On evolution kernels of twist-two operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914732533874688 |
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| author | Ji, Yao Manashov, Alexander Moch, Sven-Olaf |
| author_facet | Ji, Yao Manashov, Alexander Moch, Sven-Olaf |
| contents | The evolution kernels that govern the scale dependence of the generalized parton distributions are invariant under transformations of the $\mathrm{SL}(2,\mathrm R)$ collinear subgroup of the conformal group. Beyond one loop the symmetry generators, due to quantum effects, differ from the canonical ones. We construct the transformation which brings the {\it full} symmetry generators back to their canonical form and show that the eigenvalues (anomalous dimensions) of the new, canonically invariant, evolution kernel coincide with the so-called parity respecting anomalous dimensions. We develop an efficient method that allows one to restore an invariant kernel from the corresponding anomalous dimensions. As an example, the explicit expressions for NNLO invariant kernels for the twist two flavor-nonsinglet operators in QCD and for the planar part of the universal anomalous dimension in $ N=4$ SYM are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01763 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On evolution kernels of twist-two operators Ji, Yao Manashov, Alexander Moch, Sven-Olaf High Energy Physics - Phenomenology High Energy Physics - Theory The evolution kernels that govern the scale dependence of the generalized parton distributions are invariant under transformations of the $\mathrm{SL}(2,\mathrm R)$ collinear subgroup of the conformal group. Beyond one loop the symmetry generators, due to quantum effects, differ from the canonical ones. We construct the transformation which brings the {\it full} symmetry generators back to their canonical form and show that the eigenvalues (anomalous dimensions) of the new, canonically invariant, evolution kernel coincide with the so-called parity respecting anomalous dimensions. We develop an efficient method that allows one to restore an invariant kernel from the corresponding anomalous dimensions. As an example, the explicit expressions for NNLO invariant kernels for the twist two flavor-nonsinglet operators in QCD and for the planar part of the universal anomalous dimension in $ N=4$ SYM are presented. |
| title | On evolution kernels of twist-two operators |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2307.01763 |