There is a possible CP-violating term in the strong sector of the standard model proportional to $\theta_\text{QCD}$. In the absence of this term, the strong interactions are CP-invariant. In the weak interactions, there is CP-violation that comes from the lone phase $\delta$ appearing in the CKM quark-mixing matrix.

When the strong interactions are coupled to the weak interactions, and in the absence of new physics, do the weak interactions renormalize $\theta_\text{QCD}$?

My best guess by how this would show up diagrammatically is when the self energies of quarks pick up phases through loops, which via the U(1) anomaly could be interpreted as $\theta_\text{QCD}$. Is this guess correct?


The CP phase in the strong sector comes from a topological term (a total derivative) $$\require{cancel} \mathcal L_{\cancel{CP}} \propto \theta_\mathrm{QCD} \epsilon^{\mu \nu \rho \sigma} G_{\mu \nu} G_{\rho \sigma}, $$ where $G_{\mu \nu}$ is the gluon field-strength.

Such an operator can never be produced as an effective operator from weak interactions, therefore $\theta_\mathrm{QCD}$ will not be renormalized.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.