Production of axionlike particles in $PbPb$ collisions at the LHC, HE -- LHC and FCC: A phenomenological analysis

The production of axionlike particles (ALP) in ultraperipheral $PbPb$ collisions (UPHIC) is investigated considering the energies of the next run of the Large Hadron Collider (LHC) and of the future High Energy -- LHC (HE -- LHC) and Future Circular Collider (FCC). Assuming four different combinations for the ALP mass and coupling and the typical exclusivity cuts for central and forward detectors, we estimate the cross section and invariant mass, rapidity, transverse momentum and {acoplanarity} distributions associated to the diphoton final state produced in the $\gamma \gamma \rightarrow a \rightarrow \gamma \gamma$ subprocesses. A detailed analysis of the backgrounds is performed. We demonstrate that the backgrounds can be strongly reduced by the exclusivity cuts and that a forward detector, as the LHCb, is ideal to probe an ALP with small mass. Finally, our results indicate that a future experimental analysis of the diphoton final state in UPHIC can probe the existence and properties of axionlike particles.


I. INTRODUCTION
Over the last few years there has been a rising interest in searching for axionlike particles in e + e − , ep, νp, pp, pA and AA collisions as well in laser beam experiments (See e.g. Refs. [1][2][3][4][5][6][7][8][9][10]), mainly motivated by the fact that such particles are predicted to occur in many extensions of the Standard Model (SM). They are pseudo -Nambu -Goldstone bosons, which arise in models with spontaneous breaking of a global symmetry and are expected to be characterized by a small mass in comparison to the scale of the spontaneous breaking and by couplings to the Standard Model (SM) particles that are, at least, suppressed by the inverse of the same scale. Depending on the ALP mass and coupling structure, they can be produced at colliders and decay into photons, charged leptons, light hadrons or jets, which can be detected. In our analysis we are particularly interested in the coupling of the pseudoscalar ALP a to photons, which is described by a Lagrangian of the form where m a is the ALP mass, g a is the coupling constant andF µν = 1 2 µναβ F αβ . As a consequence, the ALP can be produced by the photon -photon fusion and can decay into a diphoton system. In Ref. [3] the authors have proposed to search by axionlike particles in ultraperipheral heavy ion collisions (UPHIC) [See also Ref. [5]], which are characterized by an impact parameter b greater than the sum of the radius of the colliding nuclei [11][12][13][14][15][16][17][18][19] and by a photon -photon luminosity that scales with Z 4 , where Z is number of protons in the nucleus. The ALP production in UPHIC is represented in Fig. 1 (a) and the associated cross section can be derived using the equivalent photon approximation [20]. In this approach, we can associated to the incident nucleus an equivalent photon spectrum N (ω i , r i ), which allows to estimate the number the photons with energy ω i at a transverse distance r i from the center of nucleus, defined in the plane transverse to the trajectory, which is determined by the charge form factor of the nucleus. Consequently, the total cross section can be factorized in terms of the equivalent photon spectrum of the incident nuclei and the elementary cross section for the γγ → a → γγ process as follows where √ s is center -of -mass energy of the P bP b collision, ⊗ characterizes a rapidity gap in the final state, W = √ 4ω 1 ω 2 = m X is the invariant mass of the γγ system and y its rapidity. Moreover, in order to exclude the overlap between the colliding nuclei and insure the dominance of the electromagnetic interaction, it is useful to include in Eq.(2) the absorptive factor S 2 abs (b), which depends on the impact parameter b of the P bP b collision. One of the main advantages of the ALP search in UPHIC is that the resulting final state is very clean, consisting of the diphoton system, two intact nuclei and two rapidity gaps, i.e. empty regions in pseudo-rapidity that separate the intact very forward nuclei from the γγ system. However, in order to probe the ALP in the γγ → a → γγ channel, it is fundamental to disentangle the associated events from those generated in the Light -by -Light (LbL) scattering, in which the diphoton final state is created by the elementary elastic γγ → γγ subprocess, represented in Fig. 1 (b). As demonstrated in Ref. [21], where the diphoton production by the LbL, Durham and double diffractive processes was estimated, the LbL process dominates the diphoton production at small invariant masses when the exclusivity cuts (see below) are taking into account. Our goal in this paper is twofold. First, to present, for the first time, a detailed analysis of the ALP production in the kinematical range probed by the LHCb detector, which is expected to be able to probe ALP's with smaller invariant masses than the central detectors. Second, to present predictions for the ALP production in P bP b collisions for the energies of the High -Energy LHC ( √ s = 10.6 TeV) [22] and Future Circular Collider ( √ s = 39 TeV) [23] considering the typical configurations of central and forward detectors and similar cuts to those used to LHC. In our analysis of the signal and the LbL background we will use superchic3 Monte Carlo event generator [24], which has been recently generalized to treat ion -ion collisions.
This paper is organized as follows. In the next Section, we present our results for the ALP production at the LHC, HE -LHC and FCC. Predictions for cross sections and the invariant mass, rapidity, transverse momentum and acoplanarity distributions are presented. The impact of the selection cuts is discussed and predictions for typical central and forward detectors are presented. Finally, in Section III, our main conclusions are summarized.

II. RESULTS
Following Ref. [24], we will assume that the photon spectrum can be expressed in terms of the electric form factor and that the absorptive corrections S 2 abs (b) for γγ interactions can be estimated taking into account the multiple scatterings between the nucleons of the incident nuclei, which allow to calculate the probability for no additional ion -ion rescattering at different impact parameters. For the background associated to the LbL scattering, the elementary cross sectionσ(γγ → γγ) will be calculated taking into account of the fermion loop contributions as well as the contribution from W bosons. In addition, we also will present the predictions for the backgrounds associated to the diphoton production by the Durham and double diffractive processes (DDP), obtained originally in Ref. [21], which are here complemented by the inclusion of new cuts on the invariant mass of the diphoton system. For a detailed discussion about the Durham and DDP channels we refer the reader to the Ref. [21]. On the other hand, the signal associated to the ALP production will be calculated following the approach discussed in Ref. [24], where the γγ → a → γγ cross sections is estimated assuming that the ALP is a narrow resonance with a mass m a that couples to the γγ system with strength g a . In what follows we will present our results for the ALP production in P bP b collisions at √ s = 5.5, 10.6 and 39 TeV. In our analysis we will use the superchic3 MC event generator [24] to estimate the processes represented in the Figs Table I we present our results for the ALP cross sections obtained at the generation level, without the inclusion of any selection in the events. We have that the cross section increases for smaller masses and larger energies, being of the order of µb at m X = 3.0 GeV and FCC energy. For comparison, we have that the LbL cross sections at √ s = 5.5/ 10.6/ 39 TeV are 1.8/ 2.7/ 5.2 × 10 4 nb, respectively. Therefore, our results indicate that the ALP cross section can be of the same order of the LbL one at smallm a and is non -negligible for larger masses. In Fig. 2 we present our predictions for the invariant mass and rapidity distributions of the diphoton system, derived at the generation level considering two possible axion masses and P bP b collisions at the LHC (left panels) and FCC (right panel) energies. The predictions for the diphoton production by the Durham and double diffractive processes, obtained taking into account of the soft survival corrections as derived in Ref. [25], are presented for comparison. As already demonstrated in Ref. [21], these two processes are subleading in comparison to the LbL one in the kinematical range considered. As expected for a resonance, the ALP production implies a peak in the invariant mass distribution. In addition, we have that for the production of an ALP with small mass (m a = 3.0 GeV), the rapidity distributions for LHC and FCC energy are very similar to the LbL one. In contrast, for m a = 15.0 GeV, the distributions are strongly suppressed and become similar to the Durham and DDP predictions, which implies that the inclusion of additional cuts is important to separate the ALP events.
In order to obtain realistic estimates for the ALP production in P bP b collisions, which can be compared with the future experimental data, we will include in our analysis the experimental cuts that are expected to be feasible in the next run of the LHC and in the future at the HE -LHC and FCC. As in Ref. [21], we will consider two distinct configurations of cuts: one for a typical central detector, as ATLAS and CMS, and other for a forward detector, as LHCb. The selection criteria implemented in our analysis are the following: • For a central detector: We will select events in which m X > 5 GeV and E T (γ, γ) > 2 GeV, where E T is the transverse energy of the photons. Moreover, we will impose a cut on the acoplanarity (1 − (∆φ/π) < 0.01) and transverse momentum of the diphoton system (p T (γ, γ) < 0.1 GeV). Finally, we only will select events where photons are produced in the rapidity range |η(γ 1 , γ 2 )| < 2.5 with 0 extra tracks.
• For a forward detector: We will select events in which m X > 1 GeV and p T (γ, γ) > 0.2 GeV, where p T is the transverse momentum of the photons. Moreover, we will impose a cut on the acoplanarity (1 − (∆φ/π) < 0.01) and transverse momentum of the diphoton system (p T (γ, γ) < 0.1 GeV). Finally, we only will select events where photons are produced in the rapidity range 2.0 < |η(γ 1 , γ 2 )| < 4.5 with 0 extra tracks with p T > 0.1 GeV in the rapidity range 3.5 < η < 1.5 and p T > 0.5 GeV in the range 8.0 < η < 5.5. Such set of cuts is considered in order to analyze the possibility of study the production of ALP's with mass in the range 1 ≤ m X ≤ 5 GeV, which cannot currently be reached by the central detectors.     Our predictions for the central and forward configurations are presented in Tables II and III, respectively. The inclusion of the exclusivity cuts strongly reduces the background, with the DDP contribution being fully eliminated and the Durham being of the order of 2 %. For a central detector, we have that the selection in the invariant mass range around the ALP mass implies that the LbL background becomes of the order or smaller the ALP signal. In particular, for m a = 40 GeV, the LbL background becomes negligible and the study of the diphoton production is a direct probe of the ALP. On the other hand, the results presented in Table III for a forward detector indicate that it is ideal to probe an ALP with small mass. Considering the expected luminosities for the next run of the LHC and future colliders, which are 10 nb −1 and 110 nb −1 , the associated number of ALP events are, respectively, ≈ 19046 and 481470, for m a = 3.0 GeV. Also, taking into account the integrated luminosity achieved by the LHCb in 2018, 210µb −1 , the significance values obtained for √ s = 5.5, 10.6 and 39 TeV are ≈ 48, 68 and 102, respectively. The expected luminosities for √ s =10.6 and 39 TeV relative to 5σ are 0.1 µb −1 and 0.004 µb −1 . Such results demonstrate the potentiality of the LHCb detector to constrain the main properties of the ALP.
In Fig. 3 we present our predictions for the invariant mass m X , transverse momentum p T (γγ), rapidity y(γγ) and acoplanarity distributions considering a central detector, m a = 15 GeV, the exclusivity cuts discussed before and P bP b collisions at the LHC (left panels) and FCC (right panels). These results have been derived before the selection in the invariant mass of the diphoton system. We have that the contribution of the Durham process is, in general, negligible, only becoming competitive for a diphoton with a large transverse momentum. The predictions for the LbL background are approximately one order of magnitude larger than ALP signal, but the shape of the p T (γγ), y(γγ) and acoplanarity distributions are similar. On the other hand, for a forward detector and assuming that m a = 3.0 GeV, the results presented in Fig. 4 indicate that the LbL and ALP predictions for the distributions are very similar, with the ALP one being slightly larger.

III. SUMMARY
The high photon -photon luminosity present in ultraperipheral heavy -ion collisions become feasible the search of New Physics in photon -induced interactions. One of more interesting final states is the diphoton system with a small invariant mass, which is dominantly produced by the Light -by -Light scattering and can also be generated by an ALP resonance in the s -channel. In this paper we have performed an exploratory study of the ALP production in P bP b collisions at the LHC, HE -LHC and FCC energies, considering four combinations for the ALP mass and coupling and taking into account the acceptance of the LHC detectors. In particular, a detailed analysis of the ALP production in the kinematical range probed by the LHCb detector was performed by the first time. Our results demonstrated that the LbL background can be strongly reduced by the exclusivity cuts and that the ALP signal is dominant for a forward detector. Consequently, a future experimental anaysis of the diphoton final state is a promissing observable to probe the existence of the Axionlike particles and its properties.