arXiv:1006.3291v1 [hep-ph] 16 Jun 2010 MIT bag model inspired partonic transverse momentum distribution for prompt photon production in pp collisions F.K. Diakonos, 1 N.K. Kaplis, 1 and X.N. Maintas 1 1 Department of Physics, University of Athens, GR-15771 Athens, Greece (Dated: June 17, 2010) We consider the prompt photon production in pp collisions using, within the framework of pertur- bative QCD, a non-gaussian distribution for the transverse momentum distribution of the partons inside the proton. Our description adopts the widely used in the literature factorization of the partonic momentum distribution into longitudinal and transverse components. It is argued that the non-gaussian distribution of the intrinsic transverse momenta of the partons is dictated by the asymptotic freedom as well as the 3D confinement of the partons in the proton. To make this as- sociation more transparent we use the MIT bag model, which plainly incorporates both properties (asymptotic freedom, confinement), in order to determine in a simplified way the partonic transverse momentum distribution. A large set of data from 6 different experiments have been fitted with this simple description using as a single free parameter the mean partonic transverse momentum 〈kT 〉. Surprisingly enough, a perfect fit of the experimental data turns out to require 〈kT 〉 values which are compatible with Heisenberg’s uncertainty relation for the proton and decrease almost smoothly as a function of the scaled variable z = p T √ s , where pT is the transverse momentum of the final photon and √ s is the beam energy in the center of mass frame. Our analysis indicates that asymp- totic freedom and 3D confinement may influence significantly the form of the partonic transverse momentum distribution leaving an imprint on the pp → γ + X cross section. PACS numbers: 13.60.Le,13.85.Ni,12.38.Qk The production of photons with large transverse mo- mentum is an excellent probe of the dynamics in hard scattering processes [1, 2]. In particular, the study of direct photon production possesses numerous and well known advantages, both theoretical and experimental [2– 9]. In the latter case the main advantage is that pho- tons are easier to detect than jets. From the theoreti- cal point of view the main advantage is the simplicity of the process allowing for an accurate determination of the gluon distribution within the proton. In the lowest order (O(αα s )) only two subprocesses, gq → γq (Comp- ton) and q ¯ q → γg (annihilation), contribute to high p T photons. Their characteristic signature is the produc- tion of a photon isolated from the hadrons in the event, accompanied by a kinematically balancing high-p T jet appearing on the opposite site. In the next-to-leading order (NLO) the process associated with the production of a photon coming from the collinear fragmentation of a hard parton produced in a short-distance subprocess, constitutes a background to the direct photon production of the same order in α s as the corresponding Born level terms [10] provided that the fragmentation scale is large enough. However, the contribution from fragmentation remains small (less than 10%) for fixed target experi- ments and becomes significant only in inclusive prompt photon production at higher collider energies [10]. Re- cently there has been observed a systematic disagreement between theoretical NLO predictions [2, 5, 8, 11–15] and experimental data [16, 17] for prompt photon production which cannot be globally improved adapting the gluon distribution function. Especially for fixed target exper- iments NLO approximation shows a significant underes- timation of the cross section for some of the measured data sets [11, 16]. A similar discrepancy can be observed between NLO calculations and the experimental data of inclusive single neutral pion production: pp → π 0 X in mostly the same experiments as in the photon case [18]. For the pion production the theoretical description is im- proved by taking into account certain large contributions to the partonic hard scattering cross section to all orders in perturbation theory using the technique of threshold resummation [18, 19]. The same technique can be applied to the photon production by calculating the QCD resum- mation contribution to the partonic processes qg → γq and q ¯ q → γg [20, 21]. However, the result is a rela- tively small enhancement, not enough to compensate for the gap between the prompt photon data in fixed tar- get experiments [11, 21] and theoretical predictions. An additional improvement can be achieved by including in the theoretical treatment resummation effect to the frag- mentation component succeeding in this way a good de- scription of UA6 and R806 pp data but still failing to reproduce the data of E706 [11]. The conclusion of this analysis is that resummed theoretical results present a residual shortfall in the description of photon and pion production data in fixed target experiments. One pos- sible explanation of this effect is the existence of a non- perturbative contribution associated with intrinsic par- tonic transverse momentum k T [4, 11, 22]. To incorpo- rate this effect in the conventional pQCD one assumes