Four-quark operators relevant toBmeson lifetimes from QCD sum rules

Abstract

At the order of 1/m 3 b , the B meson lifetimes are controlled by the hadronic matrix elements of some four-quark operators. The nonfactorizable magnitudes of these four-quark operator matrix elements are analyzed by QCD sum rules in the framework of heavy quark effective theory. The vacuum saturation for color-singlet four-quark operators is justified at hadronic scale, and the nonfactorizable effect is at a few percent level.However for color-octet four-quark operators, the vacuum saturation is violated sizably that the nonfactorizable effect cannot be neglected for the B meson lifetimes. The implication to the extraction of some of the parameters from B decays is discussed. The B meson lifetime ratio is predicted as τ (B − )/τ (B 0 ) = 1.09 ± 0.02. However, the experimental result of the lifetime ratio τ (Λ b )/τ (B 0 ) still cannot be explained.

Untitled

“…Authors in refs. [33,34] have also discussed the lifetime ratios and came to a similar result. Though the prediction for τ (B − )/τ (B 0 ) agrees with the current world average, those of τ (B To understand the above problems, one of the attempts is to assume that the local duality may be violated in the non-leptonic inclusive decays.…”

Lifetimes and heavy quark expansion

“…For τ (B + )/τ (B d ) the latest lattice number stems from 2001 [56], for τ (Λ b )/τ (B d ) we have only an exploratory lattice study from 1999 [147] and for the D-meson lifetimes we have no lattice investigations at all. For the b-hadrons also several QCD sum rule determinations of these matrix elements are available [145,146,150,151]. Concerning the power suppressed 1/m b corrections, we see that the LO-QCD term Γ (0) 4 is known for all observables and Γ (0) 5 is also known for some of the observables.…”

“…The same matrix elements can also be used for the case of τ (B s )/τ (B d ). There is also an earlier lattice study from Di Pierro and Sachrajda from 1999 [144], as well as two QCD sum rule studies from Baek, Lee, Liu and Song in 1997 [145] and one year later from Cheng and Yang [146]. Comparing these numbers, the authors [145,146] of the QCD sum rule evaluation seem to have very aggressive error estimates.…”

|Vub| AND |Vcb|, CHARM COUNTING AND LIFETIME DIFFERENCES IN INCLUSIVE BOTTOM HADRON DECAYS

“…From theoretical calculations [11,[19][20][21][22], there remain large uncertainties. For a conservative consideration, we may take following values for those parameters semileptonic decays, we find that |V ub | and |V cb | may be given, to a good approximation, by the following form…”