Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
نویسنده
چکیده
The method for obtaining functional equations, recently proposed by one of the authors [1], is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representation is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation. PACS numbers: 02.30.Gp, 02.30.Ks, 12.20.Ds, 12.38.Bx
منابع مشابه
Planar Two-loop Master Integrals for Massive Bhabha Scattering: N F = 1 and N F = 2
Recent developments in the computation of two-loop master integrals for massive Bhabha scattering are briefly reviewed. We apply a method based on expansions of exact Mellin-Barnes representations and evaluate all planar four-point master integrals in the approximation of small electron mass at fixed scattering angle for the one-flavor case. The same technique is employed to derive and evaluate...
متن کاملul 2 00 4 A complete set of scalar master integrals for massive 2 - loop Bhabha scattering : where we are ∗
We define a complete set of scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering. Among others, there are thirty three 2-loop box type MIs. Five of them have been published in (semi-)analytical form, one is determined here, the rest remains to be calculated. Further, the last four so far unknown 2-loop 3-point MIs are identified and also computed here.
متن کاملHarmonic polylogarithms for massive Bhabha scattering
Oneand two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in calculations of multi-loop integrals. We discuss them in the context of analytical solutions for two-loop master integrals in the case of massive Bhabha scattering in QED. For the GPLs we discuss analytical representations, conformal transformations, and also their transformations corresponding to relations between master ...
متن کاملDifferential equations and massive two - loop Bhabha scattering : the B
The two-loop box contributions to massive Bhabha scattering may be reduced to two-loop box master integrals (MIs) with five, six, and seven internal lines, plus vertices and self energies. The self-energy and vertex MIs may be solved analytically by the differential equations (DE) method. This is true for only few of the box masters. Here we describe some details of the analytical determination...
متن کاملOn the Massive Two-loop Corrections to Bhabha Scattering * * *
We overview the general status of higher order corrections to Bhabha scattering and review recent progress in the determination of the two-loop virtual corrections. Quite recently, they were derived from combining a massless calculation and contributions with electron sub-loops. For a massive calculation, the self-energy and vertex master integrals are known, while most of the two-loop boxes ar...
متن کامل