Eur. Phys. J. C (2018) 78: 674
https://doi.org/10.1140/epjc/s10052-018-6157-6

Regular Article - Theoretical Physics

Master integrals for double real radiation emission in heavy-to-light quark decay

¹ Dipartimento di Fisica, Sapienza, Università di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy
² INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome, Italy
³ Physik Department T31, Technische Universität München, James Franck-Straße 1, 85748, Garching, Germany
⁴ INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126, Milan, Italy
⁵ Physics Department, New York City College of Technology, The City University of New York, 300 Jay Street, Brooklyn, NY, 11201, USA
⁶ The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

^* e-mail: alessandro.broggio@tum.de

Received: 9 July 2018
Accepted: 15 August 2018
Published online: 23 August 2018

Abstract

We evaluate analytically the master integrals for double real radiation emission in the decay, where b and u are a massive and massless quark, respectively, while is an off-shell charged weak boson. Since the W boson can subsequently decay in a lepton anti-neutrino pair, the results of the present paper constitute a further step toward a fully analytic computation of differential distributions for the semileptonic decay of a b quark at NNLO in QCD. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B mesons. Our results are expressed in terms of multiple polylogarithms of maximum weight four.