Nonperturbative running of the tensor operator for Nf=3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the nonsinglet tensor operator, for N₅=3 QCD with Wilson fermions in a mixed action setup, with standard Schr\"odinger functional (SF) boundary conditions for sea quarks and chirally rotated Schr\"odinger functional () boundary conditions for valence quarks. Based on a recursive finite-size scaling technique we compute nonperturbatively 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^RGI/T (₇₀₃) ₑ, where the numerator is the scale independent (renormalization group invariant---RGI) tensor operator and the denominator is its renormalized counterpart at a hadronic scale ₇₀₃=233 (8) MeV in a given scheme. We determine the step-scaling function in four distinct renormalization schemes. We also compute the renormalization parameters of these schemes at ₇₀₃ which, combined with the RG-running factor, gives the scheme-independent quantity Zₓ^RGI (g₀^2) 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 N₅=2+1 QCD. All four results are compatible and also agree with a recent determination based on a unitary setup for Wilson quarks with Schr\"odinger functional boundary conditions arXiv: 2309. 04314. This provides a strong universality test.