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We review results concerning the theta dependence of 4D SU(N) gauge theories and QCD, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss theta dependence in the large-N limit.…

High Energy Physics - Theory · Physics 2013-02-07 Ettore Vicari , Haralambos Panagopoulos

I describe how the QCD vacuum structure, necessary to resolve the $U(1)_A$ problem, predicts the presence of a P, T and CP violating term proportional to the vacuum angle $\bar{\theta}$. To agree with experimental bounds, however, this…

High Energy Physics - Phenomenology · Physics 2011-04-11 R. D. Peccei

We discuss our study of QCD in the presence of CP-odd electromagnetic (e.m.) background fields. We investigate the propagation of the CP-odd term from the e.m. sector to the strong sector, inducing an effective $\theta$ term. We discuss the…

High Energy Physics - Lattice · Physics 2013-12-11 Claudio Bonati , Guido Cossu , Massimo D'Elia , Marco Mariti , Francesco Negro

The strong CP problem is inseparably connected with the topology of gauge fields and the mechanism of color confinement, which requires nonperturbative tools to solve it. In this talk I present results of a recent lattice investigation of…

High Energy Physics - Lattice · Physics 2023-01-11 Gerrit Schierholz

This paper presents a summary of the current status of determinations of the strong coupling constant alpha_s. A detailed description of the definition, scale dependence and inherent theoretical ambiguities is given. The various physical…

High Energy Physics - Phenomenology · Physics 2009-10-31 Ian Hinchliffe , Aneesh V. Manohar

We show that the strong CP problem can, in principle, be solved dynamically by adding extra-dimensions with compact topology. To this aim we consider a toy model for QCD, which contains a vacuum angle and a strong CP like problem. We…

High Energy Physics - Theory · Physics 2011-08-04 F. L. Bezrukov , Y. Burnier

The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update…

High Energy Physics - Lattice · Physics 2016-05-30 Arthur Dromard , Wolfgang Bietenholz , Krzysztof Cichy , Marc Wagner

We apply to the $CP^9$ model two recently proposed numerical techniques for simulation of systems with a theta term. The algorithms, successfully tested in the strong coupling limit, are applied to the weak coupling region. The results…

High Energy Physics - Lattice · Physics 2009-11-10 V. Azcoiti , G. Di Carlo , A. Galante , V. Laliena

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.…

High Energy Physics - Lattice · Physics 2021-06-30 Luigi Del Debbio , Alberto Ramos

We promote the usual QCD $\theta$-parameter to a field and interpret it as the phase of the quark condensate, which becomes nontrivial when topological defects, vortices in our formulation, are induced in the quark condensate by the QCD…

High Energy Physics - Phenomenology · Physics 2019-05-22 Chi Xiong

These lecture notes provide a self-contained, graduate-level introduction to the strong $CP$ problem and QCD axion physics from an effective field theory (EFT) viewpoint. We review the construction of the chiral EFT of QCD yielding a…

High Energy Physics - Phenomenology · Physics 2026-02-05 Francesco Sannino

We exploit the non-perturbative result that the $\theta$ angle which defines the vacuum structure is not a $c$-number free parameter, as suggested by the instanton semi-classical approximation, but instead one of the points of the spectrum…

High Energy Physics - Theory · Physics 2024-10-30 F. Strocchi

Three possible strategies have been advocated to solve the strong CP problem. The first is the axion, a dynamical mechanism that relaxes any initial value of the CP violating angle $\bar{\theta}$ to zero. The second is the imposition of new…

High Energy Physics - Phenomenology · Physics 2025-05-14 David E. Kaplan , Tom Melia , Surjeet Rajendran

I review recent results on phase structure and equation of state of strong interaction matter from lattice QCD. Particular emphasis is given to the axes where direct simulations are possible and results are obtained with sufficient control…

High Energy Physics - Lattice · Physics 2025-12-12 Bastian B. Brandt

I describe the recent success in performing accurate calculations of the effects of the strong force on particles containing bottom and charm quarks. Since quarks are never seen in isolation, and so cannot be studied directly, numerical…

High Energy Physics - Lattice · Physics 2009-11-11 Christine Davies

The properties of matter at finite baryon densities play an important role for the astrophysics of compact stars as well as for heavy ion collisions or the description of nuclear matter. Because of the sign problem of the quark determinant,…

High Energy Physics - Lattice · Physics 2017-04-05 Owe Philipsen

As an important set of thermodynamic quantities, knowledge of the equation of state over a broad range of temperatures and chemical potentials in the QCD phase diagram is crucial for our understanding of strongly-interacting matter. There…

High Energy Physics - Phenomenology · Physics 2024-03-01 Jamie M. Karthein

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD generating functional integral. We expand the perturbative boundary conditions to both perturbative and…

High Energy Physics - Phenomenology · Physics 2023-12-19 S. A. Larin

The physical origin of the strong CP problem in QCD, rooted in the structures of the vacuum of the standard model, is reviewed. The chiral solution to this problem, with its accompanying axion, is explained and various characteristics of…

High Energy Physics - Phenomenology · Physics 2011-04-11 R. D. Peccei

Lattice computations are the only first principle method capable of quantitatively assessing the topological properties of QCD at high temperature, however the numerical determination of the topological properties of QCD, especially in the…

High Energy Physics - Lattice · Physics 2018-04-18 Claudio Bonati