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

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.

Decay constants of $$ c\overline{b} $$ mesons involving the ten heavy flavor-changing currents at N3LO QCD

“…Two-loop corrections to the matching coefficients for the heavy flavor-changing pseudo-scalar, spatial vector and temporal axial-vector currents are available in the literature [55,56,105,106,110,111,115]. At the N 3 LO of α s , the matching coefficients have been numerically computed for the seven heavy flavor-changing currents: scalar [56,115], pseudo-scalar [56,115], spatial vector [56,106,115], temporal axial-vector [56,105,115], spatial axial-vector [56], spatial-temporal tensor [112] and spatial-spatial axial-tensor [112].…”

“…(2.6). At the leading-order (LO) of α s we set C LO J = C LO J = 1, while at the higher-order of α s both C J and C J are finite in D = 4 and depend on the NRQCD factorization scale µ f and QCD renormalization scale µ [112]. Note that Z OS J , Z MS J , Z J , C J and C J are gauge invariant to all orders in α s [56,112].…”

“…[98,[153][154][155][156]. Z MS t is the QCD tensor current MS renormalization constant, which is available in various literature [59,98,112,154,155,157]. Z OS t is the QCD heavy flavor-changing tensor current OS renormalization constant.…”

“…Although the complete three-loop expression of Z OS t is unknown at present, the finite (ϵ 0 ) term z g t z µ t of the ratio Z OS t /Z MS t can be calculated by eq. (2.17) and the three-loop result of z g t z µ t has been obtained by our earlier work [112]. For J ∈ {(t, i0), (t, ij), (t5, i0), (t5, ij)}, in order to calculate the matching coefficient C J , we firstly calculate Z J and C J by inputting Z MS J in eq.…”

“…[54,[102][103][104], and the S-wave B c and B * c meson decay constants involving the heavy flavor-changing pseudo-scalar, vector, axial-vector, tensor and axial-tensor currents were studied in refs. [55,56,[105][106][107][108][109][110][111][112].…”