Helicity evolution at small x: quark to gluon and gluon to quark transition operators
Abstract We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1–3]. While such transitions do not affect the large-N c version of the evolution equations for helici...
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| Format: | Article |
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SpringerOpen
2024-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2024)037 |
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| author | Jeremy Borden Yuri V. Kovchegov Ming Li |
| author_facet | Jeremy Borden Yuri V. Kovchegov Ming Li |
| author_sort | Jeremy Borden |
| collection | DOAJ |
| description | Abstract We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1–3]. While such transitions do not affect the large-N c version of the evolution equations for helicity, the large-N c & N f equations are affected. (N c and N f are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-N c & N f equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of α s ln2(1/x) with α s the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4–7]. Similar to the large-N c helicity evolution in the shock-wave approach [8], our large-N c & N f small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops. |
| format | Article |
| id | doaj-art-075c43c38d044d75a994c4148462bb4d |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-075c43c38d044d75a994c4148462bb4d2025-08-20T02:30:59ZengSpringerOpenJournal of High Energy Physics1029-84792024-09-012024915110.1007/JHEP09(2024)037Helicity evolution at small x: quark to gluon and gluon to quark transition operatorsJeremy Borden0Yuri V. Kovchegov1Ming Li2Department of Physics, The Ohio State UniversityDepartment of Physics, The Ohio State UniversityDepartment of Physics, The Ohio State UniversityAbstract We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1–3]. While such transitions do not affect the large-N c version of the evolution equations for helicity, the large-N c & N f equations are affected. (N c and N f are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-N c & N f equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of α s ln2(1/x) with α s the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4–7]. Similar to the large-N c helicity evolution in the shock-wave approach [8], our large-N c & N f small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops.https://doi.org/10.1007/JHEP09(2024)037Deep Inelastic Scattering or Small-x PhysicsResummation |
| spellingShingle | Jeremy Borden Yuri V. Kovchegov Ming Li Helicity evolution at small x: quark to gluon and gluon to quark transition operators Journal of High Energy Physics Deep Inelastic Scattering or Small-x Physics Resummation |
| title | Helicity evolution at small x: quark to gluon and gluon to quark transition operators |
| title_full | Helicity evolution at small x: quark to gluon and gluon to quark transition operators |
| title_fullStr | Helicity evolution at small x: quark to gluon and gluon to quark transition operators |
| title_full_unstemmed | Helicity evolution at small x: quark to gluon and gluon to quark transition operators |
| title_short | Helicity evolution at small x: quark to gluon and gluon to quark transition operators |
| title_sort | helicity evolution at small x quark to gluon and gluon to quark transition operators |
| topic | Deep Inelastic Scattering or Small-x Physics Resummation |
| url | https://doi.org/10.1007/JHEP09(2024)037 |
| work_keys_str_mv | AT jeremyborden helicityevolutionatsmallxquarktogluonandgluontoquarktransitionoperators AT yurivkovchegov helicityevolutionatsmallxquarktogluonandgluontoquarktransitionoperators AT mingli helicityevolutionatsmallxquarktogluonandgluontoquarktransitionoperators |