Comparison of Various Feynman Diagram Calculation Methods for the Decay b → sγ

Abstract

In recent works, the full set of three-loop diagrams (of order \(\alpha _{s}^{2}\)) associated with the current-current operators O₁ and O₂ contributing to the decay amplitude for b → sγ were calculated. In this paper, one pair of these diagrams is calculated at various values of the charm-quark mass m_c using different methods, and the numerical accuracy/ease of use of these methods are compared to the analytic results obtained by others. Using the programs AMFlow and DiffExp to solve the differential equations for the master integrals, precise numerical results were obtained across a range of charm-quark mass values. In addition, asymptotic and Taylor series expansions were performed around z = \({{m_{c}^{2}} \mathord{\left/ {\vphantom {{m_{c}^{2}} {m_{b}^{2}}}} \right. \kern-0em} {m_{b}^{2}}}\) = 0 and z = 1/10, respectively. A fully numerical evaluation of the master integrals using PySecDec was also carried out.