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Register a new userEffective Field Theories and Lattice QCD
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Authors
C. Bernard
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I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
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Effective Quantum Field Theories and QCD Lattice methods have become more and more complementary and mutually supportive in the study of Hard Probes. I present some of the progress that this alliance already delivered and I discuss future opportunities.
An approach for relating the nucleon excited states extracted from lattice QCD and the nucleon resonances of experimental data has been developed using the Hamiltonian effective field theory (HEFT) method. By formulating HEFT in the finite volume of the lattice, the eigenstates of the Hamiltonian model can be related to the energy eigenstates observed in Lattice simulations. By taking the infinite-volume limit of HEFT, information from the lattice is linked to experiment. The approach opens a new window for the study of experimentally-observed resonances from the first principles of lattice QCD calculations. With the Hamiltonian approach, one not only describes the spectra of lattice-QCD eigenstates through the eigenvalues of the finite-volume Hamiltonian matrix, but one also learns the composition of the lattice-QCD eigenstates via the eigenvectors of the Hamiltonian matrix. One learns the composition of the states in terms of the meson-baryon basis states considered in formulating the effective field theory. One also learns the composition of the resonances observed in Nature. In this paper, we will focus on recent breakthroughs in our understanding of the structure of the $N^*(1535)$, $N^*(1440)$ and $Lambda^*(1405)$ resonances using this method.
The emergence of complex macroscopic phenomena from a small set of parameters and microscopic concepts demonstrates the power and beauty of physical theories. A theory which relates the wealth of data and peculiarities found in nuclei to the small number of parameters and symmetries of quantum chromodynamics is by that standard of exceptional beauty. Decade-long research on computational physics and on effective field theories facilitate the assessment of the presumption that quark masses and strong and electromagnetic coupling constants suffice to parameterize the nuclear chart. By presenting the current status of that enterprise, this article touches the methodology of predicting nuclei by simulating the constituting quarks and gluons and the development of effective field theories as appropriate representations of the fundamental theory. While the nuclear spectra and electromagnetic responses analyzed computationally so far with lattice QCD are in close resemblance to those which intrigued experimentalists a century ago, they also test the theoretical understanding which was unavailable to guide the nuclear pioneers but developed since then. This understanding is shown to be deficient in terms of correlations amongst nuclear observables and their sensitivity to fundamental parameters. By reviewing the transition from one effective field theory to another, from QCD to pionful chiral theories to pionless and eventually to cluster theories, we identify some of those deficiencies and conceptual problems awaiting a solution before QCD can be identified as the high-energy theory from which the nuclear landscape emerges.
Our ability to resolve new physics effects is, largely, limited by the precision with which we calculate. The calculation of observables in the Standard (or a new physics) Model requires knowledge of associated hadronic contributions. The precision of such calculations, and therefore our ability to leverage experiment, is typically limited by hadronic uncertainties. The only first-principles method for calculating the nonperturbative, hadronic contributions is lattice QCD. Modern lattice calculations have controlled errors, are systematically improvable, and in some cases, are pushing the sub-percent level of precision. I outline the role played by, highlight state of the art efforts in, and discuss possible future directions of lattice calculations in flavor physics.
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio model with the entanglement vertex (EPNJL model). We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluation of screening masses is not easy in the NJL-type effective models. The method is applied to analyze temperature dependence of pion screening masses calculated with state-of-the-art lattice simulations with success in reproducing the lattice QCD results. We predict the temperature dependence of pole mass by using EPNJL model.
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