Two-loop master integrals for non-leptonic heavy-to-heavy decays

Abstract

We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that disentangles the kinematics from the space-time dimension in the differential equations, and subsequently solve the latter in terms of iterated integrals up to weight four. The solution constitutes another valuable example of the finding of a canonical basis for two-loop master integrals that have two different internal masses, and assumes a form that is ideally suited for a subsequent convolution with the light-cone distribution amplitude in the framework of QCD factorisation.

31 pages, 3 figures. v2: Minor modifications (typos etc.), matches published version

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• Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
• Next-to-Leading Order QCD Corrections to the Decay Width $H\to Z\gamma$
• Differential equations for loop integrals in Baikov representation
• Analytic results for planar three-loop integrals for massive form factors
• Two-loop QCD Corrections to $B_c$ Meson Leptonic Decays
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Three-Body Non-Leptonic Heavy-to-heavy $B$ Decays at NNLO in QCD
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• Probing new physics in class-I $B$-meson decays into heavy-light final states