T-odd Leading-Twist Quark TMDs at Small $x$

Bibliographic Details
Title:	T-odd Leading-Twist Quark TMDs at Small $x$
Authors:	Kovchegov, Yuri V., Santiago, M. Gabriel
Publication Year:	2022
Collection:	High Energy Physics - Experiment High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory
Subject Terms:	High Energy Physics - Phenomenology, High Energy Physics - Experiment, Nuclear Experiment, Nuclear Theory
More Details:	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, we are interested in revisiting the sub-eikonal correction considered by us earlier. 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 $\alpha_s \, \ln^2 (1/x)$, where $\alpha_s$ 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 $N_c$: \begin{align} f_{1 \: T}^{\perp \: NS} (x \ll 1 ,k_T^2) & = C_O (x, k_T^2) \, \frac{1}{x} + C_1 (x, k_T^2) \, \left( \frac{1}{x} \right)^{3.4 \, \sqrt{\frac{\alpha_s \, N_c}{4 \pi}}} , \notag \\ h_1^{\perp \, \textrm{NS}} (x \ll 1, k_T^2) & = C (x, k_T^2) \left( \frac{1}{x} \right)^{-1}. \notag \end{align} 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 our previous work due to the new contributions identified recently. Comment: 50 pages, 5 figures
Document Type:	Working Paper
DOI:	10.1007/JHEP11(2022)098
Access URL:	http://arxiv.org/abs/2209.03538
Accession Number:	edsarx.2209.03538
Database:	arXiv

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Items	– Name: Title Label: Title Group: Ti Data: T-odd Leading-Twist Quark TMDs at Small $x$ – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kovchegov%2C+Yuri+V%2E%22">Kovchegov, Yuri V.</searchLink><br /><searchLink fieldCode="AR" term="%22Santiago%2C+M%2E+Gabriel%22">Santiago, M. Gabriel</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2022 – Name: Subset Label: Collection Group: HoldingsInfo Data: High Energy Physics - Experiment<br />High Energy Physics - Phenomenology<br />Nuclear Experiment<br />Nuclear Theory – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22High+Energy+Physics+-+Phenomenology%22">High Energy Physics - Phenomenology</searchLink><br /><searchLink fieldCode="DE" term="%22High+Energy+Physics+-+Experiment%22">High Energy Physics - Experiment</searchLink><br /><searchLink fieldCode="DE" term="%22Nuclear+Experiment%22">Nuclear Experiment</searchLink><br /><searchLink fieldCode="DE" term="%22Nuclear+Theory%22">Nuclear Theory</searchLink> – Name: Abstract Label: Description Group: Ab Data: 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, we are interested in revisiting the sub-eikonal correction considered by us earlier. 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 $\alpha_s \, \ln^2 (1/x)$, where $\alpha_s$ 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 $N_c$: \begin{align} f_{1 \: T}^{\perp \: NS} (x \ll 1 ,k_T^2) & = C_O (x, k_T^2) \, \frac{1}{x} + C_1 (x, k_T^2) \, \left( \frac{1}{x} \right)^{3.4 \, \sqrt{\frac{\alpha_s \, N_c}{4 \pi}}} , \notag \\ h_1^{\perp \, \textrm{NS}} (x \ll 1, k_T^2) & = C (x, k_T^2) \left( \frac{1}{x} \right)^{-1}. \notag \end{align} 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 our previous work due to the new contributions identified recently.<br />Comment: 50 pages, 5 figures – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: DOI Label: DOI Group: ID Data: 10.1007/JHEP11(2022)098 – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2209.03538" linkWindow="_blank">http://arxiv.org/abs/2209.03538</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2209.03538
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RecordInfo	BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/JHEP11(2022)098 Subjects: – SubjectFull: High Energy Physics - Phenomenology Type: general – SubjectFull: High Energy Physics - Experiment Type: general – SubjectFull: Nuclear Experiment Type: general – SubjectFull: Nuclear Theory Type: general Titles: – TitleFull: T-odd Leading-Twist Quark TMDs at Small $x$ Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kovchegov, Yuri V. – PersonEntity: Name: NameFull: Santiago, M. Gabriel IsPartOfRelationships: – BibEntity: Dates: – D: 07 M: 09 Type: published Y: 2022
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