Operator Product Expansion for Inclusive Semileptonic Decays in Heavy Quark Effective Field Theory

TL;DR

The paper develops a QCD-based, systematically improvable description of inclusive semileptonic decays of heavy hadrons using HQET and an operator-product expansion in the region ${\cal Q}^2=(q-m_Q v)^2 \ll m_Q^2$. The leading term reproduces the parton-model result, with first nonvanishing corrections coming from dimension-five operators parameterized by $B_1$ and $B_2$ (mesons) and by $A_1$ (baryons), together with short-distance QCD effects encoded in Wilson coefficients and RG running. The authors compute the lepton-energy spectrum for $\overline{B}^0\to X_c e^- \bar{\nu}_e$, obtaining a smooth distribution and showing how the spectrum and total rate depend on $B_1$; this provides a way to extract nonperturbative information from data. The work clarifies the regime of validity, offering a complementary approach to previous analyses that treat regions where ${\cal Q}^2$ is of order $m_Q^2$, and establishes a framework for precision tests of heavy-quark dynamics in inclusive decays.

Abstract

Inclusive semileptonic decays are discussed in the framework of heavy quark effective field theory by employing the short distance expansion in the effective theory. The lowest order term turns out to be the parton model; the higher order terms may be regarded as correction terms to the parton model result. The first nonvanishing corrections to the parton model result are given and the lepton energy spectrum of inclusive semileptonic decays of heavy mesons is calculated.