Non-perturbative renormalization of O($a$) improved tensor currents

Abstract

We present our progress in the non-perturbative O(a) improvement and renormalization of tensor currents in three-flavor lattice QCD with Wilson-clover fermions and tree-level Symanzik improved gauge action. The mass-independent O(a) improvement factor of tensor currents is determined via a Ward identity approach, and their renormalization group running is calculated via recursive finite-size scaling techniques, both implemented within the Schrödinger functional framework. We also address the matching factor between bare and renormalization group invariant currents for a range of lattice spacings < 0.1 fm, relevant for phenomenological large-volume lattice QCD applications.

Renormalization $\&$ improvement of the tensor operator for $N_f=3$ QCD in a $χ$SF setup

“…2. Our data (red circles) are in agreement with perturbation theory at two loops (gray line) [1] and with the data obtained in a purely SF setup (circles in black) [2,17]. This demonstrates the continuum SF-𝜒SF universality.…”

Renormalization & improvement of the tensor operator for $N_f=3$ QCD in a $\chi$SF setup

“…2. Our data (red circles) are in agreement with perturbation theory at two loops (gray line) [1] and with the data obtained in a purely SF setup (circles in black) [2,17]. This demonstrates the continuum SF-SF universality.…”

Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $$N_\mathrm {f}=3$$ QCD with Wilson quarks

“…The gauge ensembles highlighted in italics were newly generated for this study, while the remaining ones were already used in previous investigations; see Refs. [14,15,[24][25][26][27]. 7 These additional ensembles allow for a more even and wider spread of bare quark masses around the chiral point for each value of β, which enables a more precise extraction of the slopes corresponding to Zr m and Z (r m − 1) as explained in Sect.…”

“…These ensembles are used for the numerical determination of the necessary renormalisation parameters and Symanzik improvement coefficients, see Refs. [14,15,[24][25][26][27] that have various applications in lattice QCD when using this discretisation of Wilson fermions. The present work provides high-precision estimates of r m obtained in the same computational framework.…”

“…Refs. [14,15,[24][25][26][27]. Some new ensembles have also been generated, in order to cover the region close to the origin of the function m(m q ) more evenly and assess its slope reliably.…”