

Y. Onel, D. Winn
Department of Physics and Astronomy, The University of Iowa, 203 Van Allen
Hall, Iowa City, Iowa 52242-1479, USA

H.A. Tanaka
SLAC National Accelerator Laboratory, 2575 Sand Hill Rd, Menlo Park, CA 94025,
USA

M. Hostert
School of Physics and Astronomy, University of Minnesota, Minneapolis, MN
55455, USA

S.A. Bogacz
Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue,
Newport News, VA 23606, USA

L. Cremaldi, D. Summers
University of Mississippi, Oxford, MS, USA

K.T. McDonald
Princeton University, Princeton, NJ, 08544, USA

G. Hanson
Department of Physics and Astronomy, University of California, Riverside, CA
92521, US

M. Palmer
Brookhaven National Laboratory, P.O. Box 5000, Upton, NY 11973 USA

M. Liu
Purdue University, 610 Purdue Mall, West Lafayette, IN, 47907, 765-494-4600,
USA