Higher-order perturbative corrections to b → c transitions at zero recoil

Abstract

We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currentsc γ µ b andc γ µ γ 5 b by calculating the terms of order n f α 2 s and substituting the dependence on the number of flavours by the first coefficient of the β-function. Both for vector and axial vector currents, we find moderate twoloop corrections below 1% in magnitude. Using the Brodsky-LepageMackenzie prescription to set the scale in the order-α s corrections in the MS scheme, we obtain µ V ≃ 0.92in the two cases. These scales are sufficiently large for perturbation theory to be well-behaved. The implications of our results to the extraction of | V cb | are briefly discussed.

Heavy-quark form factors in the large $$\beta _0$$ β 0 limit

“…At ϑ = 0 this result agrees with the result of [18] at m 1 = m 2 ; see also [5]. 2 Re-expressing the bare form factors (27) via the renormalized coupling we obtain…”

“…1) and multiply it by Z os Q with the 1/β 0 accuracy (see [5]). Reducing on-shell massive QCD integrals to off-shell HQET ones by the inversion relation (18) and then to the master integrals by IBP [15], we obtain…”

Application of heavy-quark effective theory to lattice QCD. III. Radiative corrections to heavy-heavy currents

“…[36]. When one mass becomes very large, but the other is held fixed, one can still deduce the limiting behavior from Eqs.…”

“…Because the symmetry-breaking arises at short-distances, it is more useful to focus on the operators' coefficients, noting that C lat 4 = 0, instead of C 4 = 0 as for continuum QCD. Returning to L (0) and L (1) , the coefficient of the kinetic energy becomes 36) and m 2h is called the kinetic mass. If the HQET operators are defined by minimal subtraction in dimensional regularization, then both m 1h and m 2h can be computed from the pole in the perturbative quark propagator [33], and they are infrared finite and gauge independent [34].…”

Lattice calculation of the zero-recoil form factor ofB¯→D*lνHashimoto1, Kronfeld2, Mackenzie3 et al. 2002Phys. Rev. D846530View full textAdd to dashboardCite

“…[18]. The continuum coefficients are [32] TABLE II. Double ratios, computed in the Monte Carlo, and (re)normalization factors, computed in perturbation theory to one-loop BLM order.…”