New results on Pionic Twist-3 Distribution Amplitudes within the QCD Sum Rules

TL;DR

This paper improves the calculation of pionic twist-3 distribution amplitudes using QCD sum rules, constructs better models for these wave functions, and applies them to compute the B to pi transition form factor, achieving results consistent with existing literature.

Contribution

It provides new, more accurate moments of twist-3 distribution amplitudes and develops improved models with better end-point behavior for use in perturbative QCD calculations.

Findings

Calculated moments of twist-3 distribution amplitudes with uncertainties.

Constructed models for twist-3 wave functions with improved end-point behavior.

Computed the B→π transition form factor consistent with previous results.

Abstract

We present an improved calculation on the pionic twist-3 distribution amplitudes $\phi^{\pi}_{p}$ and $\phi^{\pi}_{\sigma}$, which are studied within the QCD sum rules. By adding all the uncertainties in quadrature, it is found that $<\xi^2_p>=0.248^{+0.076}_{-0.052}$, $<\xi^4_p>=0.262^{+0.080}_{-0.055}$, $<\xi^2_\sigma>=0.102^{+0.035}_{-0.025}$ and $<\xi^4_\sigma>=0.094^{+0.028}_{-0.020}$. Furthermore, with the help of these moments, we construct a model for the twist-3 wave functions $\psi^{\pi}_{p,\sigma}(x,\mathbf{k}_\bot)$, which have better end-point behavior and are helpful for perturbative QCD approach. The obtained twist-3 distribution amplitudes are adopted to calculate the $B\to\pi$ transition form factor $f^+_{B\pi}$ within the QCD light-cone sum rules up to next-to-leading order. By suitable choice of the parameters, we obtain a consistent $f^+_{B\pi}$ with those obtained in the literature.