Three-loop matching of heavy flavor-changing (axial-)tensor currents

Abstract

Abstract We present the three-loop calculations of the nonrelativistic QCD (NRQCD) current renormalization constants and corresponding anomalous dimensions, and the matching coefficients for the spatial-temporal tensor and spatial-spatial axial-tensor currents with two different heavy quark masses. We obtain the convergent decay constant ratio up to the next-to-next-to-next-to-leading order (N3LO) for the S-wave vector meson $$ {B}_c^{\ast } $$ B c ∗ involving the tensor and axial-tensor currents. We obtain the three-loop finite (ϵ0) term in the ratio of the QCD heavy flavor-changing tensor current renormalization constant in the on-shell (OS) scheme to that in the modified-minimal-subtraction ($$ \overline{\textrm{MS}} $$ MS ¯ ) scheme, which is helpful to obtain the three-loop matching coefficients for all heavy flavor-changing (axial-)tensor currents.