QCD$\times$QED evolution of TMDs

Abstract

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 $\mathcal{O}({\alpha }_s\alpha )$ and the pure QED ones up to $\mathcal{O}({\alpha }^2)$. 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 $\mathcal{O}({\alpha }_s^0\alpha )$.

9 pages, 3 figures. v2: minor corrections, accepted for publication in Phys. Lett. B

References in corpus (13)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Measurement of the $Z/{\gamma }^{\ast }$ boson transverse momentum distribution in $pp$ collisions at $\sqrt{s}$ = 7 TeV with the ATLAS detector
• k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
• Analysis of vector boson production within TMD factorization
• Soft-/rapidity- anomalous dimensions correspondence
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• Non-perturbative QCD effects in $q_T$ spectra of Drell-Yan and $Z$-boson production
• QCD$\oplus$QED NNLO corrections to Drell Yan production
• SCET, Light-Cone Gauge and the T-Wilson Lines
• Measurement of the forward Z boson production cross-section in pp collisions at $\sqrt{s}=13$ TeV
• Transverse Momentum Distributions in the Non-Perturbative Region
• Structure of rapidity divergences in soft factors
• Analytical solutions of the QCD$\otimes$QED DGLAP evolution equations based on the Mellin transform technique in NLO approximation

Cited by in corpus (7)

• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Disentangling Long and Short Distances in Momentum-Space TMDs
• Prospects for quarkonium studies at the high-luminosity LHC
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Illuminating the nucleon spin