Year-end Sale % OFF 
Abstract
We evaluate analytically the master integrals for double real radiation emission in the b rightarrow u W^* decay, where b and u are a massive and massless quark, respectively, while W^{*} 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.
Highlights
An analytic result for the next-to-leading order (NLO) QCD corrections to the b → lνl u differential decay rate was obtained in [10]
The Master Integrals (MIs) are analytically evaluated by means of the Differential Equations (DE) method [39,40,41,42,43] and expressed in terms of generalized polylogarithms (GPLs) [44,45,46] of two variables: t, which is connected to the invariant mass of the hadronic final state, and z, which is related to the leptonic invariant mass
We evaluated MIs up to the order in the expansion where GPLs of weight four first appear in the result, since one does not expect GPLs of weight five to be present in the next-to-next-to-leading order (NNLO) differential distributions we are interested in. (Table 2 summarizes the order in at which the various MIs were evaluated.) A notable exception is represented by the MI I5
Summary
The calculation of double emission corrections to the b → uW ∗ process is first mapped into the problem of calculating three-particle cuts in two-loop bW ∗ → bW ∗ forward box-diagrams, using the method proposed in [19]. Three auxiliary topologies which encompass all of the combinations of denominators which can appear in the cut diagrams were subsequently identified. The MIs, which depend on two dimensionless parameters (defined below), are calculated by employing the DE method. The technique employed in this work is a standard method in the analytic calculation of Feynman diagrams. We describe the way in which we parameterized the kinematics of the process, we define the MIs which were identified and we discuss the way in which the integration constants arising in the DE method were fixed
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
