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arXiv · 2304.06095

Weak decay constants of the neutral pseudoscalar mesons from lattice QCD+QED

Z. R. Kordov·R. Horsley·W. Kamleh·Y. Nakamura·H. Perlt·P. E. L. Rakow·G. Schierholz·H. Stüben·R. D. Young·J. M. Zanotti
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Abstract

With increasing requirements for greater precision, it becomes essential to describe the effects of isospin breaking induced by both quark masses and electro-magnetic effects. In this work we perform a lattice analysis of the weak decay constants of the neutral pseudoscalar mesons including such isospin breaking effects, with particular consideration being given to the state mixing of the $\pi^0$, $\eta$ and $\eta^\prime$. We also detail extensions to the non-perturbative RI$^\prime$-MOM renormalization scheme for application to non-degenerate flavour-neutral operators which are permitted to mix, and present initial results. Using flavour-breaking expansions in terms of quark masses and charges we determine the leptonic decay constants for the $\pi^0$ and $\eta$ mesons, demonstrating in principle how precision determinations of all neutral pseudoscalar decay constants could be reached in lattice QCD with QED and strong isospin-breaking accounted for.

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Z. R. Kordov, R. Horsley, W. Kamleh, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, H. Stüben, R. D. Young, J. M. Zanotti. 2023-04-12. Weak decay constants of the neutral pseudoscalar mesons from lattice QCD+QED. https://arxiv.org/abs/2304.06095

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