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

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