QCD×\timesQED evolution of TMDs

We consider for the first time the QED corrections to the evolution of (un)polarized quark and gluon transverse-momentum-dependent distribution and fragmentation functions (TMDs in general). By extending their operator definition to QCD$\times$QED, we provide the mixed new anomalous dimensions up to ${\cal O}(\alpha_s\alpha)$ and the pure QED ones up to ${\cal O}(\alpha^2)$. These new corrections are universal for all TMDs up to the flavor of the considered parton, i.e., the full flavor universality of TMD evolution found in pure QCD is broken in QCD$\times$QED by the presence of the electric charge. In addition, we provide the leading-order QED corrections to the matching coefficients of the unpolarized quark TMD parton distribution function onto its integrated counterparts at ${\cal O}(\alpha_s^0\alpha)$.Comment: 9 pages, 3 figures. v2: minor corrections, accepted for publication in Phys. Lett.

Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions

In this work we consider how a parton distribution function, with an explicit transverse momentum dependence can be properly defined in a regularization-scheme independent manner. We argue that by considering a factorized form of the transverse momentum dependent spectrum for the production of a heavy lepton pair in Drell-Yan reaction, one should first split the relevant soft function into two boost invariant contributions. When those soft contributions are added to the pure collinear contributions, well-defined hadronic matrix elements emerge, i.e., the transverse momentum dependent distributions. We also perform a comparison with Collins' definition.Comment: 9 pages, 3 figures. We modified the discussion about the equivalence between Collins (JCC) and Echevarria-Idilbi-Scimemi (EIS) definitions of TMDPDF. The results remain intact. Version to appear in Phys. Lett.

Non-perturbative QCD effects in qTq_T spectra of Drell-Yan and ZZ-boson production

The factorization theorems for transverse momentum distributions of dilepton/boson production, recently formulated by Collins and Echevarria-Idilbi-Scimemi in terms of well-defined transverse momentum dependent distributions (TMDs), allows for a systematic and quantitative analysis of non-perturbative QCD effects of the cross sections involving these quantities. In this paper we perform a global fit using all current available data for Drell-Yan and $Z$-boson production at hadron colliders within this framework. The perturbative calculable pieces of our estimates are included using a complete resummation at next-to-next-to-leading-logarithmic accuracy. Performing the matching of transverse momentum distributions onto the standard collinear parton distribution functions and recalling that the corresponding matching coefficient can be partially exponentiated, we find that this exponentiated part is spin-independent and resummable. We argue that the inclusion of higher order perturbative pieces is necessary when data from lower energy scales are analyzed. We consider non-perturbative corrections both to the intrinsic nucleon structure and to the evolution kernel and find that the non-perturbative part of the TMDs could be parametrized in terms of a minimal set of parameters (namely 2-3). When all corrections are included the global fit so performed gives a $\chi^2/{\rm d.o.f.} \lesssim 1$ and a very precise prediction for vector boson production at the Large Hadron Collider (LHC).Comment: 24 pages, 11 figures. v2: new subsection added, discussion on the stability of the calculations and on higher order contributions improved, results unchange

Single spin asymmetries from a single Wilson loop

We study the leading-power gluon transverse momentum dependent distributions (TMDs) of relevance to the study of asymmetries in the scattering off transversely polarized hadrons. Next-to-leading-order perturbative calculations of these TMDs show that at large transverse momentum they have common dynamical origins, but that in the limit of small longitudinal momentum fraction $x$ only one origin remains. We find that in this limit only the dipole-type gluon TMDs survive and become identical to each other. At small $x$ they are all given by the expectation value of a single Wilson loop inside the transversely polarized hadron, the so-called spin-dependent odderon. This universal origin of transverse spin asymmetries at small $x$ is of importance to current and future experimental studies, paving the way to a better understanding of the role of gluons in the three-dimensional structure of spin-polarized protons.Comment: 5 pages, 1 figure. Various changes to the text, additional references, conclusions unchanged, version accepted for publication in Physical Review Letter