SU(2) chiral perturbation theory for Kl3 decay amplitudes

Flynn, J.M. and Sachrajda, C.T. (2009) SU(2) chiral perturbation theory for Kl3 decay amplitudes. Nuclear Physics B, 812 (1-2), 64-80. (doi:10.1016/j.nuclphysb.2008.12.001).

Abstract

We use one-loop SU(2)L×SU(2)R chiral perturbation theory (SU(2) ChPT) to study the behaviour of the form-factors for semileptonic K?? decays with the pion mass at q2=0 and at View the MathML source, where q is the momentum transfer. At q2=0, the final-state pion has an energy of approximately mK/2 (for mKmuch greater-thanm?) and so is not soft, nevertheless it is possible to compute the chiral logarithms, i.e. the corrections of View the MathML source.

We envisage that our results at q2=0 will be useful in extrapolating lattice QCD results to physical masses. A consequence of the Callan–Treiman relation is that in the SU(2) chiral limit (mu=md=0), the scalar form factor f0 at View the MathML source is equal to f(K)/f, the ratio of the kaon and pion leptonic decay constants in the chiral limit. Lattice results for the scalar form factor at View the MathML source are obtained with excellent precision, but at the masses at which the simulations are performed the results are about 25% below f(K)/f and are increasing only very slowly.

We investigate the chiral behaviour of View the MathML source and find large corrections which provide a semi-quantitative explanation of the difference between the lattice results and f(K)/f. We stress the generality of the relation View the MathML source in the SU(2) chiral limit, where P=K, D or B and briefly comment on the potential value of using this theorem in obtaining physical results from lattice simulations.

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Contributors

Author: J.M. Flynn

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