Dispersive analysis of the γ*γ*→ππ process

Abstract

In this paper, we present a dispersive analysis of the double-virtual photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this process is very sensitive to hadronic final state interaction. For the s-wave, we use a coupled-channel ππ, KK analysis which allows a simultaneous description of both f 0 (500) and f 0 (980) resonances. For higher energies, f 2 (1270) shows up as a dominant structure which we approximate by a single channel ππ rescattering in the d-wave. In the dispersive approach, the latter requires taking into account t-and u-channel vector-meson exchange left-hand cuts which exhibit an anomalous-like behavior for large space-like virtualities. In our paper, we show how to readily incorporate such behavior using a contour deformation. Besides, we devote special attention to kinematic constraints of helicity amplitudes and show their correlations explicitly.

Asymptotic behavior of meson transition form factors

“…Going beyond pseudoscalar poles, the second most important intermediate states are 2π [26,27], which require input on the amplitudes for γ * γ * → ππ [48][49][50][51][52][53]. However, some resonances in the 2π system, such as the f 0 (980) or the f 2 (1270), should be reasonably well described by a narrow-width approximation (NWA), in which case information on the respective TFFs would again be required.…”

Hadronic vacuum polarization and vector-meson resonance parameters from $$\varvec{e^+e^-\rightarrow \pi ^0\gamma }$$

“…In particular, was studied in [ 14 ] as a first step towards the doubly-virtual space-like TFF [ 15 , 16 ], which determines the strength of the pion-pole contribution in a dispersive approach to hadronic light-by-light scattering [ 51 – 54 ], to demonstrate the consistency between and data. Similarly, the and TFFs become relevant for the description of the left-hand cuts in the two-pion contributions [ 55 – 60 ].…”

$$\omega \rightarrow 3\pi $$ and $$\omega \pi ^{0}$$ transition form factor revisited

“…The same reaction together with the electromagnetic pion form factor constrain the doubly virtual pion transition form factor at low virtualities [48,49], which in turn gives the leading contribution to the HLbL process [51]. Additionally, in the calculation of the helicity partial wave amplitudes for γ * γ * → ππ [52][53][54], which are responsible for the twopion contribution to HLbL, the most important left-hand cut beyond the pion pole is almost exclusively attributed to the ω exchange. Thus, it depends on the ω → π 0 γ * TFF.…”