The document discusses the strong CP problem in particle physics. It notes that the Standard Model allows for a CP-violating interaction term that contributes to the neutron electric dipole moment. Current bounds on the neutron EDM require that the strong CP phase θ be less than 10-10, which is an unnaturally small value given the amount of CP violation seen in the weak interactions. One proposed solution is to add an axion field to the Standard Model through a Peccei-Quinn symmetry, which would generate a pseudo-Goldstone boson called the axion that could explain the smallness of θ.

1. The Strong CP Problem
Johar M. Ashfaque
The SU(3) gauge theory allows a CP-violating interaction of the form
LCP =
θαs
32π2
˜GµνGµν
to be added to the QCD Lagrangian which contributes to the neutron electric dipole moment (nEDM).
Note. Gµν
is the gluon field strength and ˜Gµν is its dual.
Note.
θ ≡ θQCD + arg det YuYd
is the strong CP phase with Yu,d being the up and down yukawas respectively.
The idea behind axions is to add fields to the Standard Model so that there is a new anomalous U(1)
symmetry which is known as a Peccei-Quinn symmetry. If this U(1)P Q is spontaneously broken, it will
generate a new Goldstone boson, the pseudo-Goldstone boson, a.
The current bound on the neutron EDM is
|dN | < 2.9 × 10−26
e cm
so that
|θ| < 10−10
which is a strikingly small value for a dimensionless natural constant given that the CP violating phase
in the CKM matrix is of order one. This smallness of θ despite the large amount of CP violation in the
weak sector is known as the strong CP problem.
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