We revisit the fermion mass problem of the <italic>SU</italic>(5) grand unified theory using machine learning techniques. The original <italic>SU</italic>(5) model proposed by Georgi and Glashow is incompatible with the observed fermion mass spectrum. Two remedies are known to resolve this discrepancy, one is through introducing a new interaction via a 45-dimensional field, and the other via a 24-dimensional field. We investigate which modification is more beautiful, defining the beauty as proximity to the original Georgi-Glashow <italic>SU</italic>(5) model. Our analysis shows that, in both supersymmetric and non-supersymmetric scenarios, the model incorporating the interaction with the 24-dimensional field is more beautiful under this criterion. We then generalise these models by introducing a continuous parameter <italic>y</italic>, which takes the value 3 for the 45-dimensional field and 1.5 for the 24-dimensional field. Numerical optimisation reveals that <italic>y</italic>&#8239;&#8776;&#8239;0.8 yields the closest match to the original <italic>SU</italic>(5) model, indicating that this value corresponds to the most beautiful model according to our definition.

India

Fayez Abu-Ajamieh

Japan

Shinsuke Kawai

United States

Nobuchika Okada

Good flavor search in SU(5): A machine learning approach

We propose a novel and minimal setup where the observed baryon asymmetry of the Universe and neutrino oscillation data can be satisfied with only one right-handed neutrino and a second Higgs doublet with the latter being also responsible for driving cosmic inflation. While inflation is realized via nonminimal coupling of the Higgs to gravity, baryon asymmetry is generated via Affleck-Dine leptogenesis. Due to the presence of only two new fields beyond the standard model (BSM), the proposed setup remains very predictive with only a small allowed parameter space consistent with the PLANCK 2018 and ACT 2025 data simultaneously. The preferred mass spectrum of the BSM particles also keeps the detection prospects alive at terrestrial experiments.

Disha Bandyopadhyay

Debasish Borah

South Korea

Suruj Jyoti Das

Leptogenesis and neutrino mass with one right-handed neutrino and Higgs inflaton

We demonstrate that the weak gravity conjecture (WGC) and the Festina-Lente conjecture (FLC) yield novel bounds on any hypothetical fifth force and millicharged particles (mCPs), as well as on the scale of inflation and on the effective Higgs quartic interaction. In particular, we find that combining the FLC with inflation leads to stronger bounds on mCPs than what the simple application of the FLC provides. Furthermore, we have explored the implications of naturalness on both the FLC and WGC, and have found that these conjectures place a lower limit on the charge of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge group.

China

Pratik Chattopadhyay

Sweden

Roman Pasechnik

Zhi-Wei Wang

Novel bounds from the weak gravity and Festina-Lente conjectures

We study a three-loop induced neutrino mass scenario from a non-holomorphic modular $\textit{A}$ $_{4}$ flavor symmetry and obtain the minimum scenario leading to predictions of the lepton masses, mixing angles, and Dirac and Majorana phases, which are shown through chi square analyses. In addition, we discuss the lepton flavor violations, muon anomalous magnetic moment, lepton universality, and relic density of the dark matter candidate. Moreover, we show that our model can be extended to satisfy the observed relic density of dark matter within the limit of perturbation by adding one singlet scalar boson without changing predictions in the neutrino sector.

Takaaki Nomura

Hiroshi Okada

Neutrino mass model at a three-loop level from a non-holomorphic modular $\textit{A}$ $_{4}$ symmetry * Takaaki Nomura is supported by the Fundamental Research Funds for the Central Universities. Hiroshi Okada is supported by Zhongyuan Talent (Talent Recruitment Series) Foreign Experts Project

We propose a unified framework that describes both the curvaton mechanism for generating primordial density fluctuations and the Affleck-Dine (AD) mechanism for baryogenesis. By introducing a complex scalar field (AD field) carrying a baryon/lepton number and its potential consisting of quadratic and quartic terms with a small baryon/lepton-number-violating mass term, we investigate the evolution of the scalar field during the radiation-dominated era following inflation. We set the initial conditions such that the quartic term dominates the scalar potential, and the angular component of the AD field is non-zero. We focus on a scenario where the AD field sufficiently dominates the energy density of the universe before its decay. We show that the radial component of the AD field can be identified with the curvaton to solely produce the Planck normalized scalar power spectrum while the evolution of the angular component is crucial for generating the observed baryon asymmetry of the universe. Additionally, we find that the amplitude of scalar bispectrum $\textit{f}$ is negative, which is consistent with the current Planck data and testable in future observations such as CMB-S4, LiteBIRD, LSS, and 21-cm experiments. In our estimation of the scalar power spectrum and bispectrum, we develop a novel analytical scheme for computing scalar fluctuations based on the $\textit{δN}$ formalism, which allows us to deal with the evolution of curvaton with polynomial potential more accurately in comparison to the existing analytical methods.

Poland

Anish Ghoshal

Abhishek Naskar

Unified origin of curvature perturbation and baryon asymmetry of the universe

We study the impact of non-thermal leptogenesis on the spectrum of gravitational waves (GWs) produced by a strong first-order phase transition in the early Universe. We consider a scenario in which a heavy scalar field, $$\phi $$ , dominates the energy density of the early Universe and decays into heavy right-handed neutrinos (RHNs). The subsequent decay of RHNs generates a lepton asymmetry, which is partially converted into the observed baryon asymmetry via the sphaleron process. The $$\phi $$ -dominated era and the entropy injection from the decays of $$\phi $$ and RHNs leave characteristic imprints on the GW spectrum, such as damping and modified frequency dependence, that distinguish it from the standard cosmological evolution. We identify the parameter space in which non-thermal leptogenesis is successful, leading to distinctive GW spectral features. We show that these GW signals can fall within the sensitivity ranges of future detectors such as ET, DECIGO and BBO. If observed, they would provide valuable insights into the thermal history and dynamics of the early Universe.

Dilip Ghosh

Koustav Mukherjee

Nimmala Narendra

Impact of non-thermal leptogenesis with early matter domination on gravitational waves from first-order phase transition

We investigate the Domain-Wall Standard Model (DWSM), a five-dimensional framework in which all Standard Model (SM) particles are localized on a domain wall embedded in a non-compact extra spatial dimension. A distinctive feature of this setup is the emergence of a Nambu–Goldstone (NG) boson, arising from the spontaneous breaking of translational invariance in the extra dimension due to the localization of SM chiral fermions. This NG boson couples via Yukawa interactions to SM fermions and their Kaluza–Klein (KK) excitations. We study the phenomenology of this NG boson and derive constraints from astrophysical processes (supernova cooling), Big Bang Nucleosynthesis (BBN), and collider searches for KK-mode fermions at the Large Hadron Collider (LHC). The strongest limits arise from LHC data: we reinterpret existing mass bounds on squarks and sleptons in simplified supersymmetric models (assuming a massless lightest neutralino), as well as limits on exotic hadrons containing long-lived squarks or long-lived charged sleptons in the regime of extremely small Yukawa couplings. From this analysis, we obtain a conservative lower bound of 1 TeV on the masses of KK-mode quarks and charged leptons. Finally, we discuss the prospects for producing KK-mode fermions at future high-energy lepton colliders and outline strategies to distinguish their signatures from those of sfermions.

Puja Das

Digesh Raut

Desmond Villalba

Nambu–Goldstone boson phenomenology in domain-wall standard model

Smooth hybrid inflation is a hybrid inflation model that is free from topological defects and predicts the density perturbation with the spectral index of about 0.97. We show that the prediction on the spectral index is robust regardless the power of nonrenormalizable terms and meets with the latest results reported by Atacama Cosmology Telescope. Viable scenarios for baryogenesis and dark matter are also discussed.

Osamu Seto

Smooth hybrid inflation in light of ACT DR6 data

We investigate several phenomenological implications of the Weak Gravity Conjecture (WGC). We find that the WGC implies that the SM neutrinos must be electrically neutral, that the electric charge in the SM must be quantized, and that the photon must be massless. In addition, we use the WGC to set lower bounds on the electric charge of milli-charged particles (mCP), the gauge coupling of several <math altimg='si1.svg'><mi>U</mi><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></math> extensions of the SM, their kinetic mixing parameter with the SM <math altimg='si2.svg'><mi>U</mi><msub><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></mrow><mrow><mtext>EM</mtext></mrow></msub></math>, and the axion couplings to photons and fermions. We also set an upper bound on the lifetime of the proton.

Sudhir K. Vempati

Implications of the weak gravity conjecture on charge, kinetic mixing, the photon mass, and more

We consider a classically conformal <inline-formula><tex-math id='TM0001' notation='LaTeX'>$U(1)$</tex-math></inline-formula> gauge extension of the Standard Model (SM), in which the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$U(1)$</tex-math></inline-formula> gauge symmetry is radiatively broken by the Coleman&#8211;Weinberg mechanism. This breaking triggers the electroweak (EW) symmetry breaking through a mixed quartic coupling between the <inline-formula><tex-math id='TM0003' notation='LaTeX'>$U(1)$</tex-math></inline-formula> Higgs field and the SM Higgs doublet. For two Higgs boson mass eigenstates after the symmetry breaking, <inline-formula><tex-math id='TM0004' notation='LaTeX'>$h_1$</tex-math></inline-formula> (SM-like Higgs boson) and <inline-formula><tex-math id='TM0005' notation='LaTeX'>$h_2$</tex-math></inline-formula> (SM singlet-like Higgs boson), we calculate the Higgs boson trilinear coupling ( <inline-formula><tex-math id='TM0006' notation='LaTeX'>$g_{h_{1} h_{2} h_{2}}$</tex-math></inline-formula>) in the model by setting the Higgs boson mass spectrum to be <inline-formula><tex-math id='TM0007' notation='LaTeX'>$M_{h_1} &gt; 2 M_{h_2}$</tex-math></inline-formula>. For a common Higgs mass spectrum and mixing angle between two Higgs fields, we find that <inline-formula><tex-math id='TM0008' notation='LaTeX'>$g_{h_{1} h_{2} h_{2}}$</tex-math></inline-formula> in the classically conformal model is highly suppressed compared to that calculated for the conventional Higgs potential, where the <inline-formula><tex-math id='TM0009' notation='LaTeX'>$U(1)$</tex-math></inline-formula> and EW symmetry breaking originate from the negative squared masses for the Higgs fields at the tree-level. Thus, this coupling suppression is a striking nature of the radiative origin of EW symmetry breaking. We then consider how to distinguish this origin at the proposed International Linear Collider (ILC) via precise measurements of anomalous SM Higgs boson couplings and the search for anomalous SM Higgs boson decay <inline-formula><tex-math id='TM0010' notation='LaTeX'>$h_1 \rightarrow h_2 h_2$</tex-math></inline-formula> followed by <inline-formula><tex-math id='TM0011' notation='LaTeX'>$h_2 \rightarrow b \bar{b}$</tex-math></inline-formula>. We conclude that once the anomalous couplings are measured at the ILC, the observation of the anomalous Higgs boson decay is promising in the conventional Higgs potential, while this decay process is highly suppressed and undetectable for the classically conformal model.