ππ→πγ*amplitude and the resonantρ→πγ*transition from lattice QCD

Abstract

We present a determination of the P -wave ππ → πγ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Lüscher formalism. We determine the amplitude for a range of discrete values of the ππ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the ρ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the ρ pole extract the ρ → πγ transition form factor. This calculation, at mπ ≈ 400 MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.

Radiative resonance couplings in γπ→ππ

“…Measuring the cross section with reduced uncertainties compared to Fig. 3 would allow one to test the narrow-width estimate of the ρ 3 → πγ decay rate, Γ ρ3→πγ = 48 (18) keV, and to improve the determination of the chiral anomaly and the ρ → πγ coupling, both without relying on model assumptions while still profiting from the full statistics of the ρ resonance. Such improved experimental information on γπ → ππ is particularly timely given its relation to hadronic light-by-light scattering in the anomalous magnetic moment of the muon as well as recent lattice calculations.…”

“…Together with a similar extraction from π − e − → π − e − π 0 [14], leading to F 3π = 9.6(1.1) GeV −3 , the low-energy theorem is now tested at the 10% level, far behind the 1.5%-level accuracy that has been reached in π 0 → γγ [15,16]. Meanwhile, a first lattice calculation of γ * π → ππ has been reported in [17,18]. In contrast to earlier measurements, the Primakoff studies at COMPASS cover not only the threshold region of γπ → ππ, but extend to much higher center-of-mass energies.…”

Meson Spectroscopy from Lattice QCD

“…There are also good prospects here with the recent appearance of the first lattice QCD calculation of a transition form factor involving a resonance [10,12].…”

“…Going beyond the resonance mass and width, recently the form factor of an unstable hadron has been calculated for the first time in lattice QCD [10,12]. From computations of the ππ → πγ * transition amplitude, the resonant ρ → πγ * transition form factor and the radiative decay width were extracted.…”

Towards a dispersive determination of the pion transition form factor

“…A better procedure would be to use the corresponding physical quantity that includes chiral corrections caused by the non-vanishing light quark masses. 3 With data from the reaction γ + π → 2π or maybe from lattice QCD [19] one could improve on this aspect. With higher-quality data at hand one could even use a twice subtracted dispersion relation and obtain additional knowledge and lower theory uncertainties as pointed out in the previous subsection.…”