Light-cone distribution functions for B decays at subleading order in 1/mb

TL;DR

The paper develops a twist-based (shape-function) framework for inclusive B decays in the high-energy, low-invariant-mass region, where the local OPE fails. It identifies four new non-local subleading operators and derives their tree-level matching for heavy-to-light currents, expressing subleading effects in terms of four distribution functions, including a spin-dependent set. Applying the formalism to \\bar B -> X_s\\gamma, the authors derive a differential rate that includes both leading and subleading contributions and show that subleading terms can be grouped into a universal function F(\omega) = f(\omega) + t(\omega)/(2m_b). A simple model demonstrates that subleading twist corrections are small in the OPE-valid region but can reach roughly 10–20% in the twist-dominated region, highlighting their potential impact on precision extractions such as |V_{ub}| and guiding future work on semileptonic decays.

Abstract

We construct the higher twist structure functions that describe inclusive b hadron decays in regions of phase space where the hadronic decay products carry high energy but have low invariant mass. We show that, for B meson decays, there are four new non-vanishing matrix elements of non-local operators. We show that to subleading twist these decays are parametrized in terms of four functions. We compute the tree-level matching for a general heavy-to-light current and apply it to B -> X_s gamma. Using a simple model for these functions we estimate the subleading twist contributions to this decay.

Figures (3)

• Figure 1: Kinematics for a general heavy to light transition.
• Figure 2: Feynman rules for non-local operators $O_0-O_4$ in $n\cdot A=0$ gauge. The Feynman rules for $P_0-P_4$ are identical except for the Dirac structure.
• Figure 3: Partially integrated Rate (\ref{['partial']}), normalized to the leading twist result, using the simple model given in (\ref{['diffmodel']}). The solid, short-dashed and long-dashed lines correspond to $\bar{\Lambda}=570$ MeV, 470 MeV and 370 MeV, respectively. The lines which rise at the endpoint correspond to $\rho_2=(500\ {\rm MeV})^3$, while those that go down correspond to $\rho_2=-(500\ {\rm MeV})^3$. The values of $\lambda_1$ has been chosen to reproduce the second moment of the leading order structure function, $\lambda_1 =-0.53\ \bar{\Lambda}^2$.