$K_{\ell 3}$ decays in Chiral Perturbation Theory

Abstract

The process $K_{\ell 3}$ is calculated to two-loop order ($p^6$) in Chiral Perturbation Theory (ChPT) in the isospin conserved case. We present expressions suitable for use with previous work in two-loop CHPT where the order $p^4$ parameters ($L_i^r$) were determined from experiment. We point out that all the order $p^6$ parameters ($C_i^r$) that appear in the value of $f_{+}(0)$ relevant for the determination of $|V_{us}|$ can be determined from $K_{\ell 3}$ measurements via the slope and the curvature of the scalar form-factor. As a by product we update the value of the CKM matrix element $|V_{us}|$.

23 pages, changes: comparison with work of Post-Schilcher extended, comparison with KEK PS E246 added and a value for V_us included, discussion of Ref. [9] changed. Some misprints corrected

References in corpus (2)

• Introduction to Chiral Perturbation Theory
• K_{l3} and pi_{e3} decays: radiative corrections and CKM unitarity

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