Momentum sum rule can be used as an inequality to estimate the lower and upper bounds of the momentum fractions of quarks and gluons in a model of proton valid in a limited x range. We compute such bounds in a self-similarity based model of proton structure function valid in the range 6.2 × 10 −7 ≤ x ≤ 10 −2 . The results conform to the asymptotic QCD expectations.
The Froissart bound implies that the total cross section (or, equivalently,
the structure function) cannot rise faster than the logarithmic growth of $
\ln^{2} \left(\frac{1}{x} \right)$. In this work, we show that such a slow
growth is not compatible with the notion of self-similarity. As a result, it
calls for the modification of the defining transverse-momentum-dependent parton
density function (TMD PDF) of a self-similarity based proton structure function
$F_{2} \left(x,Q^{2} \right)$ at small \textit{x}. Using plausible assumptions,
we obtain the Froissart saturation condition on this TMD PDF.Comment: 11 pages, 2 figures, 1 tabl
We use the path integral approach to a two-dimensional noncommutative harmonic oscillator to derive the partition function of the system at finite temperature. It is shown that the result based on the Lagrangian formulation of the problem, coincides with the Hamiltonian derivation of the partition function.
In this paper, we use momentum sum rule to compute the fractions of momentum carried by quarks and gluons in a self-similarity based model of proton. Comparison of the results with the prediction of QCD asymptotics is also made.
We construct a model for double parton distribution functions (dPDFs) based on the notion of self-similarity, pursued earlier for small x physics at HERA. The most general form of dPDFs contains total thirteen parameters to be fitted from data of proton-proton collision at LHC. It is shown that the constructed dPDF does not factorize into two single PDFs in conformity with QCD expectation, and it satisfies the condition that at the kinematic boundary x 1 + x 2 = 1 (where x 1 and x 2 are the longitudinal fractional momenta of two partons), the dPDF vanishes.
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