We present a supersymmetric solution to the strong CP problem based on spontaneous CP violation which simultaneously addresses the affects coming from supersymmetry breaking. The generated CP violating phase is communicated to the quark sector by interacting with a heavy quark a la Nelson-Barr. The Majorana mass of the right handed neutrinos is generated by interactions with the CP violating sector and so does not conserve CP. This gives the neutrino sector a non-trivial CP violating phase which can then generate the baryon asymmetry of the universe through leptogeneis. The problematic phase in the supersymmetry breaking parameters are suppressed by appealing to a particular gauge mediation model which naturally suppresses the phases of the tree-level gluino mass. This suppression plus the fact that in gauge mediation all loop generated flavor and CP violation is of the minimal flavor violation variety allows for a complete and consistent solution to the strong CP problem.
The Nelson-Barr mechanism to solve the strong CP problem requires vector-like quarks (VLQs) to transmit the spontaneous CP breaking to the SM. We study the scenario where only these VLQs are within reach at the TeV scale while the spontaneous CP breaking sector is inaccessible. We investigate how these VLQs of Nelson-Barr type differ from generic VLQs and find from parameter counting that one less parameter is needed. In particular, for one VLQ of Nelson-Barr type, there is only one CP odd quantity that is responsible for all CP violation. In this case, we solve the technical problem of parame…
The Nelson-Barr (NB) mechanism to solve the strong CP problem assumes CP conservation, arranges vanishing $\barθ$ at tree-level and requires vector-like quarks (VLQs) to transmit the CP breaking to the SM. We analyze the flavor constraints coming from the presence of one such down type VLQ of NB type by performing a global fit on the relevant flavor observables. A comparison is made to the case of one generic VLQ. We find that the allowed parameter space for the VLQ Yukawa couplings and the mixing to the SM are confined to a region much smaller than in the generic case, making the NB case fals…
We discuss composite UV completions of the Nelson-Barr(NB) solution to the strong CP problem. In our construction, the CP symmetry is broken spontaneously by the dynamics of a hidden QCD at $θ=π$. We focus on the minimal implementation of the NB construction where the visible sector contains one extra pair of vector-like up/down quarks. We show that the minimal NB theory suffers from a quality problem, and discuss how composite UV completions may resolve it. We present a simple calculable scheme, free of a quality problem, where dynamical CP violation in the hidden sector is mediated through a…
We analyze the Nelson-Barr approach to the Strong CP Problem. We derive the necessary conditions in order to simultaneously reproduce the CKM phase and the quark masses. Then we quantify the irreducible contributions to the QCD topological angle, namely the corrections arising from loops of the colored fermion mediators that characterize these models. Corrections analytic in the couplings first arise at 3-loop order and are safely below current bounds; non-analytic effects are 2-loop order and decouple as the mediators exceed a few TeV. We discuss collider, electroweak, and flavor bounds and a…
We present a solution to the strong CP problem, which relies on the horizontal gauge symmetry and CP invariance in a full theory. Similar to other Nelson-Barr type solutions, CP violation in both the strong and weak sectors in the Standard model (SM) is attributed to the condensation of complex scalars $Φ$ in the model. The model is differentiated by others in that it explains the hierarchy in quark-Higgs Yukawa coupling in the SM based on a series of sequential breaking of the horizontal $SU(3)_{f}$ gauge symmetry. The experimental constraint $\overlineθ\lesssim10^{-10}$ requires $<\!\!Φ\!\!>…
Models of spontaneous CP violation can solve the Strong CP problem without the need of an anomalous Peccei-Quinn symmetry. In this work we review the Nelson-Barr approach, quantifying a peculiar coincidence between unrelated mass scales that these models must satisfy in order to correctly reproduce the Standard Model quark masses and CP violation. We investigate the compatibility between this requirement and the induced radiative corrections to the neutron electric dipole moment, and with bounds coming from collider, electroweak and flavor observables.
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 sector or mediator sector because corrections to $\barθ$ arise only at two loops. The latter feature follows from an underlying unconventional CP symmetry of order 4 imposed in the sectors beyond the SM composed of only two vector-like quarks of charge $-1/3$ and one complex scalar singlet. No additional symmetry is necessary to implement the Nelson-Barr me…
We study spontaneous CP violation as a solution to the strong CP problem in left-right symmetric theories. The discrete CP symmetry is broken by a complex vacuum expectation value of a right-handed Higgs doublet. Heavy vectorlike down-type quarks mix with the Standard Model quarks introducing the known CP violation - realizing a variant of the Nelson-Barr mechanism. A nonvanishing QCD vacuum angle is generated at loop level. The implementation in the ultraviolet complete theory of trinification at low scales is discussed. We further comment on the phenomenology and future testability of the mo…
We present a unified relaxion solution to the five major outstanding issues in particle physics: the hierarchy problem, dark matter, matter-antimatter asymmetry, neutrino masses and the strong CP problem. The only additional field content in our construction with respect to standard relaxion models is an up-type vector-like fermion pair and three right-handed neutrinos charged under the relaxion shift symmetry. The observed dark matter abundance is generated automatically by oscillations of the relaxion field that begin once it is misaligned from its original stopping point after reheating. Th…
We examine the possibility of building a natural non-supersymmetric model of spontaneous CP violation equipped with the Nelson-Barr (NB) mechanism to address the strong CP problem. Our approach is to utilize a doubly composite dynamics where the first confinement of the CFT occurs at the scale of spontaneous CP violation (SCPV) and the second confinement at the TeV scale. A holographic dual description of this 4D set-up via a warped extra dimension with three 3-branes provides an explicit realization of this idea.In this model, radiative corrections to the strong CP phase are well under contro…
Spontaneous CP violation, such as the Nelson-Barr (NB) mechanism, is an attractive scenario for addressing the strong CP problem while realizing the observed phase of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix. However, not only the CKM phase but also the baryon asymmetric Universe requires sources of CP violation. In this study, we show that a supersymmetric NB mechanism can naturally accommodate the Affleck-Dine (AD) baryogenesis within a CP-invariant Lagrangian. The model provides flat directions associated with new heavy quarks. Focusing on one of the directions, we find that …
In a world devoid of axions, the smallness of the strong CP phase can have implications for leptonic CP violation being probed by neutrino experiments. For example, if nature adopted an axionless solution to the strong CP problem, the same symmetries that set the strong CP phase to zero at the tree-level, may also set the leptonic $CP$ phases to zero (mod π). This automatically happens in the left-right symmetric model when it is extended minimally to solve the strong CP problem by imposition of both P and CP. In the Nelson Barr solution the needed symmetries can be assigned so that leptonic C…
