Contributions of order ${\cal O}(m_{\rm quark}^2)$ to $K_{\ell 3}$ form factors and unitarity of the CKM matrix

Details Contributions of order ${\cal O}(m_{\rm quark}^2)$ to $K_{\ell 3}$ form factors and unitarity of the CKM matrix Contributions of order ${\cal O}(m_{\rm quark}^2)$ to $K_{\ell 3}$ form factors and unitarity of the CKM matrix

2000-01-18

arxiv.org/abs/hep-ph/0001188v1

Phys.Rev. D62 (2000) 033003

Physics

High Energy Physics

High Energy Physics - Phenomenology

Scientific paper

10.1103/PhysRevD.62.033003

The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_{\pi}$, $K_{\ell 3}$ decay rates and the scalar form factor slope $\lambda_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $\beta$-decays.

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