Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

Abstract

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex $(z\cdot \tensor{D})^n$ of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain $⟨{\xi }^2⟩{|}_{1\mathrm{GeV}}=0.338\pm 0.032$, $⟨{\xi }^4⟩{|}_{1\mathrm{GeV}}=0.211\pm 0.030$ and $⟨{\xi }^6⟩{|}_{1\mathrm{GeV}}=0.163\pm 0.030$. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is $a_2^{\pi }{|}_{1\mathrm{GeV}}=0.403\pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.

13 pages, 7 figures

References in corpus (9)

• Measurement of gamma gamma* --> pi0 transition form factor at Belle
• Power corrections to alpha_s(M_τ),|V_{us}| and m_s
• SVZ sum rules : 30 + 1 years later
• A Comprehensive Analysis on the Pion-Photon Transition Form Factor Beyond the Leading Fock State
• Form factors $f_{+}^{B\to \pi }(0)$ and $f_{+}^{D\to \pi }(0)$ in $QCD$ and determination of $|V_{ub}|$ and $|V_{cd}|$
• Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data
• New results on Pionic Twist-3 Distribution Amplitudes within the QCD Sum Rules
• Finding a way to determine the pion distribution amplitude from the experimental data
• Constraints on the Leading-Twist Pion Distribution Amplitude from A QCD Light-Cone Sum Rule with Chiral Current

Cited by in corpus (1)

• The $\rho$-meson longitudinal leading-twist distribution amplitude within QCD background field theory