#  Enhanced NeUtrino BEams from kaon Tagging (ENUBET)
The ENUBET Collaboration

F. Acerbi  Fondazione Bruno Kessler (FBK), Via Sommarive 18 - 38123 Povo (TN),
IT  INFN-TIFPA, Università di Trento, Via Sommarive 14 - 38123 Povo (TN), IT
I. Angelis  Aristotle University of Thessaloniki. Thessaloniki 541 24, Greece.
M. Bonesini  INFN Sezione di Milano-Bicocca, Piazza della Scienza 3 - 20133
Milano, IT  A. Branca  INFN Sezione di Milano-Bicocca, Piazza della Scienza 3
- 20133 Milano, IT  Università di Milano-Bicocca, Piazza della Scienza 3 -
20133 Milano, IT  C. Brizzolari  INFN Sezione di Milano-Bicocca, Piazza della
Scienza 3 - 20133 Milano, IT  Università di Milano-Bicocca, Piazza della
Scienza 3 - 20133 Milano, IT  G. Brunetti  Università di Milano-Bicocca,
Piazza della Scienza 3 - 20133 Milano, IT  M. Calviani  CERN, Esplanade des
particules - 1211 Genève 23, CH  S. Capelli  INFN Sezione di Milano-Bicocca,
Piazza della Scienza 3 - 20133 Milano, IT  Università degli Studi
dell’Insubria, Via Valleggio 11 - 22100 Como, IT  S. Carturan  Università di
Padova, via Marzolo 8 - 35131 Padova, IT  INFN, Laboratori Nazionali di
Legnaro, Viale dell’Università 2 - 35020 Legnaro (PD), IT  M.G. Catanesi  INFN
Sezione di Bari, Via Giovanni Amendola 173 - 70126 Bari, IT  N. Charitonidis
CERN, Esplanade des particules - 1211 Genève 23, CH  S. Cecchini  INFN Sezione
di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT  F. Cindolo  INFN
Sezione di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT  G. Collazuol
INFN Sezione di Padova, via Marzolo 8 - 35131 Padova, IT  Università di
Padova, via Marzolo 8 - 35131 Padova, IT  E. Conti  INFN Sezione di Padova,
via Marzolo 8 - 35131 Padova, IT  F. Dal Corso  INFN Sezione di Padova, via
Marzolo 8 - 35131 Padova, IT  C. Delogu  INFN Sezione di Padova, via Marzolo 8
- 35131 Padova, IT  Università di Padova, via Marzolo 8 - 35131 Padova, IT  G.
De Rosa  INFN, Sezione di Napoli, Strada Comunale Cinthia - 80126 Napoli, IT
Università “Federico II” di Napoli, Corso Umberto I 40 - 80138 Napoli, IT  A.
Falcone  INFN Sezione di Milano-Bicocca, Piazza della Scienza 3 - 20133
Milano, IT  Università di Milano-Bicocca, Piazza della Scienza 3 - 20133
Milano, IT  A. Gola  Fondazione Bruno Kessler (FBK), Via Sommarive 18 - 38123
Povo (TN), IT  B. Goddard  CERN, Esplanade des particules - 1211 Genève 23, CH
F. Iacob  INFN Sezione di Padova, via Marzolo 8 - 35131 Padova, IT  Università
di Padova, via Marzolo 8 - 35131 Padova, IT  C. Jollet  CENBG, Universitè de
Bordeaux, CNRS/IN2P3, 33175 Gradignan, FR  V. Kain  CERN, Esplanade des
particules - 1211 Genève 23, CH  B. Klic̆ek  Center of Excellence for Advanced
Materials and Sensing Devices, Ruder Boskovic Institute, HR-10000 Zagreb, HR
Y. Kudenko  Institute for Nuclear Research of the Russian Academy of Sciences,
117312 Moscow, RU  National Research Nuclear University “MEPhI”, 115409
Moscow, Russia  Moscow Institute of Physics and Technology, 141701 Moscow
region, Russia  Ch. Lampoudis  Aristotle University of Thessaloniki.
Thessaloniki 541 24, Greece.  M. Laveder  INFN Sezione di Padova, via Marzolo
8 - 35131 Padova, IT  Università di Padova, via Marzolo 8 - 35131 Padova, IT
A. Longhin  INFN Sezione di Padova, via Marzolo 8 - 35131 Padova, IT
Università di Padova, via Marzolo 8 - 35131 Padova, IT  L. Ludovici  INFN
Sezione di Roma 1, Piazzale A. Moro 2, 00185 Rome, IT  E. Lutsenko  INFN
Sezione di Milano-Bicocca, Piazza della Scienza 3 - 20133 Milano, IT
Università degli Studi dell’Insubria, Via Valleggio 11 - 22100 Como, IT  L.
Magaletti  INFN Sezione di Bari, Via Giovanni Amendola 173 - 70126 Bari, IT
Università degli Studi di Bari, Via Giovanni Amendola 173 - 70126 Bari, IT  G.
Mandrioli  INFN Sezione di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT
A. Margotti  INFN Sezione di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna,
IT  V. Mascagna  INFN Sezione di Milano-Bicocca, Piazza della Scienza 3 -
20133 Milano, IT  Università degli Studi dell’Insubria, Via Valleggio 11 -
22100 Como, IT  N. Mauri  INFN Sezione di Bologna, viale Berti-Pichat 6/2 -
40127 Bologna, IT  L. Meazza  INFN Sezione di Milano-Bicocca, Piazza della
Scienza 3 - 20133 Milano, IT  Università di Milano-Bicocca, Piazza della
Scienza 3 - 20133 Milano, IT  A. Meregaglia  CENBG, Universitè de Bordeaux,
CNRS/IN2P3, 33175 Gradignan, FR  M. Mezzetto  INFN Sezione di Padova, via
Marzolo 8 - 35131 Padova, IT  M. Nessi  CERN, Esplanade des particules - 1211
Genève 23, CH  A. Paoloni  INFN, Laboratori Nazionali di Frascati, via Fermi
40 - 00044 Frascati (Rome), Italy  M. Pari  INFN Sezione di Padova, via
Marzolo 8 - 35131 Padova, IT  Università di Padova, via Marzolo 8 - 35131
Padova, IT  CERN, Esplanade des particules - 1211 Genève 23, CH  E.G. Parozzi
INFN Sezione di Milano-Bicocca, Piazza della Scienza 3 - 20133 Milano, IT
Università di Milano-Bicocca, Piazza della Scienza 3 - 20133 Milano, IT  CERN,
Esplanade des particules - 1211 Genève 23, CH  L. Pasqualini  INFN Sezione di
Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT  Università degli Studi di
Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT  G. Paternoster
Fondazione Bruno Kessler (FBK), Via Sommarive 18 - 38123 Povo (TN), IT  L.
Patrizii  INFN Sezione di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT
M. Pozzato  INFN Sezione di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna,
IT  M. Prest  INFN Sezione di Milano-Bicocca, Piazza della Scienza 3 - 20133
Milano, IT  Università degli Studi dell’Insubria, Via Valleggio 11 - 22100
Como, IT  F. Pupilli  INFN Sezione di Padova, via Marzolo 8 - 35131 Padova, IT
Università di Padova, via Marzolo 8 - 35131 Padova, IT  E. Radicioni  INFN
Sezione di Bari, Via Giovanni Amendola 173 - 70126 Bari, IT  C. Riccio  INFN,
Sezione di Napoli, Strada Comunale Cinthia - 80126 Napoli, IT  Università
“Federico II” di Napoli, Corso Umberto I 40 - 80138 Napoli, IT  A.C. Ruggeri
INFN, Sezione di Napoli, Strada Comunale Cinthia - 80126 Napoli, IT
Università “Federico II” di Napoli, Corso Umberto I 40 - 80138 Napoli, IT  D.
Sampsonidis  Aristotle University of Thessaloniki. Thessaloniki 541 24,
Greece.  C. Scian  INFN Sezione di Padova, via Marzolo 8 - 35131 Padova, IT
Università di Padova, via Marzolo 8 - 35131 Padova, IT  G. Sirri  INFN Sezione
di Bologna, viale Berti-Pichat 6/2 - 40127 Bologna, IT  M. Stipc̆ević  Center
of Excellence for Advanced Materials and Sensing Devices, Ruder Boskovic
Institute, HR-10000 Zagreb, HR  M. Tenti  INFN Sezione di Bologna, viale
Berti-Pichat 6/2 - 40127 Bologna, IT  F. Terranova  INFN Sezione di Milano-
Bicocca, Piazza della Scienza 3 - 20133 Milano, IT  Università di Milano-
Bicocca, Piazza della Scienza 3 - 20133 Milano, IT  M. Torti  INFN Sezione di
Milano-Bicocca, Piazza della Scienza 3 - 20133 Milano, IT  Università di
Milano-Bicocca, Piazza della Scienza 3 - 20133 Milano, IT  S. E. Tzamarias
Aristotle University of Thessaloniki. Thessaloniki 541 24, Greece.  E.
Vallazza  INFN Sezione di Milano-Bicocca, Piazza della Scienza 3 - 20133
Milano, IT  F.M. Velotti  CERN, Esplanade des particules - 1211 Genève 23, CH
L. Votano  INFN, Laboratori Nazionali di Frascati, via Fermi 40 - 00044
Frascati (Rome), Italy

(15 March 2022)

###### Abstract

The ENUBET project aims at demonstrating the feasibility of a “monitored”
neutrino beam, in which the absolute normalization of the neutrino flux
produced by a narrow band meson beam can be constrained at the 1% level. The
electron neutrino component is determined by monitoring large-angle positrons
from $K_{e3}$ decays in a 40 m long instrumented decay tunnel. The $\nu_{\mu}$
flux is provided by the muons produced by two-body decays of kaons and pions
and detected along and at the end of the tunnel. Since ENUBET is a very narrow
band beam ($p=8.5$ GeV/$c$ $\pm$ 10%), the transverse position of the neutrino
interaction at the detector can be exploited to determine a priori, with
significant precision, the neutrino energy spectrum without relying on the
final state reconstruction (”narrow band off-axis technique”). Lepton
monitoring and narrow band off-axis energy reconstruction can be implemented
in a single facility based on standard accelerator technologies for a new
generation of high precision $\nu_{e}$ and $\nu_{\mu}$ cross section
measurements at the GeV scale and for precision searches of physics beyond the
standard three neutrino paradigm.

In 2019-2022 ENUBET has devised the first end-to-end simulation of the
facility and demonstrated that the precision goals can be achieved in about
three years of data taking employing neutrino detectors of moderate mass
(ICARUS at FNAL, ProtoDUNE at CERN). The technology of a monitored neutrino
beam has been proven to be feasible and cost-effective, and the complexity
does not exceed significantly the one of a conventional short-baseline beam.
The Snowmass 2021 DPF Community Planning Exercise is thus timely for the
consideration of monitored neutrino beams hosting the next generation of cross
section experiments. The ENUBET results will play an important role in the
systematic reduction programme of future long baseline experiments, thus
enhancing the physics reach of DUNE and HyperKamiokande. In this document, we
summarize the ENUBET design, physics performance and opportunities for its
implementation in a timescale comparable with DUNE.

##  1 Introduction

Neutrino oscillations at accelerators [1] play a prominent role in the study
of the Yukawa sector of the standard model and the mass generation mechanisms.
This research field has entered a new phase after the approval of DUNE [2] and
HyperKamiokande (HK) [3]. These projects have an unprecedented level of
complexity and cost, which resemble the most ambitious collider experiments
performed in the last decades as the B-factories or the LHC experiments. Like
collider experiments, the progress in the experimental precision must be
matched by the progress in theory predictions to fully reap the physics
potential of the new facilities. At the time of writing, theory predictions -
in particular the study of neutrino cross sections - lag behind what is needed
in DUNE and HK [4].

The DUNE and HK Collaborations mitigate this risk with a very careful design
of the near [5, 6] and far [7, 3] detectors. Still, the traditional near-far
cancellation technique is reaching its intrinsic limitations and the
systematic uncertainty currently dominates the physics reach.

This contribution to the Snowmass process addresses this issue in the most
direct manner and echoes the outcome of the European Strategy for Particle
Physics [8], which pointed out such weakness in the global effort to measure
neutrino properties. Instead of refining the near-far cancellation technique,
we discuss the opportunities and challenges of a new generation of short-
baseline cross section experiments, optimized to reach percent level precision
in the inclusive, differential, and doubly-differential cross-sections. These
experiments must address the region of interest for DUNE and HK but should not
be considered only ancillary facilities of long-baseline experiments. Neutrino
interactions at GeV energies [9] provide a wealth of information on the
nuclear structure at moderate $Z$ and can be extended to cover the simplest
nuclear system (e.g. hydrogen or deuteron) and explore the high-Z region of
relevance for high-density detectors. Their goals are to gain a deep
understanding of weak interactions in nuclear physics and provide high-
precision data for the study of nuclear structure. These data will inform
nuclear effective theories and, in the long term, lattice QCD. We call these
facilities a _new_ generation of cross section experiments because major
advances in this field has been achieved by the previous generation based on
dedicated experiments (SciBooNE [10], MINER$\nu$A [11, 12], WAGASCI [13],
ArgoNeuT [14], etc.), the near detectors of long-baseline (K2K [15], MINOS
[16], T2K-ND280 [17], NO$\nu$A [18]) and short-baseline experiments (MiniBooNE
[19], MicroBooNE [20]). We expect the next generation of dedicated experiments
– running on a timescale comparable with the data-taking of DUNE and HK – to
achieve major improvements on $\nu_{e}\ $, $\nu_{\mu}\ $ and
$\overline{\nu}_{\mu}$ cross-sections but also contribute to the short-
baseline program for the search of physics beyond the Standard Model.

In this document we advocate for a new facility to host the next generation of
cross section experiments. This facility should be aimed at an unprecedented
control of the neutrinos at source, their flavor, and energy to sidestep
current limitations of short-baseline experiments and improve by one order of
magnitude our knowledge of neutrino cross sections at the GeV scale.

##  2 High precision cross section measurements

Neutrino cross section measurements are currently dominated by the limited
control of the neutrinos produced at accelerators. These limitations affect
the knowledge of the flux of $\nu_{\mu}$, the size of the $\nu_{e}$ component
and the energy spectrum of the neutrinos. An ideal source would hence be a
source where the flux is known with a precision ten-times better than current
beams ($10\%\rightarrow 1\%$) so that the remaining uncertainties are only
detector-related (see below) or - for the case of $\nu_{e}$, statistics-
limited. This is particularly relevant to reduce the systematics of DUNE and
HK.

For DUNE ($L\simeq 1300$ km) and HK ($L\simeq 295$ km),
$\nu_{\mu}\rightarrow\nu_{e}\,$and
$\overline{\nu}_{\mu}\rightarrow\overline{\nu}_{e}\,$are of paramount
importance to establish CP violation in the neutrino sector and the number of
$\nu_{e}\ $charged-current (CC) interactions observed far from the source is

$N^{e}_{FD}=\tilde{M}^{\prime}\int dE\left[\phi_{\nu_{\mu}}^{FD}(E)\
\epsilon_{e}(E)\ \sigma_{\nu_{e}}(E)P(\nu_{\mu}\rightarrow\nu_{e})\
+\phi_{\nu_{\mu}}^{FD}(E)\epsilon_{\mu\rightarrow
e}\sigma_{\nu_{\mu}}(E)\right]$ (1)

where $\tilde{M}^{\prime}$ is the number of scattering centers (proportional
to the mass and material of the detector), $\phi_{\nu_{\mu}}^{FD}(E)$ is the
total flux integrated during the data taking at $L$ by the Far Detector (FD),
and $\epsilon_{e}(E)\sigma_{\nu_{e}}(E)$ is the visible cross section, i.e.,
the cross-section corrected by the efficiency of the detector.
$\epsilon_{\mu\rightarrow e}$ is the mis-identification probability of tagging
a $\nu_{\mu}\ $as a $\nu_{e}$, e.g., due to neutral-currents (NC) events or
non-reconstructed muons. For low precision experiments ($>5$% systematic
uncertainty), the uncertainties on the flux and the cross-section times
detector efficiency can be removed by an identical detector located at short
$L$, where oscillation effects are negligible, the Near Detector (ND). For the
ND, the $\nu_{\mu}\ $CC events provide an estimate of the initial flux

$N_{ND}=\tilde{M}_{N}\int dE\
\phi^{ND}_{\nu_{\mu}}(E)\epsilon_{\mu}(E)\sigma_{\nu_{\mu}}(E)$ (2)

and the $\nu_{e}\ $CC events measure the $\nu_{e}\ $ contamination at source:

$N^{e}_{ND}=\tilde{M}_{N}\int dE\left[\phi_{\nu_{e}}^{ND}(E)\ \epsilon_{e}(E)\
\sigma_{\nu_{e}}(E)\ +\phi_{\nu_{\mu}}^{ND}(E)\epsilon_{\mu\rightarrow
e}(E)\sigma_{\nu_{\mu}}(E)\right].$ (3)

In this way, the main contribution to the systematic uncertainty should come
only from the

$\frac{\epsilon_{e}(E)\sigma_{e}(E)}{\epsilon_{\mu}(E)\sigma_{\mu}(E)}$ (4)

ratio [21] and is strongly mitigated by the lepton universality, i.e. the
statement that $\sigma_{e}(E)=\sigma_{\mu}(E)$ except for calculable kinematic
corrections. Unfortunately, such an elegant solution does not work at $<5$%
level. The ND and FD are not perfectly identical. Their efficiencies are
different ($\epsilon^{ND}\neq\epsilon^{FD}$) both for $\nu_{e}\ $CC and
$\nu_{\mu}\ $CC. Even more, $\phi_{\nu_{\mu}}(E)$ and $\phi_{\nu_{e}}(E)$ are
different at the near and far location beyond the expected geometrical
reduction ($\phi\sim L^{-2}$) because the ND integrates the flux in a much
larger neutrino phase-space. The solid angle seen by the ND is much bigger
than the FD and this phase mismatch requires corrections both on flux
normalization and energy spectrum, which, in turn, increase the systematic
uncertainty.

It is worth noting that flux, efficiencies, oscillation probabilities, and
cross sections are all functions of the neutrino energy $E$. The neutrino
energy is not known a priori and must be reconstructed event-by-event by the
final-state particles of the neutrino interaction in the detector. This
reconstruction is not possible in NC events because of the outgoing neutrino
and troublesome in CC events every time a final-state particle is missed or
mis-reconstructed. Again, this procedure generates a bias affecting the
measured oscillation probability. As a consequence, assuming priors on the
neutrino beam (Monte Carlo simulation of the beamline), cross-sections
(neutrino-nucleus models), and detector response are mandatory even after the
near-far comparison. These priors, clearly, are not free of systematic
uncertainties.

Along the same line, there is little hope to predict the Standard Model
interactions with matter starting from theory, and all advances in this field
require a sophisticated interplay between model-building and high-precision
cross section measurements. A detailed account of cross-section limitations is
given in [22].

##  3 Monitored neutrino beams

Monitored neutrino beams are beams where the flux of neutrinos is directly
measured and diagnostics does not need to rely on the full simulation of the
neutrino beamline. Here, the instrumentation – mostly located in the decay
tunnel – monitors the production of the lepton associated with the neutrino at
the single-particle level. If a muon neutrino is produced by a
$\pi^{+}\rightarrow\mu^{+}\nu_{\mu}$ decay, its appearance is signaled by the
observation of the corresponding anti-muon. This observation represents a
direct estimate because the number of anti-muons produced by those decays is
equal to the number of muon neutrinos. An electron neutrino produced by a kaon
decay - for instance $K^{+}\rightarrow e^{+}\pi^{0}\nu_{e}$ \- is signaled by
the observation of a positron. Monitoring the production of leptons in the
decay tunnel of an accelerator neutrino beam is very challenging due to the
rate of secondary and tertiary particles. In the 1980s, monitored neutrino
beams were built in the USSR in the framework of the ”tagged neutrino beam
facility” [24]. This facility did not reach a flux sufficient to feed neutrino
experiments and was later de-scoped to a tagged kaon beam facility. Current
neutrino beams record muons but they have not reached single-particle
sensitivity. Their precision on flux (15%) cannot beat conventional
techniques, yet. The most advanced monitored neutrino beam project is ENUBET,
which aims at designing a monitored neutrino beam for high precision neutrino
cross-section measurements instrumenting most of the decay tunnel with fast
and radiation hard detectors, still at a marginal cost (5-10%) compared with
the total cost of the facility.

##  4 ENUBET

The ENUBET Collaboration was formed in 2015 and the feasibility study was
supported by the European Research Council in the framework of the ERC
Consolidator Grant program (PI A. Longhin). The ERC ENUBET project has
delivered the first end-to-end simulation of a monitored neutrino beams where
monitoring is performed by the detection of large angle positrons in the decay
tunnel from $K^{+}\rightarrow e^{+}\pi^{0}\nu_{e}$. Given the outstanding
results obtained in 2016-2019, ENUBET has been approved as a CERN Neutrino
Platform experiment (NP06/ENUBET) and extended significantly its physics
reach. NP06 monitors not only the kaon positrons but also muons from the
leading two body decay of kaons $K^{+}\rightarrow\mu^{+}\nu_{\mu}$ and pions
($\pi^{+}\rightarrow\mu^{+}\nu_{\mu}$). It became possible by the design of a
horn-less focusing system that can be pulsed for several seconds reducing the
particle rate at the decay tunnel by nearly two orders of magnitude. Muons
from pion decays can then be monitored by additional instrumentation located
at the end of the decay tunnel (hadron dump). The NP06 study is site-
independent and we have shown that its implementation can be carried out both
at CERN and Fermilab. A low energy version, of particular relevance for T2K,
could also be implemented in the European Spallation Source (ESS) in a longer
timescale and is being investigated in the framework of the INFRADEV EU
program. Given the maturity of the design, NP06/ENUBET is currently working in
collaboration with CERN (Physics Beyond Collider) to implement this novel
facility at the CERN SPS and exploit the existing CERN detectors (ProtoDUNE:
NP02 and NP04).

The ENUBET beam is a conventional narrow-band beam with two differences with
respect to the current beams: the decay tunnel is not located along the proton
axis of the focusing system and the proton extraction length is slow.
Particles produced by proton interactions in the target are focused, momentum
selected and transported to the tunnel entrance. Non-interacting protons are
stopped in a proton beam dump. Off-momentum particles reaching the decay
tunnel are mostly low energy particles coming from interactions in the
collimators and other beamline components together with muons that cross
absorbers and collimators. The hadron beam considered has a reference momentum
of 8.5 GeV/c with a momentum bite of 10% and we expect about 50% of $K^{+}$ to
decay in a 40 m long tunnel. A multi-momentum beamline with an optics hosting
secondaries down to a few GeV is also under study to increase the neutrino
flux below 1 GeV.

Focusing is performed by a set of dipole and quadrupoles (static focusing
system) and, in 2019, we demonstrated that the static system can achieve a
flux that allows for the measurement of $\nu_{e}$ cross section at 1% level,
while the statistical error for $\nu_{\mu}$ interactions is below 0.1% due to
the even larger $\nu_{\mu}$ flux. Such a result was obtained assuming a
neutrino detector, located about 100 m from the target of the same size of
ProtoDUNE-SP. A horn based option is now considered a backup option and
pursued to further increase the flux.

Special emphasis should be given by the possibility of developing ENUBET as an
incremental step toward muon-based neutrino sources with an outstanding
physics case on its own. In 2021, the ENUBET and nuSTORM collaborations have
started a synergic development, which is described in a dedicated contribution
to Snowmass [75].

##  5 The ENUBET implementation

We discuss here the most important outcomes of the ENUBET R&D: the development
of the hadron beamline, simulation and reconstruction algorithms for the
lepton tagger, the detector prototyping activities and the studies to assess
the reduction of systematics on the flux.

###  5.1 Burst-mode slow extraction

ENUBET must employ a slow extraction of the primary protons to mitigate pile-
up at the instrumented decay tunnel (i.e. full intensity continuously
extracted in a few seconds). However, in order not to rule out the option of
using a magnetic horn for potentially boosting the neutrino flux (Sec. 5.3),
we have studied and developed a novel pulsed slow-extraction method at CERN-
SPS, in collaboration with CERN (BE-OP-SPS and TE-ABT-BTP). In this type of
extraction, multiple ms-long pulses are slow-extracted during the flat-top at
a fixed repetition rate. The main results of this campaign have already been
reported in the previous report [26], and have been confirmed by further off-
line analysis. They can be briefly summarized as follows:

  * •

A new pulsed slow extraction method (called burst-mode slow extraction) has
been successfully implemented and tested at CERN-SPS before the Long Shutdown
2 (LS2). Our measurements showed that the scheme can be readily switched-on
and operated with the SPS control tools we developed, and that the most
critical parameter is the length of the extracted proton pulses. By upgrading
one of the existing SPS control-room applications, we have proven that the new
extraction scheme can be successfully optimized down to $10$ ms pulses
repeated at $10$ Hz, as first envisaged by ENUBET in [23].

  * •

During LS2, we developed a full simulation of this extraction scheme to
validate the experimental results and explore possible improvements, which
could not be tested in the machine before the shutdown. Using two different
methods (increase of extraction sextupole strength and amplitude extraction),
we found that pulses ranging between $3$ and $10$ ms can be produced without
any hardware modification.

The burst-mode slow extraction is a general extraction method with application
even beyond the horn-based ENUBET layout: in the static focusing option of
ENUBET, it can provide a time structure employed at the neutrino detector to
reduce cosmic-induced background. Other users of the CERN SPS and PS beamlines
can employ this method to increase and control the instantaneous particle rate
for pile-up, DAQ and PID studies.

Ripples appearing on the extracted spill, generally caused by harmonics coming
from the magnet power supplies or other electric nuisances, are a well known
issue in slow extraction. The suppression of these ripples is the subject of
long-standing efforts for both research and medical accelerators [31, 32, 33,
34, 35]. In the case of high-energy physics experiments, this noise is
detrimental because it enhances the instantaneous pile-up and counting
uncertainties [36].

We have characterized the frequency response of the slow extraction in terms
of its low-pass filter behavior. This has been performed with a full MADX [37]
model of the process, while we have also developed custom numerical models for
fast simulation, which proved to be in good agreement with MADX. We validated
our models both by performing dedicated ripple-injection measurements at the
SPS and analyzing operational data. Ultimately, we could exploit one of the
developed fast simulation models to look for possible improvements in the
suppression of ripples by scanning two of the main SPS extraction parameters:
chromaticity and sextupole strength. The results obtained so far are promising
and show that a reduction of a factor $\sim 2$ is within reach, as shown in
Fig. 1.

Figure 1: Simulated scan of the relative amplitude of power-supply ripples
compared to the nominal SPS case (unit value in the color scale), as a
function of the normalized chromaticity ($\chi$) and virtual extraction
sextupole strength ($V_{\text{ss}}$).

The present work will play an important role for future improvements of the
spill quality of the SPS slow extraction, increasing the efficiency of ENUBET
and other fixed-target experiments.

###  5.2 Target optimization

Neutrino experiments extrapolate and determine the flux of neutrinos from the
yield of secondary hadrons produced by the target. This is often the most
important source of systematic uncertainties [50]. While it is possible to
derive models for secondary production by fitting experimental data [51], the
uncertainties remain high ($>10$%), especially for the low energy region, as
reported in several surveys [52, 53, 54].

The target of ENUBET does not represent a substantial challenge compared with
focusing and instrumentation since we leverage the experience gained by long-
baseline experiments and envisage a facility with an average power of about
120 kW 111Assuming a maximal proton rate given by $4.5\times 10^{13}$ protons
over a 24 s super-cycle.. On the other hand, a re-optimization of the target
has been carried out because the project is in a very advanced state and we
are now addressing also engineering issues and costs.

Besides the choice of target material, the target geometry determines the re-
interaction probability and absorption of the secondary particles coming out
of the target after the collision with the primaries. The optimization of the
target geometry, however, is not only driven by the produced yields, but also
by mechanical constraints and cooling requirements.

The overall size of the target plays a central role in the cooling design. An
increased surface implies a larger radiative heat transfer and the change of
the size of a target is driven by the absorption/emission parameters of the
material. Increasing the size could lead to a lower production yield due to
secondary re-interactions inside the target. The optimization is then a trade-
off between mechanical robustness against heating and the effective
interaction length crossed by the secondaries.

The NP06/ENUBET team has conducted extensive optimization studies based on the
FLUKA [38, 39] and G4beamline [58] simulation codes, using graphite (density
$2.2$ g/cm3), beryllium (density $1.81$ g/cm3), Inconel (density $8.2$ g/cm3)
and various high-$Z$ materials such as gold and tungsten. Each target
prototype is modeled geometrically as a cylinder with variable radii between
$10$ and $30$ mm and lengths extending from $5$ to $140$ cm.

Initially, we analyzed the target secondary particle productions assuming
different primary energies. As expected, the number of $\pi^{+}$ per POT
linearly grows with the primary proton momenta [59], which determines the
accessible momenta for the secondaries and, hence, the neutrinos. We studied
primary protons with momenta of 400, 150, 70, and 50 GeV/c. FLUKA results
confirmed that the nominal energy of the SPS (400 GeV/c) is a good choice for
ENUBET, especially for cross section studies in the region of interest for
DUNE. This region requires a secondary mean momentum for kaons of about 8.5
GeV. We then proceeded comparing the geometry and material of the target. We
have shown that the best materials for monitored neutrino beams are graphite
(2.23 g/cm3 density), beryllium and Inconel-718. The kaon yields for graphite
are shown in Fig. 2. Higher-$Z$ materials would prove better candidates for
kaons production, however, they pose severe challenge to the cooling system
and are not an option we will pursue.

Figure 2: Kaon yields as a function of the graphite target length. The primary
beam simulated is a $400$ GeV/c proton beam. The figure of merit for this
study is the number of kaons of given energy with $10\%$ momentum bite that
enters an ideal beamline with $\pm 20$ mrad angular acceptance in both planes,
placed $30$ cm after the target. The error bars are not plotted to ease the
reading; statistical errors are negligible ($1$%), while the Monte-Carlo
systematics amounts to $\sim 20$%. Colors refer to different kaon’s momenta
while the marker style identifies the tagger radius.

Graphite is a known and well-tested material employed in several neutrino
beams thanks to its heat endurance and production yields [56]; Inconel is
quite a novel choice that is under consideration for nuSTORM [60] and ENUBET,
but already at use at CERN in other applications (like the new CERN-PS East
Area Beam Stoppers).

The most advanced ENUBET beamline (TRL6 – see Sec. 5.4) employs a graphite
target with a 3 cm radius and a length of 70 cm. An Inconel target with the
same radius and a 50 cm length is also being considered. The Collaboration is
in contact with the CERN developers, in particular the CERN SY Department, to
address a precise cost estimate of the target station, possibly in synergy
with the nuSTORM studies performed at Physics Beyond Collider.

###  5.3 Horn optimization

While the baseline option for ENUBET is a fully static beamline, the use of a
horn combined with the pulsed slow extraction described above is pursued as an
alternative option. In particular, as the magnetic horn is a complex device, a
full automatic optimization approach is required in order to find the best
geometry for maximizing the flux of focused secondaries. Since the starting
point of this work described in the past report [26], we have made important
advances.

First, a full GEANT4 [40] simulation model for the magnetic horn has been
successfully developed. Other than the MiniBooNE-like geometry previously
reported, a new double parabolic geometry has been implemented (Fig. 3).

Figure 3: Design of the double parabolic horn available in the developed
GEANT4 simulation.

We have then completed the implementation of a dedicated framework for
optimizing the magnetic horn configuration: it is composed of different
software elements and it is interfacing with a job scheduling system (Grid
Engine from the CC-IN2P3 cluster), which is required given the computational
intensive problem. Since the only way to obtain a quantitative estimation of
the horn fluxes is via a full numerical simulation, and no other crucial
information is obtained otherwise, using a meta-heuristic and stochastic-based
optimization algorithm is a good way to scan the parameter space for global
optima. For this reason, we have based the horn optimization on a Genetic
Algorithm (GA) implementation. We have inserted the handling of external
constraints on the horn parameters, in order to take into account hardware
limitations and requirements (e.g. total horn length, current, radii, etc).
The Figure of Merit (FoM) of the optimization is based on the number of
focused $K^{+}$ in the designed momentum bite, computed at two possible
locations:

  * •

At the first quadrupole after the horn. This particular FoM has the advantage
of being independent from the downstream beamline: it is used to maximize the
flux at the output of the horn and inside the acceptance of the first
quadrupole.

  * •

At the entrance of the decay tunnel. This FoM requires a further computational
intensive tracking of the particles, but it provides the quantitative gain for
the specific beamline under consideration.

In order to test the optimization framework, we have decided to first optimize
the horn in a standalone way using the beamline-independent FoM, and then to
compare the result with a full beamline tracking using the static
configuration. The main results can be summarized as follows:

  * •

The optimization framework successfully reaches an optimum in $\sim 100$
iterations (taking typically from a few hours to a day of computation time),
the constraints are also enforced correctly.

  * •

For different horn geometries and constraints, we were able to reach values of
the standalone FoM of a factor $3$ higher than the static case. These results
confirm an improvement with respect to the horn configurations used in early
studies initially performed in $2016$.

  * •

When further tracking the particles along the full static transfer line in the
current configuration, we observed an overall reduction in the gain of kaons
with respect to the standalone FoM value, up to about a factor $2$.

The most important consideration that can be drawn from the previous results
is that further studies on a dedicated beamline configuration specific for the
horn-focused beam are necessary to really determine the total achievable
increase of flux. In fact, the current implementation of the static transfer
line is not tuned to be paired with a horn: to exploit this device at best,
significant modifications could be needed. For this reason, the next step will
be to design and optimize such an alternative beamline. However, the
successful convergence of the developed optimization framework to standalone
horn optima is positive: these horn candidates satisfy basic hardware
constraints and can be used as starting point for the further beamline
optimization. On top of this, the developed optimization framework will be
upgraded to become a generic tool available for the optimization of other
components of ENUBET (e.g. collimation).

###  5.4 Transfer line

The overall concept of the ENUBET transfer line and the factors guiding our
optimization have been described in [26]. Here we present the latest design
for a static transfer line optimized for a 8.5 GeV/c reference particle. We
consider normal-conducting bending dipoles with 1.8 T field, providing a total
bending of the beam w.r.t the primary proton line of 14.8°. The quadrupoles
have an aperture radius of 15 cm. The optics is optimized considering a 10%
momentum bite and an improved target (described in 5.2) made by graphite, 70
cm long and with a radius of 3 cm. The layout is presented in Fig 4, where we
only show the focusing elements, the dumps, the copper block downstream the
first dipole with two pipes (one for the primary protons and a tilted one for
the ENUBET hadron beam), and the tagger. The absorbers placed all along the
transfer line and the rock volumes are nevertheless used in the complete
simulation that have been studied and optimized using a complete FLUKA and
GEANT4 simulation (Sec. 5.12). The design implements an INERMET180 tungsten
alloy block at the tagger entrance with a conical aperture.

Figure 4: Bending elements: dipoles are shown in red while quadrupoles are
shown in grey. Both transfer lines have the same design for the proton dump.
The hadron dump is placed downstream the tagger exit. At the tagger entrance
is placed a INERMET180 block with a conical aperture.

Downstream the target and before the first quadrupole of the transfer line we
also make use of a 5 mm thick tungsten foil to eliminate the positrons
generated by the interactions in the target. Its thickness has been chosen
after a series of simulations to optimize it by checking the ratio of positron
coming from the target and hitting the tunnel walls over the $K^{+}$ flux. The
target has been completely surrounded by concrete.

The proton dump is composed by three cylindrical layers: a 3 m long graphite
core, surrounded by aluminum, which in turn is covered by iron. The hadron
dump is placed 2 m after the tagger exit and a new design has also been
studied in order to reduce the backscattering reaching the last part of the
decay tunnel that would result in additional particles hitting the
instrumentation. A preliminary design that follows the same structure of the
proton dump and that allows to reduce the flux in the tunnel due to
backscattering is presented in Fig. 5: a graphite core of 50 cm diameter is
placed inside a layer of Iron (1 m diameter), covered by borated concrete (4 m
diameter), 1 m of additional borated concrete is placed in front of the hadron
dump leaving the opening for the beam. A more complete simulation performed
with FLUKA and GEANT4 will determine the final design but the one presented
here has already the capability to reduce by a significant amount the neutron
flux all along the tagger. In particular in the last meters of the tunnel
where the neutron fluence is more significant the ratio between neutrons from
the hadron dump hitting the tagger w.r.t those with the old design is $\sim$
0.2.

Figure 5: Preliminary new design of the hadron dump that helps reducing considerably the contribution to the background in the tagger due to the backscattering. There is 1 meter of borated concrete with an opening for the beam in front of the dump. The dump itself is composed by three cylindrical layers: the core is made by graphite, the second layer is made by iron and the last one is made by borated concrete. Transfer line |  $\pi^{+}$ [$10^{-3}$/POT] |  $K^{+}$ [$10^{-3}$/POT]
---|---|---
label |  [8.5 $\pm$ 10%] GeV/c |  [8.5 $\pm$ 10%] GeV/c
TLR6 | 4.2 | 0.4
Table 1: Fluxes obtained with G4Beamline at the tunnel entrance for $\pi^{+}$
and $K^{+}$ in the [8.5 $\pm$ 5% GeV/c] range in units [$10^{-3}$/POT]. In the
last column we report the ratio to the previous result on $K^{+}$ flux. Figure
6: Top: $\nu_{e}^{CC}$ interactions considering a 6 $\times$ 6 m2 front face
of a neutrino detector located 50 m downstream the tunnel exit divided in
categories corresponding to the position along the transfer line where the
neutrino was generated. The red spectrum corresponds to neutrinos generated
inside the tagger. Bottom: relative fraction of each category to the total
$\nu_{e}^{CC}$ rate.

In Tab. 1 the flux obtained at the tunnel entrance for 8.5 GeV/c $\pi^{+}$ and
$K^{+}$ is reported. In Fig. 6 we present the spectra for the $\nu_{e}^{CC}$
interactions seen in a far detector placed 50 m downstream of the tunnel end
with the TLR6, divided in categories depending on the origin of the neutrino
along the transfer line. The neutrinos coming from the decay tunnel are
clearly separated in energy from those generated in the proton dump and in the
first section of the beamline. Moreover, 73.5% of the total $\nu_{e}$ flux is
generated inside the tunnel, and above 1 GeV this component represent more
than 80% of the total flux. Below 1 GeV the main component is given by
neutrinos produced in the proton-dump region, which will allow us to further
improve the separation of the signal against this component by optimizing the
proton dump position. The contribution of $\nu_{e}$ coming from the straight
section in front of the tagger (i.e. from the second dipole to the tagger
entrance) amounts to $\sim$ 7% and another $\sim$5 % is given by the section
after the tunnel exit and the hadron dump. Even though indistinguishable from
the $K_{e3}$ neutrinos produced inside the decay tunnel this 12 % can be
corrected for by relying on the simulation.

By assuming 4.5$\times$1019 POT/year at the SPS the TLR6 enables to reach 104
$\nu_{e}^{CC}$ at the far detector about two years. A previous design (TLR5)
with the new optimized target would allow to reach the same statistics in
about 3 and half years.

###  5.5 Doses in the decay tunnel

The FLUKA simulation of the double-dipole beamline (TLR5) has been updated
including proper shielding to provide a sensible estimate of the ionizing
doses and neutron fluences for all the elements of the beamline. We are
particularly interested in the decay pipe where scintillators and Silicon
Photo Multipliers (SiPM) will be located and the location of the first rad-
hard focusing quadrupole. We are also evaluating the activation rates to
design engineering solutions for a possible accessibility of the instrumented
area for maintenance.

The geometry layout of active elements and shielding is shown in Fig. 7. The
FLUKA geometry description is semi-automatically generated within GEANT4. The
FLUKA model hence faithfully reproduces the GEANT4/G4Beamline one.

Figure 7: Top: FLUKA implementation of the double-dipole transfer line model
TLR5. The regions in green are those composed of borated polyethylene,
concrete is in gray, tungsten is in greenish while orange and brown represent
copper and iron, respectively. Bottom: 3D rendering of the first straight
section with a cut along a vertical plane passing through the proton beam.

The map of the accumulated dose obtained with FLUKA in Gy for 1020 POT is
shown in Fig. 8. The dose at the hottest point of the quadrupole closest to
the target is of the order of 100-300 kGy for 1020 POT. This is a totally
acceptable value in terms of operability of a suited magnet.

Figure 8: Dose map obtained in Gy for 1020 POT (FLUKA). The first quadrupole
sits roughly between $z=200$ and 500 cm.

Neutron fluences are shown in Fig. 9 for the same amount of accumulated POT.

Figure 9: Top: neutrons fluences for TLR5.

The SiPM are protected by a shielding of Borated polyethylene (BPE, 5% Boron
concentration) with a thickness of 30 cm. In Fig. 10 we show the distribution
of neutrons (neutrons/POT/cm2) as a function of the longitudinal coordinate
along the tunnel ($z$), at the inner surface of the tagger (black), at the
surface between the iron and the BPE (blue) and at the outer surface of the
BPE (red). The neutron reduction induced by adding this layer of material
amounts to a factor of $\sim$ 18, averaging over the expected energy spectrum
and it settles at about $7\times 10^{-11}$ n/POT/cm2 in the middle region of
the tagger ($3.5\times$ 109 n/cm2 for 5 $\times$ 1019 POT). This value is
about a factor 10 lower than what was estimated with the single dipole
beamline. The bulk of neutrons reaching the SiPM have kinetic energies
O(10-100) MeV/c2 (Fig. 10, right).

Figure 10: Left: FLUKA estimate of neutrons/POT/cm2 as a function of the
longitudinal coordinate along the tagger. The black line represents the inner
surface of the calorimeter, the blue one the surface after the iron absorbers
- 11 cm - and the red one the surface after additional 30 cm of BPE i.e. the
region where the SiPM will operate. Right: in Magenta the FLUKA estimate of
the kinetic energy spectrum of neutrons (GeV) reaching the SiPM in the - 25 m
long - middle section of the tagger. In red the damage function for Silicon.

At the time of writing the latest TLR6 version of the beamline is also being
implemented both in GEANT4 and FLUKA222Our GEANT4 software (Sec. 5.12)
implements a feature for semi-automatically producing the geometry input card
for FLUKA..

###  5.6 Multi-Momentum Beamline

Most of the ENUBET studies have been performed considering a beamline with a
central momentum of 8.5 GeV/c. This choice is optimal for $\pi^{+}$/e+
separation and to cover the energy range of interest for DUNE and HyperK [25].
On the other hand, the bulk of the produced neutrinos are in the multi-GeV
range (”DUNE optimized beamline”) and we aim at achieve a design flexible
enough to run lower momentum secondaries, enriching the low-energy region of
the ENUBET spectrum (”HyperK optimized beamline”).

We present in this section the ongoing R$\&$D side efforts on a beamline
design which employs a secondary multi momentum (4, 6, and 8.5 GeV/c). This
design was conceived to widen the cross-section energy range available to
ENUBET, including the region of interest of T2K/HyperK.

This beamline design is based on existing CERN magnets and on the same
principles as other low-energy secondary beamlines at CERN [62]. The
conceptual layout can be summarized as follows: downstream the optimized
Graphite target, a large-aperture quadrupole triplet defines the initial
phase-space of the charged kaons. Large aperture dipoles and iron collimators
select the particles, including the sought-for kaons, in a narrow momentum
range. In this way the majority of background particles outside the nominal
momentum band are not transported by the beamline. The 13.35∘ dipole
deflection allows for a proper dump of the 400 GeV/c primary beam without
contaminating the decay tunnel, and increase the momentum selection
resolution. The proton dump configurations are still under evaluation. The
remaining positron background is filtered by a 5 mm tungsten absorber.
Finally, another quadrupole triplet performs the final focusing of the beam so
that it enters the decay tunnel with a small divergence, and the emitted
positrons produced by the kaon decay have similar angles. The overall maximum
angular acceptance of this preliminary design is $\pm 20$ mrad in both planes.

Figure 11: Multi Momentum Beamline layout in G4Beamline. Starting with a 80 cm
long graphite target, we placed a Q200 quadrupole triplet. The bending section
is composed of two large deflection bends, a collimator of $9\times 9$ cm2
aperture followed by a 5 mm thin tungsten absorber and a QFL focusing magnet.
Before the decay tunnel, we find a final QFL quadrupole triplet.

The optics optimization for ENUBET’s multi-momentum beamline is performed at
first-order using TRANSPORT [61] and G4Beamline [58]. The results will be then
validated with MAD-X/PTC-TRACK [37] to estimate higher-order effects, while
the background reduction studies will be performed using FLUKA. Since
positrons dominate the production of secondary particles especially in the
lower energies ($<$ 6 GeV/c), we are considering placing the whole beamline
tilted with respect to the target. Placing the beamline at a horizontal angle
would drop the emission of positrons from the target with a greater factor
than the kaons. This effect is important at the desired momenta and allows for
further background suppression. However, this configuration requires special
care in the design of the dump of non-interacting protons, which is currently
under evaluation.

###  5.7 Beam background reduction studies

The search for optimal configurations with the genetic algorithm originally
developed for the horn has been extended to the full beamline. The
optimization is run with a large number of parallel jobs running on the Lyon
IN2P3 computing farm. In particular the last collimator before the tagger has
a conical aperture whose radiuses have been optimized together with the
apertures of downstream collimators. The procedure has proven to work and is
being fine tuned. A pre-selection of tracks at the target level is being
applied to make the execution speed more effective and use a larger statistic
for the figure of merit. In a first scan a figure of merit based on an
integral S/B ratio in the tagger was defined. Currently we are implementing
also some information on the shape of backgrounds to avoid picking up
configurations in which the S/B is good in terms of overall normalization but
in which background is more difficult to be separated from background due to a
similar distribution in energy and in the position along the tagger.

###  5.8 Instrumented decay tunnel and PID

In the following Sec. 5.9 and we describe the final, published, analysis of
test beam data taken during fall 2018 at CERN. With respect to last year a
more solid understanding of saturation effects has been obtained which is
providing essential guidance in the choice of the final SiPM. It should be
noted that, with respect to that design several aspects have evolved (the
layout of WLS fibers, the scintillator thickness), as we will explain when
discussing the delivery of the final demonstrator (Sec.5.17).

###  5.9 Lateral readout calorimeter

Positron tagging and $e^{+}$/$\pi^{+}$ separation require a longitudinal
segmented calorimeter with an energy resolution of
$<25\%/\sqrt{E\mbox{(GeV)}}$[41] in the energy range of interest (1-3 GeV).
The technology of choice is a sampling calorimeter, whose building element is
the LCM (Lateral Compact Module), assembled from five $3\times 3\times
1.5~{}\mbox{cm}^{3}$ steel tiles interleaved with five $3\times 3\times
0.5~{}\mbox{cm}^{3}$ plastic scintillator tiles (Eljen EJ-204 [42]). Two WLS
fibers of 1 mm diameter are inserted and glued into two grooves placed at two
opposite sides of each scintillator tiles. Each LCM has hence ten WLS fibers
that are then coupled with a Silicon PhotoMultiplier (SiPM). The SiPMs are
produced by Advansid [47], have an active area of $4\times 4~{}\mbox{mm}^{2}$
and a cell size of 40 $\mu$m. The prototype tested in fall 2018 was assembled
from 84 LCM arranged in 7 planes on a $3\times 4$ matrix (Fig. 12). The first
three longitudial planes were instrumented with Kuraray Y11 WLS fibers and the
remaining four with Saint Gobain BCF92 WLS fibers. The total length of the
calorimeter covers $30.1~{}X_{0}$ and $3.15~{}\lambda_{0}$. The transverse
dimension of $12\times 9~{}\mbox{cm}^{2}$ allows for full containment of
electromagnetic showers up to 5 GeV.

Figure 12:  The full calorimeter tested at CERN PS-T9 beamline in September
2018.

The extraction of the fibers from the lower planes of the calorimeter is made
possible by shifting the 3 longitudinal planes by 3.5 mm with respect to each
other and by extending the groove for the WLS fibers from the scintillator to
the steel tiles. The calorimeter was put under test in September 2018 at CERN
PS-T9 beamline, with a mixed beam of $e^{-}$, $\mu^{-}$ and $\pi^{-}$, with
beam momementum ranging from 1 to 5 GeV. The response to electromagnetic
showers was tested by tilting the prototype at 0, 50, 100 and 200 mrad w.r.t.
the beam axis, in order to simulate the impact angle of the positrons inside
the decay tunnel. The SiPM voltage bias was $V_{bias}=31$ V, (4 V Over Voltage
- OV). The results indicate that the performance of the calorimeter is the
same for front and inclined runs. Figure 13 shows the reconstructed energy in
the scintillator for data and MC in a 100 mrad run. Above 3 GeV it is possible
to observe a deviation from linearity, $\sim 3\%$ ($\sim 7\%$) at 4 GeV (5
GeV). This effect is caused by the saturation of the SiPMs, which is enhanced
by the rather large cross-talk at $V_{bias}=31$ V, $P_{x-talk}\simeq 44\%$, as
measured in a dedicated setup at the INFN Bologna labs. To account for these
saturation effects, the number of expected fired cells in the SiPM in the MC
has been corrected with the following equation [68]:

$N_{\rm{fired}}\simeq
N_{\rm{max}}\left(1-e^{-N_{\rm{seed}}/N_{\rm{max}}}\right),$ (5)

in which the expected average number of p.e. in an LCM ($N_{\rm{seed}}$) is
smeared for Poisson fluctuations ($N_{pe}$) and increased by the
aforementioned cross-talk effects
($N_{\rm{seed}}~{}\equiv(1~{}+~{}P_{x-talk})\cdot N_{pe}$). The SiPMs
equipping the calorimeter have 9340 cells, but the fibers are put in
mechanical contact and illuminate fewer of the available cells, namely
$N_{\rm{max}}\simeq 5000<9340$. Despite the uncertainty on $N_{\rm{max}}$, Eq.
5 manages to account for non linearities in the detector, as shown in Fig. 13.

Figure 13: Energy reconstructed in the calorimeter versus beam energy for a
100 mrad run. Testbeam data (red dots) are compared with Monte Carlo
simulation including (green triangles) and not including (blue squares) the
SiPM saturation. The horizontal errors correspond to the momentum bite of the
beam. The vertical error bars (not visible in the plot, since of
$\mathcal{O}(0.1\%)$ and covered by the marker) in “MC” and “Data” are given
by the standard error of the mean of the gaussian fit performed on the
electron peaks. The vertical error bars in “MC + SiPM saturation” are given by
the uncertainty on the number of pixels available to the light collection (the
lowest estimate is $\sim 4580$, while the highest estimate is $\sim 5400$).

The energy resolution for a 0 mrad run is shown in Fig 14. The points are
fitted to $\sigma_{E}/E=S/\sqrt{E(\rm{GeV})}\oplus C$, in which $S$ is the
sampling (stochastic) term and $C$ is the constant one. At 1 GeV the energy
resolution is 17%. At high energy the simulation deviates from the data,
mostly due to saturation effects. In particular, by the time of the
publication of these results, it was understood that the impact point of the
particle affects its contribution to saturation, which is higher for particles
impinging at the center of the module and lower for events near the edge of
the tile, as the energy is shared between two adjacent LCMs and two different
SiPMs.

Figure 14: Energy resolution versus beam energy for particles impinging on the
front face (0 mrad run) for data (red dots) and simulation (blue squares). The
fit parameters for data and simulation (MC) are shown in the top and bottom
insets.

Since the separation of signal and background in ENUBET is performed by
analyzing the energy deposit pattern in the LCMs, the simulation of this
pattern was tested with a $\pi^{-}$ beam in the same energy range as for the
electrons. The mean $\pi^{-}$ energy deposited in each plane of the
calorimeter in the data was evaluated and compared to the simulation, showing
a rather good agreement: the discrepancies do not exceed 10% and are
comparable to the uncertainty due to low-energy hadronic shower simulation
(Fig.15). These results were published on Journal of Instrumentation in August
2020 [67].

Figure 15:  Left: average energy deposited in the scintillator as a function
of calorimeter planes for 3 GeV pions. Each LCM corresponds to 0.45
$\lambda_{0}$. Right: energy ratio between data and MC.

Following the publication, an optical simulation is currently being
implemented in the simulation of the calorimeter, in order to replicate the
aforementioned SiPM saturation effect associated with the initial impact point
of the particle on the calorimeter. The first steps of this simulation, which
recreated the signal collected by a single plastic scintillator tile read with
two WLS fibers coupled to a single SiPM, have been supported by a set of
dedicated tests performed in INFN Bologna; data and simulation showed very
good agreement. Moreover, in collaboration with Fondazione Bruno Kessler
(FBK), we are currently identifying and testing different sensors as to find
the more suitable one.

###  5.10 Photon veto

In addition to the calorimeter, ENUBET is instrumented with a photon veto
detector ($t_{0}$–layer) to provide both photon identification capabilities
and precise timing of particles in the instrumented decay tunnel. In order to
achieve the main goal, the requirements are i) a photon identification
efficiency at 99%, and ii) a time resolution of $\sim$1 ns. The $t_{0}$-layer
is composed of doublets of plastic scintillator tiles (3$\times$3$\times$0.5
cm3) mounted below the LCMs and positioned every 7 cm. In this way positrons
from kaon decays in the ENUBET working condition cross five doublets on
average.

Data taken during beam-test at CERN in 2018 have been fully exploited during
2020 and the results have been published in [67] and can be summarized as
follows. The light yield for a single mip crossing a $t_{0}$ tile allow for a
collection of 25 p.e. at MPV with a time resolution estimated to be $\sim$400
ps, well within the requirements of the project.

Figure 16: (Left: The number of p.e. collected in one tile versus the number
of p.e. collected in another tile. Right: Fit on data by using a composite
model: black dots represent the data sample, the black line is the composite
model. The purple, blue and read lines are respectively dark current
contribution, the signal and the background PDF )

Moreover, the capability of the $t_{0}$-layer to separate one mip from two
mips was investigated as shown in fig. 16 A single $t_{0}$-tile is capable of
selecting the signal due to one mip with an efficiency of 87% and a background
(2-mip like) rejection efficiency of 89% are obtained with a corresponding
value for the purity of about 95%.

####  5.10.1 Waveform digitizer design

A prototype digital board to handle the signals from a 4 channel ADC board
(250 MS/s, 14 bit) and to provide a USB interface with the PC has been
designed around an Altera 5CGXBC3B6F23I7N and manufactured. It is undergoing
extensive tests in order to validate the different parts. In the readout of
the final ENUBET prototype this custom electronics will be complemented and
cross-checked with commercial digitizers and a set of 64-ch boards by CAEN
(A5202) based on the WeeROC CitiROC-1A ASICs which will only readout the
signals’ amplitude and time.

Figure 17: Layout and picture of the prototype digital board.

###  5.11 Simulation

###  5.12 Simulation packages

The ENUBET facility has been described in G4Beamline, GEANT4 and FLUKA. The
beam components are implemented in G4Beamline, that fully simulates particle
transport and interactions (described in Sec. 5.4), while FLUKA is used for
the fine tuning of collimators and shielding (Sec. 5.7) and for doses
assessment (Sec. 5.5). The GEANT4 simulation (G4TL) is redundant, since it
contains the same setup implemented in the other software packages, allowing
the cross-check of the results. It reproduces the entire facility: the
elements of the transfer line, the tagger and the neutrino detector, with the
exception of the tagger geometry. The simulation has been validated against
the G4Beamline results for one of the previous versions of the transfer line
(TLR2, single dipole version). This has been achieved by comparing the spectra
and the entering angle of particles at the tagger entrance obtained with
G4Beamline. Recently also the double-dipole transfer line (TLR5) has been
modeled in GEANT4 (Fig. 18), and the latest TLR6 version is also being
implemented.

Figure 18: GEANT4 simulation of the TLR5 double dipole beamline.

One of the strengths of this simulation is the possibility of controlling all
the parameters of the setup, from the collimator dimensions and positions to
the magnet apertures and fields, using a control card. Moreover, GEANT4 gives
access to information on particle decays and their histories.

Fig. 19 shows the output of the TLR5 simulation. The decay information about
the particles simulated throughout the beamline, such as the position of the
decay and the momenta of the secondaries, allows the reconstruction of
neutrino tracks. It is then possible to estimate the flux and the rate of
neutrinos at the far detector, and divide it according to the neutrino flavour
or to the decay mode.

Figure 19: Neutrino interaction rates at far detector, breakdown by decay
mode. It must be noted that here the implementation of the shielding was not
finalized. Hence these fluxes can be considered an upper limit for the
neutrino components from the target region. The rates are approximated by
weighting the fluxes with energy. Neutrino generators will be used in the
future.

The instrumentation of the ENUBET facility has been implemented in detail in a
GEANT4 standalone package (G4TAG) that reproduces the detectors in the decay
tunnel (the photon veto and the calorimeter modules) for the monitoring of
large angle leptons from kaon decays (Sec. 5.14, 5.15.1) and the stations
after the hadron dump for the monitoring of muons from pion decays (Sec.
5.15.2). The simulation includes the propagation and decay up to the hadron
dump of particles provided by the G4Beamline simulation of the transfer line
(Sec. 5.4) at the tunnel entrance. The response of the detectors in the tunnel
is simulated at hit level, not considering the scintillation process and light
propagation. The results concerning the lepton monitoring reported in the
following are based on the assumption of a 2 s slow extraction with
4.5$\times$1013 POT per spill.

Since the G4TAG simulation package can only account for decays in the tunnel,
we implemented a shared structure based on a ROOT TTree: by merging the
information from the transfer line (G4TL), we can trace all the decays
occurring along the entire beamline.

The assessment of the systematic uncertainties on the neutrino flux will be
performed within this GEANT4 framework, exploiting the possibility to tune all
the parameters of the simulation, following the procedure described in Sec.
5.17.1.

###  5.13 Pile-up study with waveform simulation

In order to assess the effects of the pile-up on the overall detector
performances, a software framework has been implemented to simulate the
calorimeter response at a single channel level. Each visible energy deposit
coming from the GEANT4 simulation of the instrumented tunnel (G4TAG) is
initially converted into photons hitting the SiPM using a conversion factor of
$\sim$15 photo-electrons/MeV, obtained from past test beams and cosmic rays
measurements results. Secondly, the SiPM response is simulated using the
GosSiP software tool (Generic framework for the Simulation of Silicon
Photomultiplier [63]) which allows a fine control on all the sensor operating
parameters. A waveform for each channel is generated and then processed by a
pulse detection algorithm whose results are eventually converted back into a
time series of energy deposits and returned to the event builder.

The algorithm has been optimized aiming to have a good correlation between the
measured pulse amplitude and the original visible energy deposits, a high
efficiency and an accurate time resolution in the pulse detection, which are
key parameters for the event building. The algorithm performance has been
measured for different input beam conditions and several electronics and SiPM
intrinsic parameters. In the upper part of Fig. 20 the energy spectra measured
by the detection algorithm are superimposed to the ones from the G4TAG
simulation for the different calorimeter layers; in the bottom part the
distribution of the residuals between the original hit time and the measured
ones is shown. In Tab. 2 a summary of the achieved detection efficiency is
shown.

Figure 20: Upper plots: energy spectra for the different calorimeter layers as provided by the deposited energy in the GEANT4 simulation (blue) and as measured from peak amplitudes after the waveform simulation of each SiPM (red). Bottom plots: residuals for the different calorimeter layers between the original time of the hits in the GEANT4 simulation and the pulse time as detected by the peak finding algorithm. The highlighted areas represent more stringent time intervals for the efficiency measurements (see Tab. 2). Transfer line and extraction scheme |  Hit rate per LCM |  detection efficiency |  detection efficiency limited to a $\pm$ 1 ns time range
---|---|---|---
TLR5 slow |  1.1 MHz |  97.4% |  93.7%
TLR5 fast |  10.4 MHz |  89.7% |  84.0%
TLR6 slow |  2.2 MHz |  95.3% |  89.6%
Table 2: Achieved detection efficiency as a function of the input beam
transfer line and extraction scheme (the listed data refer to the 2nd
calorimeter layer). In the last column the efficiency defined over a more
stringent time interval of $\pm$1 ns with respect to the true hit time is
shown (this corresponds to the highlighted area in the bottom plots of Fig.
20). The slow extraction scheme assumes 4.5$\times$1013 POT in 2 s; in the
fast scenario, a factor 10 increase in the particle rate is assumed.

Given the large number of channels, the simulation for the whole tagger is run
exploiting the CERN HTCondor batch system and the EOS space is used for the
data storage. This allowed us to increase the statistics by more than 100000
times from test files to a complete simulation of the output signal with over
800000 SiPMs.

Once fully debugged and properly integrated, the output of the waveform
simulation will be finally included in the lepton reconstruction chain
described in the next sections.

###  5.14 Positron monitoring

The event building is the preliminary step for the identification of leptons:
it correlates in space and time hits in the tunnel instrumentation belonging
to the same decay, dealing with mixing effects induced by beam halo particles
and other mesons’ decay modes. The algorithm setup for $K_{e3}$ monitoring is
oriented towards a preselection of positron candidate events, through the
identification of a visible energy deposit in the LCMs of the innermost layer
exceeding 28 MeV333the Landau fit of the energy released by a mip in a LCM has
a most probable value of $\sim$6.5 MeV. as “seed” for the event
reconstruction. LCM and $t_{0}$ signals correlated to the seed are then
clustered taking into account their position and timing, with cuts unchanged
with respect to the previous report [26], and the procedure is iterated over
all the signals recorded.

The positron selection and its separation from the hadronic background is
performed exploiting the longitudinal, transverse and radial segmentation of
the calorimeter, while the suppression of the residual photon background is
accomplished employing the $t_{0}$-layer. Electromagnetic showers will be more
localized than the ones initiated by hadrons from the beam halo or from other
kaon decay modes. Muons and non-interacting hadrons, already suppressed by the
request of at least one energy deposition (the event seed) largely exceeding
the mip one in the event building process, can be efficiently discarded by
their single track topology.

A set of variables describing the energy deposition pattern in the calorimeter
is implemented in a multivariate analysis, based on a Multilayer perceptron
Neural Network (NN) provided by the TMVA toolkit [64]. Unlike the previous
version of the positron selection described in the latest report, the
$e^{+}/\gamma$ separation is not accomplished anymore with a cut based
analysis of the signals in the $t_{0}$-layer. Indeed, the energy depositions
on the four most upstream tiles of the reconstructed event are used as
additional variables of the NN. The Neural Network training is performed
defining a signal sample composed by $K_{e3}$ positrons. The background
sample, that includes hadrons, muons and photons both from the beam halo and
mesons’ decays, has been enriched with electrons and positrons originated in
the transfer line, in order to exploit differences in angular and longitudinal
distributions with respect to signal positrons for their rejection.

The event classification is done according to the event seed and the
distributions refer to events reconstructed by the event builder.

Focusing on the new variables associated to the $t_{0}$-layer, the bin with a
null energy deposition in the tile is dominated by photons from the beam halo
(in orange) and kaon decays producing a $\pi^{0}$ (in yellow), with a residual
contribution from $K_{e3}$ events (golden yellow) in which the
$\pi^{0}$-related part has been reconstructed by the event builder. The
Landau-like distribution with an approximate 0.85 MeV most probable value is
well compatible with minimum ionizing particles crossing the 0.5 cm thick
plastic tiles of the $t_{0}$-layer. Finally the second small structure visible
around 1.7 MeV is due to photon conversions in the upstream tiles.

The suppression of photon like events is evident in the $t_{0}$-related
variables where almost all the events with and energy deposition not
compatible with a mip one are discarded. The variables encoding information on
the calorimeter energy strongly suppress hadronic decays of kaons (yellow) and
non-collimated pions (green), while beam induced positrons (black) are left as
the main, irreducible, component of the background.

Fig. 23 shows the overall efficiency of the selection, including the
geometrical acceptance444that amounts to $\sim$53%, as a function of the
signal-to-noise ratio (S/N), obtained for different cuts on the NN classifier.
The previous selection, with the cut-based analysis on the $t_{0}$-layer (in
dashed blue) is compared with the new one here presented (in solid blue). The
improvement is remarkable: by choosing as an example a cut on the classifier
giving an efficiency of $\sim$ 24%, the S/N significantly increases, going
from $\sim$1.6 to $\sim$ 2.1. The improved design of the proton target and of
the meson transfer line ensures a larger meson yield at the decay tunnel
entrance (Sec. 5.4), but at the same time determines an increase of the hit
rate on the tagger instrumentation of a factor $\sim$2.7. Despite the larger
mixing effects in the event building phase, that spoil the NN discrimination
capabilities, the improved selection still allows to monitor positrons with an
efficiency of $\sim$ 22% and a S/N of $\sim$ 2 (see the red line in Fig. 23,
left).

Fig. 21 shows the distributions of two relevant observables, the longitudinal
position and the total visible energy, for events at different stages of the
selection: after the event building and after the NN discrimination.

Figure 21: Longitudinal position (top) and total energy (bottom) of selected
events at different stages in the selection of $K_{e3}$ events: (left) after
the event building; (right) after the NN discrimination.

###  5.15 Muon monitoring

####  5.15.1 Tagger

A similar procedure to that applied for positron reconstruction and
discrimination is used for muons from $K_{\mu 2}$ and $K_{\mu 3}$, produced at
mean angles such that they cross the calorimetric tunnel. First of all, a
clustering of the energy deposits in the LCMs, compatible in space and time
with the expected track from a muon particle, is performed. This step, known
as muon building, is unchanged since the last report [26]: the clustering is
triggered by the identification of a seed (likewise the $e^{+}$ clustering),
an energy deposit in the innermost LCM layer compatible with a mip ($5<E<15$
MeV); the track length is required to be at least 3 LCMs in the first
calorimetric layer and at least 2 LCMs in each one of the second and third
layer, for a total of 7 LCMs all in different positions along the longitudinal
direction. The cuts on the seed energy and track length have been fine tuned
such that the product of efficiency times purity is maximized for the muon
building.

Among the built events a signal-background discrimination is achieved by
applying a NN. Different algorithms have been investigated, but like for
$e^{+}$ also the $\mu^{+}$ signal identification shows best performance with
the Multilayer perceptron. Concerning the background, the larger contribution
comes from halo muons, while second order contributions are muons from pion
decays emitted at large angles and pions either from the secondary beam or
kaon decays. A set of variables has been identified to train the NN: they
exploit the differences in the topology and in the amount of energy deposit
between signal and background. In particular, a good discrimination variable
for the halo muons is the muon impact point position along the calorimeter,
shown in Fig 22. In fact, the signal tend to be more prominent in the forward
part of the tunnel, whereas the halo muons hit the tunnel preferentially
upstream. For pions the discrimination is helped by energy related variables,
since muons (being mips) release less energy in the calorimeter.

(a)

(b)

Figure 22: (a) distribution of the impact point along the calorimeter for
muons from kaon decays. Signal contribution in red, $K_{\mu 2}$, and orange,
$K_{\mu 3}$. The main background contribution, in purple, is from halo muons.
Other colors show subdominant background contributions. (b) same as in (a) but
after applying the NN cut.

With the new version of the transfer line, a factor of $\sim 3-4$ more halo
muons in the forward region of the calorimeter is observed. This could cause a
worsening of the discrimination power for the muon impact point observable.
Moreover, a reduction of the clustering performance could be caused by the
increase in the rate of particles hitting the tunnel, inducing higher mixing
effects between different events. Anyway, a worsening of the muon building
performance has not been observed. In Fig. 23 (right) we present the signal
selection efficiency versus the signal-to-noise ratio after applying the NN on
the built muon candidates. The two curves show the comparison between the
results in the previous report and the one updated with the new transfer line:
performances are very similar, a part in the very low and high S/N regions.
The very low S/N region corresponds to looser cuts on the NN (no cut in the
lower S/N limit), the lower efficiency is then dominated by slightly lower
event building performance, probably related to the larger mixing effects
observed with the new transfer line. The very high S/N region corresponds to
tighter cuts on the NN, and selected background events are very similar to the
signal. Thus, the lower efficiency here could be related to the forward region
of the calorimeter being polluted by a higher amount of halo muons with the
new transfer line. Nevertheless, when cutting at the NN value maximizing the
efficiency times purity we get a signal efficiency of $\sim$ 34% and S/N of
$\sim$ 6 (Fig. 23, right).

Figure 23: Left: Efficiency as a function of the signal-to-noise ratio in the
selection of $K_{e3}$ events. Blue lines refers to the previous version of the
beamline (TLR5), the dashed one is obtained with the positron identification
analysis described in the previous report [26], the solid one to the improved
analysis described here (see text). The red line refers to the new beamline,
TLR6 (Sec. 5.4). Right: signal efficiency versus signal-to-noise ratio for
$K_{\mu 2}$ and $K_{\mu 3}$ events selection. The result from the new transfer
line, in red, is compared to the one from the previous report, in blue.

####  5.15.2 Muon chambers

Low energy muon-neutrinos from pions can be constrained by monitoring the
associated muons produced in the decays. These $\mu$ are emitted at low angle,
and go through the decay tunnel crossing the final hadron-dump. A measurement
of relevant physics observables can be performed by instrumenting the hadron-
dump, using different detector layers installed at increasing depth and
interleaved by absorbing material. The detector layout was presented in the
last report [26]. It allows to measure the spatial distribution of muons,
shown in Fig. 24 (a), and their energy, in Fig. 24 (b), by range-out. The
differences in the distributions between the contributions can be exploited to
disentangle the signal from the background, again dominated by halo-muons.

(a)

(b)

Figure 24: Relevant distributions for muons in the instrumented hadron-dump.
(a) spatial distribution along one of the two dimensions of a detector layer.
(b) energy distribution. Red and blue are the signal contribution, from pion
and kaon decays. Gray distribution are halo-muons.

In collaboration with the new group from University of Thessaloniki we are now
in the process of determining the best detector technology to employ for the
instrumentation of the hadron-dump. The detector needs to cope with a muon
rate of 2 MHz/cm2 and a neutron fluence of about $10^{12}~{}1~{}$MeV-neq$/$cm2
in the layer closer to the end of the decay tunnel.

###  5.16 Narrow band off-axis technique

A slow proton extraction scheme allows for the direct measurement of muons
from pion decays after the hadron dump: the combination of this information
with the one from the tagger on large angle muons from kaons provides a
complete monitoring of the $\nu_{\mu}$ flux in ENUBET (see Sec. 5.15). In
addition, the narrow momentum width of the beam ($\mathcal{O}$(5-10%)) can be
exploited to provide the neutrino energy on an event by event basis, thanks to
its correlation with the position of the interaction vertex in a detector
placed at short distance. The determination of the neutrino energy at source
with enough precision could overcome the uncertainties related to its
determination through the reconstruction of the final state, thus allowing for
a high precision differential cross section measurement.

This method, named “narrow band off-axis”, was already described in [25]. In
this report we update the related results using the realistic beam provided by
the latest version of the transfer line (Sec. 5.4), thus including also muons
and neutrinos from the beam halo and off-momentum mesons. Low energy neutrinos
from the target station and the proton dump are not included in the present
estimation, but they are expected to give a negligible contribution to the
final interaction budget, as a result of their cross section suppression. A
final re-evaluation of the technique capabilities will be performed after the
fine tuning of the complete GEANT4 simulation of the ENUBET facility (Sec.
5.11).

In order to estimate the expected number of neutrino interactions a 500 ton
liquid Argon detector (isoscalar target) placed 90 m from the entrance of the
decay tunnel (50 m from the hadron dump) and with a cross sectional area of
6$\times$6 m2 has been considered. The detailed detector response is not
included and the interaction rate is the convolution of the neutrino flux with
the CC cross section: assuming 4.5$\times$1019 POT, about 4$\times$105
$\nu_{\mu}^{CC}$ interactions will be observed at the detector and their
spectrum is shown by the black line in Fig. 25 (left). The colored lines
describe the spectra obtained selecting neutrino interactions at different
radial distances $R$ from the beam axis, in windows of $\pm$10 cm. The same
spectra, but normalized to one, are reported in the right plot.

Figure 25: (left) $\nu_{\mu}^{CC}$ interaction spectrum in black. The coloured
lines show spectra of interactions at different radial distances (R) from the
beam axis, higher frequencies of the line colour refer to larger R. (right)
Unit normalized spectra.

The low energy pion component of the spectra can be separated from the kaon
one with a loose cut on the reconstructed energy. The width of the pion peaks
at different $R$ can then be used as an estimator of the precision on the
incoming neutrino energy.

###  5.17 Demonstrator: design, procurement, construction

The layout of scintillators is shown in Fig. 26, left. All tiles are
trapezoidal in shape such that to minimize dead regions. The $t_{0}$-layer
tile (innermost radial position) holds two grooves. They are 1 mm deep such
that the full WLS diameter is enclosed in the scintillator. These two grooves
are meant for light collection (“readout” grooves) and they are propagated to
the other three outer tiles where they only have the function of letting space
to host the WLS fiber without letting the scintillation light to enter
(“transit” grooves). Transit grooves hence need to be covered with a chemical
etching treatment to make them optically opaque. The second tile has readout
grooves on the other side of the transit grooves. This pattern repeats as in
the Figure. For tile 2 and 3 readout grooves are slightly offset-ed with
respect to 0 and 1 to accommodate them with the transit ones.

Figure 26: Left: layout of the frontal grooves readout scheme. Right:
rendering of a section of the demonstrator corresponding to the extension
along the beam axis of single module (LCM). Scintillators are shown in gray,
borated polyethylene shielding in green and fiber concentrators in black.

The scintillators are in the production phase with UNIPLAST (Moskow) in
collaboration with the INR group. The tiles will be first produced with the
proper shape using injection molding. Afterwards transit grooves will be
milled and the tiles will be treated with chemical etching surface treatment
to make them white and opaque. Finally the readout grooves will be milled. The
total number of scintillator tiles for the demonstrator will be of about 10000
pieces. The scintillators will be interspersed with 15 mm thick iron slabs to
form the sampling calorimeter. Their position with respect to the other
elements of the demonstrator is shown in the right part of Fig. 26.

The procurement of Silicon Photomultipliers for the ENUBET demonstrator has
been finalized and Hamamatsu models S14160-3050HS ($3\times 3$ mm2) and
S14160-4050HS ($4\times 4$ mm2) were selected.

The final choice for the layout of the demonstrator to be exposed at CERN in
October 2022 is shown in Fig. 27 with a beam-transverse (right) and a lateral
view (left). The same is shown with a 3D rendering in Fig. 28. The object is
1.65 m long in the longitudinal direction and it spans 90∘ in azimuth. It
comprises 75 layers or iron (15 mm thick) and 75 layers of scintillators (7 mm
thick) i.e. $12~{}\times 3$ LCM. We expect to instrument the central 45∘
central region while the rest has been kept for mechanical considerations. The
structure is designed to be extendable to a full $2\pi$ object by joining four
similar detectors with minimal dead regions. The iron part extends radially
for 11 cm while the remaining 30 cm are filled with 22.5 mm thick with Borated
P.E. slabs with 5% Boron (green in the Figure).

The structure is held by a mechanical crawl sitting on four extensible legs
that are designed to allow tilting the calorimeter-beam angle in the vertical
plane and adjusting the horizontal position by means of a wheel-rail
mechanism.

Figure 27: Left: rendering of the demonstrator.

Figure 28: Left: 3D rendering of the demonstrator. Right: assembly at INFN-
LNL.

The strategy for routing the WLS and matching them to the photo-sensors is
sketched in Fig. 29. The ten WLS fibers belonging to the same LCM are routed
by passing through grooves milled in the BPE and bundled to a $4\times 4$ mm2
SiPM. The $t_{0}$-layer fibers will be read by two independent SiPMs.

Figure 29: Top: schematic view of the WLS routing thought the borated
polyethylene shielding. Bottom: the borated polyethylene shielding slabs.

The demonstrator will adopt WLS fiber “concentrators” that we developed using
3D-printing techniques. These objects (Fig. 30) are essential to ease the
process of fibers bundling. In such a way the coupling of WLS fibers to the
SiPM can be accomplished in a neat and reproducible way allowing a good,
homogeneous optical contact. After fiber polishing, five SiPM (three
4$\times$4 mm2 and two 3$\times$3 mm2 for the $t_{0}$-layer), soldered on a
small PCB, will be fixed to the top of each fiber concentrator with screws.

Figure 30: Fiber concentrators.

A pre-demonstrator small prototype comprising 3 LCMs (ENUBINO) (Fig. 31) has
been built and characterized with cosmic ray tracks at INFN-LNL laboratory and
with particle beams at CERN in November 2021 (Fig. 32). It faithfully
implements the chosen geometry and the solutions for the light readout both at
the level of scintillators and of the neutron absorber layer. The prototype
behaves according to expectations with a good uniformity and a tolerable level
of optical cross talk between the scintillator tiles.

Figure 31: Prototype of a single azimuthal section of the demonstrator
(ENUBINO) shown during its assembly to highlight the composing elements
(scintillators, iron absorbers, WLS fibers and the BPE shielding.

Figure 32: The ENUBINO prototype exposed to cosmic rays and beams at the CERN-
PS.

Efficiency maps show high efficiency and good uniformity (Fig. 33, left). The
response to m.i.p signals was also tested with the final selected Hamamatsu
SiPM model as a function of the supply voltage (Fig. 33, right).

Figure 33: ENUBINO: efficiency maps (left) and m.i.p. signals vs over-voltage
for the chosen Hamamatsu SiPMs, in mV (right).

####  5.17.1 Assessment of the systematics and physics performance

In conventional beams the systematic uncertainties impacting on the neutrino
flux are relatively large: they come from dedicated experiments to constrain
the hadro-production processes and from the precision of the parameters
characterizing the facility (for instance beamline related ones, like
currents, alignment of the magnets, etc.). As it was already mentioned,
typically, the largest systematic contribution comes from the hadro-production
uncertainties, both at the level of the target and from the re-interactions of
secondaries in the passive elements of the beamline.

Within NP06/ENUBET, the monitoring of the leptons produced together with the
neutrinos, allows to set better constraints on the neutrino flux, factorizing-
out these nuisance effects. Basically, the constraints on the parameters
inferred a posteriori by exploiting the neutrino monitoring data, imply a
reduction of the systematic uncertainties. The parameters constrained from
data are then used to reweight the Monte Carlo simulation and get in turn a
higher precision on the neutrino flux.

A model describing the measured physics observables is built from the
distributions predicted by the simulation. The model Probability Density
Function (PDF) is:

$PDF=N_{S}(\vec{\alpha},\vec{\beta})\cdot
S(\vec{\alpha},\vec{\beta})+N_{B}(\vec{\alpha},\vec{\beta})\cdot
B(\vec{\alpha},\vec{\beta})$ (6)

It is given by the sum of the signal, $S$, and background, $B$, shape
templates, normalized to the corresponding number of events $N_{S,B}$. The
systematic effects are introduced as nuisance parameters in the model: the set
of $\vec{\alpha}$ and $\vec{\beta}$ are the hadroproduction and beamline
related nuisances, respectively. As shown in Eq. 6, systematics can affect
both the normalization and shape of signal and background. An extended
likelihood for the observed data can be written using the model PDF in Eq. 6,
where the nuisance parameters are constrained by their own PDFs,
$pdf(\vec{\alpha}|0,1)$ and $pdf(\vec{\beta}|0,1)$, representing the a priori
knowledge on the hadroproduction and facility parameters discussed before. By
maximizing the extended likelihood, a specific estimation of the nuisance for
the NP06/ENUBET facility can be obtained.

This approach, has been tested using toy Monte Carlo data to study the level
of improvement in the systematic uncertainties and the consequent gain on the
neutrino flux precision. The implementation of the model PDF in Eq. 6 and of
the extended maximum likelihood on toy Monte Carlo data is done through the
RooFit package from ROOT [69]. A _RooRealSumPdf_ is used to write the model
from Eq. 6, where the signal and background templates are _RooHistPdf_ built
from the distribution predicted by the simulation. Templates normalization and
shape are allowed to change around their nominal values, following the PDFs of
the nuisance parameters $\vec{\alpha}$ and $\vec{\beta}$:

$N(\vec{\alpha},\vec{\beta})=N_{0}\cdot(1+\vec{r}_{\alpha}\cdot\vec{\alpha}+\vec{r}_{\beta}\cdot\vec{\beta})$
(7)

$T(\vec{\alpha},\vec{\beta})=T_{0}\cdot+\vec{\alpha}\cdot\Delta\vec{T}_{\alpha}+\vec{\beta}\cdot\Delta\vec{T}_{\beta}$
(8)

where $N_{0}$ and $T_{0}$ are the nominal normalization and shape,
respectively, for either a signal or background template.
$\vec{r}_{\alpha,\beta}$ and $\Delta\vec{T}_{\alpha,\beta}$ are the relative
changes in normalization and the variations in shape due to a one standard
deviation change in $\vec{\alpha},\vec{\beta}$, with respect to their nominal
values. The final model is the product of the model PDF and the constraining
PDFs for the nuisance parameters $\vec{\alpha}$ and $\vec{\beta}$. A set of
toy Monte Carlo experiments are generated by setting the nuisance parameters
to values extracted from their PDFs. A fit is then performed on each
experiment to study the improvement on nuisance parameters constraint due to
the generated pseudo-data. In order to do this the _RooMCStudy_ tool is
exploited. This implementation, using the tools available from RooFit, is
highly modular and flexible, allowing to add different systematic
contributions relatively easily, without having to rewrite the model for each
new parameter to be included.

Preliminary tests to debug the algorithm have been performed by using a toy
hadroproduction model. Mock physics observables for the fit have been sampled
using an analytical parametrization of hadroproduction and basic decay
kinematics.

(a)

(b)

(c)

Figure 34: Example of mock observable distribution for the impact point along
the tagger of muons from kaon decays. The red line is the nominal
distribution, corresponding to the mean value of 100 varied histograms
computed by sampling the toy hadroproduction parameters from their PDFs. (a)
blue lines are the ensemble of the 100 varied histograms. (b) gray band
represents the one standard deviation evaluated from the varied histograms.
(c) blue and green lines correspond to $+1~{}\sigma$ and $-1~{}\sigma$
deviation from nominal, respectively, due to the variation of one of the toy
hadro-production parameters.

As an example, let us consider the impact point distribution along the tagger,
$Z$, for muons from kaon decays. To understand how the observable changes with
the variation of the hadroproduction parameters, a distribution for each set
of the parameters value, sampled from their PDF, can be computed. This way, an
ensemble of $N$ possible realization of the distribution is obtained, as shown
in Fig. 34 (a). This approach is dubbed multi-universe method [70]. The
nominal distribution (red lines in Fig. 34) is obtained from the mean value of
the ensemble, and is used as shape template in the model PDF. From the same
ensemble, the $1~{}\sigma$ band of the distribution is also evaluated, as
reported in Fig. 34 (b). In principle, with the multi-universe method the
$1~{}\sigma$ variation of the distribution can be obtained from the sampling
of each hadroproduction parameter independently, taking into account
correlations with other parameters. In Fig. 34 (c) are shown the $\pm
1~{}\sigma$ distributions of $Z$ corresponding to the variation of one such
parameter. These varied templates can be used in the model PDF to describe the
systematic effect of that parameter: say that the parameter is $\alpha$, then
the model allows a variation of the observable around the nominal distribution
constrained by PDF$(\alpha|0,1)$, with $\pm 1~{}\sigma$ values described by
the templates in Fig 34 (c).

(a)

(b)

Figure 35: Outcome from a 500 toy Monte Carlo test. (a) distribution of the
impact point along the calorimeter for muons from kaon decays, from one of the
toy experiments. Black points are the toy Monte Carlo data. The model is built
from the signal templates for different neutrino energies, coloured
histograms, and the background template, dashed histogram. Left: model with
parameters values set to that of data generation. Right: model after
performing the extended maximum likelihood fit. (b) relative error on the
neutrino flux after the fit.

With the model PDF available, a toy Monte Carlo study can be pursued to
establish the fit stability and performance. In the model, as already pointed
out, the nuisance parameters are allowed to vary around their nominal values,
following their PDF constraints. For each toy experiment, data are generated
from the model by fixing the nuisance parameters to values sampled from their
constraints. After data generation, the same model with nominal nuisances is
used to perform an extended maximum likelihood fit. Fig. 35 reports the
outcome from a study done by generating 500 toy Monte Carlo experiments. In
this test, the model is built by considering a signal template for each energy
interval in the neutrino spectrum (in Eq. 6 the first term is a sum of more
than one signal template). The output from one of these toys is shown in Fig.
35 (a) for the $Z$ observable. Being the normalization of each signal template
the number of the neutrinos in a given energy interval, the fit provides a
constraint on the neutrino spectrum. Fig. 35 (b) reports the relative error
for the neutrino spectrum, after performing the 500 toy Monte Carlo fits: it
amounts to $\sim 1.8\%$, taking into account an initial systematic uncertainty
of $\sim 15\%$.

More recently a model based on real hadroproduction data and related
experimental systematic uncertainties is being worked out. Work in progress is
ongoing to get a re-weight of the simulation from these data: this will
provide templates for the nominal distributions of the observables.
Furthermore, the uncertainty on the data can be propagated to the re-
weighting, and by means of the multi-universe method will provide the $\pm
1~{}\sigma$ variation of the nominal templates. Basically, distributions
analogous to the one shown in Fig. 34 will be computed by correcting the Monte
Carlo simulation with real data. The full GEANT4 simulation of NP06/ENUBET
contains all the required information to build the re-weighted distribution,
since the events producing a detectable signal are linked to the hadrons
produced in the target. The hadroproduction data under consideration are the
one from the NA56/SPY experiment [71], taken with primary proton beam energy
of 400 GeV, the same as the one we are considering for our facility. With the
model obtained in this manner a realistic assessment of the hadro-production
systematics will be possible. We are also working to characterize the a priori
uncertainty of the hadroproduction by employing different generators (i.e.
hadronic physics list available in GEANT4). Figure 36 shows preliminary
results in which the reduction of the systematics uncertainties after the fit
constraint on lepton variables is visible by comparing the uncertainty
envelope before and after the fit. The machinery gas been developed for both
the $\nu_{e}$ and $\nu_{\mu}$ spectra. We are presently assessing the impact
of the facility parameters (magnetic fields, alignments) following the same
procedure.

Figure 36: Example of the reduction of hadroproduction uncertainties on
$\nu_{e}$ and $\nu_{\mu}$ spectra after the constraint given by fitting the
lepton spectra reconstructed in the tagger.

##  6 Cross section measurements with ENUBET

The impact of the ENUBET data on the $\nu_{e}$ cross-section measurement
assuming 1% flux precision is shown in Figure 37 and compared with current
data.

Figure 37: Impact of the ENUBET data on existing $\nu_{e}$ cross-section
measurements assuming 1% flux precision.

The results obtained by ENUBET fostered the possibility to constrain the low-
energy $\nu_{\mu}$ flux from pion decays by monitoring associated muons
emitted at low angles by instrumenting the hadron dump. Muons that exit the
decay tunnel and go through the hadron dump can be measured by detectors
placed between absorber layers. With a static focusing beamline and fast muon
detectors, it is possible to reconstruct muons on an event-by-event basis and
measure their momentum from their range in the detector stations. The
instrumented hadron dump allows to separate the three different components of
the muon spectrum: the measured momentum can be exploited to separate muons
from pions, and beam-halo muons from muons of $K_{\mu 2}$
($K^{+}\rightarrow\mu^{+}\nu_{\mu}$) and $K_{\mu 3}$ decays that, in turn, can
be used to determine the $\nu_{\mu}$ flux. The energy of $\nu_{\mu}$ can be
studied in bins corresponding to muon momenta reconstructed by range as they
show a clear anti-correlation due to the 2-body decay kinematics, allowing to
constrain the $\nu_{\mu}$ shape and normalization. The ENUBET collaboration is
studying a system of 8 muon stations to be placed right after the hadron dump
with iron absorbers from 2 m (upstream) to 0.5 m (downstream) depth. Muon and
neutron fluences have already been estimated: the most upstream detector needs
to cope with a muon rate of 2 MHz/cm2 and the total neutron fluence integrated
over the experiment lifetime is 1012 n(1-MeV-eq)/cm2. The radiation damage
expected in a monitored beam is much smaller compared to beams where the dump
is used to stop non-interacting primary protons. This is the reason while
instrumented dumps are not an option in conventional beams like the ones used
for long-baseline experiments.

It is worth mentioning that ENUBET is working also on a site-dependent multi-
momentum beamline to cover the lower energy region, which is of interest for
HK: the current design of the multi-momentum beamline uses existing CERN
magnets. The beamline optics is flexible enough to select hadron momenta down
to 4 GeV or less. The design consists of quadrupoles for focusing and two
dipoles for momentum selection and a large total bending to ensure the
separation of the different $\nu_{e}$ components at the neutrino detector.

The possibility of measuring the flux of $\nu_{\mu}$ with a precision
comparable with $\nu_{e}$ is a significant asset for ENUBET. Since ENUBET is a
narrow band beam and the pions produce muon-neutrinos in a two-body decay,
there is a strong correlation between the neutrino angle and its energy. As a
consequence, the measurement of the interaction vertex of the neutrino in the
detector (and, hence, its angle) provides a measurement of the energy with an
average precision of 10%. It is worth stressing that this indirect energy
measurement (narrow-band off-axis technique) can be performed at the level of
a single neutrino without resorting to the energy reconstruction at the
detector. This is the main tool to remove all reconstruction biases in the
neutrino detector and suppress the systematics on neutrino interaction
modeling that plague the Near-Detector measurements without any tuning with
data.

##  7 Other opportunities

Even if we gave special emphasis on cross section measurement, readers should
be aware that ENUBET is a full-fledged short baseline facility and can address
many items currently addressed by the US short baseline program. Thanks to an
unprecedented control of the flux, ENUBET provides a substantial improvement
in the study of Non Standard Interactions (NSI) and is a mandatory step in
case the SBN experiments at FNAL support the LSND and MiniBoone anomaly. SBN
results will be arriving in the course of the Snowmass process and beyond and
are not addressed in this document. Still they could potentially change the
neutrino program strategy in a few years from now. For a detailed discussion
of the NSI potential of ENUBET we refer to [74].

Finally, the common R&D and engineering studies pursued in coordination with
nuSTORM and the Muon Collider Collaborations are described here [75].

##  8 Conclusions

The Snowmass 2021 DPF Community Planning Exercise is particularly timely for
the consideration of monitored neutrino beams and the global strategy for the
study of neutrino physics. In 2019-2022, the ENUBET Collaboration has devised
the first end-to-end simulation of a monitored beam with a static focusing
system addressing all technology and physics (systematics) challenges. The
technology of a monitored neutrino beam has been proven to be feasible and
cost-effective, and the complexity does not exceed significantly the one of a
conventional short baseline beam. The ENUBET Collaboration is in the process
of evaluating site specific implementations at CERN, FNAL, and J-PARC, and the
CERN design is rather mature thank to NP06/ENUBET and the contributions of the
CERN PBC group.

Having ENUBET in data taking in a timescale comparable with DUNE is an
outstanding opportunity both to enhance the DUNE physics reach and to advance
substantially the study of neutrino interaction with matter and weak nuclear
physics. In particular, a neutrino facility as ENUBET complemented by a
dedicated suite of moderate-mass detectors represent the ideal playground for
the next generation of cross section experiments.

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###### Contents

  1. 1 Introduction
  2. 2 High precision cross section measurements
  3. 3 Monitored neutrino beams
  4. 4 ENUBET
  5. 5 The ENUBET implementation
    1. 5.1 Burst-mode slow extraction
    2. 5.2 Target optimization
    3. 5.3 Horn optimization
    4. 5.4 Transfer line
    5. 5.5 Doses in the decay tunnel
    6. 5.6 Multi-Momentum Beamline
    7. 5.7 Beam background reduction studies
    8. 5.8 Instrumented decay tunnel and PID
    9. 5.9 Lateral readout calorimeter
    10. 5.10 Photon veto
      1. 5.10.1 Waveform digitizer design
    11. 5.11 Simulation
    12. 5.12 Simulation packages
    13. 5.13 Pile-up study with waveform simulation
    14. 5.14 Positron monitoring
    15. 5.15 Muon monitoring
      1. 5.15.1 Tagger
      2. 5.15.2 Muon chambers
    16. 5.16 Narrow band off-axis technique
    17. 5.17 Demonstrator: design, procurement, construction
      1. 5.17.1 Assessment of the systematics and physics performance
  6. 6 Cross section measurements with ENUBET
  7. 7 Other opportunities
  8. 8 Conclusions