Non-perturbative quark mass renormalisation and running in $$N_{\scriptstyle \mathrm{f}}=3$$ N f = 3 QCD

Abstract

We determine from first principles the quark mass anomalous dimension in N f = 3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and nonperturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%.

Non-perturbative renormalization of tensor currents: strategy and results for $$N_f=0$$ N f = 0 and $$N_

“…The purpose of this work is to set up the strategy for the application of finitesize scaling techniques based on the Schrödinger Functional (SF) [21], in order to obtain a fully non-perturbative determination of both current renormalization constants at hadronic energy scales, and the running of renormalized currents to the electroweak scale. This completes the ALPHA Collaboration non-perturbative renormalization programme for nonsinglet quark field bilinears [7][8][9][10][24][25][26] and four-quark operators [27][28][29][30][31][32][33].…”

“…We have also provided values of renormalization constants at the lowest energy scales reached by the non-perturbative running, which allows to match bare matrix elements computed with non-perturbatively O(a) improved Wilson fermions and the Wilson plaquette gauge action. As part of the ALPHA programme, we are currently completing a similar study in N f = 3 QCD [39], that builds upon a high-precision determination of the strong coupling [36][37][38] and mass anomalous dimension [9,10,24]. Preliminary results indicate that a precision ∼ 1% for the running to low-energy scales is possible even for values of the hadronic matching scale well below the one reached for N f = 2.…”

“…1 We will then apply our formalism to the fully non-perturbative renormalization of non-singlet tensor currents in N f = 0 and N f = 2 QCD. Our results for N f = 3 QCD, that build on the non-perturbative determination of the running coupling [36][37][38] and the renormalization of quark masses [9,10,24], will be provided in a separate publication [39].…”

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

“…The latter step is possible based on numerical stochastic perturbation theory [31][32][33]. Finally we note that, given the coupling results, similar non-perturbative tests of perturbation theory might also be performed using the quark mass parameters [48]. g 2 (L).…”

Light quark masses in $${N_\mathrm{f}=2+1}$$ lattice QCD with Wilson fermions

“…At the physical point m q,1 , m q,2 = m u/d ≡ The bare quark masses produced by CLS [7,8] need to be combined with renormalisation and improvement coefficients in order to obtain renormalised quantities with O(a 2 ) discretisation effects. We use ALPHA collaboration results for the quark mass renormalisation and Renormalisation Group (RG) running [13] in the Schrödinger functional (SF) scheme. Symanzik improvement is implemented for the removal of discretisation effects from correlation functions, leaving us with O(a 2 ) uncertainties in the bulk and O(g 4 0 a) ones at the time boundaries.…”