# The HIBEAM program: search for neutron oscillations at the ESS

V. Santoro11footnotemark: 122footnotemark: 2 D. Milstead33footnotemark: 3 P.
Fierlinger44footnotemark: 4 W.M. Snow55footnotemark: 566footnotemark:
677footnotemark: 7 J. Barrow88footnotemark: 899footnotemark: 9 M.
Bartis1010footnotemark: 10 P. Bentley1111footnotemark: 11 L.
Björk1212footnotemark: 12 G. Brooijmans1313footnotemark: 13 N. de la
Cour1414footnotemark: 14 D.D. Di Julio1515footnotemark: 15 K.
Dunne1616footnotemark: 16 M.J. Ferreira1717footnotemark: 17 U. Friman-
Gayer1818footnotemark: 18 M. Holl1919footnotemark: 19 Y.
Kamyshkov2020footnotemark: 20 E. Kemp2121footnotemark: 21 M.
Kickulies2222footnotemark: 22 R. Kolevatov2323footnotemark: 23 H.T.
Johansson2424footnotemark: 24 B. Jönsson2525footnotemark: 25 W.
Lejon2626footnotemark: 26 J.I. Marquez Damian2727footnotemark: 27 B.
Meirose2828footnotemark: 282929footnotemark: 29 A. Nepomuceno3030footnotemark:
30 T. Nilsson3131footnotemark: 31 A. Oskarsson3232footnotemark: 32 R.
Pasechnik3333footnotemark: 33 L. Persson3434footnotemark: 34 B.
Rataj3535footnotemark: 35 J. Rogers3636footnotemark: 36 S.
Silverstein3737footnotemark: 37 R. Wagner3838footnotemark: 38 M.
Wolke3939footnotemark: 39 S.C. Yiu4040footnotemark: 40 L.
Zanini4141footnotemark: 41 European Spallation Source ERIC, Partikelgatan 5,
22484 Lund, Sweden  Department of Physics, Lund University, P.O. Box 118,
SE-221 00 Lund, Sweden  Department of Physics, Stockholm University, 106 91
Stockholm, Sweden  Physikdepartment Technische Universität München James-
Franck-Str. 1 85748 Garching, Germany  Department of Physics, Indiana
University, 727 E. Third St., Bloomington, IN, USA, 47405  Indiana University
Center for Exploration of Energy & Matter, Bloomington, IN 47408, USA  Indiana
University Quantum Science and Engineering Center, Bloomington, IN 47408, USA
Massachusetts Institute of Technology, Dept. of Physics, Cambridge, MA 02139,
USA  School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978,
Israel  Department of Physics, Columbia University, New York, NY 10027, USA
Department of Physics and Astronomy, The University of Tennessee, Knoxville,
TN 37996, USA  Instituto de Fìsica Gleb Wataghin, Universidade Estadual de
Campinas (UNICAMP), Av. Sérgio Buarque de Holanda 777, 13083-859 Campinas, SP,
Brazil  European Spallation Source Consultant, Norway  Departamento de
Ciências da Natureza, Universidade Federal Fluminense, Rua Recife, 28890-000
Rio das Ostras, RJ, Brazil  Institutionen för Fysik, Chalmers Tekniska
Högskola, Sweden  Institut Laue-Langevin, 71 Avenue des Martyrs, 38042
Grenoble, France  Department of Physics and Astronomy, Uppsala University,
Uppsala, Sweden

###### Abstract

With the construction of the European Spallation Source, a remarkable
opportunity has emerged to conduct high sensitivity searches for neutron
oscillations, including a first search for thirty years for free neutrons
converting to antineutrons. Furthermore, searches can be made for transitions
of neutrons and antineutrons to sterile neutron states. Upgrades to the ESS
infrastructure allow an improved HIBEAM design that would provide an increase
in sensitivity of an order of magnitude compared to previous work.

The HIBEAM program corresponds to baryon number violation by one and two
units. The observation of a process satisfying a Sakharov condition addresses
the open question of the origin of the matter-antimatter asymmetry in the
Universe. Sterile neutron states would belong to a ‘dark’ sector of particles
which may explain dark matter. As electrically neutral, meta-stable objects
that can be copiously produced and studied, neutrons represent an attractive
portal to a ‘dark’ sector.

This paper describes the capability, design, infrastructure, and potential of
the HIBEAM program. This includes a dedicated beamline, neutron optical
system, magnetic shielding and control, and detectors for neutrons and
antineutrons.

††journal: Journal of LaTeX Templates

##  1 Introduction

The European Spallation Source (ESS) will become the most powerful research
facility worldwide for neutron-based studies once it reaches full completion
[1]. With its exceptional capabilities, including a higher useful flux of
neutrons compared to any existing research reactor and an unprecedented level
of neutron brightness, the ESS surpasses current neutron sources.

The ESS is presently in the process of constructing 15 instruments as part of
its comprehensive suite, consisting of 22 instruments necessary to fully
achieve its scientific objectives as defined in the ESS statutes [2].
Furthermore, the ESS has a dedicated mandate for fundamental physics research.
However, one of the critical missing elements is the absence of a dedicated
beamline specifically designed for fundamental physics experiments [3] . This
identified limitation highlights the importance of establishing such a
beamline to fulfill the ESS’s comprehensive scientific mission. In this
context, taking advantage of the ESS scientific capability the HIBEAM (High-
Intensity Baryon Extraction and Measurement) collaboration aims to conduct a
program of beam neutron oscillation searches. Upgrades to the ESS
infrastructure allow an improved HIBEAM design with respect to earlier work
[4, 5].

The goals of the HIBEAM project are outlined in Ref. [4]. In this paper, a
design is given of a HIBEAM beamline with which a number of high precision
searches for neutron oscillations can be made. Neutrons converting to anti-
neutrons and/or sterile neutrons are high precision probes of baryon number
violation (BNV) and address a number of open questions in modern physics,
including baryogenesis and dark matter.

For the first time in over thirty years, a competitive search for free
neutrons converting to anti-neutrons will be made. The HIBEAM sensitivity
exceeds that of the previous search at the ILL [6] by around an order of
magnitude. The improvements are due to the capability of the ESS source, and
improvements in neutron focusing and detector technology since the last
search. Similar sensitivity improvements are expected for the HIBEAM program
of searches for sterile neutrons compared to earlier searches made at ultra-
cold neutron (UCN) facilities [7, 8, 9, 10, 11, 12, 13, 14].

This paper is organised as follows. A brief motivation for neutron conversion
is given. This is followed by an overview of the phenomenology of neutron
conversions which is used to explain the principles underpinning the design of
the search program. The ESS and HIBEAM beamline are then described. This is
followed by a description of the magnetic shielding and control
infrastructure, after which the neutron and antineutron detectors are
described.

##  2 Motivation for neutron oscillations

The observation of neutron conversions to anti-neutrons and/or sterile
neutrons at HIBEAM would be of fundamental significance. The HIBEAM program
corresponds to ‘essential scientific activities’ in 2020 Update to the
European Particle Physics Strategy [15]. The HIBEAM searches exploit unique
BNV channels for which, unlike single proton decay in which $B$ and $L$ must
be simultaneously violated to conserve angular momentum, $B$ is the only
hitherto conserved quantity which is violated. Furthermore, owing to the
experimental challenges of performing such searches there are comparatively
few searches for free neutron-antineutron conversions $(\Delta B=2,\Delta
L=0)$ compared with, for example, the leptonic equivalent process of
neutrinoless double beta decay $(\Delta B=0,\Delta L=2)$.

While the need for ‘blue sky’ exploration and high-sensitivity testing of
conservation laws strongly motivates the HIBEAM program, there also exists a
number of theoretical arguments, summarised below, outlining why BNV is
expected. Furthermore, as discussed, neutron conversions can arise as a single
phenomena addressing a specific problem, eg baryogenesis, as well as being
coupled to other signals of new physics such as neutrinoless double beta
decay.

  * 1.

The mechanism by which the matter-antimatter asymmetry in the Universe was
produced is not understood. However, it is known, as a so-called Sakharov
condition[16], that BNV is required for baryogenesis. Neutron conversions
feature in a number of scenarios of baryogenesis [17, 18, 19, 20, 21].

  * 2.

The conservation of $B$ corresponds, like $L$, to an accidental symmetry in
the SM. For theories extending the SM, BNV and lepton number violation (LNV)
therefore tend to occur generically. For example, observable low-scale BNV via
neutron conversions features in extensions of the SM, such as scenarios of
extra dimensions [22], branes [23], and supersymmetry [24, 25, 26].

  * 3.

Sterile neutrons can belong to a dark/hidden sector of particles which
interact gravitationally and not via the gauge forces of the SM [27, 28, 29,
30]. Such a sector can provide an explanation for Dark Matter. As meta-stable
and electrically uncharged objects which can be copiously produced and
studied, neutrons offer an attractive portal to a dark sector.

  * 4.

There exists a symbiosis between neutron-antineutron conversions and other key
observables for new physics sought by the community. The conversion of a
neutron to antineutron ($\Delta B=2$, $\Delta L=0$) is the baryonic equivalent
of neutrinoless double beta decay ($\Delta B=0$, $\Delta L=2$). Both processes
feature in unification scenarios and theories of neutrino masses [31, 20, 21,
32]. Furthermore, neutron-antineutron conversion, neutrinoless double decay
and single proton decay are coupled via the electroweak sphaleron interaction,
the existence of which is a fundamental prediction of the SM. The sphaleron
process can be written as $QQQQQQ\leavevmode\nobreak\ QQQL\leavevmode\nobreak\
LL$. This implies that, if any two of the following processes are observed,
then the other should exist: $n\rightarrow\bar{n}$ transition (the first six
quark operator), proton decay (the second 4-fermion operator) and
$\Delta\mathcal{L}$ =2, lepton number violation. The last term implies a low
energy process such as neutrinoless double beta decay.

##  3 Phenomenology of the neutron conversions and search principles

HIBEAM is a unique facility that can probe the full range of neutron mixing
possibilities between antineutrons and sterile states [33, 34]. The
Hamiltonian for neutrons in a $\mathbf{B}$-field is given in Equation 1.

$\hat{\mathcal{H}}=\left(\begin{array}[]{cccc}m_{n}+\vec{\mu}_{n}\vec{B}&\varepsilon_{n\bar{n}}&\alpha_{nn^{\prime}}&\alpha_{n\bar{n}^{\prime}}\\\
\varepsilon_{n\bar{n}}&m_{n}-\vec{\mu}_{n}\vec{B}&\alpha_{n\bar{n}^{\prime}}&\alpha_{nn^{\prime}}\\\
\alpha_{nn^{\prime}}&\alpha_{n\bar{n}^{\prime}}&m_{n^{\prime}}+\vec{\mu}_{n^{\prime}}\vec{B}^{\prime}&\varepsilon_{n\bar{n}}\\\
\alpha_{n\bar{n}^{\prime}}&\alpha_{nn^{\prime}}&\varepsilon_{n\bar{n}}&m_{n^{\prime}}-\vec{\mu}_{n^{\prime}}\vec{B}^{\prime}\end{array}\right)$
(1)

The terms $\varepsilon_{n\bar{n}}$ , $\alpha_{nn^{\prime}}$ and
$\alpha_{n\bar{n}^{\prime}}$ are the $n\bar{n}$ Majorana mass mixing
parameter, and mass mixing parameters for $nn{{}^{\prime}}$ and for
$n\bar{n}{{}^{\prime}}$, respectively424242A more general expression for the
Hamiltonian allows for the possibility of a transition magnetic moment (TMM)
[35]. This is not included here though a search for a TMM can be performed
with HIBEAM.. In a minimal approach, the neutron mass ($m_{n}$) and magnetic
moment ($\mu_{n}$) are assumed to the same as that in the sterile sector. The
magnetic moments for particle and anti-particle are opposite for both the
visible and sterile sectors. Magnetic fields, $B$ and $B^{\prime}$ exist in
the visible and sterile sectors, respectively.

Many different possible processes are possible. Equation 2 gives the process
probabilities as a function of propagation time $t$, in the quasi-free regime,
for free neutrons to antineutrons ($P_{n\bar{n}}$). Probabilities are also
given for sterile neutron processes434343These processes can involve sterile
neutrons and sterile antineutrons. For simplicity, only the sterile neutron
mode is written here. Physical limits and sensitivities are not dependent on
this simplification. In the event of a discovery, the ability to perform a
range of searches, including neutron-antineutron transitions via sterile
states, helps pin down the various contributions from sterile neutrons and
sterile antineutrons.: neutron-antineutron transformation ($P_{n\rightarrow
n^{\prime}\rightarrow\bar{n}}$), neutron regeneration ($P_{n\rightarrow
n^{\prime}\rightarrow n}$) and neutron disappearance ($P_{n\rightarrow
n^{\prime}}$). The characteristic oscillation times for each process
($\tau_{n\bar{n}},\tau_{n\rightarrow n^{\prime}},\tau_{n\rightarrow
n^{\prime}},\tau_{\bar{n}\rightarrow n^{\prime}}$)are the reciprocal of each
of the amplitudes. The terms $t_{1}$ and $t_{2}$ denote the propagation times
before after conversion.

$P_{n\bar{n}}(t)=\frac{t^{2}}{\tau^{2}_{n\bar{n}}};\hskip
7.11317ptP_{n\rightarrow n^{\prime}\rightarrow\bar{n}}=\frac{t_{1}^{2}\cdot
t_{2}^{2}}{\tau_{n\rightarrow
n^{\prime}}^{2}\tau_{\bar{n}\rightarrow{n}^{\prime}}^{2}};\hskip
7.11317ptP_{n\rightarrow n^{\prime}\rightarrow n}=\frac{t_{1}^{2}\cdot
t_{2}^{2}}{\tau_{n\rightarrow n^{\prime}}^{4}};\hskip 7.11317ptP_{n\rightarrow
n^{\prime}}=\frac{t^{2}}{\tau_{n\rightarrow n^{\prime}}^{2}}$ (2)

There are several notable features of neutron conversion theory that guide the
searches.

  * 1.

The probability of observing a process in the quasi-free limit is enhanced by
a power with increasing propagation time, motivating a long beamline and
sample of slow neutrons. The discovery potential of a future experiment is
often best quantified by an expression involving the propagation time raised
to a power rather than the propagation time.

  * 2.

Outside of the quasi-free limit, the above probabilities become massively
suppressed. For free neutron-antineutron conversions, to achieve the quasi-
free condition in a beam experiment requires $B<5-10$nT [36]. For transitions
to sterile neutron states, the magnetic fields in the visible ($\mathbf{B}$)
and sterile states ($\mathbf{B}$) combine such that the transition probability
has a resonant-like behaviour as the visible field is varied [37].

  * 3.

A sterile magnetic field $\mathbf{B^{\prime}}$ can be generated in a number of
ways. For example by hypothetical ionization and flow of gravitationally
captured dark material in and around the Earth [37]. Such an accumulation
could occur due to ionized gas clouds of sterile atoms captured by the Earth
e.g. due to photon–sterile photon kinetic mixing; present experimental and
cosmological limits on such mixing [38] and geophysical limits [39] still
allow the presence of a relevant amount of sterile material at the Earth for
magnetic fields less than several gauss [40].

The principles of the neutron conversion searches are illustrated in Figure 1.
The figure shows a CAD model of the HIBEAM beamline for a search for free
neutrons to antineutrons ($n\rightarrow\bar{n}$). More information of the
various features of the CAD model given in Section 6 and subsequent sections.
Neutrons are passed through a neutron guide into a free passage volume and
eventually pass through a thin ($100$ $\mu$m) carbon target, surrounded by a
detector. The detector would observe the products of the antineutron-nucleon
annihilation.

The figure also illustrates how the beamline configuration changes for sterile
neutron searches. Neutron-antineutron conversions via sterile neutrons
($n\rightarrow n^{\prime}\rightarrow\bar{n}$) require a scan over different
magnetic field values to reach the resonance regime. At an optimised magnetic
field, a sterile state in one propagation volume is induced. The sterile
neutron then passes through a beamstop which prevents the passage of neutrons.
A magnetic field in a second propagation volume then induces the transition of
the sterile neutron to an anti-neutron, the annihilation signature of which
can then be observed.

A similar set-up can be used to observe sterile neutrons via the transition of
sterile neutrons into neutrons rather than anti-neutrons following the
beamstop. The process ($n\rightarrow n^{\prime}\rightarrow\bar{n}$) provides a
classic regeneration experiment. Sterile neutrons can also be potentially
observed as an anomalous loss of neutrons at the end of a beamline
($n\rightarrow n^{\prime}$).

Figure 1: A CAD model of the HIBEAM beamline for a search for free neutrons
converting to antineutrons. It is pointed out where there would be differences
for the other experimental configurations. The principles of the various
searches are shown in the bottom left of the figure.

##  4 The European Spallation source

The ESS facility and how it relates to neutron oscillation projects is
described in Refs. [4, 41]. It employs a linear accelerator to accelerate
protons. The exceptional neutron flux achieved at ESS is a direct result of
its possession of the world’s most powerful accelerator and the utilization of
the highest beam power directed toward the target. The proton beam employed in
this process follows a pulse structure of 14 Hz, with each pulse lasting 2.86
ms. Through acceleration, the proton beam reaches an energy of 2 GeV, powered
by a current of 62.5 mA. The ESS is presently committed to delivering 2 MW
power on target by 2028, with a final aim for a beam power of 5 MW.

Figure 2: The ESS target monolith.

Once the proton beam reaches its ultimate energy, it collides with a rotating
tungsten target, resulting in spallation and the production of primarily
evaporation neutrons at around 2 MeV. The spallation neutrons undergo
moderation within the neutron moderators contained within the moderator-
reflector plug, as shown in Figure 3. Initially, the ESS will be equipped with
only a single compact low-dimensional moderator located above the spallation
target, which has been designed to deliver brightest neutron beams for
condensed matter experiments [42]. The target and moderator-reflector system
is located within a shielding configuration referred to as the monolith.
Figures 2 and 3 illustrates the proton beam, the target, and the monolith
structure.

Figure 3: Zoom in the target area. The 42 beam ports surrounding are clearly
visible, as well as the ESS moderator positioned above the spallation target.

As shown in Figure 3, the ESS possesses a total of 42 beam ports. These beam
ports play a crucial role in the facility as they serve as the neutron
extraction systems, responsible for transporting neutrons from the target to
the instrument area. Surrounding the monolith is another protective structure
known as the bunker [43]. The bunker serves as a shielding area that envelops
the ESS monolith, shielding the instrument area from the high levels of
ionizing radiation generated during operation. The roof and walls of the ESS
bunker are constructed out of heavy magnetite concrete. Within the bunker
areas, the neutron beamlines are equipped with neutron guides and other
instrument-specific equipment such as choppers or shutters.

##  5 The HIBEAM searches

The fundamental principles of the searches are shown in Figure 1. Further
details on sensitivities are given here.

###  5.1 Search for free $n\to\bar{n}$ at the HIBEAM beamline

Previous searches for free $n\rightarrow\bar{n}$ oscillations were conducted
at the Triga Mark II reactor [44, 45] and at the ILL [46, 47]. The ILL search
[47] performed almost 30 years ago provided the most stringent limit for the
free neutron oscillation time of about $8.6\times 10^{7}$ seconds. No new
searches for free $n\rightarrow\bar{n}$ oscillations have been performed
despite theoretical interest and several proposals to improve the experimental
sensitivity. These experiments require both an intense neutron source and a
team with diverse expertise in magnetic shielding, particle physics detectors,
and slow neutron optics.

The experiment involves a focused beam of free neutrons propagating in a
sufficiently field-free (or ”quasi-free”) region [33] towards a detector able
to detect the antineutron annihilation. In this detector, any antineutrons
would annihilate with a thin target (for this reason, we referred to it as the
annihilation detector), resulting in a final state of charged pions and
photons see Section 7.2. The figure of merit ($FOM$) of sensitivity for a free
$n\rightarrow\bar{n}$ search is given by:

$FOM=\sum_{i}N_{n_{i}}\cdot t_{n_{i}}^{2}\sim\langle N_{n}\cdot
t_{n}^{2}\rangle,$ (3)

where $N_{n_{i}}$ is the number of neutrons per unit time reaching the
annihilation detector after $t_{n_{i}}$ seconds of flight through a
magnetically protected, quasi-free conditioned vacuum region. The probability
of a conversion is therefore proportional to the number of neutrons times the
squared transit time. A high precision search therefore requires a large flux
of cold neutrons (i.e. neutrons with energy below 0.025 eV) which are allowed
to propagate freely over a long time to allow conversions to antineutrons.
These conditions are satisfied at the ESS.

Searches for $n\rightarrow\bar{n}$ can also be done with neutrons bound in
nuclei. $\bar{n}N$ annihilation inside a nucleus would liberate pions and
photons inside large-volume underground detectors [48, 49, 50, 51, 52, 53, 54,
55, 56, 57]. An analysis by Super-Kamiokande [56, 57, 58] infers a lower limit
on the free neutron oscillation time of $\sim 4.7\times 10^{8}$s. Atmospheric
neutrinos and other backgrounds make it more difficult for underground
detector searches to claim a discovery compared to a laboratory experiment
such as HIBEAM, where one can manipulate the magnetic field to check any
positive observation. The mean field estimates of the conversion rate may be
enhanced or suppressed by nucleon-nucleon correlation effects [32] which are
not yet fully understood. It is scientifically unwise to look for new
phenomena in only one experimental channel: the diversity of approaches
supported to discover neutrinoless double beta decay is a clear example. We
conclude that both types of searches are needed, with free neutron searches
being the cleanest from both theoretical and experimental perspectives.

###  5.2 Searches for sterile neutrons

These search modes require scans over different magnetic field configurations.
Following the procedure in [59], the sensitivity in oscillation times can be
estimated for the HIBEAM beamline for magnetic fields scans in the up-down
direction with step size 2 mG between $\pm 2$ G. Dedicated 3-D magnetic scans
with high statistics are used to investigate signal candidates.

A sensitivity on $\tau_{n\rightarrow n^{\prime}}$ up to 180 s for the neutron
regeneration experiment with the ESS at 2 MW power can be achieved for a
running period of around one ESS year for a magnetic field region up to 2 G
and background rate of 0.1 neutron/second. For the disappearance mode, this
increases to 300 s for a detector with 25% efficiency. These outstrip limits
from UCN over a wide range of magnetic field and can achieve order-of-
magnitude improvements.

The search for neutron-antineutron conversions via sterile neutrons provides a
sensitivity on ${{\tau_{n\rightarrow
n^{\prime}}\tau_{\bar{n}\rightarrow{n^{\prime}}}}}$. Unlike the other
searches, an effective background-free search can be achieved. This leads to a
sensitivity on $\sqrt{{\tau_{n\rightarrow
n^{\prime}}\tau_{\bar{n}\rightarrow{n^{\prime}}}}}$ that exceeds $1000$ s, the
precise value depending on the smallness of the expected background. HIBEAM
expects to run background-free i.e. with an expected number of background
events following selections $\ll 1$, as the ILL did. A sensitivity up to
$1000$ s is set as a benchmark. A comparison of HIBEAM sensitivities with
limits from UCN experiments is given in Figure 4.

Figure 4: Excluded regions (shaded/yellow) of $\tau_{nn^{\prime}}$ by UCN
experiments. The sensitivity of the HIBEAM program for $\tau_{nn^{\prime}}$
from regeneration and disappearance experiments is shown, as is the HIBEAM
sensitivity for $\sqrt{{\tau_{n\rightarrow
n^{\prime}}\tau_{\bar{n}\rightarrow{n^{\prime}}}}}$.

##  6 The HIBEAM beamline

To conduct the searches, a world-leading neutron beamline capable of
delivering the highest flux of free neutrons to the experimental area is
essential. Currently, a neutron extraction system that could be used for the
HIBEAM beamline is under construction. The extraction system will be located
in the ESS East sector. Figure 5 shows the ESS instrument suite, including all
the current instruments under construction. Figure 6 depicts the east sector.
HIBEAM could be positioned at beam port E6, close to the VESPA instrument. The
beamline will have a guide length of 65 m.

The layout of the HIBEAM beamline is shown in Figure 6. The neutron extraction
system is situated within the ESS target monolith see Fig 2. The neutron
extraction system plays a crucial role in transporting neutrons outside the
target, and it will be positioned between 2 meters from the moderator up to
5.5 meters.

This system comprises two main components: the Neutron Beam Port Insert (NBPI)
and the Neutron Beam Optics Assembly (NBOA), represented by the grey and
yellow structures in Figure 7, respectively. For the NBOA we are assuming a
copper substrate, but we can also consider aluminium or steel as established
alternative technologies, depending on structural factors. The preferred
option for the NBOA is an elleptical guide coated with an $m=4$ supermirror.

Following the extraction system, an additional 20-meter-long elliptical
neutron guide is required to transport the neutrons to the experimental area.
The elliptical guide is then followed by an extensive neutron flight region.
Ultimately, the neutrons will enter the experimental area, where depending on
which experiment will be carried out the neutron detector or the antineutron
detector will be installed.

Figure 5: ESS instruments suite. Figure 6: Expanded view of the location of
the HIBEAM beamline Figure 7: Neutron Extraction System CAD drawing Figure 8:
Overview of the optics system for the HIBEAM experiment. As modelled with
McStas, neutrons leave the ESS source and are focused towards the annihilation
detector.

Regarding the second optics system shown in Figure 8, located between the ESS
bunker and the guide shielding, simulations using the McStas [60] ray-tracing
package have demonstrated that, with this system, it is possible to deliver
$1.0\times 10^{12}$ n/s number of neutrons to the target, corresponding to the
$FOM$ for the neutron to antineutron search of $2.85\times
10^{9}\text{n}\cdot\text{s}$ at 5MW operating power. This $FOM$ was calculated
for the option with an annihilation target of a 40cm diameter, determined by
the compact dimensions of the WASA calorimeter (see Section 7.2). A Much
higher $FOM$ $6.9\times 10^{9}\text{n}\cdot\text{s}$ could be achieved for the
option where the annihilation target has a size of 1m see Section 7.3. The
elliptical guide is not the only option for the optics system located in the
ESS bunker; nested mirror optics similar to the one used for the NNBAR system
[61] are other possibilities. While the elliptical guide remains the current
baseline, the other options are currently under study.

###  6.1 Magnetic Infrastructure

As described above, after passing through the second optics system, the
neutrons will reach the magnetic control area. For the neutron to antineutron
search, the magnetic field in this region needs to be $<$ 5 nT to ensure the
free flight condition. This requirement imposes a technological challenge,
however prototyping for an arbitrarily extendable length detachable low
frequency shield has been pursued before [62].

Major challenges here are (i) extending the low magnetic field region to 60 m
from typically few meters length of most existing magnetic shields; (ii)
shielding in a constrained space and high radiation environment.

Figure 9: A schematic view of vacuum chamber, magnetic shield and magnetic
field coils as needed for the experiment. Inset left: Vacuum chamber and
modified end section of magnetic shield for the detector region; Inset right:
Detailed layout of a chamber and magnetic shield section. The magnetic shield
thickness is increased in the middle region of the shield. Note the ring-
shaped shield sections that “catch” magnetic flux at the ends of the shield,
at connections or access holes.

The free condition is fulfilled if the average magnetic field is below $<$ 5
nT. With a minimally particle velocity of 400 ms-1, the flight time in the low
field region is 0.1625 s, corresponding to a characteristic frequency of 6.2
Hz. It is therefore necessary that the next to a static reduction of magnetic
fields, also frequencies up to 10 Hz show an amplitude below 5 nT. To obtain a
field-free (or quasi-free) region, a combination of re-direction of magnetic
field lines and absorption of magnetic energy through Eddy currents is
required, next to interruptions of the magnetic flux in the shield to shorten
the impact of the magnetic fields of detector and spallation target.

Figure 9 shows the concept, which includes the vacuum chamber made from
aluminum, surrounded by a two-layered magnetic shield made from mumetal.

The aluminum vacuum chamber will have a thickness of 14 mm to withstand vacuum
pressure and a diameter of 0.6 m, with high material purity to avoid neutron
activation. Circling currents in the material shield external magnetic fields
above 1 Hz. Access for vacuum equipment and instrumentation will be provided
from the side, with 100 mm ID Alu tubes placed periodically at 2 m spacing,
which connect after 40 cm distance to pumps, placed outside the magnetic
shield. The branch tubes act as waveguides to prevent low frequency
distortions from entering the inside volume, while providing sufficient vacuum
conductivity to obtain $<$ 10-6 mbar inside.

The mumetal shields are composed of an octagonal assembly in two nested shells
with an inner diameter of 0.6 m and 0.75 m, from 4 individual bent segments
around the circumference of maximum 750 mm width and 300 mm length in axial
direction. The segments overlap by 50 mm and can be assembled after the vacuum
chamber is installed and provide flexible access for instrumentation of the
beam line. To achieve a residual field of $<$ 5 nT within the whole volume of
the vacuum chamber by reduction of remanent magnetization of the passive
magnetic shield, magnetic equilibration needs to be carried out. With state of
the art equilibration [63] by a sinusoidal current with linearly decreasing
envelope over 20 s into a set of toroidal coils wound around the inner
octagonal shield (also in independent sections of the shield), this goal is
feasible (as demonstrated in [62]). To obtain optimal performance along the
beam line, the enlarged diameter of the shield ensures that remanent fields
close to the shield surface do not case more than 5 nT at the inside of the
vacuum chamber. The shield will be mounted every 1.5 m with screws on
detachable plastic frames, which separate the shields mechanically and
electrically from the vacuum chamber and each other. Even with increased
thickness of the shields in the middle third of the length to compensate for
additional flux from the earth field. However, in the free flight region, the
magnetic field requirement is only $10^{-9}$ T, which is achieved by a
separated mumetal ring-section placed to catch residual flux from the
detector, while not guiding the flux into the shielded region. Also, for the
vacuum chamber, additional constraints apply to the detection region with the
annihilation target inside the vacuum chamber and the detector placed outside.
Due to the geometry of the annihilation target and the extreme background
requirement, the quality of the reconstruction of the reaction particles must
be of very high quality. In turn, the material thickness of the chamber must
be small to avoid angular broadening $\theta_{0}$ of the annihilation products
passing the material due to Moliere scattering. For aluminum with 0.5 mm wall
thickness, this effect is small enough to accommodate for the reconstruction
precision required by the 100 $\mu$m thick annihilation target, taken into
account in the design of the vacuum chamber. Here, the chamber wall is milled
down to the required thicknesses and deformed due to the vacuum pressure, with
only thick strips of material left to match the structural stability
requirements. The loss in shielding efficiency for 1-100 Hz due to the reduced
material thickness does not extend more than 0.5 m into the shield. With the
specific requirements for this setup, the experiment is also future technology
demonstrator in the magnetic aspects: Ring-geometry for field reduction were
specifically developed in preparation for this project, which enable the
modularization of magnetic shields, easy access through shields for pumping
and sensing, as well as minimization of large stray fields at the end of the
shields; Thickness variations of the shield layers and the segmentation of the
magnetic equilibration procedure was also specifically investigated and
developed as preparation for this project. Magnetic equilibration is also done
to ensure stability of applied magnetic fields inside the shield.

Regarding the sterile neutron searches where there is a need for applying
magnetic fields coil systems to generate longitudinal and transverse magnetic
fields will be installed. Transverse fields up to 300 $\mu$T are generated
with 2 sets of so-called cosine-theta coils with 90 $\deg$ rotated alignment
with a homogeneity of $\Delta B/B<10^{-3}$ ; a longitudinal field is generated
with a loosely wound solenoid axially with the shield and vacuum chamber.
Here, the homogeneity is improved by the shield, which forms a configuration
known as “magic box” when used with lids and short aspect ratio, resulting
also in close to $1.10^{-3}$ relative homogeneity. Magnetic characterization
of the shield is done using fluxgate magnetometers, which are moved through
the shield on a trolley. Magnetic equilibration resets the field distribution
and amplitude to typically within 1 nT after any arbitrary treatment in the
shield, extrapolating from experience [62]. Online magnetic characterization
is then optionally done using polarized neutrons similar to [64], where
polarized neutrons and a spin echo method were used. Here, this approach could
be advanced by deploying a small ${}^{3}He$ cell or removable polarizing
optical components at the beginning of the shielded section to polarize
neutrons at different positions in the beam. A 0.5 m long RF section operated
at few 100 Hz at 10 $\mu$T for $\pi/2$ flipping at the beginning of the beam
line and a second one at the end could for example enable spatial online
mapping while providing sensitivity to additional exotic physics cases.

##  7 Detectors

Both neutron and anti-neutron detectors are required for HIBEAM.

###  7.1 The neutron detector configuration

The very high instantaneous neutron rates in the neutron detectors needed for
different experimental configurations in this work are far too high to count
individual neutron pulses and one must use current mode detection. Since one
cannot apply the usual types of signal discrimination in this case, one must
be careful to ensure that the extra noise in the measured current from
background processes and from fluctuations in the number of current-generating
quanta from each individual neutron capture in the detector are both small
compared to $\sqrt{N}$ where $N$ is the number of neutrons. The burst of fast
neutrons from the ESS target/moderator system is gone by the time the slow
neutrons of interest arrive at the detector, so the most serious background
for neutron detectors in the direct beam comes from gammas. It is therefore
important for the detector to be able to withstand fast neutron bombardment
with no ill effects and be insensitive to gammas. It should also incorporate a
method to subtract the gamma-induced component of the neutron detector signal
without using the usual method of pulse shape discrimination.

Figure 10: Disassembled current mode 3He ion chamber used in the n-4He parity
violation experiment [65], showing the UHV vacuum chamber and the ion chamber
plates.

An ion chamber composed of 3He gas and using the $n+^{3}$He $\to^{3}$H
$+p+0.78$ MeV reaction provides a gamma-insensitive, fast neutron radiation-
damage-insensitive medium with a high absorption cross section for slow
neutrons and sufficient energy release to create enough ions per neutron
capture that the detector noise can still closely approach the $\sqrt{N}$
limit. The small fraction of the signal induced by background gammas in the
beam in such a 3He ion chamber can be subtracted by placing an identical 4He
ion chamber just in front of the 3He ion chamber. To an excellent
approximation the induced signal in the 4He ion chamber comes only from the
gammas in the beam, and a 3He ion chamber with the same dimensions and gas
pressure directly behind the 4He ion chamber will possess a nearly identical
response to gammas. Therefore one can subtract these two signals to leave only
that from the neutrons. Szymanski et. al [66] successfully demonstrated this
concept at the LANSCE pulsed spallation neutron source. Possible backgrounds
from neutron activation of ion chamber components by high energy neutrons and
gammas can be quantified at ESS using the signal from the fraction of the
time-of-flight frame outside the slow neutron arrival time and also by taking
data during dropped pulses from the ESS proton accelerator. Fast neutrons in
the beam appear to early in the time-of-flight frame to be confused with the
slow neutrons of interest for this work.

Addition of other species to the gas can reduce the range of the 3H and $p$ to
a few mm for easily-achievable gas pressures. We used a helium-argon gas
mixture in the segmented ion chamber we developed for polarized slow neutron
spin rotation measurements of parity violation [65]. The Figure shows a
picture of the detector used in this measurement. Segmentation of the detector
ion collection plates can be arranged transverse to the beam both to allow for
imaging and also to reject possible common-mode noise from pulse-to-pulse
fluctuations in the beam phase space not caught by the low efficiency monitor
upstream. The ion chamber detector can also be segmented along the beam
direction to take advantage of the fact that the slower neutrons are more
likely to be absorbed at the entrance to the chamber due to the $1/v$ behavior
of the neutron absorption cross section. Ionization signals from different
depths into the detector therefore gives information on the neutron energy
spectrum. The comparison of this data with the neutron time-of-flight
information enables a check of boundary effects in the ion chamber response
from ions that are lost to the collection plates by absorption in materials.

The required precision and stability of the total charge measurement from the
absorbed neutron beam should be ${10}^{-7\ }$ for this work. A 3He-based
neutron ion chamber of design similar to that described above was used in a
recent neutron-${}^{3}He$ parity violation experiment at SNS which reached
${10}^{-8\ }$ precision [67]. This success bodes well for our ability to meet
this specification. The stability of the efficiency of such an ion chamber can
be quite high as it depends only on chamber geometry and stability of ion
collection fields, constant gas composition and density, and electronics
properties. The current mode signals are large enough that no electronics gain
stage need be employed: one needs only a current to voltage convertor.

A detector with a variable efficiency as desired for this work can be realized
by changing the 3He gas pressure. Clean metal bellows compressors which
operate in the required pressure range and which are rated for the safe
handling of tritium gas (a nontrivial amount of tritium gas is generated in
the 3He ion chamber) are commercially available. Eventual safe extraction of
the tritium gas at the end of the measurements can easily be done by exposing
a hydrogen getter to the gas as was done in [67].

###  7.2 The annihilation detector

The signature of the neutron-antineutron transition is via the annihilation of
an antineutron on a Carbon target surrounded by an annihilation detector (see
Fig. 11). Such interactions produce a multipion state (3-5 charged pions and
photons from neutral pion decays) with momenta between 100-300 MeV [68, 69,
70]. In order to detect such a signal a dedicated annihilation detector
comprising tracking and calorimetry is needed. A schematic of the annihilation
detector that will make use of the WASA experiments [71] calorimeter can be
seen in Fig. 11. Incoming antineutrons traveling from the left in the vacuum
tube annihilate in a thin Carbon foil. Energies of annihilation products are
measured in the CsI(Na) calorimeter previously used in the WASA experiments
[71] at CELSIUS in Uppsala, at COSY in Julich and presently at FAIR,
Darmstadt. The WASA calorimeter is very compact, can be transported and will
be available for the HIBEAM project after 2027. Charged particle track
directions for event topology are measured in 3D by a cylindrical Time
Projection Chambers (TPC). Particle identification is done with a combination
of TPC and calorimeter.

Figure 11: The annihilation detector for the free neutrons converting to
antineutrons (left) and the conversion process via sterile neutrons (right)

Since the only energetic enough background that could make up an annihilation
signal is cosmic rays, an active shield of scintillator bars will surround the
experimental setup. Events coincident with a charged particle signal in the
cosmic veto will be rejected. To avoid self inhibition, an absorber thick
enough to stop all charged pions from the annihilation is needed between the
calorimeter and the scintillators. Cosmic events made by neutral particles
will be identified by missing vertex in the foil. The frequency of fake
annihilation events due to cosmics (and other natural backgrounds) will be
studied by shutting off the neutron flux at the neutron port.

The annihilation detector shall collect as much evidence as possible that a
$n-\bar{n}$ annihilation has occurred. The task is to detect and identify the
final state particles, verify the energy and momentum balance to be compatible
with $n-\bar{n}$ annihilating at rest and to verify the event topology with a
common vertex in the annihilation foil for all particles. Annihilation in a
nucleus opens additional ways to dissipate energy and momentum by re-
scattering in the nucleus. Figure 12 shows the simulated kinetic energy
distributions of particles emitted when annihilation takes place in a carbon
nucleus. Consequently the requirements on energy and momentum conservation
cannot be as strict in the $\bar{n}-C$ annihilation as in the free $n-\bar{n}$
case, as long as not all particles can be detected (neutrons and nuclear
remnant are missing) but it will anyway be in an energy regime where no
natural sources can contribute than those of cosmic origin. Around 91.5% of
the annihilations give at least one $\pi^{0}$. A good electromagnetic
calorimeter which can trigger on $\pi^{0}$ is essential. Also at least 2
charged pions are present in 98.5% of the cases and in addition protons often
come out from the nucleus. So charged particle tracking can reconstruct the
event topology with a common vertex in the foil. Both tracking and calorimetry
will have as large geometrical coverage as possible.
Figure 11 shows the detector for the mode for the $n\to\bar{n}$ and $n\to
n^{\prime}\to\bar{n}$ searches. The brown frame is a solid Iron construction
in which the CsI(Na) modules are mechanically fixed by their light guides to
Photo Multiplier (PM) tubes on the outside of the iron. The two search modes
$n\to\bar{n}$ and $\mathrm{n\to n^{\prime}\to\bar{n}}$ are quite different.
The traditional search for $n-\bar{n}$ transformation based on degenerate
states in the absence of external electromagnetic and strong (nuclear) fields
will have a very low probability and must be searched for by observing a
maximal number neutrons over as long flight time as possible. Instead, for the
$\mathrm{n\to n^{\prime}\to\bar{n}}$ mode by scanning systematically over weak
$\mathbf{B}$-fields a resonant behavior will enhance the production of
$n^{\prime}$ which in turn transforms to $\bar{n}$. If the process exists, it
should be governed by drastically higher probabilities at the proper resonance
setting for the magnetic fields. One expects rates of $\bar{n}$ annihilation
events per hour compared to events one per month or even year in the
traditional case.

Figure 12: Simulated kinetic energy spectra for different particle types in
$\bar{n}-C$ annihilations.

An important difference between the two cases is that in the standard
$n-\bar{n}$ search the neutrons beam will fly through the annihilation target
therefore the neutron induced nuclear reaction background in the annihilation
foil, a source of beam-induced pile-up background will be present. For the
$\mathrm{n\to n^{\prime}\to\bar{n}}$ case, this source of background will be
absent. It will also be possible to detect annihilation products in the very
forward direction. This gives larger solid angle covered and the annihilation
will be more completely characterized.

#### The beam tube

The beam tube will be made as thin as possible since charged particles
stopping in it will remain undetected. With 40 cm diameter the cylinder wall
is estimated to be 5 mm Al to withstand air pressure. The detection threshold
for protons will then be a few tens of MeV. As seen in the kinetic energy
spectra (Fig. 12) the threshold will only cut off the lowest 2-3 bins. For
charged pions the loss is even smaller and essentially marginal, while for
protons the effect is a little larger but still not a problem. Another effect
of the vacuum tube wall is multiple scattering. A measured direction outside
the wall will not point back correctly to the vertex due to this. The impact
on the vertex accuracy will be reduced by the thin wall and short pointing
distance to the foil. The conclusion is that no tracking will be implemented
inside the tube.

#### The Time Projection Chamber

The cylindrical TPC is compact with an outer diameter of 60 cm and inner 40
cm. The maximal drift length is about 35 cm. The short length means that the
absolute voltage on the negative terminal of the drift field (typically
200V/cm) will be 10kV at most which is rather trivial to handle. One
uncertainty for the TPC field cage and drift is that the track has to be
registered close to the edges of the field. It will be an important R&D task
to optimize the useful track length if necessary by corrections of static
distortions at the field edges so that the whole TPC thickness is usable. The
avalanche detector will be a GEM (Gas Electron Multiplier) stack with 4
layers. GEM readout is superior to wire chamber readout for this application
since the track image on the pad plane will retain the small extension of the
electron cloud after the short drift. This will give the best position
resolution. With GEMs one will also be able to run the TPC without a gating
grid and record the full track history. Also the missing 8.5% of annihilations
without without $\pi^{0}$ i.e charged particles only, would be recorded and
matched to particles in the Calorimeter. Continuous readout results in
considerable data volumes from the TPC. Another possibility with moderate loss
of annihilation events is to run in triggered mode using the excellent
performance of the calorimeter. The TPC front end chip allows a 10 microsecond
latency for such a trigger to be presented. Due to the short drift the
electron cloud at the readout plane will be only a few mm wide. To ensure
charge sharing between neighbour pads without using narrow, mm wide pads, zig-
zag shaped readout pads can be used. Then each pad will cover about 0.5square
cm on the pad plane.

The cylindrical part of the TPC with 1600 cm2 readaout area will then have
3200 pads/electronic channels. For the endcap TPC the drift length will be
about 15cm. On the area 1200 cm2 it will house 2400 pads/electronic channels.
A cylindrical TPC drift vessel with diameter 60cm should be rather
straightforward to construct with outer walls of a laminated construction of
Kapton PCB + Honeycomb structures. The inner wall can be integral with the
beam tube itself. The end cap TPC should be rather trivial from construction
point of view.

Each track will typically occupy 30 pads, 10 along the track and 3
perpendicular to it. A typical annihilation event has typically 5 tracks. A
channel can then handle multiple hits separated by a few hundred nanosecond.

The planned method for running the GEM TPC resembles the way the largest TPC
in the world, the ALICE TPC at LHC is operated after its upgrade [72].The
front end chip for ALICE TPC named SAMPA has 32 channels per chip and contains
a preamplifier, shaper, and pipeline memory for each channel. Packaged in Ball
Grid Array (BGA) package a chip is 15$\times$ 15mm2. With 32 channels per
SAMPA, each chip will serve an area of 16cm2 i.e. plenty of area available to
make a quite dense construction of the front end board fitting the limited
space available. Cooling will of course be a challenge and the arrangement
with the cylindrical and endcap TPC being read out in opposite directions
makes cooling easier.

If operated in triggered mode a powerful pulse recognition and zero-
suppression takes place already in the SAMPA chip. The SAMPA digitizes all the
time and upon receipt of a trigger the result of the previous 192 clockcycles
is avalibale for readout. At 20Mhz sampling this means a trigger latency of
about 10 microseconds is allowed. The data volumes to read out in triggered
mode with zero suppression will be of the order 1kbit per track. In continuous
mode with no zero-suppression each SAMPA will produce 6.4Gbit/s at 20 MHz
sampling.

#### The Calorimeter

The WASA calorimeter consists of about 1000 CsI(Na) modules of slightly
varying depth [71] . Typically a module is 16 radiation lengths deep and 0.8
nuclear absorption lengths. Being a scintillation detector it measures the
energy deposits by charged particles and due to the high atomic number of both
cesium and iodine it is also an excellent fully absorbing electromagnetic
calorimeter for the expected photon energies (see Fig. 12). For charged
hadrons the energy resolution is also very good but the likelihood for nuclear
reactions in the material for particles with long range into the CsI is rather
high. If no nuclear interaction takes place the CsI thickness allows stopping
400MeV protons and 190MeV charged pions. Evidently, all expected protons will
stop while a large fraction of the charged pions will go through the
calorimeter. The difficulties to measure charged hadron energies in this
regime by stopping them is a fact of nature. The only way around would be to
measure momentum instead by tracing them in a magnetic field. But a magnetic
field cannot be used in this experiment. The kinematic of the event can be
used to constraint the energy of the pions which don’t interact hadronically.
The WASA calorimeter geometry is designed to measure particles originating
from a single point in the center of the detector. But antineutron
annihilation vertices in this experiment will be distributed over the entire
area of the annihilation foil, leading to variations of incident angles that
will have some effect on the resolution. For charged hadrons the angle is
known from the TPC, which can be used for correction and for gammas the energy
measurement is likely to be less affected since it is anyway a sum of
deposited several adjacent modules. For reconstruction of the $\pi^{0}$ mass,
the opening angle between the two gammas will be enough to separate the two
energy deposits.

#### Cosmic ray veto

The only background with sufficient energy to simulate an annihilation signal
is cosmic rays. An active shield of scintillator bars will surround the
experimental setup (see Fig. 11). Events coincident with a charged particle
signal in the veto scintillators will be inhibited. To avoid self inhibition,
an absorber sufficiently thick to stop all charged pions from the annihilation
is needed between the calorimeter and the scintillators. Uninhibited cosmic
events made by neutral particles will be identified by a missing vertex in the
foil. The frequency of fake annihilation events due to cosmic particles (and
other natural backgrounds) will be studied by shutting off the neutron flux at
the neutron port. The scintillator slats will be thick (3 cm). Then minimum
ionizing particles will deposit about 6 MeV passing through the slat, well
above the energy deposit by Compton electrons from natural gamma radiation.
Light readout from the scintillators will be with wavelength shifting fibers,
sensing the light with SiPM.

####  7.2.1 Particle Identification

The identification of charged and neutral pions is strong evidence that an
annihilation event has taken place. Neutral pions are identified by their
invariant mass, calculated from the measured energies of the two final gammas
and the opening angle between them. Determining the opening angle requires
knowledge of the point of origin, which can be estimated through projection of
charged tracks in the TPC. Approximately 98.5% of annihilation events will
have at least 2 charged pions allowing a vertex to be defined. Charged
hadrons, essentially protons and pions in this case, will be identified using
dE/dx measurements in the TPC correlated with the total energy measured in the
calorimeter. The mass difference between pion and proton is large implying
that the energy loss resolution does not have to be strict. The expected
physics also helps because the proton spectrum ends at 200MeV when protons are
far from minimum ionizing while the bulk of charged pions will be minimum
ionizing. In addition negative pions will be stopped in the material and
captured by nuclei and give rise to an additional rather arbitrary energy
signal by nuclear fragments. Stopping positive pions will decay to a muon and
neutrino. The muon will add 4.2 MeV to the energy signal as the time scale of
the decay is 26ns. Subsequent decay of the muon is on a timescale of
microseconds. The energy released by the muon decay will remain unmeasured or
at least separable from the prompt event. Since the rest masses of pions
account for a sizable fraction of energy conservation balance signifying the
annihilation, it is important to identify the pions and important to know
whether the rest mass is included in the measured energy (like it is for the
neutral pions) or not.

####  7.2.2 Trigger and data acquisition system

Since the current WASA data acquisition system was commissioned in 2006, its
architecture is outdated and components lack continuous support. Therefore we
will base the WASA DAQ on a digitization layer containing self-triggering
analog-to-digital converters (ADCs) that continuously digitize all interesting
signals. The ADCs will use a design developed at University of Uppsala for the
PANDA experiment at FAIR [73]. Integrating the cosmic veto and TPC with the
WASA DAQ and event building will be accomplished by FPGA-based Data
Concentrators, based on corresponding modules designed at UU for the BESIII
CGEM readout [74]. Data will be sent over optical links using standard Gigabit
Ethernet physical link protocol. The WASA calorimeter allows several fast
triggering possibilities, based on threshold on measured energy in a module or
cluster of adjacent modules. Even the analog sum of all energies in the
calorimeter can be used for threshold discrimination. So there are many
possibilities to construct a trigger for $\pi^{0}$. Charged hadrons with
sufficient energy may also trigger but there is no harm in that if it is not
caused by cosmic particles. So these shall be rejected as described above. A
$\pi^{0}$ based trigger should find 91.5% of the annihilation events while 8.5
% have no $\pi^{0}$. Matching TPC tracks with their respective hits in the
calorimeter (in case of a trigger) is performed by using the measured trigger
pulse timing in the CsI to set the appropriate time zero for the drift time
measurement in the TPC. This is of course only applicable for particle
trajectories within the geometrical coverage of the detector, which is less
than 100% due to the entrance opening. Seen from the center of the foil the
opening has the half opening angle of about 35∘ ($\sim$1.1sr). The solid angle
coverage is thus up to 85%.

####  7.2.3 Event topology and backgrounds

The antineutron-nucleon annihilation signature is the classic pionic star [75]
i.e. around five pions isotropically produced and with momenta in the
approximate region of 100-500 MeV. The invariant mass goes up to around twice
the neutron mass and is, in practice, lower owing to nuclear scattering
effects [68, 69, 70]. The expected final state configuration can be produced
by neutrons, or other fast beam contaminants, with momenta of
$\mathcal{O}$($100$) MeV interacting with the carbon foil. However, the
arrival time of such fast neutrons at the foil is synchronotised with the
linac proton pulse arrival time on the tungsten target. For a 14Hz repetition
rate and 2.86ms pulse width, an exclusion of around 5% of operating time
suppresses fast neutrons. An irreducible isotropically produced flux of around
$\mathcal{O}$ ($10^{6}$) MeV-scale photons per second is, however, expected
from slow neutron capture on the foil. With around 1000 crystals with a
scintillation decay time of 700ns, an occupancy of less than 1% is expected.
The photons may lead to $\mathcal{O}$($10^{3}$) MeV-scale Compton electrons
per second entering the TPC after photon interactions in the beampipe. This is
a negligible background for signal candidates, for which tracks will be
matched calorimeter with a timing resolution of $\mathcal{O}$($10$) ns. As was
done in the ILL experiment, capture in the beampipe and other beam-related
infrastructure can be suppressed with 6Li neutron poison from which low energy
alpha particles are emitted which are stopped in the beampipe. The influence
of MeV-scale neutrons entering the detector can be studied with data and, if
necessary, can be suppressed with a timing cut relative to the ESS clock.
Complete measurements of beam-induced pile-up will be made with early data.

The major background is, as for the ILL experiment, expected to arise from
cosmic rays. As was done at that experiment, complete suppression is expected.
A number of selections can be made on sensitive variables to capture the
antineutron star characteristic, including final state invariant mass and
sphericity. Unlike the ILL experiment, the WASA detector provides neutral pion
tagging and reconstruction (a mass resolution of $\sim 30$ MeV can achieved
[76]) to be used as a primary selection tool. Similarly, the TPC for this
search provides precision 3-D tracking and would be expected to exceed the
vertex resolution achieved at the ILL (with limited streamer tubes). While the
full signal-to-background optimisation for WASA-based detector will be done as
part of this work, the capabilities of the individual detector components
imply a stronger performance. An efficiency of at least 50% with full
background suggestion is thus expected. As shown for the NNBAR Conceptual
Design Report [61], the use of a more advanced detector than that available at
the ILL, particularly, with respect to calorimetry, together with more
advanced analysis techniques, such as the use of machine learning, substantial
gains in efficiency can be expected.

###  7.3 Other possibilities for the annihilation detector

In the previous section, we focused on the possibility of using the WASA
calorimeter to enable the HIBEAM program with a cost-effective option.
However, the possibility of using a larger detector becomes extremely
interesting, particularly in the case of the free neutron to antineutron
oscillation option (see Section). For a larger radius annihilation detector
than the WASA-based option, a design based on the detector concept developed
for NNBAR [61] is being considered. This design incorporates a scintillator
and lead-glass calorimeter along with a TPC. As discussed in Section 7.2.3,
this technology with developments in analysis techniques can potentially
improvements by up to and beyond a factor 1.5 compared with the ILL
experiment.

###  7.4 Summary

It has been nearly three decades since the last search for neutron to
antineutron oscillations, as pursued at ILL [6]. The HIBEAM project holds the
potential to significantly extending the sensitivity by an order of magnitude.
Similar gains are expected for sterile neutron searches. It is worth
emphasizing that only ESS has the capability to achieve this. Reactor sources
are unable to provide a higher neutron flux than what has already been
achieved, and many are expected to shut down in the near future. Spallation
facilities like JPARC and SNS lack a neutron extraction system comparable to
the one currently under construction at ESS, as well as a flight path of
similar quality. ESS stands out as the sole viable option. Further, the HIBEAM
program represents pioneering searches made, for the first time, at a
spallation source, providing invaluable insights into background conditions.
It serves as a crucial and essential pilot experiment paving the way for the
full-scale NNBAR experiment.

##  8 Acknowledgements

D. Milstead, V. Santoro, B. Meirose, T. Nilsson, S. Silverstein, and M. Wolke
gratefully acknowledge support from the Council for Swedish Research
Infrastructure for the Swedish Research Council for the grant ´HIBEAM pre-
studies’.

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