Related papers: The limits of the strong $CP$ problem
QCD admits a contribution to the action, the $\theta$ term, which potentially gives rise to nontrivial phases and violates CP. This is essentially a question of how the vacuum reacts to the $\theta$ term. In this talk I will address the…
Three symmetry constraints on the CP violations in QCD are discussed in this paper. In order to generate CP violating observables from QCD, these constraints require: (1) spontaneous chiral symmetry breaking, (2) explicit chiral symmetry…
I describe how the QCD vacuum structure, necessary to resolve the $U(1)_A$ problem, predicts the presence of a P, T and CP violating term proportional to the vacuum angle $\bar{\theta}$. To agree with experimental bounds, however, this…
Some time ago Dashen pointed out that spontaneous CP violation can occur in the strong interactions. I show how a simple effective Lagrangian exposes the remarkably large domain of quark mass parameters for which this occurs. I close with…
We present a solution to the strong CP problem based on the identification of the theta angle with twice the CP violating phase present in the CKM quark matrix. This solution washes out all the unwanted issues stemming form the strong CP…
We exhibit a novel solution of the strong CP problem, which does not involve any massless particles. The low energy effective Lagrangian of our model involves a discrete spacetime independent axion field which can be thought of as a…
We investigate a controversial issue on the measure of CP violation in strong in teractions. In the presence of nontrivial topological gauge configurations, the $\theta$-term in QCD has a profound effect: it breaks the CP symmetry. The…
We briefly review the cases of forced and spontaneous chiral symmetry breaking. In particular the chiral condensate of q anti-q pairs is parametrized with two angles, phi which measures the chiral condensation, and theta which measures the…
The absence of a neutron electric dipole moment (EDM) constrains the quantum chromodynamics (QCD) theta angle to be less than one part in ten billion, posing the Strong $CP$ problem. We revisit two classes of proposed solutions. First, we…
One may argue that QCD solves the strong CP problem by itself, without having to introduce new symmetries and particles. To test this idea, a lattice simulation is performed. The problem is investigated in the CP$^3$ model first. It is…
The QCD Lagrangian contains a CP violating gluon density term with a physical coefficient $\bar{\theta}$. The upper bound on the electric dipole moment of neutron implies that the value of $\bar{\theta}$ should be extremely small rather…
We consider the effect of adding a CP-odd, theta FFdual-term to the electroweak Lagrangian without fermions. This term affects neither the classical nor perturbatively quantum physics, but can be observed through non-perturbative quantum…
It is argued that QCD might solve the strong CP problem on its own. To test this idea, a lattice simulation suggests itself. In view of the difficulty of such a calculation we have, as a first step, investigated the problem in the $CP^3$…
Recently, Ai, Cruz, Garbrecht, and Tamarit (arXiv:2001.07152, arXiv:2404.16026, arXiv:2511.04216) claimed that the strong CP problem can be avoided by adopting a particular order of limits in the Euclidean path integral, in which the…
The effects of the CP violating $\theta$ term in the QCD Lagrangian upon low energy hadronic phenomenology are reconsidered. Strong CP violating interactions among Goldstone bosons and octet baryons are incorporated into an effective chiral…
The conservation of $CP$ in QCD has been shown to follow from a careful treatment of the path integral and canonical quantization in arXiv:2001.07152 and arXiv:2403.00747. Here, we refute the critique of these results put forth in…
Owing to a different treatment of the vacuum alignment, the strong CP-violating Lagrangian obtained by Di Vecchia, Veneziano and Witten (DVW) 3 decades ago do not look quite the same as the one originally derived by Baluni at the quark or…
In the standard model QCD Lagrangian, a term of CP violating gluon density is theoretically expected to have a physical coefficient $\bar{\theta}$ of the order of unity. However, the upper bound on the electric dipole moment of neutron…
A new possibility for solving the strong CP-problem is suggested,which assumes that apart of the ordinary world of observable particles described by standard model, there exits a mirror sector of particles and two sectors share the same…
It is shown that the quark mass aligns QCD $\theta$ vacuum in such a way that the strong CP is conserved, resolving the strong CP problem.