Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

Kovchegov, Yuri V.; Santiago, M. Gabriel

doi:10.1007/jhep11(2021)200

Title: Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

Journal Article · Fri Nov 26 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep11(2021)200· OSTI ID:1835581

^[1]; Santiago, M. Gabriel ^[1]

The Ohio State Univ., Columbus, OH (United States)

We apply the formalism developed earlier for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small-x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x. We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou. We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small-x evolution equations re-summing double-logarithmic powers of α_s ln²(1/x) with α_s the strong coupling constant. We solve the corresponding novel evolution equations in the large-N_c limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by $${f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots$$ with the function C_O(x,$${k}_T^2$$) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.

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Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0004286

OSTI ID:: 1835581

Journal Information:: Journal of High Energy Physics (Online), Vol. 2021, Issue 11; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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