Determination of the pion distribution amplitude

Abstract

Right now, we have not enough knowledge to determine the hadron distribution amplitudes (DAs) which are universal physical quantities in the high energy processes involving hadron for applying pQCD to exclusive processes. Even for the simplest pion, one can't discriminate from different DA models. Inversely, one expects that processes involving pion can in principle provide strong constraints on the pion DA. For example, the pion-photon transition form factor (TFF) can get accurate information of the pion wave function or DA, due to the single pion in this process. However, the data from Belle and BABAR have a big difference on TFF in high $Q^2$ regions, at present, they are helpless for determining the pion DA. At the present paper, we think it is still possible to determine the pion DA as long as we perform a combined analysis of the most existing data of the processes involving pion such as $\pi \to \mu \bar{\nu }$, ${\pi }^0\to \gamma \gamma$, $B\to \pi l\nu$, $D\to \pi l\nu$, and etc. Based on the revised light-cone harmonic oscillator model, a convenient DA model has been suggested, whose parameter $B$ which dominates its longitudinal behavior for ${\varphi }_{\pi }(x,{\mu }^2)$ can be determined in a definite range by those processes. A light-cone sum rule analysis of the semi-leptonic processes $B\to \pi l\nu$ and $D\to \pi l\nu$ leads to a narrow region $B=[0.01,0.14]$, which indicate a slight deviation from the asymptotic DA. Then, one can predict the behavior of the pion-photon TFF in high $Q^2$ regions which can be tested in the future experiments. Following this way it provides the possibility that the pion DA will be determined by the global fit finally.

9 pages, 6 figures

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• The pion distribution amplitude and the pion-photon transition form factor in a nonlocal chiral quark model
• Reconsideration of the $B\to K^{\ast }$ Transition Form Factors within the QCD Light-Cone Sum Rules
• $a_0(980)$-meson twist-2 distribution amplitude within the QCD sum rules and investigation of $D\to a_0(980)(\to \eta \pi )e^{+}{\nu }_e$
• Investigating the ratio of CKM matrix elements $|V_{ub}|/|V_{cb}|$ from semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ and kaon twist-2 distribution amplitude
• Heavy Pseudoscalar Twist-3 Distribution Amplitudes within QCD Theory in Background Fields
• The $B\to \rho$ helicity form factors within the QCD light-cone sum rules
• The longitudinal and transverse distributions of the pion wavefunction from the present experimental data on the pion-photon transition form factor
• The ${\rm Y}(1S)$ $\to$ $B_c\rho$ decay with perturbative QCD approach
• The $B\to \pi \ell {\nu }_{\ell }$ semileptonic decay within the LCSR approach under heavy quark effective field theory
• Footprint in fitting $B\to D$ vector form factor and determination for $D$-meson leading-twist LCDA
• Constraint of $\xi$-moments calculated with QCD sum rules on the pion distribution amplitude models
• An updated determination of the pion-photon transition form factor
• $\gamma \gamma \to M^{+}{M}^{-}(M=\pi ,K)$ processes with twist-3 corrections in QCD
• Limit on the pion distribution amplitude
• Searching for $a_0(980)$-meson parton distribution function
• Covariance constraints for light front wave functions
• Status of the $D_s^{+}\to \varphi {\ell }^{+}{\nu }_{\ell }$ decay with a chiral-odd $\varphi$-meson light-cone distribution amplitude