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Absence of CP violation in the strong interactions
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Absence of CP violation in the strong interactions
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We derive correlation functions for massive fermions with a complex mass in the presence of a general vacuum angle. For this purpose, we first build the Green's functions in the one-instanton background and then sum over the configurations of background instantons. The quantization of topological sectors follows for saddle points of finite Euclidean action in an infinite spacetime volume and the fluctuations about these. For the resulting correlation functions, we therefore take the infinite-volume limit before summing over topological sectors. In contrast to the opposite order of limits, the chiral phases from the mass terms and from the instanton effects then are aligned so that, in absence of additional phases, these do not give rise to observables violating charge-parity symmetry. This result is confirmed when constraining the correlations at coincident points by using the index theorem instead of instanton calculus.
Forward citations
Cited by 6 Pith papers
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The structure of multi-axion solutions to the strong CP problem
Multi-axion theories solving the strong CP problem produce varied mass-coupling relations via a general sum rule that depends on the details of PQ symmetry breaking and anomaly alignments.
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The structure of multi-axion solutions to the strong CP problem
Multi-axion solutions to the strong CP problem produce varied mass-coupling patterns set by PQ symmetry breaking structure and QCD-EM anomaly alignment, summarized by a general sum rule for N-axion systems.
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A particle on a ring or: how I learned to stop worrying and love $\theta$-vacua
The ACGT order-of-limits prescription fails to reproduce the correct θ-dependent energy spectrum in the quantum rotor and quantum pendulum.
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On the $\uptheta$-vacua and CP violation
The θ-vacuum structure in QCD produces observable CP violation when the theory is consistently quantized with boundary degrees of freedom accounted for in the infinite-volume limit.
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CP conservation in the strong interactions
CP conservation in QCD follows from taking the infinite volume limit prior to summing over topological sectors, shown consistent with steepest-descent contours and chiral EFT.
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Quantification of the Flavor Diagonal Hadronic CP Violation
A review of progress in quantifying flavor-diagonal hadronic CP violation effects on EDMs, neutron optics, beta decay, and an attempt to address the strong CP problem without new fields or interactions.
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