International Workshop on e⁺e⁻ collisions from Phi to Psi 2017

Dispersive reconstruction of the neutral pion transition form factor obeying asymptotic constraints

27 Jun 2017, 18:30

1h 30m

Helmholtz-Institut Mainz

Board: 22

Poster Poster Session

Speaker

Long Bai (Bonn University)

Description

The neutral pion transition form factor plays prominent roles both in the hadronic light-by-light scattering corrections to the muon anomaly and in the electromagnetic rare decays of the pion. The singly-virtual transition form factor has been investigated in dispersion relations [1], where the form factor in time-like region was predicted based on the $e^+e^-\to 3 \pi$ cross section data and the high-precision space-like form factor was obtained at low energy by analytic continuation. In this work, we generalize the dispersive analysis into the doubly-virtual kinematics, incorporating the celebrated upshots obtained from perturbative quantum chromodynamics [2-6]. The resulting form factor provides a possibility to study the $\pi^0$-pole contribution to the hadronic light-by-light scattering of the muon $g-2$ in a model independent manner with well estimated uncertainty. [1] M. Hoferichter, B. Kubis, S. Leupold, F. Niecknig and S. P. Schneider, *Dispersive analysis of the pion transition form factor*, Eur. Phys. J. C **74** (2014) 3180, [arXiv:1410.4691 [hep-ph]]. [2] G. P. Lepage and S. J. Brodsky, *Exclusive Processes in Quantum Chromodynamics: Evolution Equations for Hadronic Wave Functions and the Form-Factors of Mesons*, Phys. Lett. B **87** (1979) 359. [3] G. P. Lepage and S. J. Brodsky, *Exclusive Processes in Perturbative Quantum Chromodynamics*, Phys. Rev. D **22** (1980) 2157. [4] S. J. Brodsky and G. P. Lepage, *Large Angle Two Photon Exclusive Channels in Quantum Chromodynamics*, Phys. Rev. D **24** (1981) 1808. [5] V. A. Nesterenko and A. V. Radyushkin, *Comparison of the QCD Sum Rule Approach and Perturbative QCD Analysis for $\gamma^\ast \gamma^\ast \to \pi^0$ Process*, Sov. J. Nucl. Phys. **38** (1983) 284. [6] V. A. Novikov, M. A. Shifman, A. I. Vainshtein, M. B. Voloshin and V. I. Zakharov, *Use and Misuse of QCD Sum Rules, Factorization and Related Topics*, Nucl. Phys. B **237** (1984) 525.