The strong CP problem remains one of the most important unresolved issues in the Standard Model. Spontaneous CP violation (SCPV) is a promising approach to the problem by assuming that CP is an exact symmetry of the Lagrangian but broken spontaneously at the vacuum, which enables the generation of the observed Cabibbo-Kobayashi-Maskawa (CKM) phase without reintroducing a nonzero strong CP phase. Supersymmetry (SUSY) provides a natural framework to accommodate such a mechanism, as SUSY can not only protect the scale of SCPV from radiative corrections but also suppress problematic higher-dimensional operators generating a strong CP phase. In the present study, we explore the realization of SCPV in two distinct SUSY scenarios. First, we investigate SCPV in the exact SUSY limit by extending the spurion formalism developed in non-supersymmetric theories to identify the necessary condition for stabilizing CP-violating phases, and by analyzing the stabilization of radial vacuum expectation values through R-symmetry constraints on the superpotential. Second, we construct a model in which CP is spontaneously broken at an intermediate scale along pseudo-flat directions, stabilized by soft SUSY breaking and non-perturbative effects of a gauge theory. The latter setup predicts light scalars in the SCPV sector whose masses are determined by the SUSY breaking scale.

China

Fangchao Liu

Shota Nakagawa

Yuichiro Nakai

Yaoduo Wang

Exploring the landscape of spontaneous CP violation in supersymmetric theories

The Belle II experiment and other ongoing and projected lepton facilities are expected to greatly enhance the sensitivity to the electric dipole moment (EDM) and anomalous magnetic moment (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>) for the tau lepton, making it timely to explore models that predict these observables. In this work, we study a class of models in which the tau mass is generated radiatively. As a result, sizable EDM and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> of the tau lepton arise as a natural consequence of the radiative mass generation mechanism at the electroweak scale. We present two benchmark models with different hypercharge assignments. The first model contains neutral fermions and charged scalars. We find that the model can predict a large signal of the tau EDM, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>=</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>19</mn></mrow></msup><mo stretchy="false">)</mo><mi>e</mi><mtext> </mtext><mi>cm</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>τ</mi></msub><mo>=</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo stretchy="false">)</mo></math>, which are within the reach of future updates of their measurements. In contrast, the second model, containing a charged fermion and neutral scalars, yields a similar magnitude but different sign for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>, and predicts a comparatively smaller EDM signal. Our models serve as well-motivated benchmarks for new physics scenarios in which radiative tau mass generation leads to sizable tau dipole moments.

Yoshihiro Shigekami

Peng Sun

Zhihao Zhang

Models for the electric dipole moment and anomalous magnetic moment of the tau lepton

We investigate a cosmological scenario in which the Peccei-Quinn (PQ) symmetry remains broken in the entire history of the Universe, thereby avoiding the formation of axion strings and domain walls. Contrary to the conventional expectation, it is demonstrated that appropriately chosen scalar interactions are able to keep the PQ symmetry broken at arbitrarily high temperatures. We carefully examine the finite-temperature effective potential in a model with two PQ breaking scalar fields. The existence of flat directions plays a vital role in suppressing axion isocurvature perturbations during inflation by stabilizing a PQ field at a large field value. The viable parameter space consistent with theoretical and observational constraints is identified. Our scenario provides a minimal path for PQ symmetry breaking that addresses both the axion domain wall and isocurvature problems while permitting arbitrarily high reheating temperatures accommodating high-scale baryogenesis scenarios such as thermal leptogenesis.

Yu-Cheng Qiu

Lingyun Wang

High reheating temperature without axion domain walls

A supercooled phase transition in a nearly conformal dark sector can provide a natural setting for darkogenesis via its out-of-equilibrium dynamics, where a particle-antiparticle number asymmetry in the dark sector can be reprocessed into the visible sector, yielding the observed baryon asymmetry and an asymmetric dark matter. We consider a scenario where the number asymmetry is generated from the decay of a mother particle produced via parametric resonance during the phase transition induced due to its coupling to the dilaton associated with spontaneous breaking of scale invariance. It is shown that the correct baryon asymmetry and dark matter abundance can be realized for a dark phase transition at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, which can also explain the nanohertz gravitational wave signal reported by pulsar timing array experiments. The scenario will be tested further in neutron-antineutron oscillation experiments.

Sudhakantha Girmohanta

Postsphaleron darkogenesis

We present a new framework of grand unification that is equipped with an axion solution to the strong CP problem without a domain wall problem when the Peccei-Quinn (PQ) symmetry is spontaneously broken after inflation. Our grand unified theory (GUT) is based on a symmetry breaking pattern, SU(10) × SU(5) → SU(5) ⊃ SU(3) × SU(2) × U(1) , where SU(5) and a special embedding of SU(5) ⊂ SU(10) are broken to a diagonal subgroup SU(5) . The model contains a vector-like pair of PQ-charged fermions that transform as (anti-)fundamental representations under SU(10), so that the domain wall number is one. However, after the GUT symmetry breaking, the number of vector-like pairs of PQ-charged colored fermions is larger than one, which seems to encounter the domain wall problem. This apparent inconsistency is resolved by small instanton effects on the axion potential which operate as a PQ-violating bias term and allow the decay of domain walls. We propose a domain-wall-free UV completion for an IR model where the domain wall number appears larger than one. The model gives a prediction for a dark matter axion window, which is different from that of the ordinary post-inflationary QCD axion with domain wall number one.

Shihwen Hor

Italy

Motoo Suzuki

Junxuan Xu

Small instantons and the post-inflationary QCD axion in a special product GUT

Recent cosmological observations have revealed growing tensions with the standard ΛCDM model, including indications of isotropic cosmic birefringence and deviations from <math altimg='si1.svg'><mi>w</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></math> in the dark energy equation of state, as suggested by DESI and supernova measurements. In this paper, we point out that such deviations can arise even from a subdominant energy density component. We then propose a unified framework based on a dynamical axion field that simultaneously accounts for both anomalies, providing a simple and natural extension of the standard &#923;CDM model. In our scenario, the axion field with <math altimg='si2.svg'><mn>2</mn><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&#8818;</mo><mi>m</mi><mo>&#8818;</mo><mn>7</mn><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math>, where <math altimg='si3.svg'><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math> is the current Hubble constant, induces a nonzero rotation of the CMB polarization plane and modifies the present-day dark energy equation of state. This framework accommodates recent observational data with natural parameter choices, even for a string axion with a decay constant of order 10 17 <hsp sp='0.20' />GeV.

Japan

Masaki Yamada

Interpreting cosmic birefringence and DESI data with evolving axion in ΛCDM

We construct a four-dimensional supersymmetric QCD in conformal window with a marginally relevant deformation which triggers the spontaneous breaking of (approximate) scale invariance and the subsequent confinement, generating a mass gap, at an energy scale hierarchically smaller than the Planck scale without fine-tuning. We analyze the finite temperature system and show that the phase transition associated with the breaking of conformal invariance is of the strong first order. When such a phase transition takes place at a temperature of the Universe around the electroweak scale, it generates a stochastic gravitational wave (GW) background probed by future space-based interferometers, while a conformal phase transition in a dark sector at $$ \mathcal{O}(1) $$ GeV generates GWs to explain the reported pulsar timing array signal.

Kohei Fujikura

Yufei Zhang

Conformal phase transition in supersymmetric QCD

Axion-like particles can couple to Standard Model gluons, electroweak gauge bosons, and massive fermions. A future multi-TeV muon collider provides a favorable environment to probe axion-like particles through multiple production channels, including vector boson fusion via electroweak gauge boson couplings and the top-associated production mediated by direct fermionic couplings. Motivated by the quality issue of the QCD axion, we focus on axion-like particles with masses and decay constants around the TeV scale. We explore how different axion-like particle couplings shape its production and decay modes, revealing a rich and intricate phenomenological landscape.

United States

So Chigusa

Interplay of ALP couplings at a muon collider

We propose a novel paradigm for the QCD axion with high-quality Peccei-Quinn (PQ) symmetry on the basis of electric-magnetic duality in the conformal window of a supersymmetric gauge theory. PQ breaking fields, that contain the QCD axion, emerge in the magnetic theory and possess a large anomalous dimension, which leads to not only generation of an intermediate scale of spontaneous PQ breaking but also significant suppression of explicit PQ symmetry breaking operators. The high PQ quality and the absence of a Landau pole in the color gauge coupling are achieved. The parameter space to realize the correct abundance of the axion dark matter (DM) predicts explicit PQ violation which may be probed by future measurements of the neutron electric dipole moment. In the other viable parameter space, the lightest supersymmetric particle can become a DM candidate. Since the model naturally accommodates a mechanism to suppress the axion isocurvature fluctuation, it provides a complete solution to the strong CP problem as well as the identity of DM.

High quality QCD axion via electric-magnetic duality

The dilaton emerges as a pseudo-Nambu-Goldstone boson (pNGB) associated with the spontaneous breaking of scale invariance in a nearly conformal field theory (CFT). We show the existence of a wiggly dilaton potential that contains multiple vacuum solutions in a five-dimensional (5D) holographic formulation. The wiggly feature originates from boundary potentials of a 5D axion-like scalar field, whose naturally small bulk mass parameter corresponds to a marginally-relevant deformation of the dual CFT. Depending on the energy density of a boundary 3-brane, our model can provide a relaxion potential or generate a light dilaton. However, an extremely light dilaton requires fine-tuning.