Nelson-Barr theories solve the strong CP problem with CP spontaneously broken at Λ and transmitted to the CP conserving version of the SM through vector-like quarks (VLQs). For an arbitrary number of CP breaking scalars and VLQs, we perform the full one-loop matching calculations at Λ up to dimension five operators and the relevant matching calculations at the VLQ scale relevant to tracking the contributions to the parameter $$ \overline{\theta} $$ . In the EFT after the CP breaking scalars have been integrated out, we confirm that the running of $$ \overline{\theta} $$ at $\textit{one-loop}$ is induced by CP violating dimension five operators and similarly by dimension six operator after matching to the SMEFT. In the latter, an additional contribution enters in the matching to $$ \overline{\theta} $$ at $\textit{tree-level}$ due to a dimension five operator. Analyzing the experimental constraint from $$ \overline{\theta} $$ for generic settings, we see that a large separation between Λ and the VLQ scale already suppresses the one-loop contribution to $$ \overline{\theta} $$ sufficiently. We confirm that a simple extension based on a nonconventional CP has vanishing one-loop contribution to $$ \overline{\theta} $$ . Part of our results can be also applied to generic VLQ extensions of the SM.

Brazil

Gustavo Alves

Celso Nishi

Effective description of Nelson-Barr models and the theta parameter

In this study, we numerically show that automatic Nelson-Barr models with new chiral fermions can simultaneously solve the strong CP problem and generate the observed baryon asymmetry via high-scale leptogenesis. In these models, all CP violation arises from a single spontaneous symmetry-breaking scale, linking the origin of quark and lepton CP phases. Using conservative assumptions and minimal dynamics, we identify a viable parameter window where successful leptogenesis occurs without spoiling the quality of the strong CP solution. Models with vector-like fermions face tension within this leptogenesis scenario. A key prediction is a correlation between the baryon asymmetry and the induced QCD vacuum angle shift. Remarkably, we find that the majority of the available parameter space is within reach of current and future nucleon EDM experiments.

Switzerland

C. Murgui

United States

S. Patrone

Leptogenesis in automatic Nelson-Barr models

We explore a concrete realization of a Nelson-Barr model addressing the strong CP problem with suppressed unfavorable corrections. This model has a scalar field that spontaneously breaks discrete symmetry, and its phase component can naturally be relatively light, which we call the Nelson-Barr axion. It has both a tree-level potential and the QCD instanton-induced potential like the QCD axion, each minimizing at the CP-conserving point. While one potential leads to domain wall formation, the other works as a potential bias. This model provides a natural setup for the collapse of the axion domain walls by a potential bias without spoiling a solution to the strong CP problem. We discuss the cosmological implications of domain wall collapses, including dark matter production and gravitational wave emission.

Japan

Kai Murai

Kazunori Nakayama

Domain walls in Nelson-Barr axion model

<p>Many experiments have notably reported anomalies in radioactive decay rates with periodic variations and challenged the traditional belief of time-independent decays. This periodicity could potentially be explained by the presence of a periodic dark matter (DM) candidate. In this work, we investigate the impact of time-dependent nuclear decay rates on the ultralight scalar DM 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. The light scalar DM field in this framework induces periodic modulations of both Cabibbo-Kobayashi-Maskawa matrix elements and quark mass parameters. These modulations generate corresponding periodic perturbations in the neutron-proton mass difference and nuclear binding energies. Consequently, nuclear decay rates receive oscillating residuals. By analyzing the tritium decay rate, we derive new exclusion bounds on the Nelson-Barr DM parameters.</p>

China

Chang-Jie Dai

Tong Li

Constraint on ultralight Nelson-Barr dark matter from time-dependent nuclear decay

It has recently been proposed that the extra dimension in holographic models for charmoniun is related to its internal structure. Representing the interaction between the quark anti-quark pair by a string inside the background used in these models, the linear term of the Cornell potential was obtained. More than that, the dissociation in the thermal medium is also described in a consistent way. Here we extend this study to the case of a plasma with finite density. The combined effects of density and temperature are analyzed from the point of view of quark anti-quark interaction and the results obtained are consistent with the ones derived previously using spectral functions.

Nelson R.F. Braga

William S. Cunha

Yan F. Ferreira

Holography and charmonium structure in a finite density plasma

Holographic models that consider classical vector fields in a 5-d background provide effective descriptions for heavy vector meson spectra. This is true both in vacuum and a thermal medium, such as quark gluon plasma. However, the manner in which these phenomenological models work is unclear. In particular, what is the role of the fifth dimension, and what is the relation between the holographic 5-d background and physical (4-d) heavy mesons? Hadrons, in contrast to leptons, are composite particles with some internal structure that depends on the energy at which they are observed. In this study, a static meson is represented by a heavy quark-antiquark pair with an interaction described by a Nambu Goto string existing in the same 5-d background that provides field solutions leading to masses and decay constants of charmonium states. The resulting interaction potential is linear for large distances, with a string tension consistent with the effective Cornell potential. Introducing temperature $\textit{T}$ in the background, it is found for the $J/\psi$ case that there is a deconfining transition at some critical value of $\textit{T}$. The obtained results indicate that the 5-d background effectively represents the internal structure of the (static) charmonium (quasi) states.

Holography and the internal structure of charmonium * The authors are partially supported by CNPq — Conselho Nacional de Desenvolvimento Científico e Tecnologico, by FAPERJ — Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro and by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior — Brasil (CAPES), Finance Code 001

We investigate the combined effect of rotation and finite chemical potential in the confinement/deconfinement transition of strongly interacting matter. The holographic description consists of a five-dimensional geometry that contains a black hole (BH) in the deconfined (plasma) phase. The geometry is equipped with some cut-off that introduces an infrared energy scale. We consider two possibilities: the so-called hard wall and soft wall AdS/QCD models. The transition between the plasma and hadronic phases is represented holographically as a Hawking-Page transition between geometries with and without a black hole. The gravitational dual of the rotating plasma at finite density is given by a Reissner-Nordström (RN) charged anti-de Sitter (AdS) BH with non-zero angular momentum. This analysis provides the critical temperature of deconfinement as a function of the quark chemical potential and the plasma rotational velocity. For the case of very low temperatures, the dependence of the critical values of the chemical potential for the transition to occur at <math altimg='si1.svg'><mi>T</mi><mo stretchy='false'>&#8594;</mo><mn>0</mn></math> on the rotation is found.

Octavio C. Junqueira

Holographic QCD phase diagram for a rotating plasma in the Hawking-Page approach

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.

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>

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.