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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

One of the Sakharov's condition for baryogenesis is the violation of both C and CP. In the Standard Model, gauge interactions break maximally C, but CP is only broken through the Yukawa couplings in the poorly understood scalar sector. In…

High Energy Physics - Phenomenology · Physics 2015-06-19 Jean-Marie Frère , Maxim Libanov , Simon Mollet

The Chern-Simons (CS) gravity is a modified theory of Einstein's general relativity (GR). The CS theory arises from the low energy limit of string theory which involves anomaly correction to the Einstein-Hilbert action. The CS term is given…

General Relativity and Quantum Cosmology · Physics 2023-04-12 G. G. L. Nashed , Shin'ichi Nojiri

Current upper bounds of the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|\bar\theta| \lesssim 10^{-11}$. Since QCD explains vast experimental data from the 100 MeV scale to…

High Energy Physics - Phenomenology · Physics 2020-01-08 Jihn E. Kim , Gianpaolo Carosi

Addressed is the question of whether a natural mechanism exists to resolve the strong CP problem. The analogous issue for the two-dimensional $CP^{N-1}$ models is analyzed using computer simulations.

High Energy Physics - Lattice · Physics 2007-05-23 Stuart Samuel

We examine Chern-Simons theory as a deformation of a 3-dimensional BF theory that is partially holomorphic and partially topological. In particular, we introduce a novel gauge that leads naturally to a one-loop exact quantization of this BF…

Mathematical Physics · Physics 2020-05-08 Owen Gwilliam , Brian R. Williams

In this paper we extend the results of previous work on spontaneous baryogenesis to general models involving CP violation in the Higgs sector. We show how to deal with Chern-Simons terms appearing in the effective potential arising from…

High Energy Physics - Phenomenology · Physics 2010-11-01 S. A. Abel , W. N. Cottingham , I. B. Whittingham

Models which solve the strong CP problem by employing discrete spacetime symmetries generically suffer fine-tuning and quality problems. We demonstrate that these issues are greatly ameliorated when the only source of spontaneous CP…

High Energy Physics - Phenomenology · Physics 2026-03-27 Csaba Csáki , Samuel Homiller , Taewook Youn

We discuss a simple model, based on the gauge group ${\rm SU}(3)_C\otimes {\rm SU}(2)_L \otimes \text{U}(1)_Y\otimes \text{U}(1)_R$, where the Nelson-Barr solution to the strong CP problem is implemented. This model automatically provides a…

High Energy Physics - Phenomenology · Physics 2023-07-14 Pavel Fileviez Perez , Clara Murgui , Mark B. Wise

The QCD axion stands as one of the most promising candidates for resolving the strong CP problem. However, the value of the axion's decay constant $f_a$ and, by extension, its mass $m_a$, remain uncertain within the framework of effective…

High Energy Physics - Phenomenology · Physics 2024-11-01 Qiaoli Yang , Runchao Huang

We present a new mechanism for solving the strong CP problem using a Z2 discrete symmetry and an anomalous U(1) symmetry. A Z2 symmetry is used so that two gauge groups have the same theta angle. An anomalous U(1) symmetry makes the…

High Energy Physics - Phenomenology · Physics 2015-04-16 Anson Hook

We investigate static, spherically symmetric solutions of an Einstein-Yang-Mills-Chern-Simons system with negative cosmological constant, for an SO(6) gauge group. For a particular value of the Chern-Simons coefficient, this model can be…

High Energy Physics - Theory · Physics 2013-05-29 Yves Brihaye , Eugen Radu , D. H. Tchrakian

The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in…

High Energy Physics - Theory · Physics 2015-06-11 Jorge Zanelli

Solutions of the Strong CP Problem based on the spontaneous breaking of CP must feature a non-generic structure and simultaneously explain a coincidence between a priori unrelated CP-even and CP-odd mass scales. We show that these…

High Energy Physics - Phenomenology · Physics 2021-08-04 Alessandro Valenti , Luca Vecchi

Dark matter, gauge coupling unification, and the strong CP problem find a common and simple solution (in the absence of naturalness) within axion models. We show that such solution, even without specifying the details of the model…

High Energy Physics - Phenomenology · Physics 2015-06-04 Gian F. Giudice , Riccardo Rattazzi , Alessandro Strumia

We study a non-Abelian Chern-Simons gauge theory in $ 2+ 1$ dimensions with the inclusion of an anomalous magnetic interaction. For a particular relation between the Chern-Simons (CS) mass and the anomalous magnetic coupling the equations…

High Energy Physics - Theory · Physics 2009-10-28 Armando Antillón , Joaquín Escalona , Gabriel Germán , Manuel Torres

The axion solution to the strong CP problem requires an anomalous global U(1) symmetry. We show that the existence of such a symmetry is a natural consequence of an extra dimension in which a gauged U(1) is spontaneously broken on one of…

High Energy Physics - Phenomenology · Physics 2007-05-23 Hsin-Chia Cheng , David Elazzar Kaplan

We propose a model for the QCD axion which is realized through a coupling of the Peccei-Quinn scalar field to magnetically charged fermions at high energies. We show that the axion of this model solves the strong CP problem and then…

High Energy Physics - Phenomenology · Physics 2021-06-22 Anton V. Sokolov , Andreas Ringwald

The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a…

High Energy Physics - Theory · Physics 2008-11-26 Z. Németh

Although the axion is the most compelling solution to the strong CP problem, the ad hoc introduced global Peccei-Quinn symmetry suffers from a severe fine-tuning problem known as the quality problem. In this Letter, we show that the…

High Energy Physics - Phenomenology · Physics 2026-03-05 Jie Sheng , Tsutomu T. Yanagida