Abstract
By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavour symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line disconnected terms in the 3-point correlation functions is also given. As we consider Wilson clover-like fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavour-conserving matrix elements of the vector first class form factors.
Highlights
Understanding the pattern of flavor symmetry breaking and mixing, and the origin of CP violation, remains one of the outstanding problems in particle physics
By considering a flavor expansion about the SUð3Þ flavor symmetric point, we investigate how flavor blindness constrains octet baryon matrix elements after SUð3Þ is broken by the mass difference between quarks
To hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavor symmetry breaking and proves beneficial for extrapolations to the physical point
Summary
Understanding the pattern of flavor symmetry breaking and mixing, and the origin of CP violation, remains one of the outstanding problems in particle physics. The big questions to be answered are (i) what determines the observed pattern of quark and lepton mass matrices and (ii) are there other sources of flavor symmetry breaking? In [1,2] we have outlined a program to systematically investigate the pattern of flavor symmetry breaking. The program has been successfully applied to meson and baryon masses involving up, down and strange quarks. In this article we will extend the investigation to include matrix elements
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