Pion light-cone distribution amplitude from the pion electromagnetic form factor

• Published in: Physical review. D 2020-10, Vol.102 (7), p.074022-1, Article 074022
• Main Authors: Cheng, Shan, Khodjamirian, Alexander, Rusov, Aleksey V.
• Format: Article
• Language: English
• Subjects: Amplitudes; Collaboration; Dispersion; Form factors; Pions; Polynomials; Sum rules; Uncertainty
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.102.074022

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor Fπ(Q2) and the integrated modulus of the timelike form factor. For Fπ(Q2), the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients a2,4,6,... (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BABAR collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single a2 ≠ 0 is disfavored by the fit. Considering the models with an>2 ≠ 0, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals a2(1 GeV) = (0.22–0.33), a4(1 GeV) = (0.12–0.25). The higher moments starting from a8 are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab Fπ collaboration.