Abstract
The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann–Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.
Highlights
One approach to determine the ratio |V us/V ud| of Cabibbo– Kobayashi–Maskawa (CKM) matrix elements, as suggested in [1], is by using the ratio of the experimentally determined pion and kaon leptonic decay rates (K + → μ+νμ) (π + → μ+νμ)= Vus 2 V ud fK+ 2 MK+ fπ+ Mπ+ − m2μ / M 2 K + m2μ/M π (1 + δem) (1)
This allows the development of an SU (3) flavour symmetry breaking expansion for hadron masses and matrix elements, i.e. an expansion in δmq = mq − m, with m
The unitary range is rather small so we introduce PQ or partially quenching
Summary
One approach to determine the ratio |V us/V ud| of Cabibbo– Kobayashi–Maskawa (CKM) matrix elements, as suggested in [1], is by using the ratio of the experimentally determined pion and kaon leptonic decay rates (K + → μ+νμ) (π + → μ+νμ). The QCD interaction is flavour-blind and so when neglecting electromagnetic and weak interactions, the only difference between the quark flavours comes from the mass matrix. In this article we want to examine how this constrains meson decay matrix elements once full SU (3) flavour symmetry is broken, using the same methods as we used in [11,12] for hadron masses. In particular we shall consider pseudoscalar decay matrix elements and give an estimation for f K / fπ and f K + / fπ+ (ignoring electromagnetic contributions)
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