Dynamical and thermal descriptions in parton distribution functions
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ELEMENTARY PARTICLES AND FIELDS Theory
Dynamical and Thermal Descriptions in Parton Distribution Functions* J. Cleymans1)** , G. I. Lykasov2)*** , A. S. Sorin2)**** , and O. V. Teryaev2)***** Received March 31, 2011
Abstract—We suggest a duality between the standard (dynamical) and statistical distributions of partons in the nucleons. The temperature parameter entering into the statistical form for the quark distributions is estimated. It is found that this effective temperature is practically the same for the dependence on longitudinal and transverse momenta and, in turn, it is close to the freeze-out temperature in high-energy heavy-ion collisions. DOI: 10.1134/S1063778812060099
The description of hadron production using statistical models has been pioneered several decades ago by Fermi [1], Pomeranchuk [2], Landau [3], and Hagedorn [4]. The transverse momentum spectrum of particles produced in hadron–hadron collisions can be presented in the simple form ρh ∼ exp(−mht /T ), where mht is the transverse mass of the hadron h and T is sometimes called the thermal freeze-out temperature. As is well known, the statistical (thermal) models have been applied successfully to describe hadronic yields produced in heavy-ion collisions (see, for example, [5–9] and references therein). The temperature obtained in these analyses is often referred to as chemical freeze-out temperature and is consistently slightly larger than the thermal freeze-out temperature. At the same time, the source of very fast thermalization is currently unknown and alternative or complementary possibilities to explain the thermal spectra are of much interest. Situations where statistical models have been applied, while the notion of statistical system was not obvious, are not uncommon. In particular, the statistical model was successfully applied to analyze deep inelastic lepton–nucleon scattering (DIS) [10, 11], where the statistical form [12–14] for distributions of unpolarized and polarized quarks and gluons (partons) in a nucleon was used. ∗
The text was submitted by the authors in English. UCT-CERN Research Centre and Department of Physics; University of Cape Town, South Africa. 2) JINR, Dubna, Russia. ** E-mail: [email protected] *** E-mail: [email protected] **** E-mail: [email protected] ***** E-mail: [email protected] 1)
This model may be compared with more standard parametrization of parton distributions based on the Regge theory at low x and quark counting rules at large x [15–19]. It is especially interesting to find a counterpart and give a physical meaning of the temperature introduced in the statistical model for the description of parton distribution functions. This is the main goal of this paper. Making this comparison we suggest a concept of duality between the statistical and dynamical descriptions of the DIS and strong interactions of particles and explore its consequences and implications. We do not consider the question of scaling violations for different values of Q2 , these will come into play when considering gluon or
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