A check-up for the statistical Parton model

Abstract

We compare the Parton distributions deduced in the framework of a quantum statistical approach for both the longitudinal and transverse degrees of freedom with the unpolarized distributions measured at HERA and with the polarized ones proposed in a previous paper, which have been shown to be in very good agreement also with the results of experiments performed after that proposal. The agreement with HERA data in correspondence to very similar values for the "temperature" and the "potentials" found in the previous work gives a robust confirm of the statistical model. The unpolarized distributions are compared also with the result of NNPDF. The free parameters are fixed mainly by data in the range (0.1, 0.5) for the x variable, where the valence Partons dominate, and in the small x region for the diffractive contribution. This feature makes the parametrization proposed here very attractive.

Status of the Quantum Statistical Approach to the Parton Distributions

“…Therefore for the light valence partons one should have instead of the factors 𝐴𝑋 ℎ 𝑞 the factors 𝐴 ′ ln (1 + exp 𝑌 ℎ 𝑞 ) and one could recover the form proposed in [21] for the valence quarks simply assuming the proportionality between 𝑋 ℎ 𝑞 and ln (1 + exp 𝑌 ℎ 𝑞 ) . Indeed in [24], where both 𝑋 ℎ 𝑞 and 𝑌 ℎ 𝑞 are fixed by comparing with the fermion distributions proposed in [25] the proportionality holds with a good approximation . For the non diffractive part of their antiparticles one has a slight change, since ln…”

“…Status of the Quantum Statistical Approach to the Parton Distributions In Table 1 we compare the "temperature" and the "potentials" found in [21] with the ones obtained in [26] and in [24] Instead for the gluons the agreement holds up to about 𝑥 = 0.2, while above the different parametrization lead to a faster decrease for the distribution proposed by HERA . The comparison was repeated [14] with the distributions found by [27] better in agreement with [24] than with [25] . More recently the Planck formula for the gluons was compared [28] with the distribution found by ATLAS [29] and the very good agreement shown in Fig.…”

“…When HERA presented the parton distributions derived by the combined fit to H1 and ZEUS data, Jacques Soffer immediately realized their similarity with the ones found in [21] . Therefore in [24] the free parameters introduced in [21] were fixed by minimizing the difference from the unpolarized distributions proposed by HERA and from the polarized in [21], which were…”

Low $Q^{2}$ Boundary Conditions for DGLAP Equations Dictated by Quantum Statistical Mechanics Functions

“…Some years ago a joint analysis of the DIS data measured in the H1 and ZEUS [17] experiments has been performed to give the unpolarized parton distributions and Jacques Soffer immediately realized the similarity with the statistical distributions. To perform a check for the quantum statistical parton distributions, we determine the parameters introduced [18] in order to reproduce the Hera result for the unpolarized distributions of the light parton fermions, while for the polarized ones we require to reproduce the expressions found in 2002 [19], which have been successful to describe the polarized structure functions g p,d,He 3 (x) and the production of W ± weak bosons [20]. Our results for the parton distributions are described in Figures 1-3 and the parameters are compared with the ones found in 2002 in Table 1.…”

Quantum statistical parton distribution function

“…Some years ago a joint analysis of the DIS data measured in the H 1 and ZEUS [23] experiments has been performed to give the unpolarized parton distributions and Jacques Soffer immediately realized the similarity with the statistical distributions. To perform a check for the quantum statistical parton distributions [24] the parameters introduced in the statistical approach are fixed in order to reproduce the Hera result for the unpolarized distributions of the light parton fermions, while for the polarized ones the goal is to reproduce the expressions found in [19], which have been successful to describe the polarized structure functions g p,d,He 3 1 (x) [19,14,25], and the production of the W ± weak bosons [26,28,29]. In the Table we write in the first two columns the values found in [19] and [24], respectively, in the third one the coefficients obtained with the extension to the transverse momenta are compared with the "ad hoc" factors, X h q introduced in [19]; finally in the fourth one a recent evaluation [29] of the parameters of [19].…”