TASI Lectures on The Strong CP Problem

TL;DR

The paper surveys the strong CP problem in QCD, arising from the CP-violating $\theta$ term and its physical consequences via instantons and the neutron EDM, with the empirical bound $\theta \ll 10^{-9}$. It develops intuition from a two-dimensional anomaly analysis and the $CP^N$ model, then translates these insights to real QCD, discussing the $U(1)$ problem and current algebra. It reviews proposed resolutions—massless $u$ quark, spontaneously broken CP, and the axion—highlighting the Peccei–Quinn mechanism and the axion’s cosmological role as a potential dark matter candidate, alongside experimental search strategies. The discussion emphasizes how anomalies and topological features shape CP violation in the strong sector and guide new physics beyond the Standard Model. The work connects theoretical constructs with phenomenology and cosmology, outlining promising avenues for detection and broader theoretical implications in string theory and SUSY contexts.

Abstract

These lectures discuss the $θ$ 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 models, and then explained in QCD using instantons and current algebra. Possible solutions including axions, a massless up quark, and spontaneous CP violation are discussed.

Figures (2)

• Figure 1: The triangle diagram associated with the four dimensional anomaly.
• Figure 2: Diagram in which CP-violating coupling of the pion contributes to $d_n$.