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

Abstract We apply the formalism developed earlier [1, 2] 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 lin...

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Autores principales:	Yuri V. Kovchegov, M. Gabriel Santiago
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Perturbative QCD Resummation Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/c1997b71cfd7463882c22f125025c28a
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spelling	oai:doaj.org-article:c1997b71cfd7463882c22f125025c28a2021-12-05T12:25:00ZQuark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution10.1007/JHEP11(2021)2001029-8479https://doaj.org/article/c1997b71cfd7463882c22f125025c28a2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)200https://doaj.org/toc/1029-8479Abstract We apply the formalism developed earlier [1, 2] 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 [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou [4] (see also [5]). 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 1 T ⊥ q x k T 2 = C O x k T 2 1 x + C 1 k T 2 1 x 0 + ⋯ $$ {f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots $$ with the function C O (x, k T 2 $$ {k}_T^2 $$ ) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.Yuri V. KovchegovM. Gabriel SantiagoSpringerOpenarticlePerturbative QCDResummationNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-59 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Perturbative QCD Resummation Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Perturbative QCD Resummation Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Yuri V. Kovchegov M. Gabriel Santiago Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
description	Abstract We apply the formalism developed earlier [1, 2] 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 [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou [4] (see also [5]). 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 1 T ⊥ q x k T 2 = C O x k T 2 1 x + C 1 k T 2 1 x 0 + ⋯ $$ {f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots $$ with the function C O (x, k T 2 $$ {k}_T^2 $$ ) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.
format	article
author	Yuri V. Kovchegov M. Gabriel Santiago
author_facet	Yuri V. Kovchegov M. Gabriel Santiago
author_sort	Yuri V. Kovchegov
title	Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
title_short	Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
title_full	Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
title_fullStr	Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
title_full_unstemmed	Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
title_sort	quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/c1997b71cfd7463882c22f125025c28a
work_keys_str_mv	AT yurivkovchegov quarksiversfunctionatsmallxspindependentodderonandthesubeikonalevolution AT mgabrielsantiago quarksiversfunctionatsmallxspindependentodderonandthesubeikonalevolution
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Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

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