Related papers: The $Q^2$ evolution of Soffer inequality
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…
Perturbative NLO and NNLO QCD evolutions of parton distributions are studied, in particular in the (very) small-$x$ region, where they are in very good agreement with all recent precision measurements of $F_2^p(x,Q^2)$. These predictions…
An evolving Riemannian manifold $(M,g_t)_{t\in I}$ consists of a smooth $d$-dimensional manifold $M$, equipped with a geometric flow $g_t$ of complete Riemannian metrics, parametrized by $I=(-\infty,T)$. Given an additional $C^{1,1}$ family…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
In this paper I show that it is possible to use Regge theory to constrain the initial parton distribution functions of a global DGLAP fit. In this approach, both quarks and gluons have the same high-energy behaviour which may also be used…
We review the main results on the generalization of the DGLAP evolution equations within the cut Mellin moments (CMM) approach, which allows one to overcome the problem of kinematic constraints in Bjorken $x$. CMM obtained by multiple…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
It has been pointed out that the recent BaBar data on the pi gamma^* -> gamma transition form factor F_{pi gamma}(Q^2) at low (high) momentum transfer squared Q^2 indicate an asymptotic (flat) pion distribution amplitude. These seemingly…
We present a calculation of valence double parton distributions of the pion in the framework of chiral quark models. The result obtained at the low-energy quark model scale is particularly simple, where in the chiral limit a factorized form…
Valence double parton distribution functions of the nucleon are evaluated in the framework of a simple model, where the conservation of the longitudinal momentum is taken into account. The leading-order DGLAP QCD evolution from the low…
The hadron-energy evolution (Collins and Soper) equation for all the leading-twist transverse-momentum and spin dependent parton distributions is derived in the impact parameter space. Based on the result, we present resummation formulas…
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for…
We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally…
In this work, we present an analytical solution for QCD$\otimes$QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in…
Starting from the old idea that Fermi statistics for quarks play a fundamental role to explain some features of hadron structure, we study the modification of the scaling behaviour of parton distributions due to quantum statistical effects.…
It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion…
This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded positive solution of the convolution equation…
Fourier-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position…
Supposing only that there is an effective charge which defines an evolution scheme for parton distribution functions (DFs) that is all-orders exact, strict lower and upper bounds on all Mellin moments of the valence-quark DFs of pion-like…