Lattice determinations of the strong coupling

Abstract

Lattice QCD has reached a mature status. State of the art lattice computations include $u,d,s$ (and even the $c$) sea quark effects, together with an estimate of electromagnetic and isospin breaking corrections for hadronic observables. This precise and first principles description of the standard model at low energies allows the determination of multiple quantities that are essential inputs for phenomenology and not accessible to perturbation theory. One of the fundamental parameters that are determined from simulations of lattice QCD is the strong coupling constant, which plays a central role in the quest for precision at the LHC. Lattice calculations currently provide its best determinations, and will play a central role in future phenomenological studies. For this reason we believe that it is timely to provide a pedagogical introduction to the lattice determinations of the strong coupling. Rather than analysing individual studies, the emphasis will be on the methodologies and the systematic errors that arise in these determinations. We hope that these notes will help lattice practitioners, and QCD phenomenologists at large, by providing a self-contained introduction to the methodology and the possible sources of systematic error. The limiting factors in the determination of the strong coupling turn out to be different from the ones that limit other lattice precision observables. We hope to collect enough information here to allow the reader to appreciate the challenges that arise in order to improve further our knowledge of a quantity that is crucial for LHC phenomenology.

110 pages. LaTeX

References in corpus (39)

• Measurement of the fine-structure constant as a test of the Standard Model
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• The five-loop beta function of Yang-Mills theory with fermions
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Twisted mass lattice QCD
• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• Fermionic contributions to the three-loop static potential
• Charm and Bottom Quark Masses from Perturbative QCD
• Five-loop renormalisation of QCD in covariant gauges
• Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
• Low energy moments of heavy quark current correlators at four loops
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Towards the five-loop Beta function for a general gauge group
• The strong running coupling from the gauge sector of Domain Wall lattice QCD with physical quark masses
• Update: Accurate Determinations of alpha_s from Realistic Lattice QCD
• The QCD static energy at NNNLL
• Chiral anomalies and rooted staggered fermions
• Higher Moments of Heavy Quark Correlators in the Low Energy Limit at O(alpha_s^2)
• The Realistic Lattice Determination of alpha_s(M_Z) Revisited
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Comment on "Chiral anomalies and rooted staggered fermions"
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Step scaling and the Yang-Mills gradient flow
• Topological Lattice Actions
• 't Hooft vertices, partial quenching, and rooted staggered QCD
• On the effects of heavy sea quarks at low energies
• The gradient flow running coupling with twisted boundary conditions
• Introduction to Non-perturbative Heavy Quark Effective Theory
• A massive momentum-subtraction scheme
• QCD Lambda parameter from Landau-gauge gluon and ghost correlations
• Gauge coupling beta functions in the Standard Model

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• FLAG Review 2021
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• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Memory efficient finite volume schemes with twisted boundary conditions