Log-sine evaluations of Mahler measures, II

We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in "Log-sine evaluations of Mahler measures" and "Special values of generalized log-sine integrals" by two of the authors. This motivates a detailed study of various multiple polylogarithms and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.Comment: 35 page

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added

Extension of HPL to complex arguments

In this paper we describe the extension of the Mathematica package HPL to treat harmonic polylogarithms of complex arguments. The harmonic polylogarithms have been introduced by Remiddi and Vermaseren and have many applications in high energy particle physics.Comment: 42 pages, references added, the package can be downloaded at http://krone.physik.unizh.ch/~maitreda/HPL

Two-loop QCD-EW master integrals for Z plus jet production at large transverse momentum

The production of electroweak Z bosons that decay to neutrinos and recoil against jets with large transverse momentum p$_{⊥}$ is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benet from opportunities offered by the future high-luminosity LHC, the theoretical description of the pp → Z + j process should be extended to include mixed QCD-electroweak corrections. The goal of this paper is to initiate the computation of such corrections starting with the calculation of the Feynman integrals needed to describe two-loop QCD-electroweak contributions to qq̅ → Z + g scattering amplitudes. Making use of the hierarchy between the large transverse momenta of the recoiling jet, relevant for heavy dark matter searches, and the Z boson mass m$_{Z}$, we present the relevant master integrals as a series expansion in m$_{Z}$/p$_{⊥}$

PolyLogTools - Polylogs for the masses

We review recent developments in the study of multiple polylogarithms, including the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an algorithm for finding fibration bases. We document how these algorithms are implemented in the Mathematica package PolyLogTools and show how it can be used to study the coproduct structure of polylogarithmic expressions and how to compute iterated parametric integrals over polylogarithmic expressions that show up in Feynman integal computations at low loop orders.Comment: Package URL: https://gitlab.com/pltteam/pl