Dispersive analysis of K_{L mu3} and K_{L e3} scalar and vector form factors using KTeV data

TL;DR

This paper reanalyzes K_L semileptonic decay data using dispersive methods to extract form factors and phase space integrals, testing Standard Model predictions and comparing with lattice QCD results.

Contribution

It provides a dispersive analysis of K_L decay form factors, offering new parameterizations and precise measurements of phase space integrals and the Callan-Treiman parameter C.

Findings

Phase space integrals I^e_K and I^{mu}_K are precisely determined.

The scalar form factor at the Callan-Treiman point is measured as ln C = 0.1915 ± 0.0122.

Results are consistent with Standard Model and lattice QCD calculations.

Abstract

Using the published KTeV samples of K_L --> pi^{\pm} e^{\mp} nu and K_L --> pi^{\pm} mu^{\mp} nu decays [1], we perform a reanalysis of the scalar and vector form factors based on the dispersive parameterization [2,3]. We obtain phase space integrals I^e_K = 0.15446 \pm 0.00025 and I^{mu}_K = 0.10219 \pm 0.00025. For the scalar form factor parameterization, the only free parameter is the normalized form factor value at the Callan-Treiman point (C); our best fit results in ln C = 0.1915 \pm 0.0122. We also study the sensitivity of C to different parametrizations of the vector form factor. The results for the phase space integrals and C are then used to make tests of the Standard Model. Finally, we compare our results with lattice QCD calculations of F_K/F_pi and f_+(0).