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

Abstract

We present an improved calculation on the pionic twist-3 distribution amplitudes ${\varphi }_p^{\pi }$ and ${\varphi }_{\sigma }^{\pi }$, which are studied within the QCD sum rules. By adding all the uncertainties in quadrature, it is found that $<{\xi }_p^2>=0.248_{-0.052}^{+0.076}$, $<{\xi }_p^4>=0.262_{-0.055}^{+0.080}$, $<{\xi }_{\sigma }^2>=0.102_{-0.025}^{+0.035}$ and $<{\xi }_{\sigma }^4>=0.094_{-0.020}^{+0.028}$. Furthermore, with the help of these moments, we construct a model for the twist-3 wave functions ${\psi }_{p,\sigma }^{\pi }(x,{\mathbf{k}}_{\perp })$, 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.

9 pages, 6 figures and 6 tables. To be published in Phys.Rev.D

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