# Production of meson at LHC

## Abstract

The paper is devoted to theoretical consideration of inclusive meson production at LHC. It is shown that existing experimental data on meson production at LHCb detector can be described in the framework of NRQCD formalism and color-singlet component with phenomenological value of matrix element gives main contribution. Using this model we present theoretical prediction for integrated cross sections and transverse momentum distributions for inclusive production at other LHC detectors. The case of meson production at LHC is also considered.

## I Introduction

Heavy quarkonia production can be described as production of heavy quark-antiquark pair with small relative momentum in initial partons’ interaction and subsequent projection of this pair to hadronic states with suitable quantum numbers. According to NRQCD Bodwin et al. (1995) in addition to colour singlet component (CS) one has to take also into account contributions of colour-octet components (CO) with unknown nonperturbative long-distance matrix elements (LDME), that are treated as free parameters. In NRQCD the cross section of heavy quarkonium production is written as expansion over the small relative velocity , so the number of unknown parameters is limited. As a result, one can hope that such approach could describe accurately momentum spectra of heavy quarkonia.

Unfortunately, currently NRQCD does not describe these spectra well enough, since one more problem exists. Usually integrated over transverse momenta distribution functions of initial partons are used in calculations. There is one more approach, where this drawback is removed: so called factorization Hagler et al. (2001a, b); Kniehl et al. (2006). In this approach transverse momentum dependence of partonic distribution functions is taken into account. Unfotunatelly, this technique is a little bit ambiguous, so more intensive study is required.

In our previous works Likhoded et al. (2012, 2013, 2014), devoted to -wave quarkonia states production in hadronic interaction, it was shown that in high transverse momentum region () one can use approximation to describe spectrum of final qiuarkonium, while relative contributions of CS and CO states can be determined from analysis of ratio. In this model distribution is caused by emission of additional gluon in the initial state. The same effect also makes possible the production of axial meson, that is forbidden in identical gluons’ interaction by Lanau-Yang theorem. The only opened question in this approach is the enhance of CS contribution (or, in other words, derivative of the quarkonium’s wave function in the origin). In the work Jia et al. (2014), on the other hand, it is argued that NLO corrections allows one to reproduce experimental data using CS LDME determined from decay width. Recently Collaboration LHCb has published new data on meson production, so one can test the availablilty of mentioned method in this case. Below we present the results of analysis of new LHCb data.

## Ii Inclusive Production

Recently LHCb collaboration has published new experimental work devoted to inclusive meson production Aaij et al. (2014), so it would be extremely interesting to study this process theoretically. This is the topic of the current note.

According to NRQCD scaling rules Bodwin et al. (1995) (see also Biswal and Sridhar (2012)) CS, as well as - and -wave CO components should give main contributions to the cross section of the process under consideration:

(1) | |||||

where we use results of the work Meijer et al. (2008) for the expressions of the hard cross sections, is the value of the heavy quarkonum wave function in the CS state at the origin, and the following notations for CO LDME are used Meijer et al. (2008):

(2) | |||||

(3) |

Color singlet LDME can be determined potential models Munz (1996); Ebert et al. (2003); Anisovich et al. (2007); Wang (2009); Li and Chao (2009); Hwang and Guo (2010) or leptonic width of meson:

(4) |

As for octet LDME, our analysis shows, that experimental data Aaij et al. (2014) can be described taking into account only contribution of -wave CO component with the matrix elemet

(5) |

that corresponds to

(6) |

The contribution of -wave CO competent is strongly suppressed. Using presented above parameter values it is easy to obtain the following cross section of meson production at LHCb (the cut is imposed on the transverse momentum of the final charmonium):

(7) |

The contributions of CS and -wave CO components are about 70% and 30% respectively. The value (7) is in good agreement with experimental result

(8) |

It can be seen from Fig.1a, that transverse momentum distribution are also in good agreement with experimental data. It should be noted, that presented above values of the LDMEs are strongly correlated. For example, increasing the value of the CS matrix element up to the value one can exclude the CO states completely.

It is interesting to compare our results with the results presented in Biswal and Sridhar (2012). According to Case-I fit of the last paper (see also discussion in Biswal and Sridhar (2012)) experimental data can be described by CS contributions only and -wave CO components increase the cross section by about two orders of magnitude. The value of corresponding LDME in Biswal and Sridhar (2012) is

(9) |

that is significantly larger than in (6). The reason for this discrepancy could be caused by the fact, that CO matrix elements in Biswal and Sridhar (2012) were obtained from the fit of production cross section at CDF Cho and Leibovich (1996), where CO components give main contribution.

We have mentioned above, that of production of other heavy quarkonia states is considered the situation is quite different: either contribution of CO components is dominant or the value of singlet LDME is anomalously large. So we think that independent check of LHCb results at other detectors would be desirable. Using matrix elements from eq.(4), (5) it is easy to obtain the values of the cross sections at CMS and ATLAS detectors, presented in table 1.

In the framework of the same model one can obtain also theoretical predictions for meson production at LHC. The CS matrix element is this case equals

(10) |

while CO matrix element can be estimated using dimensional arguments, as it was done in paper Likhoded et al. (2012):

(11) |

Resulting cross sections can be found in table 1 and transverse momentum distribution is shown in Fig.1b. It turns out that for all detectors the contribution of CO component is about 2%.

exp | ||
---|---|---|

LHCb | 0.58 | 0.17 |

CMS | 0.85 | 0.28 |

ATLAS | 0.63 | 0.22 |

## Iii Conclusion

The paper is devoted to theoretical analysis of inclusive heavy quarkonia production at LHC. It is shown that in the case of meson experimental data, obtained by LHCb collaboration, can be described in the framework of NRQCD model with phenomenological value of colour singlet matrix element and CS component gives main contribution. Using the same model we obtain predictions for cross sections and transverse momentum distributions at other LHCb detectors and reaction.

The work was financially supported by RFBR (grant #14-02-00096 A) and grant of SAEC “Rosatom” and Helmholtz Association.

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