| Title: |
Nonperturbative running of the tensor operator for $N_\rm{f}=3$ QCD from the chirally rotated Schrödinger Functional |
| Authors: |
Plasencia, Isabel Campos; Brida, Mattia Dalla; de Divitiis, Giulia Maria; Lytle, Andrew; Papinutto, Mauro; Pirelli, Ludovica; Vladikas, Anastassios |
| Publication Year: |
2023 |
| Collection: |
ArXiv.org (Cornell University Library) |
| Subject Terms: |
High Energy Physics - Lattice |
| Description: |
We study the Renormalisation Group (RG) running of the non-singlet tensor operator, for $N_\mathrm{\scriptstyle f}=3$ QCD with Wilson fermions in a mixed action setup, with standard Schrödinger Functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger Functional ($χ$SF) boundary conditions for valence quarks. Based on a recursive finite-size scaling technique we compute non-perturbatively the tensor step-scaling function for an energy range between a hadronic scale and an electroweak scale, above which perturbation theory may be safely applied. Our result is expressed as the RG-running factor $T^{\mathrm{RGI}}/[ T(μ_{\mathrm{had}})]_{\scriptstyle \rm R}$, where the numerator is the scale independent (Renormalisation Group Invariant - RGI) tensor operator and the denominator is its renormalised counterpart at a hadronic scale $μ_{\mathrm{had}} = 233(8)$~MeV in a given scheme. We determine the step-scaling function in four distinct renormalisation schemes. We also compute the renormalisation parameters of these schemes at $μ_{\mathrm{had}}$ which, combined with the RG-running factor, gives the scheme-independent quantity $Z^{\mathrm{RGI}}_{\mathrm T}(g_0^2)$ in four schemes and for a range of bare gauge couplings in which large volume hadronic matrix element simulations are performed by the CLS consortium in $N_\mathrm{\scriptstyle f}=2+1$ QCD. All four results are compatible and also agree with a recent determination based on a unitary setup for Wilson quarks with Schrödinger Functional boundary conditions~arXiv:2309.04314 . This provides a strong universality test. ; 35 pages, 28 figures |
| Document Type: |
text |
| Language: |
unknown |
| Relation: |
http://arxiv.org/abs/2311.15046 |
| Availability: |
http://arxiv.org/abs/2311.15046 |
| Accession Number: |
edsbas.3A583A6 |
| Database: |
BASE |