Abstract
We work out a specific class of three-loop diagrams (of order \( {\alpha}_s^2 \)) contributing to the decay amplitude for b → sγ associated with the current-current operators O1 and O2 at the physical value of the charm-quark mass mc. For many of the considered diagrams we were able to solve the master integrals using differential equations in the canonical form. For some diagrams we did not find a transformation to canonical form and therefore calculated the corresponding master integrals directly as an expansion around \( z={m}_c^2/{m}_b^2=0 \), retaining power terms up to z10 and keeping the accompanying log(z) terms to all powers. The results for the sum of all considered diagrams are given in tabular form, while contributions of individual diagrams (or combinations thereof) are given in electronic form.
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Acknowledgments
C.G. is very grateful to G. Heinrich, V. Magerya, J. Schlenk, and especially to S. Jones, for useful discussions on SecDec and PySecDec, in particular on the “method by regions” features. He also acknowledges useful discussions with Christoph Meyer on his program CANONICA as well as discussions with Johann Usovitsch on finding a “good bases” of master integrals with his program factorizeBasis.nb which extends KIRA. Further thanks go to R.N. Lee for questions on his programs LiteRed and Libra. C.G. also would like to thank J. Gasser for lecturing (a long time ago) about Fuchsian equations in his courses on quantum mechanics. Also very useful discussions with N. Schalch on various features connected with multiloop diagrams are greatfully acknowledged.
The work of C.G., C.W. and F.S. is partially supported by the Swiss National Science Foundation under grants 200020-175449 and 200020-204075.
H.M.A. is supported by the Committee of Science of Armenia Program Grant No. 21AG-1C084.
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Greub, C., Asatrian, H.M., Saturnino, F. et al. Specific three-loop contributions to b → sγ associated with the current-current operators. J. High Energ. Phys. 2023, 201 (2023). https://doi.org/10.1007/JHEP05(2023)201
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DOI: https://doi.org/10.1007/JHEP05(2023)201