Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark

Wei Tao; Ruilin Zhu; Zhen-Jun Xiao

doi:10.1140/epjc/s10052-023-11442-w

2022 Impact factor 4.4

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 294
https://doi.org/10.1140/epjc/s10052-023-11442-w

Regular Article - Theoretical Physics

Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark

Wei Tao, Ruilin Zhu^b and Zhen-Jun Xiao

Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, 210023, Nanjing, Jiangsu, China

^b rlzhu@njnu.edu.cn

Received: 3 January 2023
Accepted: 27 March 2023
Published online: 13 April 2023

Abstract

We compute the matching coefficient between the quantum chromodynamics (QCD) and the non-relativistic QCD (NRQCD) for the flavor-changing scalar current involving the heavy charm and bottom quark, up to the three-loop order within the NRQCD factorization. For the first time, we obtain the analytical expressions for the three-loop renormalization constant and the corresponding anomalous dimension for the NRQCD scalar current with the two heavy bottom and charm quark. We present the precise numerical results for those relevant coefficients with an accuracy of about thirty digits. The three-loop QCD correction turns out to be significantly large. The obtained matching coefficient is helpful to analyze the threshold behaviours when two different heavy quarks are close to each other and form the double heavy meson family.

© The Author(s) 2023

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