The B-Meson Distribution Amplitude in QCD

TL;DR

This paper computes the B-meson distribution amplitude using QCD sum rules in HQET, yielding a perturbative sum rule for the momentum-space amplitude $\phi_+(k,\mu)$ and a local-duality limit $\phi_+(k)^{\rm LD}$ that constrains the shape. It then systematically adds nonperturbative corrections via quark and gluon condensates and, crucially, nonlocal quark condensates to model long-distance effects, obtaining a robust estimate for the first inverse moment $\lambda_B^{-1}(\mu)$ and a corresponding $\lambda_B(\mu)$. The final result at $\mu=1\,\text{GeV}$ is $\lambda_B^{-1}=2.15\pm0.50\,\text{GeV}^{-1}$, i.e. $\lambda_B=460\pm110\,\text{MeV}$, complemented by a scale-dependent parameter $\sigma_B(1\,\text{GeV})=1.4\pm0.4$ and a simple, QCD-motivated $\phi_+(k,\mu)$ model governed by $\lambda_B$ and $\sigma_B$. The work provides a realistic, theoretically constrained B-meson distribution amplitude suitable for exclusive B-decay factorization and offers a concrete, testable parametrization for phenomenology.

Abstract

The B-meson distribution amplitude is calculated using QCD sum rules. In particular we obtain an estimate for the integral relevant to exclusive B-decays λ_B = 460 \pm 110 MeV at the scale 1 GeV. A simple QCD-motivated parametrization of the distribution amplitude is suggested.

Figures (8)

• Figure 1: One-loop renormalization of the nonlocal light-cone operator built of one light and one effective heavy quark field (double line). The dashed line indicates the gluon Wilson line insertion in between the quark fields.
• Figure 2: Correlation function (\ref{['T']}) in QCD perturbation theory to first order.
• Figure 3: B-meson distribution amplitude $\phi_+(k,\mu=1$ GeV$)$ calculated from the sum rule (\ref{['SR3a']}) in QCD perturbation theory to leading order (dashed curves) and next-to-leading order (solid curves) for the continuum threshold $\omega_0$=1 GeV and two values of the Borel parameter $M=0.3$ GeV (left panel) and $M=0.6$ GeV (right panel). The value of the decay constant $F(\mu)$ appearing on the l.h.s. of the sum rule is substituted by the corresponding sum rule (\ref{['SR2']}) with the appropriate accuracy (LO or NLO) and neglecting the condensate contributions.
• Figure 4: Quark condensate contribution to the correlation function (\ref{['T']}).
• Figure 5: Gluon condensate contribution to the correlation function (\ref{['T']}). Only this diagram contributes in the Fock-Schwinger gauge.