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ultrarelativistic charged hadrons ( protons or nuclei ) give rise to strong electromagnetic fields . consequently , in hadronic collisions at the lhc , the photon stemming from the electromagnetic field of one of the two colliding hadrons can interact with one photon of the other hadron or can interact directly with the other hadron @xcite .
the study of these photon - photon and photon - hadron interactions offers a unique opportunity to study fundamental aspects of quantum electrodynamics ( qed ) and quantum chromodynamics ( qcd ) .
in particular , the two - photon particle production have been extensively discussed in literature ( for reviews see , e.g. , refs .
@xcite ) , with a recent revival of interest due to the experimental results on the exclusive two - photon production of @xmath0 and @xmath4 pairs by @xmath5 interactions reported by the cms collaboration @xcite .
the observation of these processes demonstrated the feasibility of measuring such events within the current experimental apparatus available at the lhc , allowing novel studies of qcd at very high energies and searches for beyond standard model physics ( see , e.g. , ref .
@xcite ) .
the basic ingredient in the analysis of the photon - induced processes is the description of the equivalent photon distribution of the hadron , given by @xmath6 , where @xmath7 is the fraction of the hadron energy carried by the photon and @xmath8 has to be identified with a momentum scale of the process .
the equivalent photon approximation of a charged pointlike fermion was formulated many years ago by fermi @xcite and developed by williams @xcite and weizsacker @xcite .
in contrast , the calculation of the photon distribution of the hadrons still is a subject of debate , due to the fact that they are not pointlike particles . in this case
it is necessary to distinguish between the elastic and inelastic components .
the elastic component , @xmath9 , can be estimated analysing the transition @xmath10 taking into account the effects of the hadronic form factors , with the hadron remaining intact in the final state @xcite .
in contrast , the inelastic contribution , @xmath11 , is associated to the transition @xmath12 , with @xmath13 , and can be estimated taking into account the partonic structure of the hadrons , which can be a source of photons ( see , e.g. refs .
@xcite ) .    in a recent paper
@xcite we have proposed , for the first time , the study of the diffractive quarkonium photoproduction in @xmath2 collisions at lhc energies as a probe of the photon distribution of the proton .
our results indicated that , for the models considered , the contribution of the inelastic processes is of the same order or larger than the elastic one , with the predictions for the rapidity distributions being largely different , which makes the experimental discrimination feasible , with the detection of the two protons into the final state being indispensable to separate the inelastic and elastic events .
our goal in this paper is to extend our previous analysis for the @xmath0 and @xmath1 production by two - photon interactions in @xmath2 collisions at lhc energies ( for related studies see refs .
our study is strongly motivated by the recent results reported by the cms collaboration , which shows that the experimental technique currently applied allows the measurement of the two - photon production of pairs with large invariant mass in a scenario with non - negligible pileup @xcite , and by the perspective of setup of forward detectors by the cms and totem collaborations @xcite , which will enhance the kinematic coverage for such investigations , bringing more data to elucidate the proper model for the photon .
it is important to emphasize that the uncertainty present on the current measurements is an important aspect regarding the observation of rare processes that have not been measured in laboratory , like the exclusive production of photon pairs in @xmath2 , @xmath14pb and pbpb collisions , with predictions presented for the first time in ref .
then , the study of the different approaches for the photon flux is important to provide accurate predictions to be compared with data . in this sense ,
the purpose of this paper is to investigate the available approaches for the two - photon processes in @xmath2 collisions and to determine the regions of the phase space that allow the discrimination among these possible models .
this paper is organized as follows . in the next section we present a brief review of the formalism for the two - photon particle production and discuss the different models for the photon flux . in section [ sec : res ]
, we present our results for the effective photon - photon luminosities and for the two - photon @xmath0 and @xmath1 differential cross sections .
finally , in section  [ sec : sum ] we summarize our main conclusions .
following ref .  @xcite we will write the cross sections for the @xmath3 production of a final state @xmath15 @xmath16 or @xmath17 of invariant mass @xmath18 in a factorized form : @xmath19 where @xmath20 is the cross section for the hard subprocess @xmath21 and @xmath22 is the effective photon - photon luminosity for the production of the system @xmath15 at rapidity @xmath23 .
the effective luminosity is given in terms of the photon distribution of the incident hadrons as follows @xmath24 the photon distribution of a nucleon consist of two parts : the elastic and inelastic components .
in the elastic case , we have the coherent emission of photons from the hadron , without the dissociation of the incident hadron .
in contrast , in the inelastic case the photons are emitted by the quarks and antiquarks present in the hadrons , and the incident hadron is excited in a low - mass state .
consequently , we can define three different classes of @xmath3 events : ( a ) the _ elastic _ processes , where the final state @xmath15 is produced with the two incident hadrons remaining intact , and the effective luminosity is proportional to @xmath25 ; ( b ) the _ semielastic _ processes , where one of the incident hadrons remain intact and the other dissociates , with @xmath26 $ ] and ( c ) _ inelastic _ processes , where the two incident hadrons dissociates and @xmath27 .
these three classes are represented in fig .
[ diagrams ] . in all these processes
, the final state will be characterized by the presence of the state @xmath15 and two rapidity gaps , with the hadrons or the low - mass hadron beam fragments traveling in the beam direction ( for related studies see , e.g. ref .
@xcite ) .    in principle
, these different processes can be separated by the tagging of the two very forward scattered hadrons and by the requirement of the presence of large rapidities gaps in the central detector .
unfortunately , forward detectors were not available during run i of the lhc , and the next run starting in 2015 is going to produce a sizable pile - up obliterating the observation of rapidity gaps .
therefore , experimental separation of those contributions is a hard task and demands better knowledge of final - state kinematics in an observed event . in run
i , the cms collaboration have separated the signal of two - photon production of pairs ( @xmath0 and @xmath1 ) by selecting lepton tracks from the information recorded in the tracking system , which can be used to analyze exclusive events even in a scenario with large number of interaction per bunch crossing ( high pileup ) .
offline , events have been selected with no additional tracks associated to the @xmath28 vertex . since both elastic and non - elastic processes contribute in this case ,
we have higher photon luminosities , although larger uncertainties in the theoretical predictions , due to the lesser theoretically controlled inelastic photon flux ( see below ) .
currently , there is a great expectation due to the installation of the cms - totem precision proton spectrometer ( ct - pps ) @xcite , which will be setup in a first stage in one of the cms sides at about 200 metres from the interaction point .
certainly , this new detector will improve the analysis of exclusive processes and allow us to access a variety of physics topics at high luminosities .
however , a precise determination of the semielastic contribution will be still fundamental before the search of new physics in two - photon processes .    [ cols="^,^ " , ]      ( color online ) upper panels : ratio between the sum of semielastic and elastic cross sections and the elastic cross section ; lower panels : ratio between the inelastic cross section and sum of semielastic and elastic cross sections . ]
in this paper we have investigated the contribution of inelastic , semielastic and elastic processes for the @xmath0 and @xmath1 production by two - photon interactions in @xmath2 collisions considering different models for the inelastic photon distribution .
we demonstrated that these distinct models implies very distinct behaviours for the effective photon - photon luminosities and differential cross sections .
it implies that the use of the two - photon particle production mechanism to search rare events will be not a easy task before the determination of the correct description of the inelastic photon distribution .
in particular , since in a first moment only one of the very forward detectors of ct - pps will be installed , which would not eliminate the semielastic processes .
our results indicate that the analysis of the rapidity distribution for @xmath1 production can be a discriminator among the possible models for the photon distribution .
in particular , the determination of the distribution for central rapidities already differentiate the distinct models .
moreover , the analysis of the invariant mass dependence of the ratio between the sum of semielastic and elastic cross sections and the elastic one also can be used to determinate the inelastic photon distribution . finally , we believe that the analyses carried out with the data of the two - photon production of pairs , in conjunction with the exclusive vector meson production discussed in ref .
@xcite , will allow us to precisely determine the adequate description of the photon distribution , which still is an important open question in high energy physics .
this work has been supported by cnpq , capes and fapergs , brazil .
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in this paper we propose the study of the @xmath0 and @xmath1 production by two - photon interactions in @xmath2 collisions at lhc energies to constrain the photon flux associated to an ultrarelativistic proton . 
 we consider the current parametrizations for the photon distribution of the proton and estimate the effective photon - photon luminosities for elastic , semielastic and inelastic processes . 
 moreover , we present predictions for the rapidity and invariant mass distributions for the two - photon production of @xmath0 and @xmath1 in @xmath3 interactions at lhc energies . 
 we demonstrate that the semielastic and inelastic predictions are strongly dependent on the description of the inelastic photon flux , and that the relative contribution of the different processes depends on the invariant mass of the final state . 
 our results implies that a dedicated experimental analysis of the two - photon production of @xmath0 and @xmath1 with the tagging of one of the protons in the final state can be useful to constrain the magnitude of the inelastic component of the photon distribution .