Vcb determination from inclusive b → c decays: an alternative method

Abstract

The determination of V cb relies on the Heavy-Quark Expansion and the extraction of the non-perturbative matrix elements from inclusive b → c decays. The proliferation of these matrix elements complicates their extraction at 1/m 4 b and higher, thereby limiting the V cb extraction. Reparametrization invariance links different operators in the Heavy-Quark expansion thus reducing the number of independent operators at 1/m 4 b to eight for the total rate. We show that this reduction also holds for spectral moments as long as they are defined by reparametrization invariant weight-functions. This is valid in particular for the leptonic invariant mass spectrum (q 2 ), i.e. the differential rate and its moments. Currently, V cb is determined by fitting the energy and hadronic mass moments, which do not manifest this parameter reduction and depend on the full set of 13 matrix elements up to 1/m 4 b . In light of this, we propose an experimental analysis of the q 2 moments to open the possibility of a model-independent V cb extraction from semileptonic decays including the 1/m 4 b terms in a fully data-driven way.

Challenges in semileptonic $${\varvec{B}}$$ decays

“…In Refs. [326,331] it has been shown that the number of independent parameters in higher orders can be reduced by reparametrization invariance, for the total rate and the q 2 moments. While the number of HQE parameters up to order 1/m 2 b is still two, there is only one parameter at 1/m 3 b , since the spin-orbit term can be absorbed into μ 2 G .…”

QCD corrections to inclusive heavy hadron weak decays at ΛQCD3/mQ3

“…However, parametrically this correction is of the same size as the yet unknown corrections of order α 2 s Λ 2 QCD =m 2 b and α 3 s , which would need to be included in a full analysis up to order α s Λ 3 QCD =m 3 b . We note in passing that the corrections α s ρ 2 LS are not needed, since these are included in the known α s μ 2 G contributions [41]. Nevertheless, the contribution of ρ D is significant due to the large coefficient in front of ρ D and hence we expect that the impact of this correction is the largest one.…”

The heavy quark expansion for inclusive semileptonic charm decays revisited

“…Finally, we derived the total rate and spectral moments up to 1/m 4 c , and defined three new parameters that contain four-quark (weak annihilation) operators. We emphasize, that RPI observables, such as the total rate and q 2 moments, depend on a reduced set of HQE parameters [14]. Therefore, it may be useful to do an experimental analysis using q 2 moments only, as this significantly reduces the number of free parameters.…”

“…We emphasize that total rate only depends on τ 0 , while the RPI q 2 moments additionally depend on τ m . As was pointed out in [13,14], the q 2 moments have the advantage that they depend on a reduced set of 10 operators, even when including the terms up to 1/m 4 c . For the non-RPI energy moments, additional matrix elements (up to 16) have to be introduced.…”

“…Precision calculations for B meson decays rely heavily on the Heavy Quark Expansion (HQE), which makes use of the fact that for sufficiently heavy quarks, the various observables can be expressed as a double expansion in α s (m Q ) as well as in Λ QCD /m Q , where m Q is the mass of the heavy quark. For inclusive semileptonic b → c ν transitions the HQE has become quite sophisticated and high orders in both expansion parameters have been studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”