T-odd leading-twist quark TMDs at small x

• Published in: The journal of high energy physics 2022-11, Vol.2022 (11), p.98-63, Article 98
• Main Authors: Kovchegov, Yuri V., Santiago, M. Gabriel
• Format: Article
• Language: English
• Subjects: Approximation; Asymptotic properties; Carbon monoxide; Classical and Quantum Gravitation; Deep Inelastic Scattering or Small-x Physics; Elementary Particles; Evolution; High energy physics; NUCLEAR PHYSICS AND RADIATION PHYSICS; Operators (mathematics); Parton Distributions; Partons; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Resummation; String Theory; Transverse momentum
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2022)098

A bstract We study the small- x asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), the Sivers and Boer-Mulders functions. While the leading eikonal small- x asymptotics of the quark Sivers function is given by the spin-dependent odderon [ 1 , 2 ], we are interested in revisiting the sub-eikonal correction considered by us earlier in [ 3 ]. We first simplify the expressions for both TMDs at small Bjorken x and then construct small- x evolution equations for the resulting operators in the large- N c limit, with N c the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter α s ln 2 (1 /x ), where α s is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically (for the Sivers function) and analytically (for the Boer-Mulders function) we arrive at the following leading small- x asymptotics of these TMDs at large N c : f 1 T ⊥ NS x ≪ 1 k T 2 = C O x k T 2 1 x + C 1 x k T 2 1 x 3.4 α s N c 4 π h 1 ⊥ NS x ≪ 1 k T 2 = C x k T 2 1 x − 1 . The functions C O ( x, k T 2 ), C 1 ( x, k T 2 ), and C ( x, k T 2 ) can be readily obtained in our formalism: they are mildly x -dependent and do not strongly affect the power-of- x asymptotics shown above. The function C O , along with the 1 /x factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with C 1 ), our result shown above supersedes the one obtained in [ 3 ] due to the new contributions identified recently in [ 4 ].