Strong coupling from non-equilibrium Monte Carlo simulations
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Springer
Received: April 3, Revised: June 17, Accepted: July 8, Published: July 30,
2020 2020 2020 2020
Olmo Francesconi,a,b Marco Paneroc,d and David Pretid a
Physics Department, College of Science, Swansea University (Singleton Campus), Swansea SA2 8PP, United Kingdom b Universit´e Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France c Department of Physics, University of Turin, Via Pietro Giuria 1, I-10125 Turin, Italy d INFN, Turin, Via Pietro Giuria 1, I-10125 Turin, Italy
E-mail: [email protected], [email protected], [email protected] Abstract: We compute the running coupling of non-Abelian gauge theories in the Schr¨odinger-functional scheme, by means of non-equilibrium Monte Carlo simulations on the lattice. Keywords: Lattice QCD, Lattice Quantum Field Theory, Nonperturbative Effects, Renormalization Group ArXiv ePrint: 2003.13734
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)233
JHEP07(2020)233
Strong coupling from non-equilibrium Monte Carlo simulations
Contents 1 Introduction
1
2 Numerical implementation
3 7 7 18 27
4 Conclusions
34
1
Introduction
During the past few years there has been significant progress towards the understanding of quantum systems out of equilibrium and of the interplay between quantum and thermodynamics effects. Research combining theoretical tools from statistical mechanics, conformal field theory, the theory of integrable systems, and quantum information has led to a deeper comprehension of the connection between entanglement entropy and thermodynamic entropy in stationary states [1, 2], as well as a clarification of the mechanism determining the time evolution of entanglement in many-body quantum systems out of equilibrium [3]. At the same time, powerful fluctuation theorems were discovered and extensively studied in classical statistical mechanics (see refs. [4–6] for reviews), that encode analytical relations among quantities characterizing systems driven out of thermodynamic equilibrium. These include the transient fluctuation theorem describing the probability of violations of the second law of thermodynamics in non-equilibrium steady states [7–10] and Jarzynski’s identity, relating the free-energy difference between two equilibrium states of a system to the exponential average of the work done on the system to drive it out of equilibrium [11, 12]. In the present work, we show how the latter theorem can be applied to study the renormalized coupling in non-Abelian, non supersymmetric gauge theory. This quantity is of major relevance in elementary particle theory: in particular, the gauge coupling g of quantum chromodynamics (QCD) is one of the fundamental parameters in the Standard Model and plays a central rˆ ole in theoretical predictions relevant for the physics probed in 1 high-energy experiments like those at the CERN LHC [16–20]. 1
The most striking feature of the physical QCD coupling is its dependence on the momentum scale µ: the dimensionless parameter αs = g 2 /(4π) is a decrea
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