Kaon semileptonic decay (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math>) form factors from the instanton vacuum

We investigate the kaon semileptonic decay (${K}_{l3}$) form factors within the framework of the nonlocal chiral quark model ($\ensuremath{\chi}\mathrm{QM}$) from the instanton vacuum, taking into account the effects of flavor SU(3) symmetry breaking. We also consider the problem of gauge invariance arising from the momentum-dependent quark mass in the present work. All theoretical calculations are carried out without any adjustable parameter, the average instanton size ($\ensuremath{\rho}\ensuremath{\sim}1/3\text{ }\text{ }\mathrm{fm}$) and the interinstanton distance ($R\ensuremath{\sim}1\text{ }\text{ }\mathrm{fm}$) having been fixed. We also show that the present results satisfy the Callan-Treiman low-energy theorem as well as the Ademollo-Gatto theorem. Using the ${K}_{l3}$ form factors, we evaluate relevant physical quantities. It turns out that the effects of flavor SU(3) symmetry breaking are essential in reproducing the kaon semileptonic form factors. The present results are in good agreement with experiments, and are compatible with other model calculations.

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