Related papers: Momentum sum rules for fragmentation functions

This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…

The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories.…

Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been…

Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…

An "ab initio" calculation of the Carbon-12 elastic form factor, and sum rules of longitudinal and transverse response functions measured in inclusive (e,e') scattering, is reported, based on realistic nuclear potentials and electromagnetic…

Motivated by the classification of solutions of harmonic functions, we investigate Liouville type theorems for the fractional Navier-Stokes equations in $\mathbb{R}^3$ under some conditions on the boundedness of fractional derivatives. We…

We obtain a functional Erd\H os-R\' enyi law of large numbers for "nonconventional" sums of the form $\Sig_n=\sum_{m=1}^nF(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of exponentially fast $\psi$-mixing random vectors and…

The gauge invariant operator formulation of the angular momentum sum rule ${1\over2} = J_q + J_g$ for the proton is presented and contrasted with the sum rule for the first moment of the polarised structure function $g_1^p$. The decoupling…

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…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing…

We derive a sum rule for the total quark angular momentum of a spin-one hadronic system within a gauge invariant decomposition of the hadron's spin. We show that the total angular momentum can be measured through deeply virtual Compton…

Transverse-momentum dependent (TMD) light-cone wave functions of a light meson are important ingredients in the TMD QCD factorization of exclusive processes. This factorization allows one conveniently resum Sudakov logarithms appearing in…

We present a universal formalism for transverse momentum resummation in the view of soft-collinear effective theory (SCET), and establish the relation between our SCET formula and the well known Collins-Soper-Sterman's pQCD formula at the…

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…

By reanalysing transverse momentum dependence in the perturbative calculation of pion form factor an improved expression of pion form factor which takes into account the transverse momentum dependenc in hard scattering amplitude and…

This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…

Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this…

We study the $\phi$ meson at finite temperature and finite momentum using QCD sum rules. The presence of medium breaks the Lorentz invariance, and induces distinct in-medium modifications of the transverse and longitudinal modes at finite…

Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check…