In this paper we extend the supersymmetric SU(5) GUTs with the Nelson-Barr (NB) models. The NB models are a candidate for the solution of the strong CP problem. We show that the parameters in the CKM matrix are reproduced while the mass ratios of the down-type quarks and leptons in the second and third generations are explained in the minimal extension.

Japan

Junji Hisano

Moe Kuroda

Extension of SUSY SU(5) GUTs with Nelson-Barr models

<p>We show that, in the Nelson-Barr solution to the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-problem, a naturally light scalar can arise. It gives rise to a completely new phenomenology beyond that of the celebrated QCD axion, if this field constitutes dark matter, as the elements of the Cabibbo–Kobayashi–Maskawa matrix vary periodically in time. We also discuss how the model can be tested using quantum sensors, in particular using nuclear clocks, which leads to an interesting synergy between different frontiers of physics.</p>

United States

Michael Dine

Israel

Gilad Perez

Wolfram Ratzinger

Inbar Savoray

Nelson-Barr ultralight dark matter

We investigate how the solution to the strong CP problem and the explanation for the observed fermion mass hierarchies can be intrinsically related. Specifically, we explore the Nelson-Barr mechanism and identify its “seesaw limit”, where light quark masses are suppressed by large CP-violating terms. Upon adding three (two) vector-like quarks that mix with the down-type (up-type) quark sector of the Standard Model, we demonstrate how the lack of CP violation in the strong sector and the observed quark mass hierarchy can be simultaneously achieved.

Brazil

A.L. Cherchiglia

A.G. Dias

Spain

J. Leite

C.C. Nishi

Seesaw limit of the Nelson-Barr mechanism

We revisit the minimal Nelson-Barr model for solving the strong CP problem through the idea of spontaneous CP breaking. The minimal model suffers from the quality problem, which means that the strong CP angle is generated by higher-dimensional operators and one-loop effects. Consequently, it has been considered that there is a cosmological domain wall problem and that leptogenesis does not work. We point out that just imposing an additional approximate global symmetry solves the quality problem. We also propose a simple solution to the domain wall problem and show that the thermal leptogenesis scenario works.

Kai Murai

Kazunori Nakayama

Revisiting the minimal Nelson-Barr model

In the present work, we perform a comparative study of different interacting dark energy (DE) models using the Statefinder diagnostics. In particular, 17 different forms of the energy transfer rate Q between DE and dark matter (DM) were focused on, belonging to the following categories: (i) linear models in energy densities of DE and DM, (ii) non-linear models, (iii) models with a change of direction of energy transfer between DE and DM, (iv) models involving derivatives of the energy densities, (v) parametrized interactions through a function of the coincidence parameter  $$\tilde{r}$$  <math> <mover> <mi>r</mi> <mo>~</mo> </mover> </math>  , and finally we also consider (vi) two kinds of models with a self-interaction between DM, without DE. These models have been already studied in the literature and constrained with observational data available at that time. In order to discriminate between them at background level, we use the Statefinder diagnostic, based on the computation and study of the so-called Statefinder parameters r, s in addition to the deceleration parameter q. We plot the evolution trajectories for the several interacting models on the  $$r-q$$  <math> <mrow> <mi>r</mi> <mo>-</mo> <mi>q</mi> </mrow> </math>  ,  $$r-s$$  <math> <mrow> <mi>r</mi> <mo>-</mo> <mi>s</mi> </mrow> </math>   planes, and we find some distinctive features and departures from  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM and other DE models, as Quintessence, Chaplygin Gas, running vacuum models (RVM) and Galileon.

Raul Carrasco

Chile

Ángel Rincón

Joel Saavedra

Nelson Videla

Discriminating interacting dark energy models using Statefinder diagnostic

Recently, an increasing interest in UV/IR mixing phenomena has drawn attention to the range of validity of standard quantum field theory. Here we explore the consequences of such a limited range of validity in the context of radiative models for neutrino mass generation. We adopt an argument first published by Cohen, Kaplan and Nelson that gravity implies both UV and IR cutoffs, apply it to the loop integrals describing radiative corrections, and demonstrate that this effect has significant consequences for the parameter space of radiative neutrino mass models.

Germany

Patrick Adolf

Martin Hirsch

Heinrich Päs

Radiative neutrino masses and the Cohen-Kaplan-Nelson bound

Nelson-Barr models solve the strong <math><mi>C</mi><mi>P</mi></math> problem based on spontaneous <math><mi>C</mi><mi>P</mi></math> violation and generically require vectorlike quarks (VLQs) mixing with standard quarks to transmit the <math><mi>C</mi><mi>P</mi></math> violation. We devise an explicit parametrization for the case of two VLQs of either down or up type and quantitatively study several aspects including the hierarchy of the VLQ Yukawas and their irreducible contribution to <math><mover><mi>θ</mi><mo>¯</mo></mover></math>. In particular, with the use of the parametrization, we show that a big portion of the parameter space for two up-type VLQs at the TeV scale is still allowed by the constraint on <math><mover><mi>θ</mi><mo>¯</mo></mover></math>, although this case had been previously shown to be very restricted based on estimates.

G. H. S. Alves

A. L. Cherchiglia

C. C. Nishi

Explicit parametrization of more than one vectorlike quark of Nelson-Barr type

We discuss a simple model, based on the gauge group <math><mi>SU</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>C</mi></msub><mo>⊗</mo><mi>SU</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub><mo>⊗</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>Y</mi></msub><mo>⊗</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>R</mi></msub></math>, where the Nelson-Barr solution to the strong <math><mrow><mi>C</mi><mi>P</mi></mrow></math> problem is implemented. This model automatically provides a high quality solution to the strong <math><mrow><mi>C</mi><mi>P</mi></mrow></math> puzzle. Weak <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in the lepton sector arises in the same fashion as in the quark sector. We derive explicit expressions for the flavor changing couplings of the electroweak and Higgs bosons. These expressions are more general than the particular model considered. Constraints from finite naturalness are briefly discussed. We also briefly discuss related models based on the gauge group B-L.

Pavel Fileviez Pérez

Clara Murgui

Mark B. Wise

Automatic Nelson-Barr solutions to the strong <math><mi>C</mi><mi>P</mi></math> puzzle

It was recently shown that domain walls from the spontaneous breaking of <math><mi>C</mi><mi>P</mi></math> symmetry are exactly stable, and must be inflated away to recover a viable cosmology. We investigate the phenomenological implications of this result in Nelson-Barr solutions of the strong <math><mi>C</mi><mi>P</mi></math> problem. Combined with the upper bound on the scale of spontaneous <math><mi>C</mi><mi>P</mi></math> breaking necessary to suppress contributions from dangerous, nonrenormalizable operators to <math><mover><mi>θ</mi><mo>¯</mo></mover></math>, this puts an upper bound on the scale of inflation and the reheating temperature after inflation. Minimal Nelson-Barr models are therefore in tension with thermal leptogenesis, models of large-field inflation, or potential future observations of signals from topological remnants of an unrelated, subsequent phase transition. We study how extending Nelson-Barr models with a new, continuous chiral gauge symmetry can ameliorate this tension by forbidding the dangerous dimension-five operators. In particular, we show that gauging a linear combination of baryon number and hypercharge allows for an economic, anomaly-free extension of the minimal Nelson-Barr model, and discuss the phenomenological implications.

Pouya Asadi

Samuel Homiller

Qianshu Lu

Matthew Reece

Chiral Nelson-Barr models: Quality and cosmology

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 ∆N eff at a measurable level. As a function of reheating temperature, the predicted ∆N eff shows an interesting plateau behavior we dub the “flavor stairway”, which encodes information about the SM quark flavor structure.

Yang Bai

George Wojcik

Variant Nelson-Barr mechanism with minimal flavor violation