Related papers: $A_4$ modular invariance and the strong CP problem

We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real…

We investigate the possibility to describe the quark mass hierarchies as well as the CKM quark mixing matrix without fine-tuning in a quark flavour model with modular $A_4$ symmetry. The quark mass hierarchies are considered in the vicinity…

We discuss the quark mass matrices in the $A_4$ modular symmetry, where the $A_4$ triplet of Higgs is introduced for each up-quark and down-quark sectors, respectively. The model has six real parameters and two complex parameters in…

We study $A_4 \times A_4 \times A_4$ modular symmetric flavor models to realize quark mass hierarchies and mixing angles without fine-tuning. Mass matrices are written in terms of modular forms. At modular fixed points $\tau = i\infty$ and…

Recently, it was shown that modular symmetry may solve the strong CP problem without axions, by producing a vanishing QCD angle while generating a large quark CP violation phase. We extend this framework to finite modular groups,…

CP invariance is a very attractive solution to the strong CP problem in QCD. This solution requires the vanishing ${\rm arg}\,[{\rm det}\, M_d\, {\rm det} M_u]$, where the $M_d$ and $M_u$ are the mass matrices for the down- and up-type…

We study the possibility to generate the quark mass hierarchies as well as the CKM quark mixing and CP violation without fine-tuning in a quark flavour model with modular $A_4$ symmetry. The quark mass hierarchies are considered in the…

We study in the bottom-up framework the possibility to generate the quark mass hierarchies without fine-tuning, the quark mixing and CP-violation (CPV) in a flavour model with $S^\prime_4$ modular symmetry having minimal number of…

We propose a three-zero texture for the down-quark mass matrix within a $SU(5)$ GUT-inspired Standard Model, enforced by a non-invertible selection rule originating from $\mathbb{Z}_2$ gauging of $\mathbb{Z}_N$ symmetries. Assuming CP…

We find a solution to the Strong CP problem that may be testable at the LHC and future colliders. In this solution CP is broken by parity conserving terms, while parity breaking VEVs conserve CP. The quark mass matrix is Hermitian at the…

The unsuppressed CP violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle $\bar \theta$ indicates the CP invariance at…

We perform a systematical analysis of the $A_4$ modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires…

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 use a non-invertible symmetry to construct a three-zero texture for the down-type quark mass matrix, which can resolve the strong CP problem without invoking the axion, in four-dimensional spacetime with three quark families in QCD. We…

We study quark and lepton mass matrices with the common modulus $\tau$ in the $A_4$ modular symmetry. The viable quark mass matrices are composed of modular forms of weights $2$, $4$ and $6$. It is remarked that the modulus $\tau$ is close…

We study the CP violation and the CP phase of quark mass matrices in modular flavor symmetric models. The CP symmetry remains at $\tau = e^{2 \pi i/3}$ by a combination of the $T$-symmetry of the modular symmetry. However, the $T$-symmetry…

We propose an alternative to the axion mechanism for addressing the charge parity (CP) problem in quantum chromodynamics (QCD). Our approach involves imposing CP as an inherent symmetry of the Lagrangian, which is then spontaneously broken.…

A very simple model is presented where all CP violation in Nature is spontaneous in origin. The CKM phase is generated unsuppressed and the strong CP problem is solved with only moderately small couplings between the SM and the CP violation…

We study quark and lepton mass matrices in the $A_4$ modular symmetry towards the unification of the quark and lepton flavors. We adopt modular forms of weights $2$ and $6$ for quarks and charged leptons, while we use modular forms of…

I discuss several aspects of CP non-invariance in the strongly interacting theory of quarks and gluons. I use a simple effective Lagrangian technique to map out the region of quark masses where CP symmetry is spontaneously broken. I then…