Lattice QCD

Summary

Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered. Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/a, where a is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as confinement and quark–gluon plasma formation, which are intractable by means of analytic field

Official source

https://en.wikipedia.org/wiki/Lattice_QCD

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Lattice formulation of axion inflation. Application to preheating

José Roberto Canivete Cuissa, Daniel Garcia Figueroa

We present a lattice formulation of an interaction phi/Lambda F (F) over tilde between an axion and some U(1) gauge sector with the following properties: it reproduces the continuum theory up to O(dx(mu)(2)) corrections, it preserves exact gauge invariance and shift symmetry on the lattice, and it is suitable for self-consistent expansion of the Universe. The lattice equations of motion can no longer be solved by explicit methods, but we propose an implicit method to overcome this difficulty, which preserves the relevant system constraints down to arbitrary (tunable) precision. As a first application we study, in a comoving grid in (3 +1) dimensions, the last efolds of axion-inflation with quadratic potential and the preheating stage following afterwards. We fully account for the inhomogeneity and non-linearity of the system, including the gauge field contribution to the expansion rate of the Universe and its backreaction into the axion dynamics. We characterize in detail, as a function of the coupling, the energy transfer from the axion to the gauge field. Two coupling regimes are identified, sub- and super-critical, depending on whether the final energy fraction stored in the gauge field is below or above similar to 50% of the total energy. The Universe is very efficiently reheated for super-critical couplings, rapidly entering in a radiation dominated stage. Our results on preheating confirm previously published results.

IOP PUBLISHING LTD2019

Complex heavy-quark potential and Debye mass in a gluonic medium from lattice QCD

Yannis Burnier

We improve and extend our study of the complex in-medium heavy-quark potential and its Debye mass m(D) in a gluonic medium with a finer scan around the deconfinement transition and newly generated ensembles closer to the thermodynamic limit. On the lattices with larger physical volume, Re [V] shows signs of screening, i.e. a finite m(D), only in the deconfined phase, reminiscent of a genuine phase transition. Consistently Im[V] exhibits nonzero values also only above T-C. We compare the behavior of Re [V] with the color singlet free energies that have been used historically to extract the Debye mass. An effective coupling constant is computed to assess the residual influence of the confining part of the potential at T > 0. Our previous finding of a gradual screening of Re [V] around T-C on finer lattices is critically reassessed and interpreted to originate from finite volume artifacts. We discuss that deficiency of the beta = 7, xi(b) = 3.5 parameter set at N-s = 32, which has been in deployed in the literature before.

Amer Physical Soc2017

We report recent results of a non-perturbative determination of the static heavy-quark potential in quenched and dynamical lattice QCD at finite temperature. The real and imaginary part of this complex quantity are extracted from the spectral function of Wilson line correlators in Coulomb gauge. To obtain spectral information from Euclidean time numerical data, our study relies on a novel Bayesian prescription that differs from the Maximum Entropy Method. We perform simulations on quenched 32(3) x N-tau (beta = 7.0, xi = 3.5) lattices with N-tau = 24,...,96, which cover 839MeV >= T >= 210MeV. To investigate the potential in a quark-gluon plasma with light u, d and s quarks we utilize N-f = 2 + 1 ASQTAD lattices with m(l) = m(s)/20 by the HotQCD collaboration, giving access to temperatures between 286MeV >= T >= 148MeV. The real part of the potential exhibits a clean transition from a linear, confining behavior in the hadronic phase to a Debye screened form above deconfinement. Interestingly its values lie close to the color singlet free energies in Coulomb gauge at all temperatures. We estimate the imaginary part on quenched lattices and find that it is of the same order of magnitude as in hard-thermal loop perturbation theory. From among all the systematic checks carried out in our study, we discuss explicitly the dependence of the result on the default model and the number of datapoints.

Amer Inst Physics2016