Nelson-Barr Mechanism Research Articles

Variant Nelson-Barr mechanism with minimal flavor violation

Within the general framework of using spontaneous CP violation to solve the strong CP problem, we construct a variant Nelson-Barr model in which the Standard Model (SM) quark contribution to the strong CP phase is cancelled by new heavy QCD-charged fermions. This cancellation is ensured by choosing conjugate representations for the new colored states under the same global flavor symmetry of SM quarks. Choosing the global flavor symmetry to be that of minimal flavor violation, we suppress higher-order corrections to the strong CP phase to well below current experimental constraints. More than two dozen massless Goldstone bosons emerge from spontaneous flavor symmetry breaking, which yield strong astrophysical constraints on the symmetry breaking scale. In the early universe, the Goldstone bosons can be thermally produced from their interactions with the heavy colored fermions and contribute to ∆Neff at a measurable level. As a function of reheating temperature, the predicted ∆Neff shows an interesting plateau behavior we dub the “flavor stairway”, which encodes information about the SM quark flavor structure.

Low scale leptogenesis in a model with promising CP structure

We consider a simple extension of the standard model, which could give a solution to its CP issues through both the Peccei–Quinn mechanism and the Nelson–Barr mechanism. Its low energy effective model coincides with the scotogenic model in the leptonic sector. Although leptogenesis is known not to work well at lower reheating temperature than 10^9 GeV in simple seesaw and scotogenic frameworks, such low reheating temperature could be consistent with both neutrino mass generation and thermal leptogenesis via newly introduced fields without referring to the resonance effect. An alternative dark matter candidate to axion is prepared as an indispensable ingredient of the model.

Consequences of vector-like quarks of Nelson-Barr type

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 parametrizing only the new physics parameters while keeping the SM parameters as independent inputs. For one down-type VLQ, the model is largely flavor safe because the VLQ couplings to the SM up quarks and the W are hierarchically smaller for lighter quarks.

All-in-one relaxion: A unified solution to five particle-physics puzzles

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. The matter-antimatter asymmetry arises from spontaneous baryogenesis induced by the CPT violation due to the rolling of the relaxion after reheating. The CPT violation is communicated to the baryons and leptons via an operator, $\partial_\mu \phi J^\mu$, where $J^\mu$ consists of right-handed neutrino currents arising naturally from a simple neutrino mass model. Finally, the strong CP problem is solved via the Nelson-Barr mechanism, i.e. by imposing CP as a symmetry of the Lagrangian that is broken only spontaneously by the relaxion. The CP breaking is such that although an ${\cal O}(1)$ strong CKM phase is generated, the induced strong CP phase is much smaller, i.e., within experimental bounds.

Spontaneous CP violation and the strong CP problem in left-right symmetric theories

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 model.

Solving the strong CP problem with non-conventional CP

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 overline{theta} 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 mechanism.

Nelson-Barr relaxion

Cosmological relaxation models in which the relaxion is identified with the QCD axion, generically fail to account for the smallness of the strong CP phase. We present a simple alternative solution to this "relaxion CP problem" based on the Nelson-Barr mechanism. We take CP to be a symmetry of the UV theory, and the relaxion to have no anomalous coupling with QCD. The non-zero vacuum expectation value of the relaxion breaks CP spontaneously, and the resulting phase is mapped to the Cabibbo-Kobayashi-Maskawa phase of the Standard Model. The extended Nelson-Barr quark sector generates the relaxion "rolling" potential radiatively, relating the new physics scale with the relaxion decay constant. With no new states within the reach of the LHC, our relaxion can still be probed in a variety of astrophysical and cosmological processes, as well as in flavor experiments.

Challenges for the Nelson-Barr mechanism

The axion and m u = 0 solutions to the strong CP problem have been subject to the most careful scrutiny and critique. Basic theoretical issues include hierarchy and fine-tuning problems, quality and genericity of symmetries, and compatibility with solutions to the electroweak hierarchy problem. We study the similar set of challenges for solutions to strong CP based on spontaneous CP violation and the Nelson-Barr mechanism. Some of our observations have appeared in the literature previously, and others are new; our purpose is to collect and analyze the issues as a whole and provide an assessment of the most plausible settings for the Nelson-Barr solution.

Viable supersymmetric model with UV insensitive anomaly mediation

We propose an electroweak model which is compatible with the UV insensitive anomaly-mediated supersymmetry breaking. The model is an extension of the next to minimal supersymmetric standard model (NMSSM) by adding vectorlike matter fields which can drive the soft scalar masses of the singlet Higgs field negative and the successful electroweak symmetry breaking is achieved. Viable parameter regions are found to preserve perturbativity of all the coupling constants up to the Planck scale. With this success, the model becomes a perfect candidate of physics beyond the standard model without the flavor changing neutral current and $CP$ problem. The cosmology is also quite interesting. The lightest neutralino is the wino which is a perfect cold dark matter candidate assuming the nonthermal production from the gravitino decay. There is no gravitino problem because it decays before the big-bang nucleosynthesis era, and thus the thermal leptogenesis works. The cosmological domain wall problem inherent in the NMSSM is absent since the ${Z}_{3}$ symmetry is broken by the QCD instanton effect in the presence of the vectorlike quarks. We also briefly comment on a possible solution to the strong $CP$ problem \`a la the Nelson-Barr mechanism.

Supersymmetry and the Nelson-Barr mechanism.

One possible solution to the strong CP problem is that CP is an exact symmetry, spontaneously broken at some scale. Some years ago, Nelson and Barr suggested a mechanism for obtaining $\theta=0$ at tree level in this framework, and showed that radiative corrections were small in some non-supersymmetric models. Further investigations suggested that the same could be true in supersymmetric theories. In this note, we show that these analyses assumed an extraordinarily high degree of degeneracy among squark masses and among other supersymmetry breaking parameters. We argue, using naturalness as well as expectations from string theory, that this is not very plausible.