Related papers: Momentum sum rules for fragmentation functions
We prove an inversion formula for summatory arithmetic functions. As an application, we obtain an arithmetic relationship between summatory Piltz divisor functions and a sum of the M\"obius function over certain integers, denoted by…
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible…
Using soft collinear effective field theory, we derive the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) operator. We check the factorization theorem at one-loop level and compute the corresponding…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
We study the transverse momentum dependence of the Landau-Pomeranchuk-Migdal effect in QED, starting from the high energy expansion of the solution of the Dirac equation in the presence of an external field. The angular integrated energy…
We obtain functional central limit theorems for both discrete time expressions of the form $1/\sqrt{N}\sum_{n=1}^{[Nt]}(F(X(q_1(n)),\ldots, X(q_{\ell}(n)))-\bar{F})$ and similar expressions in the continuous time where the sum is replaced…
We give a description of double parton scattering with measured transverse momenta in the final state, extending the formalism for factorisation and resummation developed by Collins, Soper and Sterman for the production of colourless…
The concepts and methods of factorization using transverse-momentum-dependent (TMD) parton densities and/or fragmentation functions are summarized.
We present a fit of the transverse momentum spectrum for Drell-Yan and semi-inclusive deep inelastic scattering data, based on transverse momentum dependent (TMD) factorization at N$^4$LL accuracy. Our analysis shows good agreement with the…
We review a new approach to calculating transverse momentum distributions of the Higgs and electroweak gauge bosons using the Soft-Collinear Effective Theory. We derive a factorization theorem for transverse momentum distributions in terms…
By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schr\"odinger equation and the equations of continuum mechanics. A generalized Maxwell distribution has been used as the…
Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These…
In this paper, a sum rule means a relationship between a functional defined on a subset of all probability measures on $\mathbb{R}$ involving the reverse Kullback-Leibler divergence with respect to a particular distribution and recursion…
The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving…
We study QCD evolution equations of the first transverse-momentum-moment of the naive-time-reversal-odd fragmentation functions - the Collins function and the polarizing fragmentation function. We find for the Collins function case that the…
We investigate the momentum dependence of the extended Drell-Hearn-Gerasimov sum rule. An economical formalism is developed which allows to express the extended DHG sum rule in terms of a single virtual Compton amplitude in forward…
We extend the Collins-Soper-Sterman (CSS) formalism to apply it to the spin-dependence governed by the Sivers function. We use it to give a correct numerical QCD evolution of existing fixed-scale fits of the Sivers function. With the aid of…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
In the TMD approach, the average transverse momentum of the unpolarised TMD PDFs and FFs is crucial not only to reproduce unpolarised cross sections and hadron multiplicities, but also for the understanding of azimuthal and spin…