We propose a grand unified model in five dimensions that addresses the strong CP problem. In this framework, the boundary conditions that break the unified gauge group into the Standard Model gauge group simultaneously explain the mass splitting of the new matter content required for gauge coupling unification and the emergence of the QCD axion as the $$U(1)_\textrm{PQ}$$ gauge field. The quality of the axion solution is inherently ensured by a one-form symmetry of the model. We further investigate the implications of this setup, including its predictions for the proton decay rate, the detectability of axion dark matter, and its cosmological impact. Notably, the model predicts a proton decay signal within the sensitivity of upcoming experiments, a result driven by the trade-off between the unification scale and the reheating temperature. In our scenario, the scales of grand unification and the axion decay constant are naturally unified.

China

Norimi Yokozaki

Junhao Zhu

Five dimensional $$SU(5) \times U(1)_\textrm{PQ}$$ grand unification

We constructed a model for spontaneous CP symmetry breaking in five-dimensional space-time that has a potential to solve the strong CP problem. To explain the nature of dark matter and the baryon asymmetry of the universe, three right-handed neutrinos and <math altimg='si1.svg'><mi>U</mi><msub><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></mrow><mrow><mi>B</mi><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mi>L</mi></mrow></msub></math> gauge interaction are introduced in the bulk, in addition to the field contents of the Bento-Branco-Parada model. The wave-function profiles in the fifth dimension can suppress dangerous operators allowed by symmetries, and the scale of spontaneous CP symmetry breaking can be sufficiently large to be consistent with thermal leptogenesis. In this model, the lightest right-handed neutrino serves as dark matter with a mass of <math altimg='si2.svg'><mi mathvariant='script'>O</mi><mo stretchy='false'>(</mo><mn>10</mn><mo stretchy='false'>)</mo></math> keV. This small mass and the necessarily small mixing are explained by the exponentially localized wave-function in the fifth dimension due to a bulk mass term. The correct relic abundance is achieved thanks to the <math altimg='si1.svg'><mi>U</mi><msub><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></mrow><mrow><mi>B</mi><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mi>L</mi></mrow></msub></math> gauge interaction. The other heavy right-handed neutrinos explain the baryon asymmetry of the universe through leptogenesis, with the required CP violating phases generated by interactions involving heavy leptons.

Yanjin Jiang

Spontaneous CP violation, sterile neutrino dark matter and leptogenesis

Supersymmetry is still a viable explanation for the muon g – 2 anomaly, if the sleptons and electroweak gauginos are   <math> <mi>O</mi> <mfenced> <mn>100</mn> </mfenced> </math>  $$ \mathcal{O}(100) $$  GeV. However, for supersymmetry breaking masses this light, the SUSY flavor and CP-problem are exacerbated. To address this issue, we consider a flavor-safe gauge mediated explanation of the muon g – 2 with additional Higgs soft supersymmetry breaking mass parameters. The setup provides a generic parameter space within minimal gauge mediation. Furthermore, we show that the problematic CP violating phase can be dynamically suppressed. We find that gauge mediation models have large portions of parameter space where the muon g – 2 can be explained at 1 σ level. The interplay between the slepton and the CP-odd Higgs masses also makes the majority of this model’s parameter space testable at the LHC through searches for sleptons or additional Higgs bosons.

Jason Evans

Japan

Tsutomu Yanagida

Flavor- and CP-safe explanation of g  μ  − 2 anomaly

We consider a scenario where supersymmetry breaking, its mediation, and the cancellation of the theta parameter of <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mrow><mi>C</mi></mrow></msub></math> are all caused by a single chiral multiplet. The string axion multiplet is a natural candidate of such a superfield. We show that the scenario provides a convincing basis of focus point gaugino mediation, where the electroweak scale is explained with a moderate tuning among the parameters of the theory.

CERN

United States

Keisuke Harigaya

Tsutomu T. Yanagida

Axion induced SUSY breaking and focus point gaugino mediation

It is known that the recently reported shift of the W boson mass can be easily explained by an <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math> triplet Higgs boson with a zero hypercharge if it obtains a vacuum expectation value (VEV) of <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> GeV. Surprisingly, the addition of a TeV scale complex triplet Higgs boson to the standard model (SM) leads to a precise unification of the gauge couplings at around 10$^{14}$ GeV. We consider that it is a consequence of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> grand unification and show a possible potential for the Higgs fields yielding a weak scale complex <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> triplet scalar boson. Although it seems the proton decay constraint would doom such a low-scale unification, we show that the constraint can be avoided by introducing vector-like fermions which mix with the SM fermions through mass terms involving the VEV of GUT breaking Higgs field. Importantly, the simplest viable model only requires the addition of one pair of vector-like fermions transforming 10 and <math><mover><mrow><mn>10</mn></mrow><mo>‾</mo></mover></math>.

Jason L. Evans

W boson mass anomaly and grand unification

In this letter, we show that the wino-Higgsino dark matter (DM) is detectable in near future DM direct detection experiments for almost all consistent parameter space in the spontaneously broken supergravity (SUGRA) if the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly is explained by the wino-Higgsino loop diagrams. We also point out that the present and future LHC experiments can exclude or confirm this SUGRA explanation of the observed muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly.

Hungary

Sho Iwamoto

Wino-Higgsino dark matter in MSSM from the − 2 Anomaly

We present a supersymmetric solution to the strong <math><mi>C</mi><mi>P</mi></math> problem based on spontaneous <math><mi>C</mi><mi>P</mi></math> violation which simultaneously addresses the effects coming from supersymmetry breaking. The generated <math><mi>C</mi><mi>P</mi></math> 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 <math><mi>C</mi><mi>P</mi></math> violating sector and so does not conserve <math><mi>C</mi><mi>P</mi></math>. This gives the neutrino sector a nontrivial <math><mi>C</mi><mi>P</mi></math> 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 and Higgs bilinear masses. This suppression plus the fact that in gauge mediation all loop generated flavor and <math><mi>C</mi><mi>P</mi></math> violation is of the minimal flavor violation variety allows for a complete and consistent solution to the strong <math><mi>C</mi><mi>P</mi></math> problem.

South Korea

Chengcheng Han

Complete solution to the strong <math><mi>C</mi><mi>P</mi></math> problem: Supersymmetric extension of the Nelson-Barr model

By extending a previously proposed conformal gauge mediation model, we construct a gauge-mediated SUSY breaking (GMSB) model where a SUSY-breaking scale, a messenger mass, the μ-parameter and the gravitino mass in a minimal supersymmetric (SUSY) Standard Model (MSSM) are all explained by a single mass scale, a R-symmetry breaking scale. We focus on a low scale SUSY-breaking scenario with the gravitino mass m 3/2 =   <math> <mi>O</mi> <mfenced> <mn>1</mn> </mfenced> <mi>eV</mi> </math>  $$ \mathcal{O}(1)\mathrm{eV} $$ , which is free from the cosmological gravitino problem and relaxes the fine-tuning of the cosmological constant. Both the messenger and SUSY-breaking sectors are subject to a hidden strong dynamics with the conformality above the messenger mass threshold (and hence the name of the model “strongly interacting conformal gauge mediation”). In our model, the Higgs B-term is suppressed and a large tan β is predicted, resulting in the relatively light second CP-even Higgs and the CP-odd Higgs with a sizable production cross section. These Higgs bosons can be tested at future LHC experiments.

Gong Choi

Charms of strongly interacting conformal gauge mediation

A keV-scale gravitino arising from a minimal supersymmetric (SUSY) Standard Model (MSSM) is an interesting possibility since the small scale problems that the ΛCDM model encounters in the modern cosmology could be alleviated with the keV-scale gravitino serving as the warm dark matter (WDM). Such a light gravitino asks for a low scale supersymmetry (SUSY) breaking for which the gauge mediation (GM) is required as a consistent SUSY-breaking mediation mechanism. In this paper, we show upper bounds of the masses of the second CP-even Higgs boson H and the CP-odd Higgs boson A, assuming the keV-scale gravitino to be responsible for the current DM relic abundance: the upper bound on the mass of H/A is found to be ∼ 4 TeV for the gravitino mass of   <math> <mi>O</mi> <mfenced> <mrow> <mn>10</mn> <mo>−</mo> <mn>100</mn> </mrow> </mfenced> </math>  $$ \mathcal{O}\left(10-100\right) $$  keV. Interestingly, the mass of H/A can be as small as 2–3 TeV and the predicted tan β is as large as 55–60 for the gravitino mass of   <math> <mi>O</mi> <mfenced> <mn>10</mn> </mfenced> </math>  $$ \mathcal{O}(10) $$  keV. This will be tested in the near future Large Hadron Collider (LHC) experiments.

The upper bound of the second Higgs boson mass in minimal gauge mediation with the gravitino warm dark matter

We present a model describing the dark sector (DS) featured by two interactions remaining efficient until late times in the matter-dominated era after recombination: the interaction among dark radiations (DR), and the interaction between a small fraction of dark matter and dark radiation. The dark sector consists of (1) a dominant component cold collisionless DM (DM1), (2) a sub-dominant cold DM (DM2) and (3) a self-interacting DR. When a sufficient amount of DR is ensured and a few percent of the total DM density is contributed by DM2 interacting with DR, this set-up is known to be able to resolve both the Hubble and σ 8 tension. In light of this, we propose a scenario which is logically natural and has an intriguing theoretical structure with a hidden unbroken gauge group SU(5)X ⊗ U(1)X. Our model of the dark sector does not introduce any new scalar field, but contains only massless chiral fermions and gauge fields in the ultraviolet (UV) regime. As such, it introduces a new scale (DM2 mass, m DM2) based on the confinement resulting from the strong dynamics of SU(5)X. Both DM2-DR and DR-DR interactions are attributed to an identical long range interaction of U(1)X. We show that our model can address the cosmological tensions when it is characterized by g X =   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (10 −3)–  <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (10 −2), m DM2 =   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1)–  <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (100) GeV and T DS /T SM ≃ 0.3–0.4 where g X is the gauge coupling of U(1)X and T DS(T SM) is a temperature of the DS (Standard Model sector). Our model explains candidates of DM2 and DR, and DM1 can be any kind of CDM.