Dispersive analysis of the Primakoff reaction $γK \to K π$

Abstract

We provide a dispersion-theoretical representation of the reaction amplitudes γK → Kπ in all charge channels, based on modern pion-kaon Pwave phase shift input. Crossed-channel singularities are fixed from phenomenology as far as possible. We demonstrate how the subtraction constants can be matched to a low-energy theorem and radiative couplings of the K * (892) resonances, thereby providing a model-independent framework for future analyses of high-precision kaon Primakoff data. IntroductionThe Wess-Zumino-Witten anomaly [1,2] provides QCD predictions for processes of odd intrinsic parity at low energies. The textbook example is the two-photon decay of the neutral pion [3-5], which is determined, at zero quark masses, by the elementary charge, e, and the pion decay constant, F π . The next-more-complicated reactions involving strong and electromagnetic interactions only are three-pseudoscalars-photon processes [6] such as γπ → ππ, or η → ππγ. Low-energy theorems for these are of a very similar structure, i.e., they provide parameter-free predictions in terms of e and F π , e.g.for γπ → ππ [7][8][9]. This reaction can be investigated experimentally in a Primakoff reaction [10], with a charged-pion beam scattered off the Coulomb field of a heavy nucleus. Such experiments have been performed, with the objective to test the prediction of Eq.

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

“…Similar dispersive analyses have also been carried out for πN [122,145,146,151,152], γ ( * ) γ ( * ) → ππ [153][154][155][156][157], e + e − → π + π − [158], γπ → ππ [159,160] and γK → πK [161]. The approach for obtaining rigorous and precise poles from dispersively constrained data fits, is also well-suited for the recent lattice calculations that we hope may shed further light on these issues.…”

On the scalar $πK$ form factor beyond the elastic region

“…Given that the πK S-wave effectively stays elastic well beyond 1 GeV, with the first excited resonance, the K * 0 (1430), still predominantly coupling to the πK channel, the κ properties are thus largely encoded in the S-wave phase shift, although the full dispersive analysis involves other partial waves as well as the crossed reaction ππ → KK [3,7,9]. While πK scattering thus serves as the simplest probe of the strangeness sector of the QCD spectrum, its impact extends far beyond, with more complicated processes such as γK → πK [10], K 4 decays [11], D-meson decays such as D → ππK [12,13], or even reactions involving nucleons [14,15] depending on πK amplitudes as input.…”