K_l3 form factors at order p^6 in chiral perturbation theory

Abstract

This paper describes the calculation of the semileptonic K_l3 decay form factor at order p^6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p^4 result achieved by Gasser and Leutwyler. At order p^6 the chiral expansion contains 1- and 2-loop diagrams which are discussed in detail. The irreducible 2-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian L^6 produces direct couplings with the W-bosons. Due to these unknown couplings, one can always add linear terms in q^2 to the predictions of the form factor f_-(q^2). For the form factor f_+(q^2), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q^4 counter term, the q^4-ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q^2 our calculation shows that chiral perturbation theory converges very well in this application, as the O(p^6) corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f_+(q^2) is well described by a linear fit, but that the slope lambda_+ is smaller by about 2 standard deviations than the O(p^4) prediction. The unavoidable q^2 counter term of the O(p^6) corrections allows to bring the predictions of chiral perturbation theory into perfect agreement with experiment.

32 pages, 7 figures

References in corpus (1)

• Radiative corrections to K_{l3} decays

Cited by in corpus (42)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• FLAG Review 2019
• FLAG Review 2021
• Review of lattice results concerning low energy particle physics
• Kaon Decays in the Standard Model
• $\pi \pi$ Scattering in Three Flavour ChPT
• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• Pion and Kaon Electromagnetic Form Factors
• Low Energy Precision Test of Supersymmetry
• Chiral Perturbation Theory Beyond One Loop
• The < S P P > Green function and SU(3) breaking in K_{l3} decays
• The K -> pi vector form factor at zero momentum transfer on the lattice
• Order p^6 chiral couplings from the scalar K Pi form factor
• FLAG Review 2024
• $\pi K$ Scattering in Three Flavour ChPT
• Scalar form factors of light mesons
• V(us) Determination from Hyperon Semileptonic Decays
• High statistic measurement of the K- -> pi0 e- nu decay form-factors
• Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)
• Axial-vector Form Factors for $K_{\ell 2\gamma }$ and ${\pi }_{\ell 2\gamma }$ at $O(p^6)$ in Chiral Perturbation Theory
• Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks
• Matching Chiral Perturbation Theory and the Dispersive Representation of the Scalar Kpi Form Factor
• The Kl3 scalar form factors in the standard model
• Measurement of K^{0}_{\mu3} form factors
• Measurement of K^0_e3 form factors
• Light meson electromagnetic form factors from three-flavor lattice QCD with exact chiral symmetry
• Kaon physics: a lattice perspective
• Bounds on the slope and the curvature of the scalar Kπform factor at zero momentum transfer
• The expansion by regions in pi K scattering
• On the $\pi$ and $K$ as $q\bar{q}$ Bound States and Approximate Nambu-Goldstone Bosons
• The Ademollo-Gatto theorem for lattice semileptonic decays
• Approximating chiral SU(3) amplitudes
• Improved bounds on the radius and curvature of the K pi scalar form factor and implications to low-energy theorems
• Progress in kaon physics on the lattice
• Precision tests with Kl3 and Kl2 decays
• Analysis of the vector form factors $f_{K\pi }^{+}(Q^2)$ and $f_{K\pi }^{-}(Q^2)$ with light-cone QCD sum rules
• The role of Lattice QCD in flavor physics
• Scalar form factors $f_{\pi \pi }(Q^2)$ and $f_{KK}(Q^2)$ with light-cone QCD sum rules
• K_{l3} and pi_{e3} decays: radiative corrections and CKM unitarity
• QCD and Weak Interactions of Light Quarks
• Chiral behavior of light meson form factors in 2+1 flavor QCD with exact chiral symmetry
• Analytic Approximations for the Extrapolation of Lattice Data