The Lund $b$-jet plane

TL;DR

This paper calculates the primary Lund plane density for jets initiated by massive b-quarks in QCD, incorporating mass effects, soft logarithm resummation, and phenomenological application to $e^+e^-$ collisions at the Z boson mass.

Contribution

It provides the first resummed calculation of the Lund plane density for massive b-quark jets, including mass effects and soft logarithm resummation, with phenomenological application to $e^+e^-$ collisions.

Findings

Resummed Lund plane density for b-quark jets computed.

Mass effects and soft logarithms included in the calculation.

Application to $e^+e^-$ collisions at $ oot s=M_Z$.

Abstract

We compute the primary Lund plane density for jets initiated by a massive ($b$) quark to single logarithmic accuracy in Quantum Chromodynamics (QCD). In order to capture mass effects, we consider quasi-collinear factorisation and we include contributions from the running of the QCD coupling and from collinear evolution, in a variable flavour-number scheme. Furthermore, the resummation of soft logarithms, including clustering effects, is performed numerically, keeping the full dependence on the $b$-quark mass. While our all-order results can be applied to both hadron and lepton colliders, we present, as first phenomenological application, the resummed calculation of the Lund plane density in $e^+e^-$ collisions at $\sqrt{s}=M_Z$, matched to tree-level matrix elements.