2025/07/24 by Kuchimanchi, Ravi
#FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2507.18620
We show using the Hamiltonian formalism that if parity is a good symmetry of QCD, then the strong CP phase θ must be 0 or π. We find that for P to be a physical symmetry, it must leave the Hilbert space Hθ associated with the θ-vacuum invariant (P: Hθ→ Hθ), which is possible only for θ= 0 or π. We also show that forming linear combinations of states from different θ-sectors produces only classical statistical mixtures, consistent with superselection rules, confirming that Hθ is the most general Hilbert space for the quantum theory. Furthermore, we demonstrate that requiring [P,Ω]=0, where Ω is the generator of large gauge transformations, independently enforces θ=0 (mod π), and that for complex quark mass matrix M, if a generalized parity operator P is a symmetry, then the value of θ gets determined so that it exactly cancels Arg Det M, again giving θ=0 (mod π). These results establish the equivalence of the Hamiltonian and Lagrangian approaches to the strong CP problem.