Abstract
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Highlights
As no practical perfect lattice setup exists, different views on how to best achieve this balance lead to controversies among lattice practitioners. Another of those disputable topics is the application of perturbation theory at energies as low as those given by the low-energy window of lattice Quantum Chromodynamics (QCD) as specified in (2), including μ = ΛUV ∼ 3 GeV, see [1]
We have presented a full strategy to determine renormalized quark masses from first principle lattice calculations in three-flavour QCD
Compared to other approaches in the community, we separate and disentangle the problem of renormalization from large-scale lattice QCD simulations. In this way the massless renormalization group running for the coupling and quark masses could be mapped out non-perturbatively to high accuracy in the employed Schrödinger functional scheme, and a connection to other schemes can be established via renormalization group invariant quantities {Λ, Mi}Nf
Summary
For numerical simulations one starts from one of many valid discretisations of the (bare) Euclidean action density of Quantum Chromodynamics (QCD), LQCD. As no practical perfect lattice setup exists, different views on how to best achieve this balance lead to controversies among lattice practitioners Another of those disputable topics is the application of perturbation theory at energies as low as those given by the low-energy window of lattice QCD as specified in (2), including μ = ΛUV ∼ 3 GeV, see [1]. The natural question arises how to compare or connect our result to other determinations as summarised for instance by the Particle Data Group [2] Both naturally differ in the renormalization scheme and scale. After removing the UV cutoff dependence, we have to evolve our (continuum) result, mi(μhad), using renormalization group (RG) transformations to the same physical scale and scheme, typically MS.
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