Feasibility study to characterize the production of antineutrons in high energy $pp$ collisions through charge exchange interactions

Simulations to evaluate the feasibility of $\bar{n}$ identification and kinematic characterization via the hadronic charge exchange (CEX) interaction $n+\bar{n}\rightarrow p+\bar{p}$ are reported. The target neutrons are those composing the silicon nuclei of which inner tracking devices present in LHC experiments are made. Simulations of $pp$ collisions in PYTHIA were carried out at different energies to investigate $\bar{n}$ production and the expected $\bar{n}$ energy spectra. Then, two types of GEANT4 simulations were performed, placing an $\bar{n}$ point source at the ALICE primary vertex as a working example. In the first simulation, the $E_k$ was kept at an arbitrary (1 GeV) fix value to develop an $\bar{n}$ identification and kinematics reconstruction protocol. The second GEANT4 simulation used the resulting PYTHIA at $\sqrt{s_{pp}}=13$ TeV $\bar{n}$ energy spectra. In both simulations, the occurrence of CEX interactions was identified by the unique outgoing $\bar{p}$. The simplified simulation allowed to estimate a 0.11% CEX-interaction identification efficiency at $E_k = 1$ GeV. The $p$ CEX-partner identification is challenging because of the presence of silicon nucleus-fragmentation protons. Momentum correlations between the $\bar{n}$ and all possible $\bar{p}p$ pairs showed that $p$ CEX-partner identification and $\bar{n}$ kinematics reconstruction corresponds to minimal momentum-loss events. The use of ITS $dE/dx$ information is found to improve $\bar{n}$ identification and kinematic characterization in both simulations. The final protocol applied to the realistic simulation resulted in a $\bar{n}$ identification and kinematic reconstruction efficiency of 0.006%, based solely on $\bar{p}p $ pair observable. Thus, the expected rate of identified and kinematically reconstructed $\bar{n}$ should lie in the order of 100,000 per second, illustrating the feasibility of the method.


Introduction
To a first approximation, antiproton ( p) and antineutron ( n) productions in high-energy proton-proton () collisions should be approximately equal.Such a fact is implicit in the coalescence model [1] calculations used to characterize light anti-nuclei production in high-energy heavy-ion collisions.Yet, isotopic effects have recently been proposed [2] to significantly affect this symmetry, resulting in an enhanced n production.This is expected to have a measurable impact in the high precision cosmic ray p flux being measured by the AMS-02 experiment [2], having as background intergalactic  collisions.This led to the inclusion of an n/ p asymmetry parameter, which ranges from 1.2 to 2.0, in the cosmic ray galactic-transport code EPOS-LHC [3].Such an important effect should be measurable in  collisions carried out at the main LHC experiments, providing n production could be measured.Here we propose the use of the charge exchange reaction (CEX)  + n →  + p (see Figure 1), which produces easy-to-identify charged particles.Indeed, this technique led to the n discovery [4], and shortly after, to measure its mass, based on the kinematic analysis of the same reaction [5].The feasibility of using CEX to identify and reconstruct the kinematic properties of antineutrons produced by LHC experiments via CEX interactions on their silicon inner tracking devices is explored here, taking as a working example ALICE and its Inner Tracking System (ITS).This document is organized as follows: Section 2 describes the details of the PYTHIA and GEANT4 simulations carried out to explore the feasibility of using CEX to detect The six inner circles represent the 2 mm [7] sensitive silicon layers.The tracker simulation limit corresponds to the seventh circle.The corresponding radii () are listed in Table 1.See Figure 3 for an isometric view.
n.The resulting data are presented and analyzed in section 3. Momentum correlations between the n and the p pair produced in CEX events are studied to establish viable n identification and kinematic characterization protocols, improved by using the magnitude of ∕ signals generated by CEX-induced silicon nuclei fragmentation.Conclusions are given in section 4.

Simulations
The ITS and Time Projection Chamber (TPC) detectors constitute the main ALICE charge-particle tracking devices, providing high-resolution information about interactionvertex positions and the momentum components of the charged particle residues.The technique proposed here consists in using the ITS silicon-nuclei neutrons as CEX targets (Figure 1) to produce easier-to-identify p pairs.The following simulations are specifically based on the ALICE RUNs 1 and 2 ITS geometrical configuration [6], composed of 6 concentric cylindrical layers with an integrated silicon thickness of 12 mm.A first simulation was performed using the event generator PYTHIA [8] to obtain the emitted antineutrons' energy distribution.Three million  collision events were generated at √   = 0.9, 2.7, 5.02, 7, 8, and 13 TeV at which ALICE [9] experimental data exists.The number of antineutrons produced per event, as well as their corresponding total energy, were recorded.The results are shown in ALICE ITS [6] layer numbers are listed from inner to outer, together with their corresponding radial () and longitudinal () dimensions (cm), as well as the total sensitive surface area (m 2 ).The tracker simulation-limit dimensions are associated to the seventh layer.
simulation, at 13 TeV an average of 3 n´s per collision is produced (Table 2).As a reference, the LHC Run 2 produced 600 million  collisions per second [10].Hence, on average, 10 9 n´s per second were produced at the LHC maximum energy.Figure 5 shows that the resulting n yields increase with energy, but the monotonically decreasing shape of the corresponding energy distributions remains fairly independent of the collision energy, having total energy maxima at  ≈ 1 GeV.Thus, in what follows, we assume that most of the n yields have kinetic energies between 0 and 2 GeV.
With the above information, a simplified GEANT4 [11,12,13] simulation was implemented, in which a monoenergetic   = 1 GeV (i.e.,  n = 1.697GeV), isotropic point n source is placed at the center of the six-layer silicon detector, hereon the primary vertex.The geometry and dimensions of the ALICE-ITS (Table 1) used are shown in figures 2, 3 and 4. In the GEANT4 simulations, the first ITS silicon layer is defined as the CEX target, while the remaining five layers are defined as the sensitive detectors.This, however, does not prevent CEX interactions from occurring in all six layers.Note that, in full (e.g., PYTHIA)  collision simulations, the presence of p pair vertices (hereon the interaction vertices) located in outer ITS layers, with no corresponding ∕ (ionization) signals in inner ones, shall help differentiate n produced in the primary vertex from other  collision residues.This scenario, on which we are presently working, is beyond the scope of the present feasibility study, where only n are generated at the primary vertex.
The present GEANT4 simulations consider an isotropic point source located at the primary vertex and emitting n of a given kinetic energy   distribution.The simplified version considers the generation of 10 8 fix   = 1 GeV n's.The second GEANT4 simulation consists of 10 7 events, where the n's now have the actual 13 TeV PYTHIA energy distribution (see Fig. 5).The results of both simulations are presented and analyzed in the next section.

Analysis and results
The simulated data were analyzed using ROOT [14].As a first step, p´s generated by primary n´s are required to generate ionization signals in at least one of the ITS layers.In the n kinetic energy domain produced by GEANT4,  + n →  + p +  + and  + n →  + p +  0 constitute the sole background sources to the CEX interaction considered here.In order to exclude them in both GEANT4 simulations, the following  veto was implemented.Distinguishing between the  + p and the  + p +  0 outgoing channels is difficult experimentally due to the short  0 half-life ( = 0.26×10 −9 m), decaying dominantly (99%) into two photons.However, in the 10 8 events analyzed here, not a single one had + p+ 0 as an outgoing channel.Thus, the cross-section of this CEXbackground channel is expected to be less than 0.1 b, i.e., negligible compared to the above quoted   value.Concerning the  + p +  + channel, 34,657 events of this type were observed in the same data sample, yielding a more significant cross-section of 5.76±0.12mb.However, in what follows, it is assumed that those events can be discriminated through the charged-particle identification of a p +  + pair using downstream tracking devices (eg. the ALICE-TPC).

Mono-energetic n Simulation
Although the CEX interaction of interest is included in GEANT4 [15] as a physical process, its probability is not explicitly provided.Therefore, the corresponding   (1) at   = 1 GeV cross section was deduced from the n + 28  interaction simulation described next.The resulting value is, then, used to estimate the corresponding   efficiency at this energy.The simplified GEANT4 simulation, consisting of 10 8 events, produced a total of 113,355 p's events resulting from CEX interactions.This corresponds to an identification efficiency of 0.11%, indicating that approximately one of every 1000 antineutrons produced at the primary vertex could be identified via the p produced in the CEX reaction.This yields a CEX cross-section in silicon of   = 18.85 ± 0.11 mb, at this kinetic energy.Its ratio to the measured cross section for the inverse CEX reaction p +  → n +  on carbon (8 mb) [4], scales approximately as their geometrical cross sections.
When a CEX interaction occurs, a certain amount of energy is transferred to the silicon nucleus fragments.The simulation allowed to estimate an upper limit of ∕ ≈ 300 ionization energy loss per event.Because of it, the n momentum may only be recovered within this limitation from a CEX-based kinematic analysis.Also, an average of 5 protons per event were found among those fragments, limiting the ability to identify the actual CEX .To improve the possibility of recovering momenta information of the incident n, a selection criterion was proposed to aid in identifying the CEX  in each event.Based on the assumption that the primary and the interaction vertices (Figure 6) can be reconstructed using downstream tracking, momentum conservation implies that the primary vertex, the CEX interaction vertex, as well as the p  and the p p vectors, should lie on a common plane.In practice, energy loss to silicon fragmentation breaks this symmetry.Hence, the best one can do is to identify as the  CEXpartner that fulfilling the following three conditions.First, the equation of the plane formed by the interaction vertex, the p p vector, and the p  vector of each  is determined.The most likely  should be that for which the distance to the primary vertex is minimal.Second, to reduce kinematic reconstruction uncertainty, events characterized by a large loss of n energy and momentum were discarded.To do so, for every event, the quantities  p  +    and |(p p + p  )| were calculated.The proton having the maximum values of each quantity, corresponding to the second and third conditions, was selected.Thus, the  meeting all three conditions was identified as the most likely CEX .With the above criteria, the most likely CEX  was identified in 14,969 events, i.e., 0.015% of the mono-energetic data sample.The reconstructed n momentum norm |p p + p  |∕|p n| from these events is shown in Figure 7, where a peak standing over a broader distribution is observed.A Gaussian fit to the peak yields a maximum at 0.90 ± 0.05.The underlying correlation can also be observed componentby-component in Figure 8, where the normalized value  recovered by this technique, being consistent with the ∼ 90% obtained in Figure 7.This simplified exercise already illustrates the feasibility of the technique to identify n´s, allowing to count ≈ 0.1% of them, while being able to reconstruct 90% (± 5%) of the energy for 0.007% of them.
The amount of energy deposited by the silicon nucleus fragments can be used to select those events characterized by a low energy transfer.Studying the corresponding ∕ signals in events where the most likely CEX  identification was possible, it was empirically determined that selecting events with ∕ > 100 MeV improved the kinematic reconstruction with minimal reconstructed n yield loss.These results are shown in Figure 9 for the fix   distribution.As can be seen, when comparing the results before and after applying the ∕ condition, events with |p p + p   |∕|p n| values between 0.5 and 0.9 were reduced, while increasing the percentage of energy that can be reconstructed from 84% to 89%.The percentage of events where the most likely CEX proton can be identified, which also satisfied the ∕ condition, turned out to be 0.011%.A Gaussian fit to this distribution revealed an improved uncertainty of ± 0.04, i.e., a 20% resolution improvement with a 26% yield loss.

PYTHIA 13 TeV n energy distribution simulation
The proposed method was also applied to a realistic n source, one having the PYTHIA 13 TeV energy distribution between 0 and 10 GeV, as described in Section 2. This data sample comprised 10 7 events, where 5,795 were identified as CEX interactions.From them, the most likely  was identified in 815 cases.The corresponding efficiencies were 0.06% for antineutron identification and 0.008% for kinematic information reconstruction.The resulting normalized quantity |p p + p   |∕|p n| is plotted in Figure 10.A Gaussian fit to the peak of this distribution yields a standard deviation value of 0.08, which is assumed to be the error associated with the method proposed in this case.
The same ∕ < 100 MeV condition, as in the fixed energy GEANT4 simulation, was used.The results obtained are shown in Figure 11.Once again, comparing the results before and after applying this condition, there is a decrease in events with a |p p + p  |∕|p n| value between 0.4 and 0.8, increasing the percentage of energy that can be reconstructed from 85% to 89%.The percentage of events where the most likely CEX proton can be identified and satisfy the ∕ < 100 MeV condition is 0.006%.This is similar to what was found for the mono-energetic case in figures 8 and 7.The fit yielded an improved uncertainty of 0.06.

Conclusions
Simulations to estimate the identification efficiency, and kinematics-reconstruction precision, in n detection using the Charge Exchange interaction (CEX) n +  →  + p occurring in silicon nuclei of tracking devices in main LHC experiments, are presented.The n production rate in  collisions at the LHC was estimated via PYTHIA  simulations in the √   = 0.9 -13 TeV energy range, obtaining n∕ = 0.9 -2.6, respectively.The simulated n energy spectra show maxima at the lowest energy, followed by a power law yield-decay as a function of energy.Using the ALICE-ITS detector configuration of RUN´s 1& 2, a simplified GEANT4 simulation, locating an isotropic source emitting 1 GeV n's at the primary vertex, was carried out to estimate the CEX cross-section.Assuming all charged particles can be identified by downstream tracking, CEX-interaction identification is univocally associated to the presence of an outgoing p, with no charged 's in the event.The resulting cross section is   = 18.97 ± 0.11, corresponding to an n identification efficiency of 0.11%.The competing n +  →  + p +  0 interaction cross section is found to be, at least, three orders of magnitude smaller.Momentum correlations between the initial n and the outgoing p pair were also studied.The criterion to distinguish CEX 's from silicon nuclei fragmentation protons is based on momentum conservation.Yet, a high energy and momentum transfer to silicon nucleons distorts the CEX  identification.The problem is reduced by discarding events with significant losses of energy and momentum, at the cost of identification efficiency.As an example, here the n momentum could be reconstructed with an uncertainty of 5%, while reducing the identification efficiency to 0.015%.ITS ∕ information can also be used to reject events characterized by large momentum transfers to silicon nuclei, which produce a larger number of ionizing fragments.The addition of this selection criteria reduced the identification efficiency to 0.011%, with an improved resolution of 4%.A second GEANT4 simulation using a more realistic n energy distribution yielded an n identification efficiency of 0.06% and a 0.008% kinematic reconstruction efficiency.Should this identification and kinematic reconstruction protocol be applied to LHC Run 2  data, the expected rate of identified and kinematically reconstructed n's should lie in the order of 100,000 per second, illustrating the feasibility of the method.

Figure 2 :
Figure 2: ITS geometry, frontal view, used in the simulations.The six inner circles represent the 2 mm[7] sensitive silicon layers.The tracker simulation limit corresponds to the seventh circle.The corresponding radii () are listed in Table1.See Figure3for an isometric view.

Figure 3 :
Figure 3: Isometric view of the geometry used in the GEANT4 simulations.Lines are auxiliary contours that help to improve the visualization.

Figure 4 :
Figure4: Isometric view of simulated n trajectories, 10 events, generated at the primary vertex.The six ITS layers ± borders (see Table1) are included to provide a geometrical reference.

Figure 5 :
Figure 5: Total energy  =   +  0  2 of the antineutrons produced in events  collisions at different √   values generated by PYTHIA.

Figure 6 :
Figure 6: Momentum vectors of  and p together with the interaction vertex form a single plane that, without considering energy losses due to fragmentation, should contain the primary vertex.
y,z) is plotted versus  n  .The corresponding mean values in this figure are 0.85, 0.86, and 0.85, respectively, representing the fractions of the n momentum

Figure 7 :
Figure 7: Mono-energetic case.The histogram shows the distribution of the reconstructed antineutron momentum magnitude p p + p  normalized by the antineutron momentum p n, coming from CEX events.The discontinuous line represents a Gaussian fit.See text.

Figure 8 :
Figure 8: For events in which it is possible to identify the CEX  through the method proposed, the value    +  n  ( = , , ) normalized by the corresponding component of the n momentum is shown versus the value  n  .Correlation factors of ∼ 0.9 between momentum components of the CEX products and the n ones were obtained.

Figure 9 :
Figure 9: Mono-energetic case.Distribution of the reconstructed antineutron momentum magnitude normalized, (p p + p  )∕p n, for events in which the CEX proton can be selected and for those in which ∕ < 100 MeV.

Figure 10 :
Figure 10: Realistic case.The reconstructed-to-initial antineutron momentum ratio distribution is plotted for the proton selected by the proposed method.A gaussian fit to the distribution with parameters  = 0.90 and  = 0.11 is shown.

Figure 11 :
Figure 11: Realistic case.Distribution of the reconstructed antineutron momentum magnitude normalized, (p p + p  )∕p n, for events in which the CEX proton can be selected and for those in which ∕ < 100 MeV.

Table 2 ,
and Figure5, respectively.According to this

Table 1 )
are included to provide a geometrical reference.