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These lectures discuss the $\theta$ parameter of QCD. After an introduction to anomalies in four and two dimensions, the parameter is introduced. That such topological parameters can have physical effects is illustrated with two dimensional…

High Energy Physics - Phenomenology · Physics 2007-05-23 Michael Dine

The recent lattice QCD calculations of the neutron and proton electric dipole moments (EDMs) and the CP-violating $\pi {\rm NN}$ coupling constant due to the $\theta$ term are reviewed. Progress towards nucleon EDM calculations, including…

High Energy Physics - Lattice · Physics 2024-11-26 Keh-Fei Liu

Effective field theory arguments suggest that if BSM sectors contain new sources of CP-violation that couple to QCD, these sources will renormalize the $\theta$ term and frustrate ultraviolet solutions to the strong CP problem.…

High Energy Physics - Phenomenology · Physics 2021-10-04 Jordy de Vries , Patrick Draper , Kaori Fuyuto , Jonathan Kozaczuk , Benjamin Lillard

The atomic, nuclear, and nucleon electric dipole moments (EDMs) have significant sensitivity to the CP violation of elementary particle physics, but its quantification has for long been obstructed by the nonperturbative physics of quantum…

High Energy Physics - Phenomenology · Physics 2023-10-17 Nodoka Yamanaka

The behaviour of the broken CP symmetry at finite temperature is examined. This is achieved through the investigation of the neutron electric dipole moment $d_n$ induced by $\theta$-term. By using thermal QCD sum rules, we find that below…

High Energy Physics - Phenomenology · Physics 2016-09-06 Mohamed Chabab

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

These TASI lectures where given in 2018 and provide an introduction to the Strong CP problem and the axion. I start by introducing the Strong CP problem from both a classical and a quantum mechanical perspective, calculating the neutron eDM…

High Energy Physics - Phenomenology · Physics 2023-11-21 Anson Hook

We investigate the direct and indirect bounds on dipole operators involving the top quark. A careful analysis shows that the experimental upper limit on the neutron electric dipole moment strongly constrains the chromo-electric dipole of…

High Energy Physics - Phenomenology · Physics 2013-08-05 Jernej F. Kamenik , Michele Papucci , Andreas Weiler

In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $\theta$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($\eta^\prime$…

High Energy Physics - Lattice · Physics 2026-05-04 Claudio Bonanno , Claudio Bonati , Massimo D'Elia

It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta-angle term in the QCD action…

High Energy Physics - Phenomenology · Physics 2011-01-27 J. Bordes , H. M. Chan , S. T. Tsou

One often hears that the strong $CP$ problem is the one problem which cannot be solved by anthropic reasoning. We argue that this is not so. Due to nonperturbative dynamics, states with a different $CP$ violating paramenter $\theta$ acquire…

High Energy Physics - Theory · Physics 2017-12-11 Nemanja Kaloper , John Terning

We present a solution to the strong CP problem based on the identification of the theta angle with twice the CP violating phase present in the CKM quark matrix. This solution washes out all the unwanted issues stemming form the strong CP…

High Energy Physics - Phenomenology · Physics 2018-02-23 Renata Jora

Motivated by recent claims questioning the existence of strong CP violation, we present a pedagogical review of CP violation in Quantum Chromodynamics (QCD). Using fundamental properties of the QCD partition function, we analyze the…

High Energy Physics - Phenomenology · Physics 2026-01-09 Andreas Ringwald

One of the yet unsolved questions of QCD in the context of the Standard Model is to explain the strong CP problem. A way to look for a better understanding of it is to investigate the theory in the presence of a non-zero topological theta…

High Energy Physics - Lattice · Physics 2014-11-05 Lorenzo Bongiovanni , Gert Aarts , Erhard Seiler , Denes Sexty

Lattice QCD is rapidly progressing toward being able to reliably compute the electric dipole moment of the neutron as a function of the strong CP-violating parameter theta. Present day calculations are performed at unphysical values of the…

High Energy Physics - Lattice · Physics 2014-11-17 Donal O'Connell , Martin J. Savage

A recent work combined the popular left-right parity (LR) and Peccei-Quinn (PQ) symmetries to explain the alignment in quark masses. Since axions may not exist, we break PQ softly and discover a new solution to the strong CP problem.…

High Energy Physics - Phenomenology · Physics 2018-05-04 Ravi Kuchimanchi

We analyze the impact of the $\theta$-angle and axion dynamics for two-color (in fact any $Sp(2N)$) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry…

High Energy Physics - Theory · Physics 2022-11-30 Jahmall Bersini , Alessandra D'Alise , Francesco Sannino , Matías Torres

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

On the basis of allowed local gauge symmetries, the QCD Lagrangian admits a CP-violating term proportional to the topological charge density, commonly referred to as the $\theta$ term. A priori, any value of $\theta$ is consistent with the…

High Energy Physics - Phenomenology · Physics 2026-03-26 Anthony G. Williams

According to the present understanding, the observed diversity of the strong interaction phenomena is described by Quantum Chromodynamics, a gauge field theory with only very few parameters. One of the fundamental questions in this context…

High Energy Physics - Phenomenology · Physics 2009-11-07 Martin Lüscher