EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2022-091 LHCb-PAPER-2022-006

Measurement of antiproton production from antihyperon decays in ${p}{\rm He}$
collisions at $\sqrt{s_{\scriptscriptstyle\rm NN}}=110$ GeV

LHCb collaboration

The interpretation of cosmic antiproton flux measurements from space-borne
experiments is currently limited by the knowledge of the antiproton production
cross-section in collisions between primary cosmic rays and the interstellar
medium. Using collisions of protons with an energy of $6.5$ TeV incident on
helium nuclei at rest in the proximity of the interaction region of the LHCb
experiment, the ratio of antiprotons originating from antihyperon decays to
prompt production is measured for antiproton momenta between $12$ and
$110\text{\,Ge\kern-1.00006ptV\\!/}c$. The dominant antihyperon contribution,
namely ${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays from promptly
produced $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$
particles, is also exclusively measured. The results complement the
measurement of prompt antiproton production obtained from the same data
sample. At the energy scale of this measurement, the antihyperon contributions
to antiproton production are observed to be significantly larger than
predictions of commonly used hadronic production models.

Submitted to Eur. Phys. J. C

© 2024 CERN for the benefit of the LHCb collaboration. CC BY 4.0 licence.

##  1 Introduction

In recent years, the space-borne experiments PAMELA [1] and AMS-02 [2] greatly
improved measurements of the abundance of the antiproton, $\overline{p}$,
component in cosmic rays, which is sensitive to a possible dark matter
contribution [3, 4, 5]. In the 10–100 GeV $\overline{p}$ energy range, the
interpretation of their measurements requires accurate knowledge of the
$\overline{p}$ production cross-sections in the spallation of cosmic rays in
the interstellar medium [6], which is mainly composed of hydrogen and helium.
The LHCb experiment has the unique ability to study collisions of the LHC
beams with fixed gaseous targets, including helium, reaching the
$100\text{\,Ge\kern-1.00006ptV}$ scale for the nucleon-nucleon centre-of-mass
energy, $\sqrt{s_{\scriptscriptstyle\rm NN}}$, unprecedented for fixed-target
experiments [7]. Using a sample of proton-helium (${p}{\rm He}$) collisions
collected in 2016, the production of prompt antiprotons directly in the
collisions or through decays of excited states was measured by the LHCb
collaboration [8]. These results were the first to use a helium target, and,
covering an energy scale where significant violation of Feynman scaling [9]
occurs, contributed to a better modelling of the secondary $\overline{p}$
cosmic flux [10, 11, 4].

The uncertainties on $\overline{p}$ production from weak decays still limit
the interpretation of cosmic $\overline{p}$ data [10]. The largest of these
contributions is due to antineutron decays, which cannot be directly observed
in LHCb but can be estimated from the antiproton measurements and the
assumption of isospin symmetry. Another significant contribution, which is
less constrained theoretically, comes from decays of antihyperons, $\kern
1.79993pt\overline{\kern-1.79993ptH}$. Antiprotons produced in this way are
referred to as detached in the following as they can experimentally be
distinguished from prompt antiprotons in the LHCb experiment by the separation
between their production vertex and the primary ${p}{\rm He}$ collision vertex
(PV).

This paper reports a determination of the ratio

$R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}\equiv\dfrac{\sigma({p}{\rm
He}\rightarrow\kern
1.79993pt\overline{\kern-1.79993ptH}X\rightarrow{\overline{p}}X)}{\sigma({p}{\rm
He}\rightarrow{\overline{p}}_{\text{prompt}}X)}$ (1)

of detached to prompt antiprotons in ${p}{\rm He}$ collisions at
$\sqrt{s_{\scriptscriptstyle\rm NN}}=110\text{\,Ge\kern-1.00006ptV}$ with
momentum, $p$, ranging from $12$ to $110$$\text{\,Ge\kern-1.00006ptV\\!/}c$
and transverse momentum, $p_{\mathrm{T}}$, between $0.4$ and
$4$$\text{\,Ge\kern-1.00006ptV\\!/}c$, where X stands for any arbitrary set of
unreconstructed particles. Two approaches to the measurement, presented in
Secs. 4 and 5, are followed as described below.

The dominant process, namely ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ with promptly produced
$\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ particles, is
measured relying only on the secondary vertex displacement from the PV and on
the decay kinematics. The ratio

$R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}\equiv\dfrac{\sigma({p}{\rm He}\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}X\rightarrow{\overline{p}}{{\pi}^{+}}X)}{\sigma({p}{\rm
He}\\!\rightarrow{\overline{p}}_{\text{prompt}}X)}$ (2)

is then determined using the prompt production result [8], obtained from the
same dataset.

In the second approach, an inclusive measurement of detached antiprotons is
performed by exploiting the particle identification (PID) capabilities of the
LHCb detector. Prompt and detached $\overline{p}$ are distinguished by the
minimum distance of their reconstructed track to the PV, the impact parameter
(IP). As $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}/R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ is predicted
more reliably than the single ratios, the consistency of these two
complementary approaches is verified.

The available measurements of the $R_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ ratio, though
affected by large uncertainties, hint at a significant increase of this ratio
for $\sqrt{s_{\scriptscriptstyle\rm NN}}>100\text{\,Ge\kern-1.00006ptV}$ [10].
The LHCb fixed-target configuration is capable of exploring the energy scale
where the $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}$ enhancement occurs. The contribution to $\overline{p}$
production from charm and beauty hadron decays is estimated to be three orders
of magnitude smaller than the prompt one, using the measured
${c}{\overline{c}}$ cross-section in the same fixed-target configuration at
LHCb [12] and the known charm branching fractions to baryons [13]. This is
negligible compared to the accuracy of this measurement.

##  2 The LHCb detector and its fixed-target operation

The LHCb detector [14, 15] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector (VELO) surrounding the
proton-proton ($p$ $p$) interaction region [16], a large-area silicon-strip
detector located upstream of a dipole magnet with a bending power of about 4
Tm, and three stations of silicon-strip detectors and straw drift tubes [17]
placed downstream of the magnet. The tracking system provides a measurement of
the momentum of charged particles with a relative uncertainty that varies from
0.5% at low momentum to 1.0% at 200$\text{\,Ge\kern-1.00006ptV\\!/}c$. The IP
is measured with a resolution of $(15+29/p_{\mathrm{T}})\,\upmu\text{m}$,
where $p_{\mathrm{T}}$ is measured in $\text{\,Ge\kern-1.00006ptV\\!/}c$.
Different types of charged hadrons are distinguished by using information from
two ring-imaging Cherenkov (RICH) detectors [18], whose acceptance and
performance define the $\overline{p}$ kinematic range accessible to this
study. The first RICH detector has an inner acceptance limited to $\eta<4.4$
and is used to identify antiprotons with momenta between $12$ and
$60\text{\,Ge\kern-1.00006ptV\\!/}c$. The second RICH detector, whose
Cherenkov threshold for protons is $30\text{\,Ge\kern-1.00006ptV\\!/}c$,
covers the range $3<\eta<5$ and is used for antiproton momenta up to
$110\text{\,Ge\kern-1.00006ptV\\!/}c$. The scintillating-pad detector (SPD) of
the calorimeter system is also used in this study. The SMOG (System for
Measuring Overlap with Gas) system [19, 20] enables the injection of noble
gases with pressure of $\mathcal{O}(10^{-7})$ mbar in the beam pipe section
crossing the VELO, allowing LHCb to be operated as a fixed-target experiment.
The online event selection is performed by a trigger [21], which consists of a
hardware stage, requiring any activity in the SPD detector, and a software
stage asking for at least one reconstructed track in the VELO. To avoid
background from $p$ $p$ collisions, fixed-target events are acquired only when
a bunch in the beam pointing toward LHCb crosses the nominal interaction
region without a corresponding colliding bunch in the other beam.

##  3 Data sample and simulation

This measurement is performed on data specifically collected for
$\overline{p}$ production studies in May 2016. Helium gas was injected when
the two beams circulating in the LHC accelerator consisted of proton bunches
separated by at least 1 $\,\upmu\text{s}$, 40 times the nominal value. In this
configuration, spurious $p$ $p$ collisions are suppressed. A sample of
${p}{\rm He}$ collisions with a $6.5$ TeV proton-beam energy
($\sqrt{s_{\scriptscriptstyle\rm NN}}=110.5$ GeV) and corresponding to an
integrated luminosity of about $0.5\text{\,nb}^{-1}$ was collected [8].

Selected events are required to have a reconstructed PV within the fiducial
region $-700<z<+100$ mm, where the $z$ axis is along the beam direction and
$z=0$ mm corresponds to the LHCb nominal collision point in the central part
of the VELO. The fiducial region is chosen to achieve a high efficiency for PV
reconstruction in fixed-target collisions and a significant probability that
antihyperon decays occur within the VELO. Antiproton candidates are
reconstructed in the full tracking system exploiting the excellent $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ invariant-mass
resolution and IP determination. The PV position is required to be compatible
with the beam profile and events must have fewer than 5 tracks reconstructed
in the VELO with negative pseudorapidity. This selection suppresses to a
negligible level the background from interactions with material, decays, and
particle showers produced in beam-gas collisions occurring upstream of the
VELO. A sample of $33.7$ million reconstructed ${p}{\rm He}$ collisions
satisfying these requirements is obtained from the data.

Simulated data samples of ${p}{\rm He}$ collisions are produced with the Epos-
lhc generator [22]. The interaction of the generated particles with the
detector, and its response, are implemented by using the Geant4 toolkit [23,
*Agostinelli:2002hh] as described in Ref. [25]. The collisions are uniformly
distributed along $z$ in the range $-1000<z<+300$ mm, wide enough to cover the
fiducial region. When estimating efficiencies, a $z$-dependent weight is
applied to simulated events to account for the measured gas pressure
variation.

This study uses a sample of unbiased simulated inelastic collisions and
several $\overline{p}$-enriched samples, where the simulation of the detector
response is performed only if the event generated by Epos-lhc contains a
suitable $\overline{p}$ candidate. In the sample used for the inclusive
analysis, events must include at least one $\overline{p}$ with
$p_{\mathrm{T}}>0.3\text{\,Ge\kern-1.00006ptV\\!/}c$ and $1.9<\eta<5.4$. In
the sample used for the exclusive analysis, the antiproton must also come from
a $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decay
occurring within the acceptance of the VELO. To study the cascade baryon
contribution, a sample where the $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decay follows from a
${{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}}\\!\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{{\pi}^{+}}$ decay is
also simulated.

##  4 Exclusive $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}$ measurement

About 70% [26] of the detached antiprotons are expected to originate from
decays of promptly produced $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}$ baryons and can be selected in the LHCb detector by exploiting
the detached decay vertex and the invariant-mass resolution. The decay
kinematics allow the antiproton to be identified from the charge and the
asymmetry of the longitudinal momenta of the final-state particles with
respect to the $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}$ flight direction ($p_{\text{L}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$),

$\alpha_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}\equiv\dfrac{p_{\text{L}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}({{\pi}^{+}})-p_{\text{L}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}({\overline{p}})}{p_{\text{L}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}({{\pi}^{+}})+p_{\text{L}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}({\overline{p}})},$
(3)

which is always negative for $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decays [27].
Therefore, the RICH detectors are not used in this approach. In order to
minimise systematic uncertainties in the measurement of $R_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$, the selection
follows as much as possible that used for the prompt measurement [8]. In
particular, the same fiducial volume, where the PV reconstruction efficiency
cancels in the ratio, and the same kinematic region for the $\overline{p}$
candidate, $12<p<110$$\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$0.4<p_{\mathrm{T}}<4$$\text{\,Ge\kern-1.00006ptV\\!/}c$, are required. The
analysis is performed in intervals of $p$ and $p_{\mathrm{T}}$. These
intervals are aligned with those used in the prompt measurement, except that
some are merged to improve the statistical accuracy.

###  4.1 Selection and invariant-mass fit

Table 1:  Selection requirements for ${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays. Symbols are defined in the text. Detector acceptance | $2<\eta({\overline{p}})<5$
---|---
$2<\eta({{\pi}^{+}})<5.5$
$2<\eta({\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}})<5.5;~{}p_{\mathrm{T}}({\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}})>0.3\text{\,Ge\kern-1.00006ptV\\!/}c$
Decay geometry | IP($\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$) $<5$ mm; $\chi^{2}_{\text{DOCA}}$ $<$ 10
$\log[\chi^{2}_{\text{IP}}({\overline{p}})]>1$;
$\log[\chi^{2}_{\text{IP}}({{\pi}^{+}})]>2$
$\mathcal{F}_{\text{IP}}>1.5;~{}\mathcal{F}_{\text{$\chi^{2}_{\text{IP}}$}}>4$
${K}^{0}_{\mathrm{S}}$ veto |  $M_{{p}\rightarrow\pi}<490$ or $M_{{p}\rightarrow\pi}>511\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
Armenteros-Podolanski | $\Big{|}\Big{(}\frac{\alpha_{{\kern 0.89996pt\overline{\kern-0.89996pt\mathchar 28931\relax}}}+0.69}{0.18}\Big{)}^{2}+\Big{(}\frac{p_{\text{T}{\kern 0.89996pt\overline{\kern-0.89996pt\mathchar 28931\relax}}}({{\pi}^{+}})}{100.4\text{\,Me\kern-0.70004ptV\\!/}c}\Big{)}^{2}-1\Big{|}<0.39$

The $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decay
candidates are reconstructed from two oppositely charged tracks, which
comprise segments in the VELO and in the downstream tracking stations, have a
good fit quality and are incompatible with being produced at the PV. The two-
track combinations are selected only if their distance of closest approach is
compatible with zero using a $\chi^{2}$ test ($\chi^{2}_{\text{DOCA}}$).
Following previous $\mathchar 28931\relax$ production studies in LHCb [28],
large discrimination against combinatorial background is obtained by combining
the IP information of the $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}$ and the final-state particles into the linear discriminant

$\mathcal{F}_{\text{IP}}\equiv\log\left(\frac{\text{IP}({\overline{p}})}{1\text{\,mm}}\right)+\log\left(\frac{\text{IP}({{\pi}^{+}})}{1\text{\,mm}}\right)-\log\left(\frac{\text{IP}({\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}})}{1\text{\,mm}}\right).$ (4)

To take into account the uncertainty on their measurements, a second
discriminant $\mathcal{F}_{\text{$\chi^{2}_{\text{IP}}$}}$ is constructed by
replacing IP in Eq. (4) with the $\chi^{2}_{\text{IP}}$ variable, defined as
the difference in the vertex-fit $\chi^{2}$ of the PV reconstructed with and
without the track(s) under consideration. To veto
${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}$ decays, the
misreconstructed invariant-mass $M_{{p}\rightarrow\pi}$, obtained by assigning
the pion mass to both final-state particles, is required to be incompatible
with the ${K}^{0}_{\mathrm{S}}$ mass. Finally, a requirement on the
Armenteros-Podolanski plane [27] $\left(\alpha_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}},\,p_{\text{T}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}({{\pi}^{+}})\right)$, where $p_{\text{T}{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ is the transverse
momentum with respect to the $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ direction, is used.
The selection requirements are listed in Table 1.

The purity of the selected sample is above $90\%$ in the unbiased simulation.
To subtract the residual background, the invariant-mass distribution of the
$\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ candidates is
fitted with the sum of one Voigtian [29] and two Gaussian functions for the
signal and a second-order polynomial for the background. This model, validated
with simulation, takes into account the bias to the background distribution
from the Armenteros-Podolanski plot requirement and is able to describe the
data in all kinematic intervals. The invariant-mass distribution for selected
${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ candidates is shown in Fig.
1 together with a fit integrated over all $p$ and $p_{\mathrm{T}}$ intervals,
which results in a yield of $(50.7\pm 0.3)\cdot 10^{3}$ ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays.

Figure 1: Invariant-mass distribution for the ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ candidates selected in the
${p}{\rm He}$ data. The fit model is overlaid on the data.

###  4.2 Tracking efficiency

The yields of the selected candidates in each kinematic interval are corrected
for the total reconstruction and selection efficiencies. These are determined
as the ratio of signal yields obtained by the invariant-mass fit of the $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ candidates in the
$\overline{p}$-enriched simulated sample to the number of actual candidates
generated by the Epos-lhc model in the same interval of $p$ and
$p_{\mathrm{T}}$. With this procedure, the efficiency takes into account the
resolution effects resulting in migration across kinematic intervals. The
largest inefficiency comes from decays occurring downstream of the VELO and
can be accurately predicted. For the upstream decays, the average track
reconstruction efficiency is determined in simulation to be $(95.84\pm
0.04)\%$ for the antiprotons and $(85.40\pm 0.06)\%$ for the pions, which tend
to have a lower momentum. The quoted uncertainties are only due to the finite
simulated sample size. These efficiencies are corrected by factors determined
from calibration samples in $p$ $p$ data, which are consistent with unity in
all kinematic intervals within their systematic uncertainty of $0.8\%$ [30].

As illustrated in Fig. 2, the tracks considered in this study exhibit a
different topology, notably in the VELO, with respect to the prompt tracks
from $p$ $p$ collisions used for calibration, because of the larger spread of
the fixed-target collision position and the long $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ flight distance.

Figure 2: Normalised distributions of the production vertex $z$ coordinate for
simulated prompt and detached $\overline{p}$ in ${p}{\rm He}$ collisions and
for prompt $\overline{p}$ in simulated $p$ $p$ collisions in the kinematic
range explored in this paper. For ${p}{\rm He}$ collisions, all antiprotons
originate in the $-100<z<700$ mm PV fiducial region.

The validation of the VELO tracking efficiency is therefore extended using
partially reconstructed ${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decay candidates in the
${p}{\rm He}$ collision sample, where the candidate $\overline{p}$ is
reconstructed in the tracking stations upstream and downstream of the magnet
but ignoring the information from the VELO. To take into account the degraded
resolution of the decay vertex, the selection is loosened by requiring
$\mathcal{F}_{\text{IP}}>1$ and
$\mathcal{F}_{\text{$\chi^{2}_{\text{IP}}$}}>3$, while the pion, reconstructed
using the whole tracking system, is required to be identified by the RICH
detectors to compensate for the larger background. The VELO tracking
efficiency is estimated from the fraction of candidates in this sample where
the partially reconstructed track satisfies the quality requirements for a
fully reconstructed track when including the information from the VELO. The
VELO efficiencies measured in data and simulation with the same analysis are
compared in Fig. 3, notably as a function of the $\overline{p}$ production
vertex position. No significant differences are observed.

Figure 3: VELO tracking efficiency for $\overline{p}$ in ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays as a function of
(top left) the particle momentum, (top right) the transverse momentum, (bottom
left) the production vertex $z$ coordinate and (bottom right) the number of
reconstructed long tracks in the event.

The uncertainty on the $\overline{p}$ reconstruction efficiency in each
kinematic interval is expected to cancel in the $R_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ ratio. Therefore,
a 0.8% systematic uncertainty on $R_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ from the
${\pi}^{+}$ tracking efficiency is assigned.

###  4.3 Other systematic uncertainties

A fit model uncertainty is evaluated by repeating the fit with an additional
Gaussian component in the signal model or with an Argus function [31] for the
background model. In both cases, the variation of the result is smaller than
the statistical uncertainty in both data and simulation. The online selection
requirements are found to be fully efficient in a control sample with randomly
selected events. Each of the offline selection requirements listed in Table 1
has an efficiency larger than 90%, with a total selection efficiency of 70%.
The largest inefficiencies are attributed to the requirements on
$\mathcal{F}_{\text{IP}}$, $\mathcal{F}_{\text{$\chi^{2}_{\text{IP}}$}}$ and
$M_{{p}\rightarrow\pi}$. The normalised distributions of the two $\mathcal{F}$
discriminants are compared between data and simulated signal. The background
contamination is statistically subtracted from the data by modelling the
$\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ invariant-
mass distributions and by applying the sPlot technique [32] with
$m({\overline{p}}{{\pi}^{+}})$ as discriminating variable. The efficiencies of
the requirements in Table 1 are measured on the resulting distributions and
the difference between data and simulation, amounting to 1%, is assigned as
systematic uncertainty. As a further cross-check of the reliability of the
simulation in the wide fiducial region for fixed-target collisions, the
analysis is repeated in four equally populated intervals of the PV $z$
position. The efficiency-corrected signal yields are found to agree within the
statistical uncertainties. To check that the $\overline{p}$-enriched simulated
sample does not bias the efficiency estimation, a simulated sample with a
looser $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$
selection is used. The total signal efficiencies are found to agree in all
kinematic intervals.

###  4.4 Results

The ratio $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}$ is determined in each kinematic interval from the measured
yield $N_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$
of ${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays, the total
efficiency $\epsilon_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}$ and the corresponding quantities for prompt $\overline{p}$
production [8] as

$R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}=\dfrac{N_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}}{N_{\text{{$\overline{p}$}}}}\dfrac{\epsilon_{\text{{$\overline{p}$}}}}{\epsilon_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}}.$ (5)

The $N_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$
yields determined from the fits to the $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ invariant-mass
distributions are corrected by $0.6\%$ to account for the contribution from
collisions on the residual gas of the LHC vacuum contaminating the helium
target, as estimated in Ref. [8]. The related uncertainty is expected to
cancel in the ratio. All significant sources of systematic uncertainty on the
$R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ ratio
are listed in Table 2. The leading contributions relate to the particle
identification of prompt antiprotons and to the limited size of the produced
$\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ sample. The
$R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ results
are illustrated in Fig. 4 and reported in Appendix A for the kinematic
intervals that are common to this and the prompt antiproton production
analysis. The results as a function of $p$ ($p_{\mathrm{T}}$), integrated over
the $0.55<p_{\mathrm{T}}<1.2$$\text{\,Ge\kern-1.00006ptV\\!/}c$
($12<p<50.5$$\text{\,Ge\kern-1.00006ptV\\!/}c$) region, are shown in Fig. 5
and compared to widely used hadronic collision models included in the Crmc
package [26]. The data indicate that all considered generators significantly
underestimate the $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}$ contribution to the $\overline{p}$ production.

Table 2: Relative uncertainties on the $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ measurement. Particle identification ($N_{\text{{$\overline{p}$}}}$) |  $0\%-36\%$ $(<5\%$ for most intervals)
---|---
Statistical uncertainty ($N_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$) |  $2.2\%-11\%$ $(<4\%$ for most intervals)
Statistical uncertainty ($N_{\text{{$\overline{p}$}}}$) |  $0.5\%-11\%$ $(<2\%$ for most intervals)
Simulated sample size ($\epsilon_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$) |  $1.8\%-4.1\%$ $(<2\%$ for most intervals)
Simulated sample size ($\epsilon_{\text{{$\overline{p}$}}}$) |  $0.4\%-11\%$ $(<2\%$ for most intervals)
Background subtraction ($N_{\text{{$\overline{p}$}}}$) | $1.1\%$
Selection efficiency ($\epsilon_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$) | $1\%$
Tracking efficiency for ${\pi}^{+}$ ($\epsilon_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$) | $0.8\%$
Figure 4:  Measured $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}$ in each of the considered $p$ and $p_{\mathrm{T}}$ intervals.

Figure 5: Measured $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}$ as a function of (top) the $\overline{p}$ momentum for
$0.55<p_{\mathrm{T}}<1.2$$\text{\,Ge\kern-1.00006ptV\\!/}c$ and (bottom) the
$\overline{p}$ transverse momentum for
$12<p<50.5$$\text{\,Ge\kern-1.00006ptV\\!/}c$. The measurement is compared to
the predictions, in the same kinematic regions, from the Epos 1.99 [33], Epos-
lhc [22], Hijing 1.38 [34] and Pythia 6 [35] models, included in the Crmc
package [26].

##  5 Inclusive $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ measurement

An alternative inclusive approach to the measurement of the detached
$\overline{p}$ yield relies on the PID capabilities of the RICH detectors and
on the IP resolution of the VELO, rather than on the reconstruction of the
$\kern 1.79993pt\overline{\kern-1.79993ptH}$ decays. In this second analysis,
a high-purity $\overline{p}$ sample is selected through a tight PID
requirement. Prompt and detached antiprotons are statistically resolved
through a template fit to the distribution of the $\chi^{2}_{\text{IP}}$
variable. Figure 6 shows the $\log(\chi^{2}_{\text{IP}})$ distribution for all
simulated $\overline{p}$ in the $\overline{p}$-enriched sample. Three
contributions can be clearly distinguished, mainly corresponding to prompt,
detached, and antiprotons produced in secondary collisions with the detector
material. A non-Gaussian tail of the prompt distribution, extending towards
the detached $\overline{p}$ region, is attributed to scattering in the
material separating the primary LHC vacuum and the VELO, as further discussed
in Section 5.2.

Figure 6: Distributions of the $\log(\chi^{2}_{\text{IP}})$ variable for all
simulated antiprotons in the $\overline{p}$-enriched simulated sample. The
contributions from prompt, detached and antiprotons produced in the detector
material are separately shown.

Antiproton candidates are selected from negatively charged tracks
reconstructed with a high-quality fit including segments in the VELO and in
the tracking stations upstream and downstream of the magnet. The analysis is
performed in the ($p$, $p_{\mathrm{T}}$) plane, with ten momentum intervals
between $12$ and $110$$\text{\,Ge\kern-1.00006ptV\\!/}c$ and five for
$p_{\mathrm{T}}$ between $0.4$ and $4\text{\,Ge\kern-1.00006ptV\\!/}c$. The
$\overline{p}$ identification is based on two quantities determined from the
response of the RICH detectors: the difference between the logarithm of the
likelihood of the proton and pion hypotheses, $\mathrm{DLL}_{{p}{\pi}}$, and
that between the proton and kaon hypotheses, $\mathrm{DLL}_{{p}{K}}$ [18]. A
tight selection is used, requiring $\mathrm{DLL}_{{p}{\pi}}>20$ and
$\mathrm{DLL}_{{p}{K}}>10$, to suppress contamination from misidentified
particles. Kinematic intervals at the boundaries of the RICH capabilities,
where the $\overline{p}$ purity predicted in simulation is below 80%, are
removed from the analysis. The overall predicted purity of the resulting
$\overline{p}$ sample is 97%. The numbers of reconstructed prompt and detached
$\overline{p}$, $N_{\text{prompt}}$ and $N_{\text{det}}$, are determined from
the fit and then corrected for the corresponding efficiencies as estimated
from simulation. These are then used to calculate

$R_{\kern
1.25995pt\overline{\kern-1.25995ptH}}=\dfrac{N_{\text{det}}}{N_{\text{prompt}}}\dfrac{\epsilon_{\text{prompt}}}{\epsilon_{\text{det}}}.$
(6)

Efficiencies are determined from the simulation as the ratio between the
number of selected candidates in each interval of reconstructed $p$ and
$p_{\mathrm{T}}$, and the number generated by the Epos-lhc model in the same
kinematic interval.

###  5.1 Template fit

Templates for the $\chi^{2}_{\text{IP}}$ distributions are drawn from the
$\overline{p}$-enriched simulation in each kinematic interval for different
categories of candidates: three templates for the prompt, detached and
secondary $\overline{p}$ and four templates for misidentified particles,
consisting of pions, kaons, electrons and fake tracks. Smoothed curves are
obtained through a parametrisation of the probability density functions as a
sum of Gaussian functions, whose parameters are obtained from a fit to the
simulated event distributions, as illustrated in Fig. 7. For each template the
number of Gaussian components, whose parameters are initialized to random
values in the appropriate range, is increased, up to 15, until a good fit is
obtained.

Figure 7: Distributions of $\log(\chi^{2}_{\text{IP}})$ for (top) prompt and
(bottom) detached antiprotons in the $\overline{p}$-enriched simulated sample
for a kinematic interval in the central region of the considered phase-space.
The fit model is overlaid on the data.

The template fits are performed with the fractions of the three $\overline{p}$
components left free to float, while the small contributions from
misidentified particles are fixed to the values predicted by the unbiased
simulation. The procedure is validated by performing the fit to the unbiased
simulated sample and verifying that the obtained abundance for each of the
three $\overline{p}$ categories agrees with the actual value within the
statistical uncertainties. The fit is then applied to the data. Figure 8 shows
the fit result integrated over all kinematic intervals. The raw ratio of
detached to prompt reconstructed candidates is found to be
$R_{\text{raw}}\equiv N_{\text{det}}/N_{\text{prompt}}=0.1247\pm 0.0005$,
where the uncertainty is statistical only. This is significantly larger than
the value predicted by the unbiased simulated sample, $0.0848\pm 0.0014$,
confirming a sizeable underestimation of the antihyperon component by the
Epos-lhc generator.

Figure 8: Distributions of the $\log(\chi^{2}_{\text{IP}})$ variable in the
data sample integrated over all kinematic intervals. The fit model is overlaid
on the data.

###  5.2 Scattered prompt antiprotons

Figure 6 shows that a significant fraction of simulated prompt $\overline{p}$
candidates are reconstructed with an IP value well above the expected
resolution, compatible with the detached $\overline{p}$ typical values. As
illustrated in Fig. 9, this is due to scattering that may change the track
trajectory of the prompt $\overline{p}$ when the particle crosses the
aluminium foil, shown in Fig. 10, separating the primary LHC vacuum from the
VELO sensor volume. The tail is indeed found to be strongly dependent on the
azimuthal angle $\phi$. The simulation of the material geometry and of the
scattering cross-section is therefore critical to the determination of
$R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$.

Figure 9: Normalised distributions of the prompt $\overline{p}$
$\log(\chi^{2}_{\text{IP}})$ variable in different ranges of the azimuthal
angle $\phi=\text{atan}(p_{y}/p_{x})$. Figure 10: Sketch of the VELO [36],
where the aluminium foils crossed by the particles before entering the VELO
volume is visible. The crossed material is maximum for $|\phi|>1$.

A validation using data of the predicted prompt $\overline{p}$ template is
performed by selecting ${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}(1520)\\!\rightarrow{\overline{p}}{{K}^{+}}$ decays. These happen
at the primary interaction vertex and, tagged by the invariant-mass of the
parent particle and by the kaon identification, provide a prompt
$\overline{p}$ sample in data. Since a small sample size of these decays is
selected in the ${p}{\rm He}$ collision sample, the analysis is performed on
the largest fixed-target sample collected during the LHC Run 2, namely a
sample of proton-neon (${p}{\rm Ne}$) collisions with beam energy of 2.5 TeV
acquired in 2017. The $\overline{p}$ candidate is selected with the same
requirements as for the inclusive study, while the tagging kaon must satisfy
$\mathrm{DLL}_{{K}{\pi}}\equiv\mathrm{DLL}_{{p}{\pi}}-\mathrm{DLL}_{{p}{K}}>20,\mathrm{DLL}_{{p}{K}}<0$
and $\log(\chi^{2}_{\text{IP}})<3$ to enforce prompt decays. Events are
weighted according to the $\overline{p}$ transverse momentum and the SPD hit
multiplicity to equalize these distributions with those observed for the
prompt $\overline{p}$ candidates in ${p}{\rm He}$ data. The ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}(1520)\\!\rightarrow{\overline{p}}{{K}^{+}}$ yield is determined
in intervals of the $\overline{p}$ $\log(\chi^{2}_{\text{IP}})$. The
background is subtracted by fitting the ${\overline{p}}{{K}^{+}}$ invariant-
mass distribution with a Voigtian function for the signal and an exponential
function for the background, as illustrated in Fig. 11. The mass resolution
for the signal in each interval is independent, as it degrades for increasing
values of $\chi^{2}_{\text{IP}}$. Figure 12 shows the resulting reconstructed
$\log(\chi^{2}_{\text{IP}})$ distribution for the prompt $\overline{p}$
candidates. A reasonable agreement with the template from simulation is found,
though differences are expected due to the simplification of the material
geometry in the simulation. To estimate the related systematic uncertainty,
the inclusive template fit for the sample integrated over all intervals is
repeated using this template drawn using data for the prompt $\overline{p}$
component. The relative variation of $R_{\text{\text{raw}}}$ is 4.8% and is
assigned as systematic uncertainty.

Figure 11: Invariant-mass distributions for the ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}(1520)\\!\rightarrow{\overline{p}}{{K}^{+}}$ candidates selected
in the ${p}{\rm Ne}$ data within two intervals of the $\overline{p}$
$\log(\chi^{2}_{\text{IP}})$ variable. The fit model is overlaid on the data.
Figure 12: Distributions of the number of signal candidates determined in each
interval of the antiproton $\log(\chi^{2}_{\text{IP}})$ compared to the
prediction of the ${p}{\rm He}$ simulation for selected prompt antiprotons.

###  5.3 Antihyperon decays

The detached $\overline{p}$ efficiency, in particular the fraction of $\kern
1.79993pt\overline{\kern-1.79993ptH}$ decays occurring within the VELO,
strongly depends on the assumed relative production yields of the different
antihyperons contributing to the inclusive $\overline{p}$ yield. The Epos-lhc
model predicts that, in the measured kinematic range, 72% of the
$\overline{p}$ candidates originate from ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays of promptly produced
$\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ particles,
17% from ${{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28934\relax}}}{}^{-}}\\!\rightarrow{\overline{p}}{{\pi}^{0}}$ decays, 11% from
${{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}}\\!\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{{\pi}^{+}}$ and
${{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{0}}\\!\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{{\pi}^{0}}$ cascade
decays, and less than 1% from ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28938\relax}}^{+}$ decays. These
predictions are expected to be accurate within a relative uncertainty of
approximately $20\%$ [37]. The assumed values of ${{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28934\relax}}}{}^{-}}/\kern
1.79993pt\overline{\kern-1.79993ptH}$ and ${{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}^{+}}/{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}$ ratios are verified
with the collision data.

The template fit is expected to have sensitivity to the contribution of
${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28934\relax}}}{}^{-}$
decays, as illustrated in Fig. 13. Indeed, when compared to $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decays, the ${{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar
28934\relax}}}{}^{-}}\\!\rightarrow{\overline{p}}{{\pi}^{0}}$ decay Q-value is
larger and antiprotons show on average a larger IP. The fit is repeated with
two independent detached $\overline{p}$ components: the ${\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28934\relax}}}{}^{-}$ decays and
all other decays. The best fit fraction of ${\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28934\relax}}}{}^{-}$ is larger
than the Epos-lhc prediction by a factor $1.13\pm 0.02$. This correction
factor, compatible with the expected theoretical uncertainty, is applied to
the simulated sample to recompute the efficiency and correct the detached
$\overline{p}$ templates. While the fit results for $R_{\text{raw}}$ change
less than 1%, the variation of $\epsilon_{\text{det}}$ implies a change to
$R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ between $1.2\%$ and $3.8\%$,
depending on the kinematic interval. This is assigned as a systematic
uncertainty on $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ due to the
relative ${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28934\relax}}}{}^{-}$ production.

Figure 13: Distribution of the $\log(\chi^{2}_{\text{IP}})$ variable in the
data sample integrated over all kinematic intervals modelled with independent
components for ${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28934\relax}}}{}^{-}$ decays (labelled as $\overline{p}$ from ${\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28934\relax}}}{}^{-}$) and all
other antihyperon decays ($\overline{p}$ from $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$).

To check the cascade contribution, the ${{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}}\\!\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{{\pi}^{+}}$ yield is
directly measured and compared to the ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ one. Candidates are
selected combining a reconstructed $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decay with a
${\pi}^{+}$ candidate track with a distance of closest approach to the $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ trajectory
compatible with zero. Similarly to the prompt $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ selection, prompt
${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}^{+}$
decays are selected using a linear discriminant:
$\log[\chi^{2}_{\text{IP}}({\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}})]+\log[\chi^{2}_{\text{IP}}({{\pi}^{+}})]-\log[\chi^{2}_{\text{IP}}({{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}^{+}})]>0$. To
minimise the systematic bias in the ${\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}^{+}$/$\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ ratio, the final-
state $\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$
selection follows the same requirements as the prompt $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ candidates, except
that on $\chi^{2}_{\text{IP}}$, and a loose selection is chosen for the
${\pi}^{+}$ candidate, without any PID requirement. The $z$ distribution of
the decays is also equalised, by weighting the prompt $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ candidates to
reproduce the observed distribution of $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ decay vertices from
the reconstructed ${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}$ decays. The invariant-mass distribution of the ${{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}}\\!\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{{\pi}^{+}}$
candidates is displayed in Fig. 14, where the fit to determine the signal
yield is also shown. The fit model, verified on simulation, uses a Voigtian
function for the signal and an exponential function for the background. The
same analysis is performed on the simulated sample and the yield ratio
$\sigma({{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}})/\sigma({\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}})$ is found to be larger in data with respect to the Epos-lhc
model by a factor $1.09\pm 0.09$. This factor is used to weight the relative
production yield of both ${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}$ and ${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{0}$ baryons in the simulation. The related uncertainty
corresponds to a systematic uncertainty on $R_{\kern
1.25995pt\overline{\kern-1.25995ptH}}$ from cascade production, varying
between $0.6\%$ and $0.9\%$, depending on the kinematic interval.

Figure 14: Invariant-mass distribution for the ${{\kern
1.79993pt\overline{\kern-1.79993pt{\mathchar
28932\relax}}}^{+}}\\!\rightarrow{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{{\pi}^{+}}$
candidates selected in the ${p}{\rm He}$ data. The fit model is overlaid on
the data.

###  5.4 Other systematic uncertainties

The fit model uncertainty is estimated by repeating it with the raw binned
distributions as templates and is found, in most intervals, to be below 2%.

Once the probability that antihyperon decays occur within the VELO is taken
into account, the reconstruction and selection efficiencies are expected to
mostly cancel in the $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ ratio.
Residual differences are still expected from the different distributions of
the production vertex position due to the decaying antihyperons flight
distance. The overall tracking efficiency is measured in the simulation as
$(94.85\pm 0.01)\%$ for prompt and $(93.47\pm 0.05)\%$ for detached
antiprotons, with the quoted uncertainties due to the finite simulated sample
size. The small difference is mainly due to the lower average number of hits
in the VELO for the latter. As discussed in Section 4.2, these geometrical
effects are verified to be predicted reliably and no significant systematic
uncertainty is assumed.

A larger bias could be induced by the tight PID selection. In the simulation,
its efficiency is measured to be $(64.90\pm 0.03)\%$ and $(57.74\pm 0.11)\%$
for for prompt and detached antiprotons, respectively. The quoted
uncertainties correspond to the finite simulated sample size. These
predictions are validated using high-purity $\overline{p}$ samples from
${\kern 1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays, where the
antiproton is identified without using the RICH. A large sample of these
decays is selected from the ${p}{\rm Ne}$ collision sample acquired in 2017. A
machine-learning-based approach, documented in Ref. [38], is used to model the
PID response as a function of 12 variables related to the particle trajectory,
its reconstruction quality and the event occupancy. This model, applied to the
simulated events, is able to reproduce the predicted PID efficiency for the
two $\overline{p}$ categories within the statistical uncertainties, which are
lower than 1%. This demonstrates that the predicted difference is due to
geometrical effects and that the RICH response for a given track topology and
detector occupancy is accurately simulated. On the other hand, the RICH
detector response is affected by low-energy background that is not accurately
simulated. For the selected ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\rightarrow{\overline{p}}{{\pi}^{+}}$ decays in the ${p}{\rm He}$
sample, the distributions of RICH hit multiplicities differ from those
predicted in simulation, and the efficiency of the PID requirement is found to
be larger by a relative 8% than the predicted value. When the PID requirement
is loosened to increase its efficiency by this 8% for the detached component,
the $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ value changes by 0.9%,
which is assigned as the systematic uncertainty on the PID selection. The
systematic uncertainties on the predicted fraction of misidentified particles
is also evaluated from this check and its effect on $R_{\kern
1.25995pt\overline{\kern-1.25995ptH}}$ is found to be negligible.

A systematic uncertainty on the assumed longitudinal profile of the gas target
density is assigned from the change of the
$\varepsilon_{\text{det}}/\varepsilon_{\text{prompt}}$ ratio when introducing
the weights to equalize the PV $z$ distribution in data and simulation. It
amounts to less than 0.5% in most kinematic intervals.

###  5.5 Results

Table 3: Relative uncertainties on the $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ measurement.  Prompt $\overline{p}$ template | $4.8\%$
---|---
Statistical uncertainty |  $1.9\%-6.2\%$ $(<2.5\%$ for most intervals)
Template parametrisation |  $0-5.3\%$ $(<2\%$ for most intervals)
Simulated sample size |  $1.5\%-5.8\%$ $(<1.8\%$ for most intervals)
Production of ${\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28934\relax}}}{}^{-}$ | $1.2-3.8\%$
Particle identification | $0.9\%$
Production of $\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}$ | $0.6-0.9\%$
Gas $z$ profile simulation |  $0.1-1.5\%$ $(<0.5\%$ for most intervals)
Figure 15: Measured $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ in each
of the considered $p$ and $p_{\mathrm{T}}$ intervals.

Figure 16: Measured $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ as a
function of (top) the $\overline{p}$ momentum for
$0.4<p_{\mathrm{T}}<4\text{\,Ge\kern-1.00006ptV\\!/}c$ and (bottom) the
$\overline{p}$ transverse momentum for
$12<p<110\text{\,Ge\kern-1.00006ptV\\!/}c$. The measurement is compared to
predictions, in the same kinematic regions, from the Epos 1.99 [33], Epos-lhc
[22], Hijing 1.38 [34], Pythia 6 [35] and Qgsjet-ii04 [39] models, included in
the Crmc package [26].

The results for each kinematic interval are illustrated in Fig. 15 and the
numerical values are provided in Appendix A. Table 3 summarises the
uncertainties in the $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$
measurement. The inclusive results as a function of $p$ or $p_{\mathrm{T}}$,
integrated in the other variable, are shown in Fig. 16. As already observed in
the $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$
measurement, the most commonly used hadronic collision generators are shown to
underestimate the antihyperon contribution to $\overline{p}$ production at
$\sqrt{s_{\scriptscriptstyle\rm NN}}=110\text{\,Ge\kern-1.00006ptV}$.

##  6 Conclusions

Figure 17: Fraction of antiprotons from decays of promptly produced $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ particles to the
total yield of detached antiprotons as a function of (top) their momentum for
$0.55<p_{\mathrm{T}}<1.2\text{\,Ge\kern-1.00006ptV\\!/}c$ and (bottom) their
transverse momentum for $12<p<50.5\text{\,Ge\kern-1.00006ptV\\!/}c$. The data
are compared to the Epos-lhc [22] prediction for this quantity.

The ratio $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar
28931\relax}}}/R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ measured with
the inclusive and exclusive approaches is compared with the Epos-lhc
prediction in Fig. 17. As this ratio is predicted more reliably than the
inclusive detached $\overline{p}$ yield, the good agreement between the
measured and predicted values provides a mutual validation for the results of
the two complementary approaches followed in this paper.

In conclusion, the production of antiprotons from antihyperon decays relative
to the prompt $\overline{p}$ production is measured in the fixed-target
configuration of the LHCb experiment from ${p}{\rm He}$ collisions at
$\sqrt{s_{\scriptscriptstyle\rm NN}}=110\text{\,Ge\kern-1.00006ptV}$. The
results confirm previous findings from colliders [40, 41, 42] for an increased
$\kern 1.79993pt\overline{\kern-1.79993ptH}$ contribution with respect to the
$\sqrt{s_{\scriptscriptstyle\rm NN}}~{}\sim~{}10\text{\,Ge\kern-1.00006ptV}$
scale probed in past fixed-target experiments and indicate a sizeable
underestimation of this contribution in most hadronic production models used
in cosmic ray physics. A significant dependence of $R_{\kern
1.25995pt\overline{\kern-1.25995ptH}}$ on the $\overline{p}$ momentum is
observed. This effect is not usually considered in the modelling of the
secondary $\overline{p}$ component in cosmic rays, where $R_{\kern
1.25995pt\overline{\kern-1.25995ptH}}$ is assumed to depend only on
$\sqrt{s_{\scriptscriptstyle\rm NN}}$ [10, 11]. These results are thus
expected to provide a valuable input to improve the predictions for the
secondary $\overline{p}$ cosmic flux.

##  Appendix A Numerical results

The numerical results for the measurements of the $R_{{\kern
1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ and $R_{\kern
1.25995pt\overline{\kern-1.25995ptH}}$ ratios, presented in Secs. 4 and 5, are
reported in Table 4 in intervals of the antiproton momentum and transverse
momentum.

Table 4: Measured $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ and
$R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ ratios
in intervals of the antiproton momentum and transverse momentum, measured in
$\text{\,Ge\kern-1.00006ptV\\!/}c$ units. The average momentum and transverse
momentum, as predicted by the Epos-lhc generator for prompt antiprotons, are
also listed for each interval in $\text{\,Ge\kern-1.00006ptV\\!/}c$ units. The
uncertainty is split into an uncorrelated component, denoted with
$\delta_{\text{uncorr}}$, and a component that is fully correlated among the
kinematic intervals, denoted $\delta_{\text{corr}}$.

$p$${}^{\text{min}}$ | $\langle p\rangle$ |  $p$${}^{\text{max}}$ | $p_{\mathrm{T}}^{\text{min}}$ | $\langle p_{\mathrm{T}}\rangle$ | $p_{\mathrm{T}}^{\text{max}}$ | $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ | $\delta_{\text{uncorr}}$ | $\delta_{\text{corr}}$ | $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ | $\delta_{\text{uncorr}}$ | $\delta_{\text{corr}}$
---|---|---|---|---|---|---|---|---|---|---|---
12.0 | 12.98 | 14.0 | 0.40 | 0.47 | 0.55 | 0.477 | 0.013 | 0.025 | — | — | —
12.0 | 12.99 | 14.0 | 0.55 | 0.62 | 0.70 | 0.433 | 0.012 | 0.023 | 0.429 | 0.019 | 0.022
12.0 | 12.99 | 14.0 | 0.70 | 0.79 | 0.90 | 0.371 | 0.012 | 0.020 | 0.395 | 0.036 | 0.019
12.0 | 12.99 | 14.0 | 0.90 | 1.02 | 1.20 | 0.337 | 0.016 | 0.019 | 0.377 | 0.042 | 0.013
12.0 | 13.00 | 14.0 | 1.20 | 1.47 | 4.00 | 0.303 | 0.026 | 0.018 | — | — | —
14.0 | 15.08 | 16.2 | 0.40 | 0.47 | 0.55 | 0.546 | 0.018 | 0.029 | — | — | —
14.0 | 15.09 | 16.2 | 0.55 | 0.62 | 0.70 | 0.423 | 0.011 | 0.022 | 0.370 | 0.017 | 0.019
14.0 | 15.09 | 16.2 | 0.70 | 0.79 | 0.90 | 0.387 | 0.010 | 0.021 | 0.317 | 0.012 | 0.016
14.0 | 15.09 | 16.2 | 0.90 | 1.02 | 1.20 | 0.383 | 0.014 | 0.022 | 0.290 | 0.018 | 0.011
14.0 | 15.10 | 16.2 | 1.20 | 1.48 | 4.00 | 0.311 | 0.022 | 0.019 | — | — | —
16.2 | 17.43 | 18.7 | 0.40 | 0.47 | 0.55 | 0.518 | 0.022 | 0.027 | — | — | —
16.2 | 17.43 | 18.7 | 0.55 | 0.62 | 0.70 | 0.442 | 0.012 | 0.024 | 0.395 | 0.018 | 0.019
16.2 | 17.43 | 18.7 | 0.70 | 0.79 | 0.90 | 0.412 | 0.010 | 0.022 | 0.317 | 0.012 | 0.016
16.2 | 17.44 | 18.7 | 0.90 | 1.02 | 1.20 | 0.374 | 0.012 | 0.021 | 0.273 | 0.015 | 0.011
16.2 | 17.44 | 18.7 | 1.20 | 1.49 | 4.00 | 0.352 | 0.020 | 0.020 | — | — | —
18.7 | 20.03 | 21.4 | 0.40 | 0.47 | 0.55 | 0.447 | 0.024 | 0.025 | — | — | —
18.7 | 20.03 | 21.4 | 0.55 | 0.62 | 0.70 | 0.458 | 0.013 | 0.024 | 0.342 | 0.028 | 0.017
18.7 | 20.03 | 21.4 | 0.70 | 0.79 | 0.90 | 0.417 | 0.010 | 0.023 | 0.320 | 0.014 | 0.016
18.7 | 20.04 | 21.4 | 0.90 | 1.03 | 1.20 | 0.406 | 0.012 | 0.023 | 0.280 | 0.014 | 0.011
18.7 | 20.05 | 21.4 | 1.20 | 1.49 | 4.00 | 0.344 | 0.017 | 0.021 | — | — | —
21.4 | 22.88 | 24.4 | 0.55 | 0.62 | 0.70 | 0.456 | 0.015 | 0.025 | 0.316 | 0.015 | 0.015
21.4 | 22.89 | 24.4 | 0.70 | 0.79 | 0.90 | 0.446 | 0.011 | 0.024 | 0.312 | 0.013 | 0.015
21.4 | 22.88 | 24.4 | 0.90 | 1.03 | 1.20 | 0.382 | 0.011 | 0.022 | 0.277 | 0.023 | 0.011
21.4 | 22.89 | 24.4 | 1.20 | 1.50 | 4.00 | 0.370 | 0.017 | 0.022 | — | — | —
24.4 | 26.02 | 27.7 | 0.40 | 0.47 | 0.55 | — | — | — | 0.180 | 0.065 | 0.009
24.4 | 26.02 | 27.7 | 0.55 | 0.62 | 0.70 | 0.400 | 0.016 | 0.022 | 0.260 | 0.016 | 0.013
24.4 | 26.02 | 27.7 | 0.70 | 0.79 | 0.90 | 0.407 | 0.011 | 0.023 | 0.283 | 0.015 | 0.013
24.4 | 26.03 | 27.7 | 0.90 | 1.03 | 1.20 | 0.405 | 0.012 | 0.023 | 0.280 | 0.016 | 0.011
24.4 | 26.04 | 27.7 | 1.20 | 1.51 | 4.00 | 0.321 | 0.014 | 0.019 | — | — | —
$p$${}^{\text{min}}$ | $\langle p\rangle$ |  $p$${}^{\text{max}}$ | $p_{\mathrm{T}}^{\text{min}}$ | $\langle p_{\mathrm{T}}\rangle$ | $p_{\mathrm{T}}^{\text{min}}$ | $R_{\kern 1.25995pt\overline{\kern-1.25995ptH}}$ | $\delta_{\text{uncorr}}$ | $\delta_{\text{corr}}$ | $R_{{\kern 1.25995pt\overline{\kern-1.25995pt\mathchar 28931\relax}}}$ | $\delta_{\text{uncorr}}$ | $\delta_{\text{corr}}$
---|---|---|---|---|---|---|---|---|---|---|---
27.7 | 29.52 | 31.4 | 0.40 | 0.47 | 0.55 | — | — | — | 0.226 | 0.059 | 0.011
27.7 | 29.52 | 31.4 | 0.55 | 0.62 | 0.70 | 0.349 | 0.019 | 0.023 | 0.224 | 0.034 | 0.011
27.7 | 29.53 | 31.4 | 0.70 | 0.79 | 0.90 | 0.430 | 0.014 | 0.024 | 0.273 | 0.012 | 0.014
27.7 | 29.53 | 31.4 | 0.90 | 1.03 | 1.20 | 0.394 | 0.012 | 0.023 | 0.253 | 0.011 | 0.010
27.7 | 29.53 | 31.4 | 1.20 | 1.52 | 4.00 | 0.357 | 0.015 | 0.021 | — | — | —
31.4 | 35.55 | 40.0 | 0.40 | 0.47 | 0.55 | — | — | — | 0.279 | 0.050 | 0.017
31.4 | 35.56 | 40.0 | 0.55 | 0.62 | 0.70 | 0.398 | 0.017 | 0.023 | 0.247 | 0.032 | 0.013
31.4 | 35.57 | 40.0 | 0.70 | 0.79 | 0.90 | 0.412 | 0.013 | 0.024 | 0.257 | 0.012 | 0.014
31.4 | 35.58 | 40.0 | 0.90 | 1.03 | 1.20 | 0.385 | 0.010 | 0.022 | 0.268 | 0.009 | 0.009
31.4 | 35.60 | 40.0 | 1.20 | 1.52 | 4.00 | 0.350 | 0.010 | 0.021 | — | — | —
40.0 | 45.08 | 50.5 | 0.55 | 0.62 | 0.70 | 0.326 | 0.019 | 0.025 | 0.261 | 0.016 | 0.015
40.0 | 45.08 | 50.5 | 0.70 | 0.79 | 0.90 | 0.362 | 0.014 | 0.022 | 0.280 | 0.014 | 0.016
40.0 | 45.08 | 50.5 | 0.90 | 1.03 | 1.20 | 0.382 | 0.013 | 0.023 | 0.272 | 0.037 | 0.012
40.0 | 45.12 | 50.5 | 1.20 | 1.54 | 4.00 | 0.364 | 0.012 | 0.022 | 0.229 | 0.011 | 0.005
50.5 | 76.35 | 110.0 | 0.70 | 0.79 | 0.90 | 0.351 | 0.021 | 0.025 | — | — | —
50.5 | 76.50 | 110.0 | 0.90 | 1.03 | 1.20 | 0.323 | 0.013 | 0.019 | — | — | —
50.5 | 76.97 | 110.0 | 1.20 | 1.55 | 4.00 | 0.336 | 0.010 | 0.020 | 0.244 | 0.010 | 0.012

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