SU(2) chiral perturbation theory for Kl3 decay amplitudes

SU(2) chiral perturbation theory for Kl3 decay amplitudes

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.

kaon physics, weak decays, chiral perturbation theory, lattice QCD, non-perturbative effects

64-80

Flynn, J.M.

d8e90963-ba56-415c-bbd4-496b7d91d343

Sachrajda, C.T.

0ed6568b-f52f-4314-8677-4aeeb925d6f7

1 May 2009

Flynn, J.M.

d8e90963-ba56-415c-bbd4-496b7d91d343

Sachrajda, C.T.

0ed6568b-f52f-4314-8677-4aeeb925d6f7

## 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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## More information

Submitted date: 7 September 2008

Published date: 1 May 2009

Additional Information:
Report number: SHEP-08-26

Keywords:
kaon physics, weak decays, chiral perturbation theory, lattice QCD, non-perturbative effects

Organisations:
High Energy Physics

## Identifiers

Local EPrints ID: 143309

URI: https://eprints.soton.ac.uk/id/eprint/143309

ISSN: 0550-3213

PURE UUID: 9017fbec-dd18-4442-a911-0d366773a513

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Date deposited: 26 May 2010 08:06

Last modified: 20 Jul 2019 01:21

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