π−N\pi-N Drell-Yan process in TMD factorization

This article presents the review of the current understanding on the pion-nucleon Drell-Yan process from the point of view of the TMD factorization. Using the evolution formalism for the unpolarized and polarized TMD distributions developed recently, we provide the theoretical expression of the relevant physical observables, namely, the unpolarized cross section, the Sivers asymmetry, and the $\cos2\phi$ asymmetry contributed by the double Boer-Mulders effects. The corresponding phenomenology, particularly at the kinematical configuration of the COMPASS $\pi N$ Drell-Yan facility, is displayed numerically.Comment: Version published in Advances in High Energy Physic

Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the latest model gradient. The complexity of STRME method in non-convex, convex and strongly convex settings has all been analyzed, which matches the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods

Transverse momentum spectrum of dilepton pair in the unpolarized π−N\pi^-N Drell-Yan process within TMD factorization

We study the transverse momentum spectrum of dilepton produced in the unpolarized $\pi^- N$ Drell-Yan process, using transverse momentum dependent factorization up to next-to-logarithmic order of QCD. We extract the nonperturbative Sudakov form factor for the pion in the evolution formalism of the unpolarized TMD distribution function, by fitting the experimental data collected by the E615 Collaboration at Fermilab. With the extracted Sudakov factor, we calculate the normalized differential cross section with respect to transverse momentum of the dimuon and compare it with the recent measurement by the COMPASS Collaboration.Comment: 17 pages, 3 figure