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arXiv · 2502.08797

$\mathrm{O}(a)$ improvement of the flavour singlet scalar density in a setup with Wilson fermions

Pia Leonie Jones Petrak·Jochen Heitger·Fabian Joswig
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Abstract

We report on our Ward identity determination of the $\mathrm{O}(a)$ improvement coefficient for the flavour singlet scalar density, namely $g_\mathrm{S}$, from three-flavour lattice QCD with Wilson-clover fermions and the tree-level Symanzik improved gauge action. We employ five couplings, $g_0^2 \in [1.5,1.77]$, that cover the range used in large-volume CLS simulations. While $g_\mathrm{S}$ itself is for instance relevant for the $\mathrm{O}(a)$ improvement of meson and baryon sigma terms, a relation to $b_\mathrm{g}$, the $\mathrm{O}(a)$ improvement parameter of the gauge coupling, can also be established, allowing for its non-perturbative extraction as well. With Wilson fermions, $b_\mathrm{g}$ is in principle required for full $\mathrm{O}(a)$ improvement at non-vanishing sea quark masses. We outline our procedure for extracting $b_\mathrm{g}$.

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Pia Leonie Jones Petrak, Jochen Heitger, Fabian Joswig. 2025-02-12. $\mathrm{O}(a)$ improvement of the flavour singlet scalar density in a setup with Wilson fermions. https://doi.org/10.22323/1.466.0290

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