Quark and gluon helicity evolution at small x: revised and updated
Abstract
We revisit the problem of small Bjorken-x evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave (s-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength F12 and quark “axial current” $$\overline{\psi}\gamma$$+γ5ψ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, $${}_D{}^{\leftarrow i} {}_D{}^{i}$$, also sandwiched between the light-cone Wilson lines (with the repeated transverse index i = 1, 2 summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, $${}_D{}^{i} {}_D{}^{\leftarrow i}$$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this new operator into small-x helicity evolution, and construct novel evolution equations mixing all three operators ($${}_D{}^{i} {}_D{}^{\leftarrow i}$$, F12, and $$\overline{\psi}\gamma$$+γ5ψ), generalizing the results of . We also construct closed double-logarithmic evolution equations in the large-Nc and large-Nc&Nf limits, with Nc and Nf the numbers of quark colors and flavors, respectively. Solving the large-Nc equations numerically we obtain the following small-x asymptotics of the quark and gluon helicity distributions ΔΣ and ΔG, along with the g1 structure function, $$$$ \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {g}_1\left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2\pi }}} $$$$ in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.
- Authors:
-
- Univ. of Jyvaskyla (Finland)
- The Ohio State Univ., Columbus, OH (United States)
- The Ohio State Univ., Columbus, OH (United States); Stony Brook Univ., NY (United States)
- Publication Date:
- Research Org.:
- The Ohio State Univ., Columbus, OH (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); European Research Council (ERC)
- OSTI Identifier:
- 1968877
- Grant/Contract Number:
- SC0004286; ERC-2015-CoG-681707
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2022; Journal Issue: 7; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Deep Inelastic Scattering or Small-X Physics; Resummation
Citation Formats
Cougoulic, Florian, Kovchegov, Yuri V., Tarasov, Andrey, and Tawabutr, Yossathorn. Quark and gluon helicity evolution at small x: revised and updated. United States: N. p., 2022.
Web. doi:10.1007/jhep07(2022)095.
Cougoulic, Florian, Kovchegov, Yuri V., Tarasov, Andrey, & Tawabutr, Yossathorn. Quark and gluon helicity evolution at small x: revised and updated. United States. https://doi.org/10.1007/jhep07(2022)095
Cougoulic, Florian, Kovchegov, Yuri V., Tarasov, Andrey, and Tawabutr, Yossathorn. Fri .
"Quark and gluon helicity evolution at small x: revised and updated". United States. https://doi.org/10.1007/jhep07(2022)095. https://www.osti.gov/servlets/purl/1968877.
@article{osti_1968877,
title = {Quark and gluon helicity evolution at small x: revised and updated},
author = {Cougoulic, Florian and Kovchegov, Yuri V. and Tarasov, Andrey and Tawabutr, Yossathorn},
abstractNote = {We revisit the problem of small Bjorken-x evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave (s-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength F12 and quark “axial current” $\overline{\psi}\gamma$+γ5ψ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, ${}_D{}^{\leftarrow i} {}_D{}^{i}$, also sandwiched between the light-cone Wilson lines (with the repeated transverse index i = 1, 2 summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, ${}_D{}^{i} {}_D{}^{\leftarrow i}$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this new operator into small-x helicity evolution, and construct novel evolution equations mixing all three operators (${}_D{}^{i} {}_D{}^{\leftarrow i}$, F12, and $\overline{\psi}\gamma$+γ5ψ), generalizing the results of . We also construct closed double-logarithmic evolution equations in the large-Nc and large-Nc&Nf limits, with Nc and Nf the numbers of quark colors and flavors, respectively. Solving the large-Nc equations numerically we obtain the following small-x asymptotics of the quark and gluon helicity distributions ΔΣ and ΔG, along with the g1 structure function, $$ \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {g}_1\left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2\pi }}} $$ in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.},
doi = {10.1007/jhep07(2022)095},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2022,
place = {United States},
year = {Fri Jul 15 00:00:00 EDT 2022},
month = {Fri Jul 15 00:00:00 EDT 2022}
}
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