Related papers: On the Evolution of Sum Rules for T-Odd Distributi…
Consider the sequence of continued fraction convergents $p_n/q_n$ to a random irrational number. We study the distribution of the sequences $p_n \pmod{m}$ and $q_n \pmod{m}$ with a fixed modulus $m$, and more generally, the distribution of…
We show how to consistently construct initial conditions for the QCD evolution equations for double parton distribution functions in the pure gluon case. We use to momentum sum rule for this purpose and a specific form of the known single…
We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-$\frac{1}{2}$ and spin-0 hadrons. We derive exact non-perturbative identities decomposing the…
The Parton Branching (PB) approach describes the evolution of transverse momentum dependent (TMD) parton densities. We propose to extend the PB method by including TMD splitting functions, instead of the DGLAP splitting functions which…
We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain…
A generic physical situation is considered where Im $\Pi$, the imaginary part of polarization operator (generalized susceptibility), can be measured on a finite interval and the high frequency asymptotics (up to a few orders) of $\Pi$ can…
Using momentum sum rule for evolution equations for Double Parton Distribution Functions (DPDFs) in the leading logarithmic approximation, we find that the double gluon distribution function can be uniquely constrained via the single gluon…
The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$,…
Transverse-momentum-dependent parton distribution functions are analyzed in semi-inclusive deep inelastic scattering at low transverse momentum using soft-collinear effective theory. The transverse-momentum-dependent parton distribution…
The Birkhoff Ergodic Theorem establishes pointwise convergence for integrable observables, but for $f\notin L^1$, no normalization yields almost sure convergence. This paper investigates trimmed ergodic sums, where the largest observations…
We give an overview of the current status of perturbative QCD factorization theorems in processes that involve transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FF). We enumerate those…
We show that the Collins-Soper-Sterman resummation approach to the derivation of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is gauge invariant. The special gauge-dependent parton distribution function employed in the…
We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…
We study the evolution behavior of generalized parton distributions at small longitudinal momentum fraction. Particular attention is paid to the ratio of a generalized parton distribution and its forward limit, to the mixing between quarks…
I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. I summarize basic results while attempting to trace their development over that…
We calculate the leading twist pion unpolarized transverse momentum distribution $f_1(x,k_T^2)$ and the Boer-Mulders function $h_1^\perp(x,k_T^2)$, using leading Fock-state light front wave functions (LF-LFWFs) based on Dyson-Schwinger and…
The spin-dependent structure functions $g_1(x)$, $g_2(x)$, ${g}_2^{WW}(x)$ and ${\bar g}_2(x)$ and their moments are studied in the CM bag model. The results show that (i) $\int_0^1g_2(x)dx=0$, i.e. the Burkhardt-Cottingham sum rule holds,…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…