Diffractive $\gamma \gamma$ production in $pp$ collisions at the LHC

In this letter we estimate the contribution of the double diffractive processes for the diphoton production in $pp$ collisions at the Large Hadron Collider (LHC). The acceptance of the central and forward LHC detectors is taken into account and predictions for the invariant mass, rapidity and, transverse momentum distributions are presented. A comparison with the predictions for the Light -- by -- Light (LbL) scattering and exclusive diphoton production is performed. We demonstrate that the events associated to double diffractive processes can be separated and its study can be used to constrain the behavior of the diffractive parton distribution functions.

The study of diphoton production in exclusive processes in hadronic collisions became an active field of research during recent years, strongly motivated by the possibility to observe one of the main consequences of the Quantum Electrodynamics (QED): the Light-by-Light (LbL) scattering. Although several attempts were made to detect such rare phenomenon, e.g., the high precision measurements of the electron and muon anomalous magnetic moment [1,2], direct observations in the laboratory remained challenging until CMS and ATLAS Collaboration have observed, for the first time, the LbL scattering in ultraperipheral P bP b Collisions [3,4]. Such collisions are characterized by an impact parameter b greater than the sum of the radius of the colliding nuclei [5][6][7][8][9][10][11][12][13] and by a photon -photon luminosity that scales with Z 4 , where Z is number of protons in the nucleus. As a consequence, in ultraperipheral heavy ion collisions (UPHIC), the elementary elastic γγ → γγ process, which occurs at one -loop level at order α 4 and have a tiny cross section, is enhanced by a large Z 4 (≈ 45 × 10 6 ) factor. In addition, the contribution of gluon initiated processes can be strongly reduced in nuclear collisions [14], becoming the LbL scattering feasible for the experimental analysis [15,16]. On the other hand, for pp collisions, due the absence of the Z 4 enhancement, the diphoton production by gluon initiated processes are expected to significantly contribute and can be dominant in some regions of the phase space. Our goal in this letter is to estimate the contribution of the double diffractive processes, represented in Figs. 1 (a) and (b), for the diphoton production in pp collisions at √ s = 13 TeV. In such reactions, the diphoton system is generated by the interaction between partons (quarks and gluons) of the Pomeron (IP ), which is a color singlet object inside the proton. The associated final state will be characterized by the diphoton system, two intact protons and two rapidity gaps, i.e. empty regions in pseudo-rapidity that separate the intact very forward protons from the γγ system. In principle, these events can be separated by tagging the intact protons in the final state using forward detectors, as e.g. the AFP/ATLAS and the CT -PPS, and/or by measuring the rapidity gaps. In addition, to separate the double diffractive processes, we must to control the background associated to the LbL scattering and the exclusive diphoton process, represented in Figs. 1 (c) and (d), respectively. In our analysis, we will estimate all these processes using the Forward Physics Monte Carlo (FPMC) [17] and SuperChic event generator [18], taking into account the acceptance of the LHC detectors. In particular, we will consider the typical set of cuts used by the ATLAS and CMS Collaborations to separate the exclusive events. In addition, we will present, for the first time, the predictions for the diphoton production in double diffractive processes for the kinematical range probed by the LHCb detector. As we will show below, the events associated to double diffractive processes can be separated by imposing a cut on the transverse momentum of the diphoton system, which allow us to investigate the dependence of the predictions on the modelling of the diffractive parton distributions.
Initially, let's present a short review of the main aspects need to to describe the diphoton production in the double diffractive processes (DDP), represented in Figs expressed by are the diffractive gluon, quark and antiquark densities of the proton i with a momentum fraction x i . The parton distributions have its evolution in the hard scale µ 2 given by the DGLAP evolution equations and should be determined from events with a rapidity gap or a intact hadron. In the Resolved Pomeron model [19] the diffractive parton distributions are expressed in terms of parton distributions in the pomeron and a Regge parametrization of the flux factor describing the pomeron emission by the hadron. In particular, the diffractive gluon distribution can be expressed as follows where ξ is the momentum fraction of the proton carried by the Pomeron, f p I P (ξ) stands for the associated flux distributions in the proton and g I P (β ≡ x/ξ, µ 2 ) is the Pomeron gluon distribution (A similar definition is valid for the diffractive quark distribution). Furthermore, β is the momentum fraction carried by the gluon inside the Pomeron. It is useful to assume that the Pomeron flux is given by where t min , t max are kinematic boundaries. The flux factors are motivated by Regge theory, where the pomeron trajectories are assumed to be linear, α I P (t) = α I P (0)+α I P t, and the parameters B I P , α I P and their uncertainties are obtained from fits to the data. In our analysis, we will consider different parametrizations for g I P (β, µ 2 ) and q I P (β, µ 2 ) in order to investigate the sensitive of the predictions on the description of the Pomeron structure. In order to derive realistic predictions for the diphoton production in double diffractive process, we need to take into account of the nonperturbative effects associated to soft interactions which imply the breakdown of  the collinear factorization [20] and lead to an extra production of particles that destroy the rapidity gaps in the final state [21]. The treatment of these soft survival corrections is still strongly model dependent (recent reviews can be found in Refs. [22,23]). In our analysis, we will assume that the hard process occurs on a short enough timescale such that the physics that generate the additional particles can be factorized and accounted by an overall factor. As a consequence, the soft survival effects can be included in the calculation by multiplying the cross section by a global factor S 2 eik (denoted eikonal factor in Fig. 1). It is important to emphasize that the validity of this assumption is still an open question and should be considered a first approximation for this difficult problem. As in Refs. [24][25][26], we will assume that S 2 eik = 0.03 for pp collisions at √ s = 13 TeV. In what follows, we will estimate the diphoton production in double diffractive processes using the Forward Physics Monte Carlo (FPMC) [17], which allow us to estimate the associated cross sections and distributions taking into account of the detector acceptances. In this event generator, the hard matrix elements are treated by interfacing FPMC with HERWIG v6.5 [27] which includes perturbative parton showering followed by the hadronization. In order to estimate the impact of the Pomeron structure in the predictions, we will consider four different parametrizations for the diffractive parton distributions, which are based on different assumptions for the β -behavior and have been obtained using distinct sets of data [28,29]. For the calculation of the LbL scattering and exclusive gg → γγ production (Durham model) it is employed a dedicated event generator for exclusive processes: SuperCHIC3 [18]. The soft survival effects S 2 eik have been include in our calculations of the exclusive process assuming the model 4 implemented in the SuperChic3. On the other hand, for the LbL scattering, we assume that S 2 eik = 1. For the proton tagging at the LHC, a region of 0.015 ≤ ξ ≤ 0.15 for both protons is chosen for a center of mass energy of 13 TeV considering the standard acceptance in the central detectors. For the final state selection we use HepMC2 [30] with a plugin called HepPDT 1 which has been designed to be used by any Monte Carlo particle generator or decay package. HepPDT has the function to store particle information such as charge and nominal mass in a table which is accessed by a particle ID number. The particle ID number is defined according to the Particle Data GroupâĂŹs Monte Carlo numbering scheme [31]. The final analysis and distributions are done with ROOT [32]. Two distinct configurations of experimental offline cuts are considered: one refers to a typical central detector as ATLAS and CMS, and other for a forward detector such as LHCb. The protons are assumed to be intact in the interaction, allowing to measure the central mass, m X = √ ξ 1 ξ 2 s, where ξ 1,2 is the proton fraction momentum loss given by 1 − (p Z1,2 /6500) and √ s is the center of mass energy. This quantity can be studied in dedicated very forward detectors AFP and CT-PPS [33].
Initially, in Table I we present our results for the cross sections associated to the different channels, obtained at the generation level, without the inclusion of any selection in the events. The predictions for the double diffractive processes are presented considering four distinct parametrizations for the diffractive parton distributions. We have that the gluon -induced processes (Durham and DDP) are dominant, with the DDP predictions being strongly dependent on the Pomeron structure. In Fig. 2 we present our results for the invariant mass m γγ , transverse momentum p T (γγ) and rapidity y(γγ) distributions of the diphoton system. The DDP and Durham predictions are larger than the LbL one in the kinematical range considered. Such result contrast with that presented in Ref. [14] for P bP b collisions, where the LbL scattering is dominant due to the Z 4 enhancement. For m γγ ≤ 40 GeV and transverse momentum p T (γγ) ≤ 2 GeV, the Durham process dominates. On the other hand, for larger values of m γγ and p T (γγ), the main contribution for the diphoton production comes from double diffractive processes.
In order to obtain realistic estimates of the diphoton production in pp 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. The selection criteria implemented in our analysis of double diffractive and exclusive diphoton processes are the following:  • For a central detector: We will select events in which m(γγ) > 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 transverse momentum of the diphoton system (p T (γγ) > 3 GeV). Finally, we only will select events where photons are produced in the rapidity range |η(γ 1 , γ 2 )| < 2.5 and the central mass m X is larger than 195 GeV, which is the kinematical range covered by the forward detectors AFT and CT -PPS [33].
• For a forward detector: We will select events in which m(γγ) > 1 GeV and p T (γ, γ) > 0.2 GeV, where p T is the transverse momentum of the photons. A additional cut is applied on transverse momentum of the diphoton system (p T (γγ) > 3 GeV). Finally, we will select only events where photons are produced in the rapidity range 2.0 < |η(γ 1 , γ 2 )| < 4.5, allowing particles with p T > 0.5 GeV in the range −8.0 < η < −5.5 corresponding to the HERSCHEL selection in the LHCb.
The impact of each of these cuts on the total cross sections is summarized in Tables II and III for the central and forward detectors, respectively. Our results indicate that the inclusion of all cuts fully suppress the contribution of the LbL scattering and exclusive process for the diphoton production. We have that these contributions are completely removed by the cut on the transverse momentum of the diphoton system (p T (γγ) ≥ 3 GeV). Therefore, the events after cuts are a clean probe of the diphoton production in double diffractive processes. The results also indicate that the associated predictions are strongly dependent on the diffractive parton distribution considered. In particular, the DDP predictions for central and forward detectors are a direct probe of the diffractive quark distributions, since the diphoton production in the kinematical range considered is dominated by the qq → γγ subprocess, as demonstrated in Fig. 3, where we have calculated the distributions using the H1 -Fit A parametrization. Results for a central (forward) detector are presented in the upper (lower) panels. In order to estimate the dependence of our predictions for the distributions on the modeling of the Pomeron structure, we present in Fig. 4 the results for the distinct parametrizations and the cuts for central (upper panels) and forward (lower panels) detectors. One has that the predictions can differ by a factor larger than two, with the slope of the transverse momentum distribution being sensitive to the modeling of the diffractive quark distribution. Such result indicates that a future experimental analysis of the diphoton production in double diffractive processes can be useful to constrain this distribution.
Finally, let's summarize our main results and conclusions. In this letter we have investigated the diphoton production in diffractive and exclusive processes present in pp collisions at the LHC. Our main focus was in the possibility of separate the events associated to the double diffractive processes, where the diphotons are produced by the interaction between quarks and gluons of the Pomeron. We have demonstrated that the background associated to the LbL scattering and the exclusive process can be strongly reduced by a cut on the transverse momentum of the diphoton system. As a consequence, the study of the diphoton production with   p T (γγ) ≥ 3 GeV becomes a direct probe of the diffractive mechanism and the underlying assumptions associated to the treatment of the gap survival as well as to the description of the Pomeron structure. We shown that the diphoton production is dominated by the qq → γγ subprocess. Moreover, our results indicated that the analysis of the invariant mass, transverse momentum and rapidity distributions are sensitive to the modeling of the diffractive quark distribution.