Partonic transverse momenta in non-relativistic hyper-central quark potential models

• Published in: arXiv.org
• Main Authors: Diakonos, F K, Kaplis, N K, Maintas, X N
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 16.06.2010
• Subjects: Collision dynamics; Dependence; Gaussian distribution; Mathematical models; Normal distribution; Parameters; Partons; Physics - High Energy Physics - Phenomenology; Protons; Quarks; Three body problem; Transverse momentum
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1006.3294

We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schr\"odinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization ansatz, we incorporate the obtained transverse-momentum distribution in a perturbative QCD scheme for the calculation of the cross-section for prompt photon production in pp collisions. A large set of experimental data is fitted using as a single free parameter the mean partonic transverse momentum. The dependence of <k T> on the collision characteristics (initial energy and transverse momentum of the final photon) is much smoother when compared with similar results found in the literature using a Gaussian distribution for the partonic transverse momenta. Within the considered class of hyper-central quark potentials the one with the weaker dependence on the hyper-radius is preferred for the description of the data since it leads to the smoothest mean partonic transverse-momentum profile. We have repeated all the calculations using a two-body potential of the same form as the optimal (within the considered class) hyper-central potential in order to check if the presence of three-body forces is supported by the experimental data. Our analysis indicates that three-body forces influence significantly the form of the parton transverse-momentum distribution and consequently lead to an improved description of the considered data.