EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

SHADOWS

Search for Hidden And Dark Objects With the SPS

Expression of Interest

W. Baldini(1), A. Balla(2), J. Bernhard(3), A. Calcaterra(2), V. Cafaro(4), A.
Ceccucci(3), V. Cicero(4), P. Ciambrone(2), H. Danielsson(3), G.
D’Alessandro(3), G. Felici(2), L. Gatignon(5), A. Gerbershagen(3), V.
Giordano(4), G. Lanfranchi(2), A. Montanari(4), A. Paoloni(2), G. Papalino(2),
T. Rovelli(4), A. Saputi(2), S. Schuchmann(6), F. Stummer(7), N. Tosi(4)

(1) INFN, Sezione di Ferrara, Ferrara, Italy
(2) INFN, Laboratori Nazionali di Frascati, Frascati (Rome), Italy,
(3) CERN
(4) INFN, Sezione di Bologna, Bologna, Italy
(5) University of Lancaster, Lancaster, UK
(6) University of Mainz, Germany
(7) University of Vienna, Austria

Executive Summary

We propose a new beam-dump experiment, SHADOWS, to search for a large variety
of feebly-interacting particles possibly produced in the interactions of a 400
GeV proton beam with a high-Z material dump. SHADOWS will use the 400 GeV
primary proton beam extracted from the CERN SPS currently serving the NA62
experiment in the CERN North area and will take data off-axis when the P42
beam line is operated in beam-dump mode. SHADOWS can accumulate up to a $\sim
2\cdot 10^{19}$ protons on target per year and expand the exploration for a
large variety of FIPs well beyond the state-of-the-art in the mass range of
MeV-GeV in a parameter space that is allowed by cosmological and astrophysical
observations. So far the strongest bounds on the interaction strength of new
feebly-interacting light particles with Standard Model particles exist up to
the kaon mass; above this threshold the bounds weaken significantly. SHADOWS
can do an important step into this still poorly explored territory and has the
potential to discover them if they have a mass between the kaon and the beauty
mass. If no signal is found, SHADOWS will push the limits on their couplings
with SM particles between one and four orders of magnitude in the same mass
range, depending on the model and scenario.

###### Contents

  1. 1 Introduction
  2. 2 SHADOWS at the CERN SPS
  3. 3 The K12/P42 Beam line
  4. 4 The ECN3/TTC8 experimental complex
  5. 5 The detector concept
  6. 6 Physics reach
    1. 6.1 Sensitivity to light dark scalars
    2. 6.2 Sensitivity to ALPs with fermion couplings
    3. 6.3 Sensitivity to Heavy Neutral Leptons
  7. 7 Backgrounds
    1. 7.1 Reduction of the muon background: The magnetic muon sweeping system
    2. 7.2 Reduction of the muon background: detector-based methods
  8. 8 The SHADOWS detector
    1. 8.1 Tracking system
    2. 8.2 Timing detector
    3. 8.3 Electromagnetic calorimeter
    4. 8.4 Hadronic calorimeter
    5. 8.5 Muon system
    6. 8.6 Upstream Veto
  9. 9 Tentative schedule
  10. 10 Conclusions and Outlook

##  1 Introduction

Feebly-interacting particles (FIPs) with masses below the electroweak (EW)
scale and possibly belonging to a rich dark sector represent a complementary
approach with respect to the traditional Beyond the Standard Model (SM)
physics explored at the LHC. They can be the answer to many open questions in
modern particle physics: the baryon asymmetry of the Universe, the nature of
dark matter (DM), the origin of the neutrino masses and oscillations, the
cosmological inflation, the strong $CP$ problem, the hierarchy of scales, and
the cosmological constant Lanfranchi:2020crw .

Prominent examples of FIPs are: i) the axions, that may be responsible for the
conservation of CP symmetry in strong interactions, and constitute a fraction
or entirety of DM and its extensions axion-like particles (ALPs), that can be
mediators between DM and SM particles; ii) DM candidates and related mediators
with thermal origin and masses in the MeV-GeV range that can arise from new
gauge groups added to the SM; iii) heavy neutrinos with masses below the EW
scale that could account for the origin of neutrino masses and the matter
anti-matter asymmetry via a leptogenesis mechanism based on neutrino
oscillations; iv) Light scalar particles mixed with the Higgs boson that might
provide some novel ways of addressing the hierarchy problem (e.g. via the so-
called relaxion mechanism), or could have been responsible for cosmological
inflation.

The interest for FIPs in the broader particle and astroparticle communities is
continuously growing, and a multitude of initiatives has emerged in the recent
years. The profound interest in this emerging field is reported in many
important reports and documents from the community at large: the Cosmic
Feng:2014uja  and Intensity Hewett:2014qja  Frontier Reports of the 2013
Snowmass Process, the Dark Sector community report Alexander:2016aln  , the
Cosmic Vision report Battaglieri:2017aum , the LHC Long-Lived Particle
community white paper Alimena:2019zri , the Physics Beyond Colliders (PBC) BSM
report Beacham:2019nyx , the White Paper on new opportunities for next
generation neutrino experiments Arguelles:2019xgp , the Briefing Book of the
European Strategy for Particle Physics
EuropeanStrategyforParticlePhysicsPreparatoryGroup:2019qin , and the Report
from the FIPs2020 workshop Agrawal:2021dbo .

The recent recommendations of the European Strategy for Particle Physics
(ESPP) Update ESPP  include the physics of feebly-interacting particles among
the essential scientific activities for particle physics to be pursued in the
next decade: ”The quest for dark matter and the exploration of flavour and
fundamental symmetries are crucial components of the search for new physics.
This search can be done in many ways, for example through precision
measurements of flavour physics and electric or magnetic dipole moments, and
searches for axions,  dark sector candidates and feebly interacting
particles.”.

SHADOWS aims to be a main player in the searches for FIPs in the range of the
familiar matter (MeV-GeV) by exploiting the potential of the existing CERN
accelerator complex.

In the range of MeV-GeV, the strongest bounds on the interaction strength of
new light particles with SM particles exist up to the kaon mass; above this
mass the bounds weaken significantly. SHADOWS can do an important step into
this still poorly explored territory and has the potential to discover them if
they have a mass between the kaon and the beauty mass. If no signal is found,
SHADOWS will push the limits on their couplings with SM particles between one
and four orders of magnitude in the same mass range, depending on the model
and scenario, opening new directions in model building.

This paper is organized as follows. Section 2 explains why SHADOWS should be
placed in the ECN3/TCC8 area currently hosting the NA62 experiment
NA62:2017rwk  served by a primary proton beam line (P42/K12) from the CERN
SPS. Sections 3 and Section 4 introduce the characteristics of the P42/K12
proton beam line and the ECN3/TCC8 experimental complex, respectively. The
main requirements for the detector are described in Section 5 and a
description of the main detector components is provided along with suitable
detector technologies. The physics reach of the experiment for one and five
integrated years of data taking is shown in Section 6 following the benchmarks
proposed by the Physics Beyond Colliders BSM working group Beacham:2019nyx .
In Section 7 the most important beam-induced backgrounds are examined and a
solution found for their reduction. A tentative schedule of the experiment is
sketched in Section 9. Finally Section 10 draws the conclusions.

##  2 SHADOWS at the CERN SPS

Feebly-interacting particles can be originated from the decay of beauty, charm
and strange hadrons and from photons produced in the interaction of protons
with a target. Their couplings to SM particles are very suppressed leading to
expected production rates of $10^{-10}$ or less. Since the charm and beauty
cross-sections steeply increase with the energy Lourenco:2006vw ; ZEUS:2013fws
, a high-intensity, high-energy (but slowly extracted) proton beam is required
to improve over the current results Agrawal:2021dbo .

To date the world best beam line to produce high intensity fluxes of beauty
and charm hadrons through the interactions of protons on a high-$Z$ dump is
the 400 GeV P42/K12 primary proton beam line extracted from the CERN SPS and
serving the NA62 experiment hosted in the TCC8/ECN3 experimental area. FIPs
emerging from the decays of charm and beauty hadrons have a non negligible
transverse momentum and therefore can be detected by an experiment placed off-
axis with respect to the direction of the impinging beam on the dump. This
feature opens up the possibility of installing SHADOWS in the ECN3/TTC8 area
and taking data when the P42 line is operated in beam-dump mode NA62_Addendum
. The SHADOWS project has to be compatible with future plans for kaon physics
in the ECN3/TCC8 area currently investigated by the NA62 collaboration.

The smallness of the couplings implies that FIPs are also very long-lived (up
to 0.1 sec) compared to the bulk of the SM particles. Therefore the decays to
SM particles can be optimally detected using an experiment with tens of meter
long decay volume and with tracking and particle identification capabilities.
The long ($\sim~{}200$ m) ECN3/TTC8 experimental hall allows such an
experiment to be installed.

SHADOWS main goal is to detect FIPs produced in charm and beauty decays and
decaying to visible SM final states. The striking experimental signature will
be two (or more) tracks and/or photons originating from the same point in the
decay volume and nothing else. The experimental challenge is to disentangle
the signal from backgrounds that mimic the same signature.

##  3 The K12/P42 Beam line

Figure 1 shows the schematic layout of the extracted beam lines from the SPS
in the CERN North Area complex NA_note . Primary protons extracted from the
SPS impinge on three different targets, T2, T4 and T6. The T2 target produces
the H2 and H4 beam lines which are normally operated as versatile secondary or
tertiary beams but may occasionally be configured as attenuated primary beams.
The T6 target produces the M2 beam for the COMPASS experiment in the EHN2
hall.

Figure 1: A schematic layout of the North Area complex. The blue arrows show
the path of the protons towards the T10 target in ECN3. Figure taken from Ref.
Montbarbon:2020lcf .

The P42 line is served by primary slowly-extracted protons from the SPS that
impinge on the T4 target. Secondaries produced in the T4 target provide the
secondary or tertiary H4 and H6 beams to test beam areas. Non-interacting
protons are transported to the T10 target located almost 900 m downstream of
T4.

The K12 beam line is derived from a 400 GeV primary proton beam impinging on a
400-mm long, 2-mm diameter cylindrical Beryllium (Be) target that is used to
produce a secondary positively charged hadron beam of 75 GeV/c momentum. In
normal (kaon) operation, only 40% of the protons interact with the Be target
and the remaining 60% is dumped onto the NA62 dump collimators (TAXes) that
act as a hadron stopper $\sim$ 23 m downstream of the target. The TAXes are
made of blocks of Cu-Fe for a total $\sim$ 21$~{}\lambda_{I}$ and a length of
3.2 m.

The K12 beam line can be operated also in beam-dump mode. In beam-dump mode
the T10 target is lifted and the proton beam is fully dumped onto the K12
TAXes. This is illustrated by the red arrow in Figure 2.

Figure 2: The P42/K12 beam line serving NA62. Primary 400 GeV protons from the
P42 beam line impinge on the T10 target and create a mixed (pion, kaon,
proton) beam (K12 line, light blue arrows) serving the NA62 experiment. If the
T10 target is lifted, the primary proton beam (red arrow) impinges directly on
the TAX collimators that are used as a dump.

The switching between kaon-mode to dump-mode is a quick and fully reversible
operation: it has been already performed in the 2017-2018 run and about
$3\cdot 10^{16}$ protons-on-target (pot) successfully recorded by NA62 in
dump-mode. NA62 aims to collect additional o$(10^{18})$ pot in dump mode
during the current run (2021-2024) NA62_Addendum .

About $2\cdot 10^{18}$ pot are delivered by the P42 line to NA62 every year.
This assumes about 200 days of SPS up time per year, a beam intensity of
$3.3\cdot 10^{12}$ protons per 4.8 sec long spill and about 3000 spills
delivered per day111This is a typical number averaged over the past few years.
It takes into account the SPS super-cycle structure, the LHC filling, and the
SPS efficiency..

With some upgrade of the target and dump complex, the intensity of the P42
primary proton beam can be increased up to a factor 6-7 and still being
compatible with the operation of all the other existing projects/experiments
in the North Area. This is illustrated in Figure 3 where up to $2-2.5\cdot
10^{19}$ protons can be delivered to the North Area experiments every year
assuming that no protons are delivered to the Beam Dump Facility (BDF). The
current plan is that the BDF can be considered for approval only in 2027 after
the next update of the European Strategy for Particle Physics.

Figure 3: Intensity limitations (shaded areas) from SPS slow extraction and
operationally achieved protons on target in 2018 (red dot). The secondary $y$
axis shows the number of spills. From Ref. CERN-ACC-NOTE-2018-0082 .

Recent studies have shown that an intensity up to $8\cdot 10^{12}$ protons per
spill would be compatible with the current NA62 target and dump complex and
with the radiation protection classification of the TCC8/ECN3 area. For higher
beam intensities, instead, a new design of the TAXes is required with
optimised block materials and cooling. Higher beam intensities are currently
requested by the KLEVER project KLEVERProject:2019aks  that requires an
increase in the primary proton beam intensity up to a factor 6-7 for
generating a neutral kaon beam suitable for the measurement of the branching
fraction of the rare decay $K_{L}\to\pi^{0}\nu\overline{\nu}$ with 20%
accuracy.

Studies are ongoing within the BE-EA CERN department to assess the thermal
load on the target and TAXes for a beam up to $\times 7$ the nominal NA62
intensity and related radiation protection issues.

In evaluating SHADOWS sensitivity for FIPs, we assume that the P42 primary
proton beam is dumped on TAXes for 200 days per year for a maximum of five
integrated years of data taking. Two scenarios are considered:

  * -

scenario n.1: one integrated year (200 days) of data taking at $\times 4$ the
nominal NA62 beam intensity, corresponding to $N_{\rm pot}\sim 10^{19}$;

  * -

scenario n.2: five integrated years of data taking at $\times 4$ the nominal
NA62 beam intensity (or three integrated years at the KLEVER nominal
intensity) for a total number $N_{\rm pot}\sim 5\times 10^{19}$.

In scenario n.1 (n.2), about $2(10)\cdot 10^{16}$ $D-$mesons and $\sim
1(5)\cdot 10^{12}$ $b-$hadrons are produced. This large amount of charm and
beauty hadrons opens up the possibility to search for feebly-interacting
particles emerging from their decays in the dump, as heavy axions, ALPs, dark
scalars, and heavy neutral leptons (HNLs).

##  4 The ECN3/TTC8 experimental complex

The ECN3/TTC8 experimental hall is placed 15 m underground in the CERN North
Area and hosts the NA62 experiment. This is shown in Figure 4. The blue wall
at the very end of the picture defines the separation between the experimental
hall and the target area, a supervised zone in the TCC8 tunnel hosting the
target and the TAX collimators.

Figure 5 shows a layout of the target area in the TCC8 tunnel, with the T10
target and the TAXes complex 23 m downstream of the T10 target. A picture of
the 3.2 m long water-cooled Cu-Fe based TAXes is shown in Figure 6.

A larger view of the target area including the beginning of the NA62
experimental area is shown in Figure 7. The two labels zone 1 and zone 2 show
two possible zones suitable to host the SHADOWS experiment. Zone 1 could be
immediately available with minor modifications provided no show-stoppers arise
from radiation protection issues. Zone 2 would be available with non-
negligible (but likely addressable) changes in the area setup. A picture of
the space available in zone 1 and zone 2 is shown in Figure 8 and 9,
respectively. The two concrete walls shown in zone 1 could be moved upstream
to free space for the detector. The blue wall also should be moved closer to
the target and TAX area to allow the access to the SHADOWS detector area.

The SHADOWS experiment in its first phase aims to install a first spectrometer
in zone 1, leaving to an optional second phase the installation of a second
spectrometer in zone 2, as detailed in Section 5 .

After the EoI stage, a detailed integration/engineering design will be needed
to address important integration issues related to zone 1, namely: i) the
access to the magnets of the beam line; ii) the radiation protection
constraints in particular upstream of the blue wall. On a longer term, for the
second phase of the experiment after the long-shutdown LS4, other important
issues would need to be addressed for zone 2 (eg: accessibility to other
magnets of the K12 beam line).

Figure 4: View of the ECN3 hall hosting the NA62 experiment. Figure 5:
Schematics of the target/dump area, with the T10 Be target and the TAXes
complex in the TCC8 tunnel. The proton beam direction goes from left to right.
Figure 6: Picture of the 3.2 m long, water cooled, Fe-Cu based TAXes. Figure
7: Schematics of the TCC8 tunnel comprising the target area and a fraction of
the NA62 zone. The SHADOWS experiment could be placed in the zones marked as
zone 1 and zone 2. The beam runs from left to right. Figure 8: Picture of the
zone adjacent to the beam line in the target area (zone 1) . The two concrete
shielding walls visible in the picture can be moved closer to the dump to free
the space for SHADOWS. Figure 9: Picture of the zone adjacent to the beam line
in the NA62 experimental hall (zone 2).

##  5 The detector concept

The detector requirements are defined by the characteristics of FIPs produced
in the interactions of 400 GeV proton beam with a dump. At these energies,
FIPs with masses above the kaon mass are mostly produced in the decays of
charmed and beauty hadrons and in proton bremsstrahlung and/or Primakoff
effect occurring in the dump. The smallness of the couplings implies that FIPs
are naturally long-lived, eg. at the SPS energies they can fly on average from
a few meters to several tens or hundreds of km, depending on the model and
scenario. On the other side the SPS centre-of-mass energy ($\sqrt{s}\sim 23$
GeV) implies that the hadrons are produced with a relatively small boost and
therefore FIPs emerging from their decays have a large polar angle. Figure 10
shows the illumination of the $\pi^{+}\mu^{-}$ pair from the decay of a HNL of
mass 1.5 GeV in a scoring plane placed at $\sim 50$ m from the dump. The HNL
is assumed to be created in the decays of charmed hadrons (Figure 10, left)
and beauty hadrons (Figure 10, right) produced in the interactions of the 400
GeV proton beam with the dump. The pions and muons illuminate the plane up to
several meters away from the beam axis, validating the concept of an off-axis
detector.

Figure 10: Illumination at the first SHADOWS tracking layer ($\sim 50$ m from
the dump) of the $\pi^{+}\mu^{-}$ pair from the decay of a HNL of mass 1.5 GeV
from charm (left) and from beauty (right) hadron decays.

The distance of the detector with respect to the impinging point of the proton
beam onto the dump is a compromise between the maximisation of FIP flux in
acceptance (that requires short distances) and the maximisation of the
probability that the FIP decays before reaching the detector (that requires
long distances). The optimal distance varies as a function of the FIP model
and benchmark: for example, HNLs with very long lifetimes (hundreds of km at
the SPS energy) require long decay volumes in order to increase the
probability of their decay before reaching the spectrometer. Light dark
scalars, instead, have a lifetime of order of meters for a large majority of
the available parameter space for a mass in the GeV range, and therefore
require relatively short decay volumes.

There is another consideration to be taken into account. On the one hand, the
detector should be placed on-axis with respect to the beam in order to
maximise the acceptance for FIPs. On the other hand, an on-axis detector is
hindered by the large flux of muon and neutrino backgrounds induced by the
interactions of the protons with the dump. A detector placed off-axis is less
affected by these backgrounds that are mostly produced in the forward
direction and can profit of the non negligible polar angle of a FIP coming
from the decay of a hadron containing a heavy quark (charm or beauty). The
transverse distance with respect to the beam axis is a compromise between the
loss of signal acceptance and the background reduction.

The interplay between these diverse requirements defines the driving
principles for the design of the detector. Ultimately, an optimal detector for
FIPs at a proton beam dump is made of a series of spectrometers, each preceded
by a decay volume whose length is a function of the spectrometer transverse
dimensions. If the series of spectrometers is placed off-axis the loss in
acceptance is mitigated by a large background reduction with respect to an on-
axis setup and by the fact that the detector can be placed much closer to the
FIP production point.

This proposal describes the implementation of the first of a series of
spectrometers that could be placed off-axis in the ECN3/TTC8 area. The first
spectrometer could be placed in zone 1. However physics sensitivities are
computed also for the case of two spectrometers, placed one after the other in
zone 1 and zone 2, respectively, to show in perspective the physics potential
of the SHADOWS proposal. Going beyond two spectrometers is not considered in
the present study, but it is a compelling option that will be studied in the
future.

The dimension of the first spectrometer is driven by the dimensions of the
available space in zone 1 and by the constraints coming from safety rules and
accessibility. The baseline SHADOWS detector in zone 1 consists of a decay
volume and a spectrometer. The decay cvolume is 20 m long with transverse
dimensions of 2.5$\times$2.5 m2, placed $\sim 1.5$ m off-axis with respect to
the beam direction, and starting 10 m downstream of the dump. The spectrometer
of about the same transverse dimensions and a length of about 7-8 m follows
the decay volume. Figure 11 show the 3D view (top) and the top view (bottom)
of the SHADOWS decay volume and spectrometer in zone 1.

Figure 11: 3D view of the SHADOWS detector located in zone 1 adiacent to the
beam line and close to the TAX shielded zone. Top plot: 3D view. Bottom plot:
top view.

About $\sim$40 m of space could be available in zone 2, before the beginning
of the decay volume of the NA62 experiment. This space could be used in the
future to build another detector, with a 30 m long, 3 m wide and 4 m high
decay volume followed by a spectrometer with the same transverse dimensions. A
possible layout with the two spectrometers is shown in Figure 12 and a zoom of
the second spectrometer is shown in Figure 13. In the following Sections we
will discuss the physics reach mostly for one spectrometer, but we include the
study of the performance that can be obtained also with a second spectrometer
for FIPs with very long lifetimes, as for example Heavy Neutral Leptons, in
order to provide a projection of the full SHADOWS potential.

Figure 12: 3D view (top) and top view (bottom) of the SHADOWS detectors
located both in zone 1 and zone 2 adjacent to the beam line in the TCC8 area.
The end point of the two spectrometers is defined by the beginning of the
decay volume of the NA62 experiment, clearly visible after the second
spectrometer. Figure 13: Detail of the second SHADOWS spectrometer. The
beginning of the decay tank of the NA62 experiment (Blue tube) is clearly
visible after the spectrometer.

##  6 Physics reach

The SHADOWS detector, being off-axis, is sensitive to FIPs emerging from the
dump with a sizeable polar angle. This can occur in the decay of
mesons/baryons containing heavy quarks (charm and beauty) produced in the
interactions of 400 GeV protons with the $Cu$-based dump. The probability of
producing a $b\overline{b}$ and $c\overline{c}$ pair is given by
$\chi_{c\overline{c}}=\sigma_{c\overline{c}}/\sigma_{pp}\sim 3.9\cdot 10^{-3}$
and $\chi_{b\overline{b}}=\sigma_{b\overline{b}}/\sigma_{pp}\sim 2.7\cdot
10^{-7}$Lourenco:2006vw ; Hans-Thomas , which include also secondary
production. The kinematic distributions of charmed and beauty mesons are
obtained with Pythia 6 by simulating the interactions of 400 GeV protons with
a $Cu$-based dump following the study in Ref. Hans-Thomas .

In the following Sections we will present SHADOWS sensitivity for light dark
scalars, ALPs with fermion couplings, and Heavy Neutral Leptons, as they are
representatives benchmarks for FIPs emerging from charm and beauty decays.
More benchmarks are certainly possible and will be considered in the future.
In evaluating the sensitivity for the benchmark channels we closely follow the
prescriptions of the PBC-BSM working group Beacham:2019nyx .

###  6.1 Sensitivity to light dark scalars

A light scalar particle mixing with the Higgs with angle $\theta$ can be a
mediator between DM and SM particles. The overall Langrangian is of the form:

${\cal L}_{\rm scalar}={\cal L}_{\rm SM}+{\cal L}_{\rm DS}-(\mu S+\lambda
S^{2})H^{\dagger}H.$ (1)

where ${\cal L}_{\rm SM}$ is the SM lagrangian, ${\cal L}_{\rm DS}$ is a
overall dark sector lagrangian that can include a light dark scalar among
several other states, and the remaining terms represent the interactions of a
light dark scalar with the Higgs boson. The minimal scenario assumes for
simplicity that $\lambda=0$ and all production and decay processes of the dark
scalars are controlled by the same parameter $\mu$. At low energy, the Higgs
field can be substituted for $H=(v+h)/\sqrt{2}$, where v = 246 GeV is the
electroweak vacuum expectation value and $h$ is the field corresponding to the
physical 125 GeV Higgs boson. The nonzero $\mu$ leads to the mixing of $h$ and
$S$ states. In the limit of small mixing it can be written as follows:

$\theta=\frac{\mu v}{m^{2}_{h}-m^{2}_{S}}.$

For $m_{h}>>m_{S}$, $\theta\sim\mu$ and the parameter space for this model is
$(\theta,m_{S})$. A more general approach consists in having both $\lambda$
and $\sin\theta$ being different from zero: in this case, the parameter space
is $\\{\lambda,\theta,m_{S}\\}$, and $\lambda$ is assumed to dominate the
production via e.g. $h\to SS$, $B\to K^{(*)}SS$, $B^{0}\to SS$ etc. In this
study we consider only the minimal scenario which gives the dominant
contribution at the SPS energy.

At the SPS energy the dominant production process for a light dark scalar is
via decay of secondary mesons containing a $s$ or $b$ quark, while the
production via charmed mesons is CKM suppressed. Since we are interested in
decays emerging with a large polar angle we concentrate to the case of
production via $b$ decays. In that case the inclusive production probability
for a light dark scalar is:

$P_{\rm scalar}\sim 2\chi_{b\overline{b}}\times{\rm BR}(b\to Ss)\sim
13\,\theta^{2}\,\chi_{b\overline{b}}\left(1-{m^{2}_{S}\over
m^{2}_{b}}\right)^{2}.$ (2)

The main visible decay channels of the light dark scalar are photons, leptons
and hadrons. Below the $\pi\pi$ threshold, the scalar decays into photons,
electrons and muons. We follow Ref. Winkler:2018qyg  for the evaluation of the
partial decay widths that can be computed perturbatively. As example of
perturbative partial decay width is the one for leptonic decays:

$\Gamma(S\to\ell^{+}\ell^{-})={\sin^{2}\theta G_{F}m_{S}\over
4\sqrt{2}\pi}m^{2}_{\ell}\beta^{3}_{\ell}$ (3)

where $\ell=(e,\mu,\tau$), $G_{F}$ is the Fermi constant, and
$\beta_{\ell}=\sqrt{1-4m^{2}_{\ell}/m^{2}_{S}}$. Hadronic decays are instead
more involved due to the presence of strong interactions in the final state,
namely in the proximity of the $f_{0}(980)$ resonance, where non-perturbative
computations are needed. There is a vast literature about the evaluation of
the hadronic widths near the $\sim 1$ GeV threshold (see for example Ref.
Winkler:2018qyg ). In this work we follow the PBC recommendations and use the
computation done by Donoghue et al. Donoghue:1990xh  for the partial decay
widths for $\pi\pi$ and $KK$ final states around the 1 GeV threshold. The
scalar branching fractions for scalar decays into two charged track final
states ($e^{+}e^{-},\mu^{+}\mu^{-},\pi^{+}\pi^{-},K^{+}K^{-}$) and the scalar
lifetime (computed for $\sin\theta=1$) are shown in Figure 14 (left and right,
respectively) as a function of the scalar mass.

Figure 14: Scalar branching fractions in two charged track final states (left)
and scalar lifetime (for $\sin\theta=1$) (right) as a function of the scalar
mass.

In this study we consider only final states with two charged tracks,
neglecting for the time being, multi pion and $\tau\tau$ final states. On this
respect the sensitivity evaluation should be considered conservative.

The number of events of $S\to X^{+}X^{-}$ ($X=e,\mu,\pi,K$) reconstructed in
the SHADOWS detector is given by:

$N_{\rm obs}=N_{\rm pot}\times P_{\rm
scalar}\times\sum_{X=ee,\mu\mu,\pi\pi,KK}BR(S\to f)\times{\cal
A}(f)\times\varepsilon(f)$ (4)

where $N_{\rm pot}$ is the number of protons on dump, $P_{\rm scalar}$ is
given by Eq. 2, ${\cal A}(f)$ is the acceptance for a light scalar particle of
a given mass $m_{S}$ and coupling parameter $\sin^{2}\theta$ decaying into a
final state $f=X^{+}X^{-}$.

The acceptance is given by the product of the probability that the light
scalar particle decays inside the fiducial volume and the probability ${\cal
P}(X^{+}X^{-})$ that the two charged tracks in the final state are
reconstructible in the magnetic spectrometer. The efficiency $\varepsilon(f)$
is the product of the trigger, reconstruction and selection efficiencies for
the final state. We consider $\varepsilon(f)=1$ in the present study, knowing
that for reasonable values of $\varepsilon(f)$ the results could change by a
factor of two at most.

The position of the decay vertex of the scalar is required to be inside the
decay volume. The decay volume starts 10 m after the production point of the
$b$-hadrons into the dump. The decay products of the scalar are required to be
within the acceptance of the magnet, placed 2.5 m after the end of the
fiducial volume with an aperture of $2.5\times 2.5$ m2. We assume that all the
decay products reaching the magnet aperture will hit the muon detector placed
at the end of the SHADOWS spectrometer, about 5 m away from the magnet. This
is a reasonable assumption given the fact that the spectrometer is very
compact.

Figure 15 shows the sensitivity of SHADOWS first spectrometer for
$N_{pot}=10^{19}$ (scenario 1) and $N_{pot}=5\times 10^{19}$ (scenario 2)
along with the current bounds and future projections for other
experiments/proposals. SHADOWS with $N_{pot}=10^{19}$ is competitive with
FASER2 with 3 ab-1 and with $N_{pot}=5\times 10^{19}$ covers a sizeable
fraction of the parameter space that could be possibly explored by SHiP (with
$N_{pot}=2\times 10^{20}$), MATHUSLA (with 3 ab-1) and CODEX-b (with 3 ab-1)
below the $b-$mass. It is worth noting that SHADOWS could cover this parameter
space much earlier than FASER2, CODEX-b, and SHiP.

Figure 15: Sensitivity of SHADOWS experiment for light feebly-interacting
scalars for $N_{pot}=10^{19}$ (scenario 1) and $N_{pot}=5\cdot 10^{19}$
(scenario 2). SHADOWS with $N_{pot}=10^{19}$ is competitive with FASER2 with 3
ab-1 and with $N_{pot}=5\times 10^{19}$ covers a sizeable fraction of the
parameter space that could be possibly explored by SHiP (with $N_{pot}=2\times
10^{20}$), MATHUSLA and CODEX-b (with 3 ab-1) below the $b-$mass.

###  6.2 Sensitivity to ALPs with fermion couplings

Light pseudo-scalars with fermion couplings can be produced in meson decays,
most notably in $K\to\pi a$ and $B\to K^{*}a$, as $D$ decays are suppressed by
CKM.

As for the scalar case, in order to avoid uncertainties due to the form
factors, in the present study we consider the inclusive decays $b\to X_{s}a$,
as documented in Ref Dolan:2014ska :

$P(b\to X_{s}a)={1\over 8\pi}\left({m_{b}^{2}-m_{a}^{2}\over
m_{b}^{3}}\right)^{2}|h^{S}_{sb}|^{2}$ (5)

where $X_{s}$ can be any strange meson, $a$ the light pseudo-scalar, $b$ the
$b-$quark. Here $|h_{sb}^{S}|^{2}=(h_{sb}^{R}+h_{sb}^{L})/2$ contains the ALP
fermionic coupling to quarks $g_{Y}=v/f_{a}$ with $v$ is the Higgs vev and
$f_{a}$ is the scale of spontaneous symmetry breaking. Here we report the
explicit expression of $h_{sb}^{R}$ ($h_{sb}^{L}$ is analogous to $h_{sb}^{R}$
with $m_{b}\to m_{s}$):

$h_{sb}^{R}=-{\alpha g_{Y}m_{b}m^{2}_{t}\over 4\sqrt{2}\pi
m^{2}_{W}\sin(\theta_{W})^{2}v}V_{tb}V^{*}_{ts}\log\left({\Lambda^{2}\over
m^{2}_{t}}\right).$ (6)

In this expression $m_{b}$, $m_{t}$, $m_{W}$ are the masses of the bottom, top
quarks and $W$, respectively, $\theta_{W}$ is the Weinberg angle, and
$V_{tb}V^{*}_{ts}$ are the CKM matrix values.

It is important to note that the production rate of an ALP depends on a cut-
off scale $\Lambda$ that cures the divergency in the FCNC diagram. This
divergency is absent in the scalar case. This means that numerical
computations depend on the specific chosen UV completion. Here we follow what
proposed in Dolan:2014ska  and use $\Lambda=$ 1 TeV. Also the analytic
formulae for the branching fractions are taken from the same reference.

Below $2\cdot m_{\mu}$ the ALPs decay rate is dominated by the electron and
photon mode, above $2\cdot m_{\mu}$ by the muon mode and above $2\cdot
m_{\tau}$ by the $\tau$ modes. The branching fraction in hadrons is instead
negligible and open only above the $3\pi$ threshold as a consequence of the
pseudoscalar nature of the ALP that cannot decay in two pions. In the current
study we consider only the $e^{+}e^{-}$ and $\mu^{+}\mu^{-}$ final states
which are the dominant ones (apart a small window between 100 and 200 MeV
which is dominated by $\gamma\gamma$ final state) below $\sim 3$ GeV.

As for the light scalar case, the number of events of $S\to X^{+}X^{-}$
($X=e,\mu$) reconstructed in the SHADOWS detector is given by:

$N_{\rm obs}=N_{\rm pot}\times P(b\to X_{s}a)\times\sum_{X=ee,\mu\mu}BR(a\to
f)\times{\cal A}(f)\times\varepsilon(f)$ (7)

where we use the same notations as in Eq. 4 and $P(b\to X_{s}a)$ is defined in
Eq. 5. Figure 16 shows the SHADOWS sensitivity with one spectrometer for
$N_{\rm pot}\sim 10^{19}$ (scenario 1) and $5\cdot 10^{19}$ (scenario 2)
compared against projections from other experiments Agrawal:2021dbo . In both
scenarios SHADOWS is better than FASER2 with $3$ ab-1, equivalent to CODEX-b
(with 3 ab-1) and SHiP (with $2\cdot 10^{20}$ pot), and covers a sizeable part
of the parameter space below the $b$-mass that could be possibly covered by
MATHUSLA. It is worth noting also in this case that SHADOWS could cover this
parameter space much earlier than FASER2, CODEX-b, and SHiP.

Figure 16: Sensitivity of SHADOWS experiment for light feebly-interacting
axion-like particles with fermion couplings for $N_{pot}=10^{19}$ (scenario 1)
and $N_{pot}=5\times 10^{19}$ (scenario 2). SHADOWS is better than FASER2 with
$3$ ab-1, equivalent to CODEX-b (with 3 ab-1) and SHiP (with $2\cdot 10^{20}$
pot), and covers a sizeable part of the parameter space below the $b$-mass
that could be possibly covered by MATHUSLA.

###  6.3 Sensitivity to Heavy Neutral Leptons

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

${\cal L}_{\rm vector}={\cal L}_{\rm SM}+{\cal L}_{\rm DS}+\sum F_{\alpha
I}(\bar{L}_{\alpha}H)N_{I}$ (8)

where ${\cal L}_{\rm SM}$ is the SM Lagrangian, ${\cal L}_{\rm DS}$ is the
Lagrangian describing a dark sector that includes HNL as one of the possible
states, and the remaining term describe the interactions of HNL with the SM.
Here $H$ is the Higgs field and the summation goes over the flavour of lepton
doublets $L_{\alpha}$, and the number of available HNLs, $N_{I}$. The
$F_{\alpha I}$ are the corresponding Yukawa couplings. The dark sector
Lagrangian $\mathcal{L}_{\rm DS}$ should include the mass terms for HNLs, that
can be both Majorana or Dirac type. For a more extended review, see Ref.
Gorbunov:2007ak ; Alekhin:2015byh .

Setting the Higgs field to its vacuum expectation value (vev), and
diagonalizing mass terms for neutral fermions, one arrives at $\nu_{i}-N_{J}$
mixing, that is usually parametrized by a matrix called $U$. Therefore, in
order to obtain interactions of HNLs, inside the SM interaction terms one can
replace $\nu_{\alpha}\to\sum_{I}U_{\alpha I}N_{I}$. In the minimal HNL models,
both the production and decay of an HNL are controlled by the elements of
matrix $U$.

Following the PBC prescriptions as in Ref. Beacham:2019nyx , we evaluate
SHADOWS sensitivity to HNLs assuming the single-flavor dominance, eg: we
assume only one HNL state N that mixes with electron or muon or tau neutrinos,
separately. Under this assumption all HNL production and decay probability can
be determined as a function of the parameters ($m_{N},|U^{2}_{e}|$,
($m_{N},|U^{2}_{\mu}|$) and ($m_{N},|U^{2}_{\tau}|)$, depending on the chosen
flavor. The single flavor dominance approximation is currently being
reconsidered in the PBC and multiple HNL states with comparable couplings to
different flavours are now introduced to make HNL physics compatible with the
parameters describing mixing and oscillations of the active neutrinos
Agrawal:2021dbo . The determination of the SHADOWS sensitivity in this updated
scenarios will be performed in the coming months following the PBC activities.

Heavy neutral leptons at the SPS energy arise from the decays of charmed and
beauty mesons. The production rates and possible final states are taken from
Ref. Gorbunov:2007ak . An example of HNL branching fractions as a function of
the HNL mass for a specific choice of the ratios of the couplings is shown in
Figure 17. Figures 18, 19, and 20 show SHADOWS sensitivity for the coupling to
the first, second and third lepton generation for the two considered
scenarios, $10^{19}$ pot and $5\cdot 10^{19}$ pot. The top and bottom plots
correspond to SHADOWS with one and two spectrometers, respectively. For the
HNL case the addition of the second spectrometer is equivalent to an increase
of the proton intensity of a factor $\sim(5-6)$.

Below the charm threshold for all considered scenarios (electron, muon, and
tau coupling) SHADOWS with one spectrometer is better than any existing or
proposed experiment in same mass range apart MATHUSLA and SHiP. SHADOWS with
two spectrometers is competitive with MATHUSLA and only one order of magnitude
above the SHiP sensitivity. Above the charm threshold and below the b-mass,
SHADOWS with one (two) spectrometer(s) allows to improve the current bounds by
2.0 (2.5) orders of magnitude in all the considered scenarios and is better of
any experiment in the same timescale.

Figure 17: Production modes (top) and branching fractions (bottom) of HNL
decaying in several final states as a function of the HNL mass for a specific
choice of the ratios of the HNL couplings.

Figure 18: Top: Sensitivity of SHADOWS experiment with one spectrometer for
light feebly-interacting heavy neutral leptons coupled to the first lepton
generation. Bottom: same as above but with two spectrometers. Below the charm
threshold, SHADOWS with one spectrometer is better than any existing or
proposed experiment in same mass range apart MATHUSLA and SHiP. Below the
charm threshold SHADOWS with one (two) spectrometer(s) is competitive with
MATHUSLA and only one (1.5) order of magnitude above the SHiP sensitivity.
Above the charm threshold and below the b-mass, SHADOWS with one (two)
spectrometer(s) allows to improve the current bounds by 2.0 (2.5) orders of
magnitude and is better of any experiment in the same timescale.

Figure 19: Top: Sensitivity of SHADOWS experiment with one spectrometer for
light feebly-interacting heavy neutral leptons coupled to the second lepton
generation. Bottom: same as above but with two spectrometers. Below the charm
threshold SHADOWS with one (two) spectrometer(s) is competitive with MATHUSLA
and only one (1.5) order of magnitude above the SHiP sensitivity. Above the
charm threshold and below the b-mass, SHADOWS with one (two) spectrometer(s)
allows to improve the current bounds by 2.0 (2.5) orders of magnitude and is
better of any experiment in the same timescale.

Figure 20: Top: Sensitivity of SHADOWS experiment with one spectrometer for
light feebly-interacting heavy neutral leptons coupled to the third lepton
generation. Bottom: same as above but with two spectrometers. Below the charm
threshold SHADOWS with two spectrometers is competitive with MATHUSLA and only
one order of magnitude above the SHiP sensitivity. Above the charm threshold
and below the b-mass, SHADOWS with one (two) spectrometer(s) allows to improve
the current bounds by 2.0 (2.5) orders of magnitude and is better of any
experiment in the same timescale.

##  7 Backgrounds

The proton interactions with the dump, along with feebly-interacting
particles, give rise to a copious direct production of short-lived resonances,
and pions and kaons. While the TAX length ($\sim 22\,\lambda_{\rm I}$) is
sufficient to absorb the hadrons and the electromagnetic radiation produced in
the proton interactions, the decays of pions, kaons and short-lived resonances
result in a large flux of muons and neutrinos. Muons and neutrinos from the
dump are the two major sources of background for FIP searches.

For an off-axis detector, however, the background originated by neutrino
interactions with the air or the detector material are fully negligible as the
neutrinos emerging from the decays of pions and kaons are intrinsically
produced in the forward direction. The most relevant backgrounds for SHADOWS
are those originated by the beam-induced muon flux.

In order to study the rate, composition, and evolution of the beam and related
backgrounds, a Geant4-based simulation of the P42/K12 beam line including the
target and TAX area and all the magnetic elements placed along the beam has
been developed by the NA62 collaboration and the BE-EA-LE team. This
simulation is based on the package Beam Delivery Simulation or BDSim
Nevay:2018zhp . The products of the interactions of the 400 GeV proton beam
with the TAX material are simulated, transported across the magnetic elements
of the K12 beam line, and their kinematics and composition stored for further
processing. The results of the simulation have been cross-checked with data
when the experiment is operated in kaon-mode and the agreement between data
and simulation has been found to be within a factor of two.

Figure 21 shows the simulated momentum distribution of the particles produced
in the dump and scored immediately upstream of the beginning of the decay
vessel ($z=34.4$ m with respect to the target) for: i) any $x,y$ (left plot);
ii) $1.5<x<4.0$ m, $-1<y<1.5$ m (right plot) which define the transverse
dimensions of the decay vessel. As expected, most of the background is
produced on-axis and misses the SHADOWS acceptance. The only relevant
background emerging with a non-negligible $p_{T}$ due to multiple scattering
in the TAX material are low momentum ($<20$ GeV) muons (see Figure 21, right).

Figure 21: Left: Simulated momentum distribution of particles emerging from
TAXes scored immediately upstream of the beginning of the decay vessel of the
SHADOWS detector. Right: Same as left plot but requiring that the particles
are in SHADOWS acceptance ($1.5<x<4.0$ m and $2.5<y<-1$ m).

The origin point of the muons emerging from the dump is shown in Figure 22, in
the three possible views. Most of the muons, as expected, are originated in
the decay of pions and kaons produced by the (primary and secondary) inelastic
interactions of the protons within the first few interaction lengths of the
dump. This origin point is contained within a radius of a few cm with respect
to the beam impinging point. A small fraction is due to the decays of kaons
and pions produced in the proton interactions with the target box,
corresponding to the long tail starting at z=0 m.

Figure 22: Origin point of the muons emerging from TAXes. Top: $(x,z)$ view.
Center: $(y,z)$ view. Bottom: $(y,x)$ view. The T10 target is placed at z=0,
the TAXes start at z=23 m. Most of the muons are originated in the decay of
pions and kaons produced by the (primary and secondary) inelastic interactions
of the protons in the first interaction lengths of the dump. A small fraction
is originated by kaons and pions produced in the proton interactions with the
target box, as shown by the long tail in the top and middle plot. The target
box will be removed during SHADOWS operation.

Muons originated in the dump can produce either combinatorial background and
secondary tracks and $V^{0}$ through inelastic interactions in the last TAX
interaction lengths and in the decay vessel material. Both backgrounds are
described below.

  * -

Muon inelastic interactions: muons emerging from the TAXes can interact
inelastically with the material upstrean of or forming the decay volume. These
interactions can generate particles, including $V^{0}$ ($K_{\rm S},K_{\rm L}$
and $\Lambda$), that enter the decay volume and mimic signal events.

  * -

Combinatorial muon background: A dangerous source of background comes from
random combinations of opposite charged muon tracks entering the decay vessel
and mimicking signal events with dimuon final state by forming a fake vertex
in the fiducial volume.

As detailed in Ref. NA_note , the front end of the K12 beam consists of a
strong quadrupole triplet followed by a dogleg, called ‘achromat’ of four
identical dipoles. The first two dipoles provide a vertical offset of 110 mm
and the last pair brings back the beam to the straight axis. Once back on the
original axis, the beam is collimated and the momentum definition refined in
another collimator, COLL3. After COLL3, a series of three 2 m long dipoles
with the gap filled with soft iron, except for a 40 mm diameter field-free
hole for the beam passage, sweeps away muons (both $\mu^{+}$ and $\mu^{-}$)
produced in the region around the T10 target and TAX dumps.

When operated in beam dump mode the T10 target head is lifted up and the
proton beam is dumped on the TAXEs. The configuration of the beam line magnets
used for studying the background hitting the SHADOWS acceptance is the
standard NA62 magnet configuration with the only difference putting the second
pair of dipoles at the same polarity with a nominal field strength of
approximately -1.67 T in the iron (and perhaps switching off the first pair of
dipoles). This configuration was already studied in the Physics Beyond
Colliders Conventional Beam Working Group for the operation of NA62 in dump
mode CERN-PBC-REPORT-2018-002 .

The illumination of the muon background immediately after the ’achromat’ is
shown in Figure 23, for both muon charges together and for each charge
separately. Muons emerging from the dump and the achromat have a non-
negligible divergence: Figure 24 shows the evolution of the muon flux as a
function of the distance from the dump. At z = 55 m (which corresponds roughly
to the position of the first tracking station of the first SHADOWS
spectrometer) the muon flux extends up to several meters with respect to the
beam axis. The rate expected within the tracker acceptance is $\sim$ 10-15 MHz
at the NA62 nominal intensity.

Figure 23: Top: Muon illumination at the plane z=34.4 m. Bottom: same but
divided per charge (left: positive muons, right: negative muons).

Figure 24: Evolution of the muon illumination emerging from TAXes. Top:
illumination at the plane z=34.4 m. Center: illumination at z=43.3 m (middle
of the SHADOWS decay volume). Bottom: illumination at z=55 m (position of the
first station of the SHADOWS tracker).

###  7.1 Reduction of the muon background: The magnetic muon sweeping system

The muon flux evolution detailed in Figure 24 shows that is paramount to get
rid of off-axis muons immediately after the second dipole, where they are
still concentrated in a small transverse area. Luckily enough, an analysis of
their momentum distribution shows that off-axis muons are typically made of
low-momentum ($<20$ GeV) tracks. This is shown in Figure 25 where muons
emerging from the second dipole at z=34.4 m are shown in the plane $p$ versus
$x$: for $|x|>500$ mm the muons have $p<20$ GeV. This observation suggests
implicitly also the solution: low-p muons can be swept away using a magnetic
field in a magnetised iron block.

Figure 25: Muons at z=34.4 m in the plane momentum versus lateral
displacement: muons with a lateral displacement of more than 50 cm have
momentum below 20 GeV.

The SHADOWS muon sweeping system based on magnetic elements is currently being
conceptually designed by the BE-EA-LE group. A preliminary sketch of the
magnetized iron block (MIB) is shown in Figure 26. Assuming a maximum field
value of 1.7 T/m, a MIB 5 m long produces an effective field of 8.5 Tm. The
sweeping iron block will be placed immediately after the BEND2 dipole and will
be part of the shielding structure of the TAXes area. Preliminary results show
that the muon flux hitting the SHADOWS spectrometer can be reduced already by
a factor of $\sim$20 without detailed optimization, bringing the muon flux
below $\sim$1 MHz total rate in the SHADOWS acceptance. When normalized to the
detector active area, this flux is only about a factor of three higher than
what has been measured in the NA62 acceptance when NA62 is operated in beam-
dump mode. A measurement of the muon flux in the SHADOWS area will be
performed during the current NA62 run, when NA62 will be operated in beam-dump
mode to collect $o(10^{18})$ pot as planned in Ref. NA62_Addendum .

Figure 26: Schematic view of the position of a magnetised iron block to sweep
out the muons emerging from the BEND2 dipole with a lateral displacement in
the SHADOWS direction.

Figure 28 shows the simulated muon illumination of the first SHADOWS tracking
station with the MIB added to the setup. The non-muon background is fully
negligible and the muon one is reduced by more than one order of magnitude
already at the first attempt. A closer look at the residual flux shows that
the residual muon flux within the SHADOWS acceptance is due to muons of the
same charge, see Figure 29. This is due to the fact that whilst muons bent
towards the beam line do not encounter any other magnetic fields, those bent
in the opposite direction towards the cavern wall are back-scattered by the
field of opposite polarity present in the external part of the MIB (see Figure
26). An improved design of the MIB is currently ongoing within the BE-EA-LE
group.

Figure 27: Magnetized iron block for muon background sweeping placed right
after the end of the last dipole of the achromat. The grey structure defines
the concrete blocks used to shield the TAX area. Top and centre plot: 3D view;
Bottom plot: top view. The yellow block defines the last dipole.

Figure 28: Residual background at z=55.3 m (position of the first tracking
station). Left: non-muon background; Right: muon background. In the SHADOWS
acceptance the non muon background is fully negligible and the muon one is
reduced by more than an order of magnitude with respect to the one without
sweeping system.

Figure 29: Residual background at z=55.3 m (position of the first tracking
station). Left: muon background with positive charge. Right: muon background
with negative charge. The residual background is due to the bending of tracks
back into the SHADOWS acceptance due to the opposite field in the other side
of the magnetized block.

###  7.2 Reduction of the muon background: detector-based methods

In addition to the muon sweeping system, an active veto in front of the decay
vessel can tag charged tracks coming from the dump: an active veto with an
efficiency of $\sim 99.5\%$ would reduce the untagged flux to a few permille
of the total flux.

Beyond the muon sweeping system and the active veto, additional handles are
available for further reducing the background. The backgrounds arising from
inelastic interactions of the residual muon flux hitting SHADOWS detector
material and from combinatorial mixing of two (or more) muon tracks are
expected to have the following characteristics:

  1. 1.

The total momentum of selected tracks when extrapolated backward to the dump
does not point to the position of the proton beam impinging point;

  2. 2.

combinatorial tracks form rarely a fake vertex in the 20 m long fiducial
volume;

  3. 3.

combinatorial tracks are mostly non coincident in-time. This is particularly
true for the case of the combinatorial muon background, because muons
generated in the interactions of the primary proton beam with the dump
remember the timing structure of the proton spill and therefore are almost
uniformly spread along the 3.3-sec effective spill duration.

These characteristics allow us to draw also the guidelines for reducing these
backgrounds efficiently. The spectrometer must have:

  * a)

a tracking system able to reconstruct the vertex of 2-opposite charged tracks
with $o(1)$ cm resolution in the transverse view over 20 m long decay volume
and an impact parameter with respect to the impinging point of the proton beam
onto TAXes with a resolution of $\sim$ 1 cm.

  * b)

A timing detector able to measure the track arrival times with a resolution
$\sigma_{t}\sim$ o(200) ps will reduce out-of-time combinatorial tracks by a
factor about $6\cdot\sigma_{t}/3.3$ sec.

  * c)

An electromagnetic calorimeter with a good time resolution and the capability
also of reconstructing the direction of the photons.

  * d)

A muon detector with a time resolution comparable to the one of the timing
detector in order to identify and reject combinatorial muon tracks.

These characteristics can be easily satisfied by the detector options outlined
in the next Section.

##  8 The SHADOWS detector

The SHADOWS detector must be able to reconstruct and identify most of the
visible final states of FIPs decays. These are listed in Table 1 for the main
portals used in the Physics Beyond Colliders exercise Beacham:2019nyx .

Table 1: Main decay modes for FIPs represented in the four portals of the PBC exercise. $\ell=e,\mu,\tau$. Scalar portal |  $\ell^{+}\ell^{-}$, $\pi^{+}\pi^{-}$, $K^{+}K^{-}$
---|---
Pseudo-scalar portal |  $\ell^{+}\ell^{-}$, $\gamma\gamma$, $\pi^{+}\pi^{-}$, $K^{+}K^{-}$
Vector portal | $\ell^{+}\ell^{-},\pi^{+}\pi^{-},K^{+}K^{-}$
Fermion (neutrino) portal | $\ell^{\pm}\pi^{\mp},\ell^{\pm}K^{\mp},\ell^{\pm}\rho^{\mp}(\rho^{\mp}\to\pi^{\pm}\pi^{0}),\ell^{+}\ell^{-}\nu$

To this aim a standard spectrometer with excellent tracking and timing
performance and some particle identification capability is required. The
spectrometer should be made of:

  * -

a tracking system able to reconstruct with high accuracy the mass, the decay
vertex and the impact parameter with respect to the impact point of the beam
on the dump for FIP decays with at least two charged tracks in the final
state. We require: i) a mass resolution of a few MeV for masses of the order
of a few GeV; ii) a vertex resolution of $\sim 1$ cm in the transverse plane
over a volume length of $\sim$ 20 m; iii) an impact parameter resolution of
$\sim 1$ cm for FIP decays into two charged tracks when the total momentum is
extrapolated backward at the impact point of the beam onto the dump. All these
requirements are important to separate the signal from the background;

  * -

a timing detector with $\sim(100-200)$ ps time resolution in order to reduce
any combinatorial background (and in particular the muon one) by requiring the
tracks to be coincident in time. Combinatorial tracks are in fact
intrinsically respectively out-of-time as they have a origin time spread over
the 3.3 sec effective duration of a typical P42 proton spill;

  * -

an electromagnetic calorimeter able to reconstruct the energy, the position
and (possibly) the direction of photons coming from FIP decays.

  * -

a hadron calorimeter for efficient $\mu$/hadron separation;

  * -

a muon detector to positively identify muons and with timing capabilities to
reinforce the rejection of the combinatorial muon background in combination
with the timing detector.

A schematic layout of the spectrometer is shown in Figure 30.

Figure 30: Schematic layout of the spectrometer. The beam runs from right to
left.

The front face of the decay volume should be equipped with a high-efficient
veto system able to tag beam-induced charged tracks emerging from the dump.
Since the detector is off-axis the inelastic interactions of neutrinos with
the air of the decay volume are not a concern. However charged tracks not
tagged by the veto system could still enter the decay volume, make inelastic
interactions with the air contained in it, and mimic a FIP decay. In order to
reduce such a background the decay volume could be either placed in a mild
($\sim 10^{-2}-10^{-3}$ mbar) vacuum or filled with $He$.

In the following Sections we describe possible technologies suitable for the
SHADOWS sub-detectors. The list should be considered only indicative as other
options could be equally viable. The final choice of the technologies will be
driven by the overall detector optimisation and the interest of experimental
groups. While the R&D of new technologies is certainly encouraged, this is not
mandatory: in fact the relatively low background rate at the spectrometer
level (see Section 7) allows the SHADOWS detectors to be built using existing
technologies already available on the market.

###  8.1 Tracking system

The design of the tracking system and the dipole magnet is driven by the
requirement of achieving $\sim 1$ cm (or less) resolution on the transverse
position of the decay vertex of a feebly-interacting particle in two charged
tracks over a decay volume length of about 20 m. This is in fact one of most
effective handles to reduce the combinatorial background. A preliminary study
shows that this resolution can be achieved by a tracking system with a dipole
magnet with a bending power of about 1.5 T$\cdot$m and four tracking stations
with a single station resolution of about 250 $\mu$m. The four stations should
be placed two before and two after the magnet, with a distance between the two
stations placed at the same side of the magnet of $\sim 500$ mm and a gap of
1500 mm between the two stations adjacent to the dipole.

Table 2 shows the dependence of the momentum resolution as a function of the
track momentum for a tracking system able to reconstruct with 1 cm accuracy in
the transverse plane the decay vertex in any position along the 20 m long
decay volume.

Table 2: Dependence of the momentum resolution and the curvature angle $\rho$ inside the magnetic field as a function of the momentum of the tracks for a fixed resolution in the decay vertex over 20 m long decay volume. p [GeV] |  $\sigma_{xy}$ [mm] |  $\sigma_{z}$ [mm] |  $\rho$ [m] |  $\sigma(p)/p$ (%)
---|---|---|---|---
1 | 10.6 | 500.0 | 3.33 | 0.2
2 | 10.6 | 500.0 | 6.67 | 0.4
5 | 10.6 | 500.0 | 16.67 | 1.1
10 | 10.6 | 500.0 | 33.33 | 2.2
20 | 10.6 | 500.0 | 66.67 | 4.4
50 | 10.6 | 500.0 | 166.67 | 11.1
100 | 10.6 | 500.0 | 333.33 | 22.2
200 | 10.6 | 500.0 | 666.67 | 44.4

Possible technologies already available on the market are:

  1. 1.

NA62 tracking system Danielson:2010fta : Straw tubes in vacuum, 10 mm
diameter, based on a gas mixture Ar(70%): CO2 (30%). One straw chamber is
composed of four views $(X,Y,U,V)$, with one double-layer per view. The hit
resolution is better than $400\mu$m over most of the straw diameter per single
layer, and there are eight layers per tracking station. The warm dipole magnet
provides 0.9 Tm bending power. This system achieves a mass resolution of 3-4
MeV for a long-lived particle of mass of 1 GeV decaying in two charged tracks.
The decay vertex resolution is better than 1 cm over a 100 m long decay volume
and the accuracy of the impact parameter with respect to the beam impinging
onto the TAXes is better than 1 cm for a distance between the decay vertex and
the dump of (100-180) m.

  2. 2.

LHCb Outer Tracker LHCbOuterTrackerGroup:2013epe : gas-tight straw-tube
modules based on Ar(70%): CO2 (30%) gas mixture. Each module contains two
staggered layers of drift-tubes with inner diameters of 4.9 mm. The drift
coordinate resolution per layer is $\sim 200$ $\mu$m. The mass resolution for
a $B_{s}\to\mu^{+}\mu^{-}$ decay at the LHC energies is $\sim$ 20 MeV.

  3. 3.

Fibre Tracker (LHCb upgrade phase 1) LHCbSciFi : The LHCb SciFi tracker
consists of three tracking stations (T1,T2,T3) each with four detection planes
aligned with different stereo angles $(0^{\circ},\pm 5^{\circ})$ with respect
to the vertical. Each detection plane is made of 250 $\mu$m diameter, 2.5 m
long scintillating fibres. The system is expected to provide a hit resolution
per station of $<80\mu$m with 4 Tm bending magnet.

###  8.2 Timing detector

The timing detector has to provide a time resolution of $o(100-150)$ ps to
reject combinatorial backgrounds made of out-of-time charger tracks, mostly
muons. Several options are possible on the market, here we simply list some of
them.

  1. 1.

Scintillating bar timing detector: scintillating bars read out by arrays of
silicon photomultipliers. This option has been considered for the SHiP timing
detector. The detector comprises more than 500 bars of EJ200 scintillating
material with dimensions 168 cm$\times$6 cm$\times$1 cm broken. The end of
each bar is read out by an array of eight SiPM attached to custom PCBs. A time
resolution of $\sim$80 ps almost uniform along the bar length has been
demonstrated on prototypes SHiP:2019hap .

  2. 2.

Glass Multigap Resistive Plate Chambers, glass-RPC: This option is based on
the RPC technology derives from a novel concept of Multigap Resistive Plate
Chambers (MRPC) with a Sealed Glass Stack (SGS). Also this option has been
considered for the SHiP timing detector. A time resolution of $<60$ ps has
been measured on prototypes.

  3. 3.

Scintillating pad detector: a double layer of the redesigned scintillating
pads considered for the muon detector (see below) could provide a timing
detector with about 150 ps time resolution.

###  8.3 Electromagnetic calorimeter

The electromagnetic calorimeter must be able to reconstruct the energy, the
position and (possibly) the direction of photons coming from FIP decays,
either directly or via intermediate resonances (eg. $\pi^{0}$s).

Given the relatively low rate and low energies involved, no radiation issues
are expected. Several technologies fit SHADOWS requirements and are listed
here below. Other technologies can be certainly considered.

  * -

$PbWO_{4}$ crystals (CMS electromagnetic calorimeter):
The CMS ECAL CMS_ECAL  is a homogeneous and hermetic calorimeter containing
61200 lead tungstate ($PbWO_{4}$) scintillating crystals mounted in the
barrel, closed at each end by end-caps each containing 7324 crystals.

The high-density(8.28 g/cm3), short radiation length ($X_{0}$=0.89 cm), and
small Molière radius (R=2.2 cm) of $PbWO_{4}$ allow the construction of a
compact calorimeter with fine granularity. The crystals emit blue-green
scintillation light with a broad maximum at wavelengths 420–430 nm. They are
read out by APD (barrel) Baccaro:1999ns  and vacuum phototriodes (endcaps)
Bell:2004eu . The light yield is about 4.5 photo-electrons for 1 MeV of
deposited energy in the crystals. The barrel is made of 23 cm long crystals
with front face cross sections of around 2.2 cm$\times$2.2 cm, whilst the
endcaps comprise 22 cm long crystals with front face cross sections of 2.86
cm$\times$2.86 cm. The energy resolution is $\sigma(E)/E=2.8\%/\sqrt{E(\rm
GeV)}\oplus 12\%/E({\rm GeV})\oplus 0.3\%$.

The CMS ECAL endcaps will be dismounted during long shutdown 3 and a fraction
of the crystals can be reconditioned for their use in the SHADOWS experiment.
This opportunity makes this choice particularly attractive for SHADOWS.

  * -

Shashlik technology (LHCb ECAL):
The LHCb electromagnetic calorimeter Machikhiliyan:2009zz  structure employs
the shashlik technology Atoian:1992ze  , when interleaving scintillator-
absorber layers are pierced by optical fibers of light collection system. The
light readout devices are photomultipliers (PMTs). The LHCb ECAL is made of
3312 separate modules of square section, of different sizes. The sampling
stack comprises 66 lead plates and 67 scintillator (BASF-165H polystyrene
basedplastic doped with 2.5% p-terphenyl and 0.01% POPOP) planes, separated by
thin ($120\,\mu$m) TYVEC paper sheets. Wavelength-shifting (WLS) fibers
(KURARAY Y-11(250) MSJ, 1.2 mm diameter) of the light collection system run
parallel to the beam axis and penetrate the entire module body. Fibers serving
the same cell are grouped together at the rear of the module and are read out
by the same PM. The cells have transverse dimensions of $4.04\times
4.04/6.06\times 6.06/12.12\times 12.12$ cm2 depending on the zone. This
calorimeter has an energy resolution $\sigma(E)/E\sim 10\%/\sqrt{e}\oplus 1\%$
and a fast time response in order to cope with the LHC bunch spacing of 25 ns.

  * -

The ”SplitCal” calorimeter (SHiP proposal) Bonivento:2018eqn
The SplitCal calorimeter proposed for the SHiP experiment is a lead sampling
calorimeter, with absorber plates orthogonal to the incoming beam direction,
and two types of active layers: scintillator layers for the energy and time
measurement, with coarse spatial segmentation and high resolution layers to
determine the transverse position and direction of the shower. Preliminary
studies show that a moderate energy resolution of $\sigma(E)/E\sim
10-15\%/\sqrt{(}E({\rm GeV})$, a time resolution of a few ns and photon
direction measurement are achievable with this design.

###  8.4 Hadronic calorimeter

The hadron calorimeter has to positively identify hadrons and measure their
energy. A detailed study of its requirements and related performance will be
done in the future, but we expect that a traditional structure of a sampling
calorimeter made from alternate layers of iron and scintillator, as for
example the MUV1 and MUV3 system of the NA62 experiment NA62:2017rwk , could
be adequate for SHADOWS requirements.

###  8.5 Muon system

The muon system has to identify muons with high efficiency ($>$ 95%), reduce
the hadron contamination to less than 1% in a momentum range between 5 - 100
GeV/c, and reject the combinatorial muon background pairs from the beam muon
halo together with the Timing detector. The combinatorial muon background from
beam halo is spread along spills 3.3-sec long and can be controlled by
requiring a tight ($<3\cdot\sigma_{t}$, $\sigma_{t}\sim 150$ ps) time
coincidence of the two tracks.

The detector could be made of four active stations, of $\sim(2.5\times 2.5)$
m2 transverse area, interleaved by iron filters $\sim 3.0\lambda_{I}$ thick.
In order to achieve a time resolution of $o$(150) ps over the four stations, a
time resolution of $\sim$ 300 ps per station is required. The baseline
technology consists of scintillating tiles with direct SiPM readout. The basic
unit is a $\sim$225 cm2 area (15$\times$ 15) cm2 and $\sim$ 10 mm thick tile
of organic scintillator, read out by four SiPMs. Tests performed at the
Laboratori Nazionali di Frascati of INFN and INFN Bologna Balla:2021njd  show
that a time resolution of 250-300 ps per tile can be achieved with an
efficiency of $>99.8\%$ and a light yield of $\sim 230$ photo-electrons per
minimum-ionizing particle. Figure 31 shows the first 4-tile prototype.

Figure 31: Prototype of the SHADOWS muon system: 4-scintillating tiles with
direct SiPM readout equipped with a customized front-end electronics.

In the SHADOWS muon detector the tiles will be grouped in modules of 16 (32)
tiles each. Each stations will be equipped with 16 (8) modules.

The modules are installed on both sides of a supporting structure (Al wall) in
a staggered chess structure: such a design allows both the dead zones to be
minimised and the weight on the supporting wall to be equally shared between
the two wall sides. Each station can slide on rails to ease the access to the
modules during installation/repair. A schematic layout of the SHADOWS muon
system is shown in Figure 32.

Figure 32: Schematic layout of the SHADOWS muon system. The system is made of
four active stations interleaved by passive filters. Each station is made by
16 or 8 modules, 16- or 32-tile each, respectively. The modules are organised
in a chess-like structure. Each tile has an area of $\sim 225$ cm2.

###  8.6 Upstream Veto

The Upstream Veto should be installed in the front face of the decay volume to
tag the residual muon background emerging from the TAXes and not yet swept out
by the magnetized iron block (see Section 7). The veto must have high
efficiency, excellent time resolution and a few cm granularity to stand the
high rate expected in that region. A possibility could be to install a double
layer of scintillating tiles similar to those developed for the muon system
but of smaller area. Other technologies are clearly possible and can be
considered.

##  9 Tentative schedule

Figure 33 shows the tentative time schedule for the installation and operation
of the SHADOWS experiment in the first phase (one spectrometer installed in
zone 1). This assumes the current schedule for the CERN accelerator complex.
Assuming the presentation of a Technical Proposal from the Collaboration
within 2022 and a positive recommendation from the CERN SPS Committee and
Research Board, we could aim at installing the detector during the Long
Shutdown 3 and start with a pilot run at the beginning of Run 4. The goal is
to integrate $5\cdot 10^{19}$ pot in beam-dump mode within Run 5, with at
least one spectrometer.

Figure 33: SHADOWS tentative timescale for the installation of the first
spectrometer in zone 1.

##  10 Conclusions and Outlook

Feebly-interacting particles (FIPs) may provide an answer to many open
questions inparticle physics, astrophysics, and cosmology. These include the
origin of the neutrino masses and oscillations, the baryon asymmetry of the
universe, the dark matter, the strong CP problem, the cosmological inflation,
and the apparent fine tuning of the EW scale.

In the coming years a wealth of experimental results for FIPs are expected
from all the major laboratories in the world. These include accelerator based
experiments (ATLAS,CMS, LHCb, NA64, NA62 at CERN; MEG-II and Mu3e at PSI;
Belle II at KEK; BDX and HPS at JLab; MiniBooNE at FNAL; T2K ND280 and KOTO at
J-Park) as well as dark matter direct detection experiments and dedicated
experiments searching for axions/ALPs in Europe and US.

In addition to established experimental efforts, a multitude of new
initiatives has recently emerged both at CERN (NA62 in dump mode, SHiP,
MATHUSLA,FASER, CODEX-b) and elsewhere (LDXM at SLAC, long baseline neutrino
near detectors at Fermilab and in Japan, Beam Dump experiment at Mainz, and
others) aiming at covering in the coming decade uncharted regions of FIPs
parameter space inaccessible to traditional experiments at colliders.

SHADOWS, profiting of the unique P42 beam line characteristics in terms of
intensity and energy and of the profound expertise related to its operation of
the CERN BE-EA-LE group and the NA62 collaboration, aims at becoming one of
the leading experiments worldwide in the field during this decade.

The experiment is currently being designed. Groups or individuals interested
to contribute to the SHADOWS physics case and/or to the SHADOWS detector can
contact:
<EMAIL_ADDRESS><EMAIL_ADDRESS>.

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