In this letter, we construct an explicit rephasing transformation that converts an arbitrary unitary matrix into the Kobayashi–Maskawa (KM) parametrization and identify all independent CP phases in the mixing matrix as the arguments of its matrix elements. Furthermore, by applying this rephasing transformation to the fermion diagonalization matrices <inline-formula><tex-math id='TM0001' notation='LaTeX'>$U^{\nu , e}$</tex-math></inline-formula>, we show that the Majorana phases are represented by fermion-specific phases <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\delta ^{\nu , e}_{\rm KM}$</tex-math></inline-formula> and their relative phases. In particular, by neglecting the 3-1 elements <inline-formula><tex-math id='TM0003' notation='LaTeX'>$U_{31}^{\nu ,e}$</tex-math></inline-formula> of the diagonalization matrices for the two fermions, the KM phase <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\delta _{\rm KM}$</tex-math></inline-formula> is concisely expressed as <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\delta _{\rm KM} = \arg \left[1 + ({U^{e * }_{21} U^{\nu }_{21} / U^{e * }_{11} U^{\nu }_{11} }) \right] + \arg \left[ - { U_{32}^{e *} U_{32}^{\nu } / U^{e * }_{22} U^{\nu }_{22} } \right]$</tex-math></inline-formula> by fermion-specific rephasing invariants representing two relative phases.

Japan

Masaki J S Yang

Explicit Rephasing to Kobayashi–Maskawa Representation and Fundamental Phase Structure of CP Violation

In this analysis, we examine the angular distribution of low-mass dimuon pairs produced in simulated electron–positron collisions at the proposed International Linear Collider (ILC), which operates at a center-of-mass energy of 500 GeV and has an integrated luminosity of 4 ab <inline-formula><tex-math id='TM0003' notation='LaTeX'>$^{-1}$</tex-math></inline-formula>. Our focus is on the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\cos\theta _{\text{CS}}$</tex-math></inline-formula> variable, which is defined in the Collins&#8211;Soper frame. In the Standard Model, the production of low-mass dimuon pairs is primarily driven by the Drell&#8211;Yan process, which exhibits a notable forward&#8211;backward asymmetry. However, many scenarios beyond the Standard Model predict different shapes for the <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\cos\theta _{\text{CS}}$</tex-math></inline-formula> distribution. This angular distribution can be valuable for distinguishing between these models, especially in the event of observing excesses beyond the Standard Model expectations. We utilized the mono-Z <inline-formula><tex-math id='TM0006' notation='LaTeX'>$^{\prime }$</tex-math></inline-formula> model to interpret the simulated data. In the absence of any discoveries of new physics, we establish upper limits at the 95% confidence level on the masses of various particles in the model, which includes the spin-1 <inline-formula><tex-math id='TM0007' notation='LaTeX'>$\mathrm{Z}^{\prime }$</tex-math></inline-formula> boson and fermionic dark matter.

Egypt

S Elgammal

Spin Identification of the Mono-Z′ Resonance in Muon-Pair Production at the ILC with Simulated Electron–Positron Collisions at √s = 500 GeV

We study a quasi-two-zero neutrino texture based on a type-II seesaw model with modular <inline-formula><tex-math id='TM0002' notation='LaTeX'>$A_4$</tex-math></inline-formula> symmetry to evade the cosmological bound on the sum of neutrino masses while keeping some predictability in the neutrino sector. Working on three fixed points for the modulus, we discuss predictions of the model and show the allowed points satisfying the cosmological bound on neutrino mass from both cosmic microwave background (CMB) and CMB + baryon acoustic oscillation data.

China

Takaaki Nomura

Hiroshi Okada

Quasi-Two-Zero Texture in Type-II Seesaw at Fixed Points from Modular <italic>A</italic> <sub>4</sub> Symmetry

For general one-matrix models in the large- <italic>N</italic> limit, we introduce the cap amplitude <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\psi (b)$</tex-math></inline-formula> as the expansion coefficient of the 1-form <inline-formula><tex-math id='TM0003' notation='LaTeX'>$ydx$</tex-math></inline-formula> on the spectral curve. We find that the dilaton equation&#160;for the discrete volume <inline-formula><tex-math id='TM0004' notation='LaTeX'>$N_{g,n}$</tex-math></inline-formula> of the moduli space of genus- <italic>g</italic> Riemann surfaces with <italic>n</italic> boundaries is interpreted as gluing the cap amplitude along one of the boundaries. In this process, one of the boundaries is capped and the number of boundaries decreases by one. In a similar manner, the genus- <italic>g</italic> free energy <inline-formula><tex-math id='TM0008' notation='LaTeX'>$F_g$</tex-math></inline-formula> is obtained by gluing the cap amplitude to <inline-formula><tex-math id='TM0009' notation='LaTeX'>$N_{g,1}$</tex-math></inline-formula>.

Kazumi Okuyama

Cap Amplitudes in Random Matrix Models

This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a “radial basis function” expansion of the interaction term that appears in the Euclidean path integral formalism. By constructing a corresponding “multilayered perceptron”-type neural network with exponential nonlinearities in the hidden layer, the original path integral can be approximated by a linear combination of Gaussian path integrals that can be solved analytically. The method has been tested for the double-well potential that includes a quadratic and a quartic term, giving very good, within a few percent, agreement between the true and estimated bound state wave functions that are extracted from the propagator at large Euclidean times. The proposed method can also be used to describe potentials that have imaginary parts, which is tested for a simple Gaussian path integral with complex frequencies, where the model uncertainty stays below 1% for both the real and imaginary parts of the propagator.

South Korea

Gábor Balassa

On the Solution of Euclidean Path Integrals with Neural Networks

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.

Nagisa Hiroshima

Mitsuru Kakizaki

Shuhei Ohzawa

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

We study collective excitations in a relativistic collisionless plasma composed of massless fermions subject to an external magnetic field. We include dynamical electromagnetism and fluctuations of the chiral charge, while maintaining a vanishing net chiral charge. Within the framework of chiral kinetic theory, we find that the chiral anomaly gives a correction to the transverse photon self-energy and that a novel type of dynamical screening can emerge. In the strong magnetic field limit, we also show that the collective mode has a gap using the lowest Landau level approximation. We further discuss implications of the anomalous dynamical screening for neutron star phenomenology.

Sota Hanai

Anomalous Dynamical Screening of Relativistic Plasma in a Magnetic Field

We investigate crosscap states in 2D rational conformal field theories (RCFTs), with an emphasis on the role of noninvertible symmetries. In particular, we argue for the existence of crosscap states labeled by each Verlinde line in the RCFT, extending previous constructions involving simple currents. Evidence for the existence of these new states is obtained by deriving a generalized Cardy condition incorporating both crosscaps and topological defects, which we check in some concrete examples. Finally, we briefly discuss how these crosscap states transform under the action of Verlinde lines, as well as the connection to mixed anomalies between parity and internal symmetries.

Wataru Harada

Justin Kaidi

Yuya Kusuki

Yuefeng Liu

New Crosscap States

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.

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.