Structure functions of the nucleon in a statistical model

Abstract

Deep inelastic scattering is considered in a statistical model of the nucleon. This incorporates certain features which are absent in the standard parton model such as quantum statistical correlations which play a role in the propagation of particles when considering Feynman diagrams containing internal lines.The inclusion of the O(α s ) corrections in our numerical calculations allows a good fit to the data for x ≥ 0.25. The fit corresponds to values of temperature and chemical potential of approximately T = 0.067 GeV and µ = 0.133 GeV. The latter values of parameters, however, give rise, for all x, to a large value for R = σ L /σ T .

Nuclear EMC effect in a statistical model

“…with the upper sign for fermions (quarks, anti-quarks), and nether sign for bosons (gluons); g f is the degree of color-spin degeneracy, which is 6 for quark (anti-quark) and 16 for gluon; µ f is the corresponding chemical potential, while for anti-quark µ q = −µ q , and for gluon µ g = 0; x is the light-front momentum fraction of the nucleon carried by the specific parton; M is the mass of the nucleon, and the value is taken as 938.27 MeV; and Li 2 (z) is the polylogarithm function, defined as Li 2 (z) = ∞ k=1 z k /k 2 . Note that the analytic expression above is different from those attained in the previous statistical models [31,32,33,34,35,36,37,38,39,40,41,42].…”

“…On the other hand, due to the complicated non-perturbative effect, it is still difficult to calculate the parton distribution functions (PDFs) of the free nucleon absolutely from the first principle theory of the quantum chromodynamics (QCD) at present. Various models according to the spirit of QCD have been brought forward, therein statistical ones, providing intuitive appeal and physical simplicity, have made amazing success [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 Actually, as can be speculated, with partons bound in the wee volume of the nucleon, not only the dynamic, but also the statistical properties, for example, the Pauli exclusion principle, should have important effect on PDFs. Angelini and Pazzi [29,30], as pioneers, found that the nucleon valence quark distribution has a thermodynamical behavior for x > 0.1 with the temperature decreasing for different Q 2 .…”

“…Angelini and Pazzi [29,30], as pioneers, found that the nucleon valence quark distribution has a thermodynamical behavior for x > 0.1 with the temperature decreasing for different Q 2 . Cleymans and Thews [31,32,33] explored a statistical way to generate compatible PDFs. Mac and Ugaz [34] incorporated first order QCD correction, and afterwards Bhalerao et al [35,36,37,38,39] introduced finite-size correction; they both referred to the infinite-momentum frame (IMF).…”

Statistical effect in the parton distribution functions of the nucleon

“…Various models according to the spirit of QCD have been brought forward, therein statistical ones, providing intuitive appeal and physical simplicity, have made amazing success [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Actually, as can be speculated, with partons bound in the wee volume of the nucleon, not only the dynamic, but also the statistical properties, for example, the Pauli exclusion principle, should have important effect on the PDFs.…”

Measurements of the Double-Spin Asymmetry A₁ on Helium-3: Toward a Precise Measurement of the Neutron A₁

“…Other statistical approaches to nucleon structure exist; in 1994, for example, a statisticalmechanical extension of the MIT bag model (Section 2.3.8) was used to compute the unpolarized structure functions of the proton, but the results failed to agree with experiment [84]. Bhalerao et al [85,86] had better success with a model wherein calculations are performed in the nucleon rest frame and eventually boosted to the infinite-momentum frame; they also make explicit corrections for the finite size of the nucleon.…”