The strong CP problem is a question in particle physics, which brings up the following quandary: why does quantum chromodynamics (QCD) seem to preserve CP-symmetry?
According to the current mathematical formulation of quantum chromodynamics, a violation of CP-symmetry in strong interactions could occur.
However, no violation of the CP-symmetry has ever been seen in any experiment involving only the strong interaction.
"[1][2] There are several proposed solutions to solve the strong CP problem.
The most well-known is Peccei–Quinn theory,[3] involving new pseudoscalar particles called axions.
The symmetry is known to be broken in the Standard Model through weak interactions, but it is also expected to be broken through strong interactions which govern quantum chromodynamics (QCD), something that has not yet been observed.
To illustrate how the CP violation can come about in QCD, consider a Yang–Mills theory with a single massive quark.
while the second term is the so-called θ-term or “vacuum angle”, which also violates CP-symmetry.
Quark fields can always be redefined by performing a chiral transformation by some angle
due to a change in the path integral measure, an effect closely connected to the chiral anomaly.
For example, the CP violation due to the mass term can be eliminated by picking
If instead the θ-term is eliminated through a chiral transformation, then there will be a CP violating complex mass with a phase
Practically, it is usually useful to put all the CP violation into the θ-term and thus only deal with real masses.
In the Standard Model where one deals with six quarks whose masses are described by the Yukawa matrices
Since the θ-term has no contributions to perturbation theory, all effects from strong CP violation is entirely non-perturbative.
Notably, it gives rise to a neutron electric dipole moment[5] Current experimental upper bounds on the dipole moment give an upper bound of
The strong CP problem is solved automatically if one of the quarks is massless.
[7] In that case one can perform a set of chiral transformations on all the massive quark fields to get rid of their complex mass phases and then perform another chiral transformation on the massless quark field to eliminate the residual θ-term without also introducing a complex mass term for that field.
This then gets rid of all CP violating terms in the theory.
The problem with this solution is that all quarks are known to be massive from experimental matching with lattice calculations.
Even if one of the quarks was essentially massless to solve the problem, this would in itself just be another fine-tuning problem since there is nothing requiring a quark mass to take on such a small value.
[8] This introduces a new global anomalous symmetry which is then spontaneously broken at low energies, giving rise to a pseudo-Goldstone boson called an axion.
The axion ground state dynamically forces the theory to be CP-symmetric by setting
Axions are also considered viable candidates for dark matter and axion-like particles are also predicted by string theory.
at some high energy scale where CP-symmetry is exact but the symmetry is then spontaneously broken.
remains small at low energies while the CP breaking phase in the CKM matrix is large.