Master integrals for the two-loop penguin contribution in non-leptonic B-decays

Abstract

We compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results for all master integrals in terms of iterated integrals with rational weight functions. It is the first application of this method to the case of two different internal masses.

41 pages, 3 figures. The analytic results for all master integrals are attached in electronic form to the source file of the present submission

References in corpus (38)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Differential Equations for Feynman Graph Amplitudes
• Numerical evaluation of multiple polylogarithms
• Automatized analytic continuation of Mellin-Barnes integrals
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Magnus and Dyson Series for Master Integrals
• Calculation of two-loop virtual corrections to b --> s l+ l- in the standard model
• Extension of HPL to complex arguments
• SecDec: A general program for sector decomposition
• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• The rare decay B --> X_s l^+ l^- to NNLL precision for arbitrary dilepton invariant mass
• Evaluating single-scale and/or non-planar diagrams by differential equations
• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes
• The Two-Loop Master Integrals for $q\bar{q}\to VV$
• NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part
• Analytic calculation of two-loop QCD corrections to b\to s\ell^+\ell^- in the high q^2 region
• Analytic results for two-loop master integrals for Bhabha scattering I
• Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• NNLO vertex corrections in charmless hadronic B decays: Real part
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Hard spectator interactions in B to pi pi at order alpha_s^2
• Adequate bases of phase space master integrals for $gg\to h$ at NNLO and beyond
• Radiative corrections to hard spectator scattering in $B\to \pi \pi$ decays
• The two-loop soft function for heavy quark pair production at future linear colliders
• Higher order QCD corrections in exclusive charmless B decays
• On a two-loop crossed six-line master integral with two massive lines
• Penguin Loops for Nonleptonic B-Decays in the Standard Model: Is there a Penguin Puzzle?
• Order alpha_s^2 magnetic penguin correction for B decay to light mesons

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• Two loop virtual corrections to $b\to (d,s){\ell }^{+}{\ell }^{-}$ and $c\to u{\ell }^{+}{\ell }^{-}$ for arbitrary momentum transfer
• Exact NLO Matching and Analyticity in $b\to s\ell \ell$
• Efficient Evaluation of Massive Mellin--Barnes Integrals
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• Three-Body Non-Leptonic Heavy-to-heavy $B$ Decays at NNLO in QCD
• Long distance effects in inclusive rare $B$ decays and phenomenology of $\bar{B}\to X_d{\ell }^{+}{\ell }^{-}$
• Two-loop master integrals for non-leptonic heavy-to-heavy decays
• On the calculation of soft phase space integral
• Two-Loop integrals for CP-even heavy quarkonium production and decays
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• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
• Soft-collinear factorization in B decays
• Charmless Non-Leptonic Multi-Body B decays
• Non-leptonic B-decays at two loops in QCD Factorization
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays