<p>Radiative symmetry breaking provides an appealing explanation for electroweak symmetry breaking and addresses the hierarchy problem. We present a comprehensive phenomenological study of this scenario, focusing on its key feature: the logarithmic-shaped potential. This potential gives rise to a relatively light scalar boson that mixes with the Higgs boson and leads to first-order phase transitions (FOPTs) in the early Universe. Our study includes providing exact and analytical solutions for the vacuum structure and scalar interactions, classifying four patterns of cosmic thermal history, and calculating the supercooled FOPT and gravitational waves (GWs). A detailed treatment of the FOPT dynamics reveals that an ultra-supercooled FOPT does not always imply strong GW signals, due to its short duration. By combining future collider and GW experiments, we can probe the conformal symmetry breaking scales up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>5</mn></msup><mi>–</mi><msup><mn>10</mn><mn>8</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.</p>

China

Wei Liu

Ke-Pan Xie

Probing radiative electroweak symmetry breaking with colliders and gravitational waves

Nontopological fermionic solitons exist across a diverse range of particle physics models and have rich cosmological implications. This study establishes a general framework for calculating fermionic soliton profiles under arbitrary scalar potentials, utilizing relativistic mean field theory to accurately depict the interaction between the fermion condensate and the background scalar field. Within this framework, the conventional “fermion bound states” are revealed as a subset of fermionic solitons. In addition, we demonstrate how the analytical formulae in previous studies are derived as special cases of our algorithm, discussing the validity of such approximations. Furthermore, we explore the phenomenology of fermionic solitons, highlighting new formation mechanisms and evolution paths, and reconsidering the possibility of collapse into primordial black holes.

Revisiting the fermion-field nontopological solitons

The self-interacting dark matter (SIDM) paradigm offers a potential solution to the small-scale structure problems faced by collisionless cold dark matter. This framework incorporates self-interactions among dark matter particles, typically mediated by a particle with a MeV-scale mass. Recent evidences of nano-Hertz gravitational waves from pulsar timing arrays (PTAs) such as NANOGrav, CPTA, EPTA, and PPTA suggest the occurrence of a first-order phase transition (FOPT) at a MeV-scale temperature. Considering the close proximity between these two scales, we propose that the mediator mass in the SIDM model originates from the spontaneous breaking of a <math><mi>U</mi><mo>(</mo><mn>1</mn><msup><mo>)</mo><mo>′</mo></msup></math> symmetry, which is driven by the FOPT indicated by PTA data. Consequently, the alignment of these two scales is believed to be deeply connected by the same underlying physics. By extensively exploring the parameter space, remarkably, we find that the parameter space favored by SIDM just provides an explanation for the PTA data.

Chengcheng Han

Jin Min Yang

Mengchao Zhang

Self-interacting dark matter implied by nano-Hertz gravitational waves

We investigate the formation of primordial black holes (PBHs) through delayed vacuum decay during slow cosmic first-order phase transitions. Two specific models, the polynomial potential and the real singlet extension of the Standard Model, are used as illustrative examples. Our findings reveal that models with zero-temperature scalar potential barriers are conducive to the realization of this mechanism, as the phase transition duration is extended by the U-shaped Euclidean action. We find that the resulting PBH density is highly sensitive to the barrier height, with abundant PBH formation observed for sufficiently high barriers. Notably, the phase transition needs not to be ultra-supercooled (i.e. the parameter α ≫ 1), and the commonly used exponential nucleation approximation Γ(t) ~ e  βt  fails to capture the PBH formation dynamics in such models.

Japan

Shinya Kanemura

Masanori Tanaka

Primordial black holes from slow phase transitions: a model-building perspective

We investigate the reach for resonances of the composite Higgs models at a 10 TeV μ + μ  −  collider with up to 10 ab −1 luminosity. The strong dynamics sector is modeled by the minimal coset SO(5)/SO(4), where vector resonances are in (3, 1) of SO(4) and fermions are in (2, 2). Various production and decay channels are studied. For the spin-1 resonances, the projections are made based on the radiative return and vector boson fusion production channels. The muon collider can cover most of the kinematically allowed mass range and can measure the coupling g  ρ  to percent level. For the fermionic resonances (i.e. the top partners), pair production easily covers the resonance mass below 5 TeV, while single production extends the reach to 6 TeV for a small ξ = 0.015.

United States

Da Liu

Lian-Tao Wang

Composite resonances at a 10 TeV muon collider

We propose a novel scenario for DM in which weakly interacting massive particles (WIMPs) can freeze-in due to a first-order phase transition (FOPT) in the early Universe. The FOPT dilutes the preexisting DM density to zero and leads to a sudden change in DM mass, preventing WIMPs from reequilibrating due to their large mass-to-temperature ratio. Following the FOPT, WIMPs are produced via a freeze-in process, even though their interactions are not feeble. We demonstrate this concept using a simplified model and then apply it to a realistic model with a delayed electroweak phase transition. Our work presents a promising new direction for the freeze-in mechanism, and also extends the category of WIMP DM.

Xiao-Rui Wang

Freeze-in of WIMP dark matter

A cosmic first-order phase transition occurring at the MeV scale provides an attractive explanation for the nano-Hertz gravitational wave (GW) background, which is indicated by the recent pulsar timing array data from the NANOGrav, CPTA, EPTA, and PPTA Collaborations. We propose this explanation can be further tested at the colliders if the hidden sector couples to the Standard Model sector via the Higgs portal. Through a careful analysis of the thermal history in the hidden sector, we demonstrate that in order to explain the observed GW signal, the portal coupling must be sizable so that it can be probed through Higgs invisible decay at the LHC or future lepton colliders such as CEPC, ILC, and FCC-ee. Our research offers a promising avenue to uncover the physical origin of the nano-Hertz GWs through particle physics experiments.

Shao-Ping Li

Collider test of nano-Hertz gravitational waves from pulsar timing arrays

In the minimal supersymmetric standard model (MSSM) extended by a singlet superfield, when the coupling between the singlet sector and the MSSM sector is tiny, the singlet sector can be a quasi dark sector with supersymmetry (SUSY). We investigate the cosmological phenomena in this scenario and obtain the following observations: (i) In the parameter space solving the small cosmological scale anomalies via self-interacting singlino dark matter (SIDM), a first-order phase transition (FOPT) can readily happen but requires rather light dark matter below MeV; (ii) The corresponding parameter space indicated by FOPT and SIDM can be partially covered by detecting the phase-transition gravitational waves (GWs) at the near-future projects, such as LISA, TianQin and Taiji. Therefore, the recently developed GW astronomy could be a novel probe to such a SUSY scenario.

Wenyu Wang

Wu-Long Xu

Jin Yang

Cosmological phase transitions, gravitational waves and self-interacting dark matter in the singlet extension of MSSM

We discuss domain walls from spontaneous breaking of Abelian discrete symmetries <math><msub><mi>Z</mi><mi>N</mi></msub></math>. A series of different domain wall structures are predicted, depending on the symmetry and charge assignments of scalars leading to the spontaneous symmetry breaking (SSB). A widely existing type of domain walls are those separating degenerate vacua which are adjacent in the field space. We denote these walls as adjacency walls. In the case that <math><msub><mi>Z</mi><mi>N</mi></msub></math> terms are small compared with the <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> terms, the SSB of <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> generates strings first and then adjacency walls bounded by strings are generated after the SSB of <math><msub><mi>Z</mi><mi>N</mi></msub></math>. For symmetries larger than <math><msub><mi>Z</mi><mn>3</mn></msub></math>, nonadjacent vacua exist, and we regard walls separating them as nonadjacency walls. These walls are unstable if <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> is a good approximation. If the discrete symmetry is broken via multiple steps, then we arrive at a complex structure where one kind of wall is wrapped by another type. On the other hand, if the symmetry is broken in different directions independently, then walls generated from the different breaking chains are blind to each other.

Yongcheng Wu

Ye-Ling Zhou

Classification of Abelian domain walls

We propose a new scenario of leptogenesis, which is triggered by a first-order phase transition (FOPT). The right-handed neutrinos (RHNs) are massless in the old vacuum, while they acquire a mass in the new vacuum bubbles, and the mass gap is huge compared with the FOPT temperature. The ultra-relativistic bubble walls sweep the RHNs into the bubbles, where the RHNs experience fast decay and generate the lepton asymmetry, which is further converted to the baryon asymmetry of the Universe (BAU). Since the RHNs are out of equilibrium inside the bubble, the generated BAU does not suffer from the thermal bath washout. We first discuss the general feature of such a FOPT leptogenesis mechanism, and then realize it in an extended B − L model. The gravitational waves from U(1) B−L  breaking could be detected at the future interferometers.