We investigate the trilinear Higgs boson coupling derived from the functional forms of various extended Higgs potentials. In light of experimental constraints on Higgs boson couplings, we focus on extended Higgs models in which the trilinear Higgs boson coupling is predominantly determined by the Standard Model Higgs field. Such models include the nearly aligned Higgs Effective Field Theory, classically scale-invariant models, pseudo-Nambu–Goldstone boson scenarios, tadpole-induced models, and others. We also consider higher-order corrections, including top quark and new particle contributions that are often neglected, and discuss their impact on the trilinear Higgs boson coupling. Finally, we show to what extent the functional forms of the Higgs potentials can be probed at future colliders.

Japan

Nagisa Hiroshima

Mitsuru Kakizaki

Shuhei Ohzawa

Classifying Extended Higgs Models through the Trilinear Higgs Boson Coupling Measurement at Future Colliders

We study the augmentation of the Standard Model (SM) with another <inline-formula><tex-math id='TM0001' notation='LaTeX'>$SU(2)$</tex-math></inline-formula> Higgs doublet and right-handed neutrinos. The second Higgs doublet ( <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\Phi _2$</tex-math></inline-formula>) is defined as odd under the <inline-formula><tex-math id='TM0003' notation='LaTeX'>$Z_2$</tex-math></inline-formula> symmetry, and hence the lightest stable neutral particle from the additional doublet becomes the cold dark matter candidate. The right-handed neutrino field coupled to the Higgs field provides nonzero mass for the neutrinos. The inert doublet field coupled nonminimally to gravity as <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\zeta _2 \Phi _2^\dagger \Phi _2 R$</tex-math></inline-formula> also acts as an inflaton field. The inflationary bounds restrict the interaction couplings as <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\lambda _2/\zeta _2^2 \approx 4\times 10^{-10}$</tex-math></inline-formula>. After inflation ends, the scalar bosonic degrees of freedom from the inert doublet can contribute to the electroweak phase transition. The strongly first-order phase transition bound, i.e. <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\frac{\phi _{+}(T_c)}{T_c} \ge 1.0$</tex-math></inline-formula>, restricts the bare mass parameter of the additional doublet to <inline-formula><tex-math id='TM0007' notation='LaTeX'>$m_{22}=400.0$</tex-math></inline-formula> GeV, demanding GUT-scale perturbative unitarity for <inline-formula><tex-math id='TM0008' notation='LaTeX'>$Y_N=0.01$</tex-math></inline-formula>. The right-handed neutrino effect is studied here only through the running of Yukawa coupling, i.e. <inline-formula><tex-math id='TM0009' notation='LaTeX'>$Y_N$</tex-math></inline-formula>. The running of Yukawa coupling for different values at the electroweak scale restricts the perturbative unitarity at different scales, and affects the strength of the phase transition. The increase in <inline-formula><tex-math id='TM0010' notation='LaTeX'>$Y_N$</tex-math></inline-formula> reduces the strength of the phase transition, and it is no longer satisfied even for a vanishing bare mass parameter. The Planck-scale perturbative unitarity allows for the first-order phase transition, <inline-formula><tex-math id='TM0011' notation='LaTeX'>$\frac{\phi _{+}(T_c)}{T_c} \ge 0.6$</tex-math></inline-formula>, up to <inline-formula><tex-math id='TM0012' notation='LaTeX'>$m_{22}=70.0$</tex-math></inline-formula> GeV for <inline-formula><tex-math id='TM0013' notation='LaTeX'>$Y_N=0.01$</tex-math></inline-formula>, and none of the mass values satisfy the first-order phase transition for <inline-formula><tex-math id='TM0014' notation='LaTeX'>$Y_N=0.4$</tex-math></inline-formula>. The thermal corrections also affect the probability of tunneling from the false vacuum to the true vacuum, and hence the finite-temperature stability of the electroweak vacuum has been studied including the finite-temperature effects.

South Korea

Seong Chan Park

India

Shilpa Jangid

Finite-Temperature Stability from a Doublet Inflation Field with Right-Handed Neutrinos

We discuss the phenomenological implications of noninvertible selection rules in the framework of the supersymmetric standard model. We find that a remnant <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\mathbb {Z}_2$</tex-math></inline-formula> symmetry of fusion algebras that holds at all-loop order plays the role of <italic>R</italic>-parity, forbidding baryon- and lepton-violating operators. In addition, a combination of Standard Model gauge symmetry and the noninvertible selection rules lead to baryon triality and proton hexality that can protect the proton from decay. In general, our selection rules cannot realize the same results as conventional <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\mathbb {Z}_N$</tex-math></inline-formula> symmetries in the supersymmetric standard model. We also clarify the assignments of matter fields under the fusion algebras that are consistent with <inline-formula><tex-math id='TM0004' notation='LaTeX'>$SU(4) \times SU(2) \times SU(2)$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0005' notation='LaTeX'>$SU(5)$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0006' notation='LaTeX'>$SO(10)$</tex-math></inline-formula> grand unified theories.

Tatsuo Kobayashi

Hironobu Mita

Hajime Otsuka

Riku Sakuma

Matter Symmetries in Supersymmetric Standard Models from Noninvertible Selection Rules

This paper investigates the scattering states of spin-(1/2) particles in the spacetime of a spinning cosmic string with spacelike disclination and dislocation, with and without a Coulomb interaction. Working within the tetrad formalism, we solve the Dirac equation for several configurations of angular-momentum density <inline-formula><tex-math id='TM0001' notation='LaTeX'>$J_{t}$</tex-math></inline-formula> and the torsion parameter <inline-formula><tex-math id='TM0002' notation='LaTeX'>$J_{z}$</tex-math></inline-formula> that are relevant from a physical perspective. These configurations include balanced torsion ( <inline-formula><tex-math id='TM0003' notation='LaTeX'>$J_{t}=J_{z}$</tex-math></inline-formula>), pure spinning strings ( <inline-formula><tex-math id='TM0004' notation='LaTeX'>$J_{z}=0$</tex-math></inline-formula>), pure screw dislocations ( <inline-formula><tex-math id='TM0005' notation='LaTeX'>$J_{t}=0$</tex-math></inline-formula>), and the general case. In all cases, the geometry modifies an effective azimuthal quantum number, and for strong rotation it introduces a geometric radial cutoff <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\rho _{c}$</tex-math></inline-formula> that acts as a hard wall. These factors lead to closed-form expressions for the radial wavefunctions, phase shifts, and differential cross sections, which are expressed in terms of confluent hypergeometric and Bessel functions. We demonstrate that conical curvature, rotation, and torsion generate Aharonov&#8211;Bohm-like contributions, as well as energy- and momentum-dependent asymmetries in Dirac&#8211;Coulomb scattering. This results in topology-renormalized Mott/Rutherford patterns. In the Coulomb-free limit, scattering becomes purely geometric yet still exhibits characteristic forward enhancement, which is governed by defect parameters and the cutoff. We briefly discuss possible realizations in Dirac materials, such as strained or defective graphene, where lattice disclinations and dislocations mimic the cosmic-string geometry.

Algeria

Abdelmalek Boumali

Analysis of Spin-1/2 Particle Scattering in a Spinning Cosmic-String Spacetime with Torsion, Curvature, and a Coulomb Potential

The extension of the Standard Model Higgs doublet with three nonzero hypercharge triplets is examineled in this article. The triplets are charged under additional <inline-formula><tex-math id='TM0002' notation='LaTeX'>$U(1)_{L_{\mu }-L_{\tau }}$</tex-math></inline-formula> symmetry. We investigate the stability of the electroweak vacuum at both the tree level and the two-loop level. It is observed that the vacuum stability can be satisfied up to the Planck scale using two-loop <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\beta$</tex-math></inline-formula>-functions. In contrast, due to the increase in the positive effect from triplet degrees of freedom, the perturbative unitarity can be satisfied only up to <inline-formula><tex-math id='TM0004' notation='LaTeX'>$10^{12}$</tex-math></inline-formula> GeV. The parameter space allowed from the Planck scale stability is checked for the strongly electroweak first-order phase transition. The model satisfies the strongly first-order phase transition for the triplet bare mass parameters up to the TeV scale due to the sufficient contribution to the cubic term from the triplet degrees of freedom. It is observed that this model foresees a strongly first-order phase transition for all mass ranges until the degrees of freedom become heavy enough to decouple from the thermal bath. The benchmark points satisfying the strongly first-order phase transition are tested for gravitational-wave signatures. The benchmark points that are allowed from the Planck scale stability, strongly first-order phase transition also comes out to lie in the detectable frequency range of the LISA and BBO experiments.

Anirban Biswas

Strongly Electroweak Phase Transition with <italic>U</italic>(1) <italic>L</italic>&#956;&#8211;<italic>L</italic>&#964; Gauged Nonzero Hypercharge Triplet

The Lanczos algorithm offers a framework for constructing wave functions in closed and open quantum systems from their Hamiltonians. Since the early universe is inherently an open system, we employ this algorithm to investigate Krylov complexity across various cosmological phases: inflation, radiation domination (RD), and matter domination (MD). Our results highlight a clear distinction in Krylov complexity between the closed- and open-system methodologies. To accurately capture the influence of potentials during RD and MD, we examine a set of inflationary potentials, including the Higgs potential, <inline-formula><tex-math id='TM0001' notation='LaTeX'>$R^2$</tex-math></inline-formula> inflation, and chaotic inflation, while incorporating violations of slow-roll conditions. This study is conducted in conformal time through the preheating stage. Numerically, we find that the evolution of Krylov complexity and Krylov entropy shows remarkable similarity across different potentials during RD and MD. Furthermore, we rigorously construct an open two-mode squeezed state using the second kind of Meixner polynomial. Based on this construction, we derive for the first time the evolution equations&#160;for the squeezing parameter <inline-formula><tex-math id='TM0002' notation='LaTeX'>$r_k$</tex-math></inline-formula> and phase <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\phi _k$</tex-math></inline-formula> in terms of the scale factor. Our analysis indicates that dissipative effects lead to rapid decoherence-like behavior. In addition, we observe that the inflationary universe behaves as a strongly dissipative system, whereas during the RD and MD epochs the universe exhibits weak dissipative characteristics. This work opens new perspectives for studying the universe from a quantum-informational viewpoint.

China

Ke-Hong Zhai

Lei-Hua Liu

Krylov Complexity in Early Universe

Primordial black holes (PBHs) are significant sources of axions and axion-like particles, provided their Hawking temperature exceeds the particles’ masses. Given the predominant decay of axions into photons, the enhanced photon spectrum they generate can be feasibly detected using sensitive detectors. This paper introduces a novel methodology that elucidates the decay process by which particles traverse and decay over cosmological timescales. Specifically, we derive estimations for the photon spectrum and flux, assuming a monochromatic mass spectrum and isotropic distribution for PBHs. Encouragingly, forthcoming detectors like e-ASTROGAM are well positioned to capture this signal.

Yongsoo Jho

Tae-Geun Kim

Jong-Chul Park

Yeji Park

Primordial Black Holes as a Factory of Axions: Extragalactic Photons from Axions

We consider a class of spontaneously broken <inline-formula><tex-math id='TM0001' notation='LaTeX'>$SU(2)$</tex-math></inline-formula> gauge theories with an adjoint scalar and look for exact magnetic monopole solutions in the Bogomol&#8217;nyi&#8211;Prasad&#8211;Sommerfield (BPS) limit. We find that some of the resulting solutions exhibit a new internal degree of freedom (a moduli space parameter) that controls the energy density profile of the monopole while keeping the total energy (mass) constant.

Czechia

Petr Beneš

Filip Blaschke

Magnetic Monopoles with an Internal Degree of Freedom

The matter operator in the double-scaled Sachdev–Ye–Kitaev model exhibits special properties when its dimension is analytically continued to <inline-formula><tex-math id='TM0001' notation='LaTeX'>$-\frac{1}{2}$</tex-math></inline-formula>. At this dimension, the operator is in a degenerate representation of the <italic>q</italic>-deformed oscillator algebra and satisfies a null vector equation. Its peculiar fusion property gives rise to recursion relations among matter correlation functions. We find that these relations allow us to determine the two-point function without having to sum over infinitely many chord diagrams.

Kazuo Hosomichi

Masayoshi Sato

Degenerate Chords in Double-Scaled SYK

We investigate the response of the Kaluza–Klein (KK) mass spectrum to various deformations of the rugby-ball background in 6D supergravity. We derived the mode equations that contain the 3D scale factor and the lapse function. By solving these, we numerically evaluate the KK masses for a bulk scalar and a spinor when the background has a nontrivial dependence on the position in the compact space. We clarify some qualitative features of the spectrum deformation for some perturbations of the rugby-ball background. For perturbations of a supersymmetric background, we find that the mass-splitting between bosonic and fermionic modes is much smaller than the deviation from the values of the supersymmetric mass eigenvalues.