Improved factorization for threshold resummation in heavy quark to heavy quark decays

U. G. Aglietti; G. Ferrera

doi:10.1140/epjc/s10052-023-11440-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 335
https://doi.org/10.1140/epjc/s10052-023-11440-y

Regular Article - Theoretical Physics

Improved factorization for threshold resummation in heavy quark to heavy quark decays

U. G. Aglietti¹ and G. Ferrera²^b

¹ Dipartimento di Fisica, Università di Roma “La Sapienza”, 00185, Rome, Italy
² Dipartimento di Fisica, Università di Milano and INFN Sezione di Milano, 20133, Milan, Italy

^b giancarlo.ferrera@mi.infn.it

Received: 5 December 2022
Accepted: 27 March 2023
Published online: 27 April 2023

Abstract

We consider the resummation of soft-gluon effects in heavy quark to heavy quark decays, namely the processes $Q_{1} \to Q_{2} + (non QCD partons)$ $Q_1 \rightarrow Q_2 \, + \, \mathrm {(non\,QCD\, partons)}$ , where $Q_{1}$ $$Q_1$$ and $Q_{2}$ $$Q_2$$ are two different heavy quarks. We construct a new factorization scheme for threshold resummed spectra, which allows us to consistently evaluate the distribution of the final hadron invariant mass $m_{X}$ $$m_X$$ in all the kinematic regions, i.e. when $m_{X}$ $$m_X$$ is smaller, of the same order, or larger than the mass of the final quark $Q_{2}$ $$Q_2$$ . A dependence of the improved Coefficient function on the threshold variable is introduced, which can however be relegated to a small interval of this variable by means of the so-called Partition of Unity. We explicitly apply our improved scheme to the $b \to X_{s} + γ$ $b \rightarrow X_s \, + \gamma$ decay at next-to-leading logarithmic accuracy.

© The Author(s) 2023

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