Helicity Evolution at Small $x$: Quark to Gluon and Gluon to Quark Transition Operators
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916289826521088 |
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| author | Borden, Jeremy Kovchegov, Yuri V. Li, Ming |
| author_facet | Borden, Jeremy Kovchegov, Yuri V. Li, Ming |
| contents | 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. 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 $α_s \, \ln^2 (1/x)$ 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. Similar to the large-$N_c$ helicity evolution in the shock-wave approach, our large-$N_c \& N_f$ small-$x$ splitting functions agree with those obtained in the infrared evolution equations framework up to three loops, but appear to slightly disagree at four loops. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Helicity Evolution at Small $x$: Quark to Gluon and Gluon to Quark Transition Operators Borden, Jeremy Kovchegov, Yuri V. Li, Ming High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory 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. 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 $α_s \, \ln^2 (1/x)$ 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. Similar to the large-$N_c$ helicity evolution in the shock-wave approach, our large-$N_c \& N_f$ small-$x$ splitting functions agree with those obtained in the infrared evolution equations framework up to three loops, but appear to slightly disagree at four loops. |
| title | Helicity Evolution at Small $x$: Quark to Gluon and Gluon to Quark Transition Operators |
| topic | High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2406.11647 |