# Meson production in two-photon interactions at energies available at CERN Large Hadron Collider

###### Abstract

The meson production cross sections are estimated considering photon-photon interactions in hadron - hadron collisions at CERN LHC energies. We consider a large number of mesons with photon-photon partial decay width well constrained by the experiment and some mesons which are currently considered as hadronic molecule and glueball candidates. Our results demonstrate that the experimental analysis of these states is feasible at CERN - LHC.

###### pacs:

12.40.Nn, 13.85.Ni, 13.85.Qk, 13.87.CeThe Large Hadron Collider (LHC) at CERN started high energy collisions two years ago. During this period a large amount of data have been collected considering collisions at = 0.9, 2.36 and 7 TeV as well as collisions at = 2.76 TeV. Currently, there is a great expectation that LHC will discover new physics beyond the Standard Model, such as supersymmetry or extra dimensions. However, we should remember that the LHC opens a new kinematical regime at high energy, where several questions related to the description of the Quantum Chromodynamics (QCD) remain without satisfactory answers. Some open questions are the search for non- resonances, the determination of the spectrum of states and the identification of states with anomalous couplings. A possible way to study these problems is the study of meson production in two-photon interactions brodsky ; achasov . In general, this process is studied in leptonic colliders. An alternative is to use ultra-relativistic protons and nuclei, which give rise to strong electromagnetic fields and estimate the production of a given final state considering the photon - photon and photon - hadron interactions. In particular, it is possible to study photon - photon interactions in proton - proton and nucleus - nucleus collisions at LHC (For a review see Ref. baur ). Recently, Bertulani bertulani revisited this subject and proposed the study of the meson production in ultraperipheral heavy ion collisions at LHC in order to constrain the two-photon decay widths. In this letter we extend this previous study for the meson production in two-photon interactions in proton - proton collisions. Initially we calculate the cross sections for mesons with photon-photon partial decay width well constrained by the experiment, which allows to constrain the theoretical methods and calibrates the experimental techniques. After we predict the cross sections for mesons which are currently considered as glueball and hadronic molecule candidates. Our results shows that LHC can be used to investigate these states.

Lets consider the hadron-hadron interaction at large impact parameter () and at ultra relativistic energies (For recent reviews see, e.g., Ref. uphic ). In this regime we expect the electromagnetic interaction to be dominant. In heavy ion colliders, the heavy nuclei give rise to strong electromagnetic fields due to the coherent action of all protons in the nucleus, which can interact with each other. In a similar way, it also occurs when considering ultra relativistic protons in colliders. The photon stemming from the electromagnetic field of one of the two colliding hadrons can interact with one photon of the other hadron (two-photon process) or can interact directly with the other hadron (photon-hadron process). The total cross section for a given process can be factorized in terms of the equivalent flux of photons of the hadron projectile and the photon-photon or photon-target production cross section. In the case of the production of a neutral state in two-photon interactions the total cross section is given by (See, e.g., serbo )

(1) |

where characterizes the presence of a rapidity gap in the final state, is the squared center of mass energy, is the distribution function which is associated to the flux of photons generated by the hadron (), , with and the photon and hadron energies, respectively. Moreover, is the photon-photon cross section given by

(2) |

where , and are the spin, mass and the photon-photon partial decay width of the final state , respectively, and the function enforces energy conservation.

The main input in our calculations are the equivalent photon flux for a ultrarelativistic proton, , and the two photon partial decay widths, . Currently there are different models for the equivalent photon flux available in the literature (See e.g. Ref. nystrand ). The general expression for the equivalent photon flux of an extended object is given by serbo

(3) |

where is the momentum transfer from the projectile and its form factor. Moreover, with the mass of the projectile. The presence of the form factor cuts off the photon flux above GeV. As its dependence on the photon virtuality is , the average virtuality is very small, which allow us to treat the processes as due to quasi-real photon photon collisions.

Considering only the electric dipole form factor for the proton, GeV, the following expression for the equivalent photon flux can be obtained

(4) |

where . We denote this model by Electric in what follows. If the term containing in Eq. (3) is disregarded, the equivalent photon spectrum of high energy protons is given as follow

(5) |

This expression was derived originally by Dress and Zeppenfeld in Ref. dz and will be denoted DZ hereafter. In Ref. kniehl , the author studied the effect of including the magnetic dipole moment and the corresponding magnetic form factor of the proton, obtaining a spectrum (denoted Electric + Magnetic hereafter) which is smaller than the DZ one at small . Another model considered in literature is the use of a minimum impact parameter, = 0.7 fm, in the photon energy spectrum produced by a point particle, which is given by

(6) |

where and are modified Bessel functions and . In Fig. 1 we present a comparison between these different models for the photon flux. A basic characteristic of the distinct models for the photon spectrum is that they diminish with energy approximately like . Consequently, the photon spectrum is strongly peaked at low , so that the photon - photon center of mass energy, , is much smaller than the center of mass energy of the proton - proton system. Therefore, the main contribution for the total cross section, Eq. (1) comes from the small behaviour of the photon spectrum. In this region, the DZ model predicts a larger photon flux. In contrast, the Electric one, predicts the lower photon flux. The other two models, the Electric + Magnetic and = 0.7 fm models, predict intermediate values for the photon flux. At low () the difference between the models is ever smaller than 20 %. However, the difference increases at larger values of . At the difference among the DZ and Electric models is 25 %, increasing for 100 % at . In this letter we will use the and photon fluxes in our calculations, which allow us to estimate the theoretical uncertainty in our predictions.

State | (keV) | (pb) | (pb) | ||
---|---|---|---|---|---|

TeV | TeV | TeV | TeV | ||

In what follows we present our predictions for the total cross section considering proton - proton collisions at LHC and center-of-mass energies of TeV and TeV. We consider either taken from experiment or from theory. Initially, we present in Table 1 our predictions for the mesons which have partial decay ratio reasonably well constrained by the experiment, which allows to use the values present in the Particle Data Group PDG . As emphasized before, the study of mesons which have its decay ratio well known is fundamental to constrain the theoretical methods and calibrate the experimental techniques, for in a second moment investigate the production of exotic particles. As expected from Eqs. (1) and (2), the cross sections decrease at larger values of the meson mass and increase at larger values of . Moreover, the cross sections increase by when the center of mass energy increases from 7 to 14 TeV. The difference between the and depends of the final state and it is of the order of . Assuming the design luminosity mbs the corresponding event rates will be larger than events/year at TeV, making the experimental analysis of these final states feasible at LHC.

State | (keV) | (pb) | (pb) | ||
---|---|---|---|---|---|

TeV | TeV | TeV | TeV | ||

In Tables 2, 3 and 4 we present our predictions for some mesons that does not have two photon partial decay rates well constrained by the experiment. Our goal now is to verify if the study of the meson production in two-photon interactions at LHC can be used to constrain the partial decay rates and, consequently, the theoretical models considered in our calculations. In Table 2 we consider the theoretical values for as given in bertulani . The small values of for the and states implies that the experimental analysis of these states is a hard task.

Recently, several new observed states have been interpreted as being hadronic molecules, i.e bound states of two or more mesons (For a review see, e.g., review_mol ). In these models two photon radiative decays are considered diagnostic tools which are sensitive to the inner structure of the short-lived molecules. Here we consider the model proposed in Refs. mol1 ; mol2 ; mol3 , where the decay rates are obtained considering an effective Lagrangian which includes both the coupling of the molecular bound state to their hadronic constituents and the coupling of the constituents to other hadrons and photons. For instance, in this model the meson is considered as a superposition of the molecular and states, while the meson is a bound state of and mesons. In Table 3 we present our predictions for some hadronic molecule candidates considering the two-photon decay rates given in Refs. mol1 ; mol2 ; mol3 . We assume that the masses of the mesons , , and are given by , , and MeV, respectively. For the lighter state, , we predict large values for the total cross sections and event rates larger than events/year at TeV. For the heavy states we predict event rates larger than events/year with a strong dependence on the quantum numbers of the state. The large values predicted by this model imply that the experimental analysis of these final states can be useful to constrain the underlying physics.

State | Mass | (keV) | (pb) | (pb) | ||
---|---|---|---|---|---|---|

(MeV) | TeV | TeV | TeV | TeV | ||

Finally, in Table 4 we present our predictions for mesons which are glueball candidates, i.e., particles dominantly made of gluons. It is important to emphasize that none of them was up to now unambiguously identified. However, the existence of glueballs is predicted in many theoretical calculations, including lattice QCD (For a recent review see, e.g., review_glueball ). In our calculations we use the two-photon decay rates proposed in Ref. magno_mario , where the glueball production was estimated in ultraperipheral heavy ion collisions. Due to the small values of for glueball states, we predict a low value for the total cross section and event rates smaller than events/year.

State | (eV) | (pb) | (pb) | ||
---|---|---|---|---|---|

TeV | TeV | TeV | TeV | ||

Some comments are in order before the summary of our main results. Firstly, meson production in two-photon interactions are clean events, with a final state characterized by two very forward protons, the meson (or its decay products) in the central detector and the presence of two rapidity gaps. Two rapidity gaps in the final state also are generated in central exclusive processes (CEP) by Pomeron - Pomeron interactions, where a Pomeron () is associated to a colorless object (See, e.g., forshaw ). The magnitude of meson production in antoni ; magno ; harland1 ; harland . In particular, in Ref. harland1 , the central exclusive heavy quarkonia ( and ) production at the LHC has been studied in detail. In comparison with our predictions for production, the results presented in harland1 are at least three orders of magnitude larger. It is important to emphasize that the CEP predictions describe the CDF data for the exclusive production cdf . In the case of production, the CEP predictions are a factor two larger. Consequently, we expect that for these final states the production to be dominated by antoni ; magno ; harland ). Moreover, interactions are much less sensitive to these effects. They are under theoretical control and can be considered a lower bound for the event rates of these final states. Another aspect which we would like to comment is the experimental separation among interactions. For both cases the -distribution is of the type . The main distinction is associated to the slope which is almost 4 (40) GeV for ) interactions forshaw ; tagging ; denterria . It implies that photon - induced interactions take place larger impact parameters (i.e. are less central) than Pomeron induced processes and, consequently, the exchanged squared momentum is smaller. As a consequence it is expected that the transverse momentum distribution of the scattered protons to be different and values. This expectation is corroborated by the results presented, for instance, in the Refs. tagging ; kepka , where the transverse momentum distribution has been quantified considering different final states. Certainly, this subject deserves more detailed studies. However, it is important to emphasize that the ATLAS and CMS collaborations have a program of forward physics with extra detectors located in a region away from the interaction point, which probably can eliminate many serious backgrounds. interactions, with the latter predicting large ( and cross sections are strongly dependent on the treatment of the soft final states interactions and the associated survival probability. In contrast, the predictions for light meson production in interactions still is an open question, since in this case the main contribution for the cross section comes from non-perturbative regime, which implies the use of phenomenological models in order to estimate the total cross section (For some related studies see, e.g., Refs. interactions. On the other hand, the production of light mesons in interactions has been estimated in Refs.

In summary, in this letter we estimated the the meson production in two-photon interactions at CERN-LHC, which is characterized by two rapidity gaps in the final state. We have obtained non-negligible values for the total cross sections, which implies that the experimental study is feasible. In particular, our results indicate that this process can be useful to test the glueball and hadronic molecule models.

## Acknowledgments

This work was supported by CNPq, CAPES and FAPERGS, Brazil.

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