2023/11/25 by Plasencia, Isabel Campos, Brida, Mattia Dalla, de Divitiis, Giulia Maria +4
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat)
paper · doi:10.48550/arxiv.2311.15046
We study the Renormalisation Group (RG) running of the non-singlet tensor operator, for N_\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 (χSF) 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 TRGI/[ T(μhad)]\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 μhad = 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 μhad which, combined with the RG-running factor, gives the scheme-independent quantity ZRGI\mathrm T(g02) 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_\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.