We investigate the properties of domain walls arising from non-Abelian discrete symmetries, which we refer to as non-Abelian domain walls. We focus on $\textit{S}$ , one of the most commonly used groups in lepton flavour mixing models. The spontaneous breaking of $\textit{S}$ leads to distinct vacua preserving a residual $\textit{Z}$ or $\textit{Z}$ symmetry. Five types of domain walls are found, labelled as SI, SII, TI, TII, and TIII, respectively, the former two separating $\textit{Z}$ vacua and the latter three separating $\textit{Z}$ vacua. We highlight that SI, TI and TIII may be unstable for some regions of the parameter space and decay to stable domain walls. Stable domain walls can collapse and release gravitational radiation for a suitable size of explicit symmetry breaking. A symmetry-breaking scale of order 100 TeV may explain the recent discovery of nanohertz gravitational waves by PTA experiments. For the first time, we investigate the properties of these domain walls, which we obtain numerically with semi-analytical formulas applied to compute the tension and thickness across a wide range of parameter space. We estimate the resulting gravitational wave spectrum and find that, thanks to their rich vacuum structure, non-Abelian domain walls manifest in a very interesting and complex phenomenology.

China

Bowen Fu

United Kingdom

Stephen King

Spain

Luca Marsili

Italy

Silvia Pascoli

Jessica Turner

Ye-Ling Zhou

Non-Abelian domain walls and gravitational waves

We study thermal leptogenesis in realistic supersymmetric flipped SU(5) × U(1) unification. As up-type quarks and neutrinos are arranged in the same multiplets, they exhibit strong correlations, and it is commonly believed that the masses of right-handed (RH) neutrinos are too hierarchical to fit the low-energy neutrino data. This pattern generally predicts a lightest RH neutrino too light to yield successful leptogenesis, with any lepton-antilepton asymmetry generated from heavier neutrinos being washed out unless special flavour structures are assumed. We propose a different scenario in which the lightest two RH neutrinos $\textit{N}$ and $\textit{N}$ have nearby masses of order 10 GeV, with thermal leptogenesis arising non-resonantly from both $\textit{N}$ and $\textit{N}$ . We show that this pattern is consistent with all data on fermion masses and mixing and predicts the lightest physical left-handed neutrino mass to be smaller than about 10 eV. The Dirac phase, which does not take the maximal CP-violating value, plays an important role in leptogenesis.

Greece

George Leontaris

Leptogenesis in realistic flipped SU(5)

The spontaneous breaking of a U(1) symmetry via an intermediate discrete symmetry may yield a hybrid topological defect of domain walls bounded by cosmic strings. The decay of this defect network leads to a unique gravitational wave signal spanning many orders in observable frequencies, that can be distinguished from signals generated by other sources. We investigate the production of gravitational waves from this mechanism in the context of the type-I two-Higgs-doublet model extended by a U(1) R  symmetry, that simultaneously accommodates the seesaw mechanism, anomaly cancellation, and eliminates flavour-changing neutral currents. The gravitational wave spectrum produced by the string-bounded-wall network can be detected for U(1) R  breaking scale from 1012 to 1015 GeV in forthcoming interferometers including LISA and Einstein Telescope, with a distinctive f 3 slope and inflexion in the frequency range between microhertz and hertz.

Poland

Anish Ghoshal

Moinul Rahat

Type-I two-Higgs-doublet model and gravitational waves from domain walls bounded by strings

The flavor structure of quarks and leptons and quark-lepton unification are studied in the framework of Pati-Salam models with A 4 modular symmetry. The three generations of the left-handed and right-handed fermions are assigned to be triplet or singlets of A 4. The light neutrino masses are generated through the type-I seesaw mechanism. We perform a systematic classification of Pati-Salam models according to the transformations of matter fields under the A 4 modular symmetry, and the general form of the fermion mass matrix is given. We present four phenomenologically viable benchmark models which provide excellent descriptions of masses and flavor mixing of quarks and leptons, including neutrinos. In such models we find that the normal ordered neutrino mass spectrum is preferred over the inverted case, with neutrinoless double beta decay predicted to be too small to be observed by the next generation of experiments.

Gui-Jun Ding

Si-Yi Jiang

Jun-Nan Lu

Bu-Yao Qu

Pati-Salam models with A4 modular symmetry

The observed excesses in the search for neutralinos and charginos by ATLAS and CMS can be fitted simultaneously in the minimal supersymmetric standard model (MSSM) assuming a light higgsino mass, of magnitude less than about 250 GeV, and a compressed higgsino dominated neutralino and chargino spectrum, with 5–10% mass splittings. However, light higgsinos as dark matter would have far too large direct detection cross sections. We consider the Next-to-MSSM (NMSSM) with an additional singlino-like lightest supersymmetric particle (LSP) a few GeV below the next-to-lightest supersymmetric particle (NLSP). Sparticles prefer to decay first into the NLSP and remnants from the final decay into the LSP are too soft to contribute to the observed signals. Co-annihilation in the higgsino-sector can generate a relic density in the WMAP/Planck window. The singlino-like LSP has automatically a direct detection cross section below present and future sensitivities: a direct detection signal in the near future would exclude this scenario. The singlet-like Higgs scalar of the NMSSM can have a mass around 95 GeV and signal cross sections in the  $$b\bar{b}$$  <math> <mrow> <mi>b</mi> <mover> <mrow> <mi>b</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   channel at LEP and in the  $$\gamma \gamma $$  <math> <mrow> <mi>γ</mi> <mi>γ</mi> </mrow> </math>   channel at the LHC compatible with the respective observations.

France

Ulrich Ellwanger

Cyril Hugonie

Sweden

Stefano Moretti

NMSSM explanation for excesses in the search for neutralinos and charginos and a 95 GeV Higgs boson

The tri-hypercharge proposal introduces a separate gauged weak hypercharge assigned to each fermion family as the origin of flavour. This is arguably one of the simplest setups for building “gauge non-universal theories of flavour” or “flavour deconstructed theories”. In this paper we propose and study two minimal but ultraviolet complete and renormalisable tri-hypercharge models. We show that both models, which differ only by the heavy messengers that complete the effective theory, are able to explain the observed patterns of fermion masses and mixings (including neutrinos) with all fundamental coefficients being of   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1). In fact, both models translate the complicated flavour structure of the Standard Model into three simple physical scales above electroweak symmetry breaking, completely correlated with each other, that carry meaningful phenomenology. In particular, the heavy messenger sector determines the origin and size of fermion mixing, which controls the size and nature of the flavour-violating currents mediated by the two heavy Z′ gauge bosons of the theory. The phenomenological implications of the two minimal models are compared. In both models the lightest Z′ remains discoverable in dilepton searches at the LHC Run 3.

Mario Fernández Navarro

Avelino Vicente

Minimal complete tri-hypercharge theories of flavour

In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model  $${\text{U}}{\left(1\right)}_{Y}^{3}$$  based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e + π 0 channel.

Mario Navarro

Tri-unification: a separate SU(5) for each fermion family

We explore the origin of Majorana masses within the majoron model and how this can lead to the generation of a distinguishable primordial stochastic background of gravitational waves. We first show how in the simplest majoron model only a contribution from cosmic string can be within the reach of planned experiments. We then consider extensions containing multiple complex scalars, demonstrating how in this case a spectrum comprising contributions from both a strong first order phase transition and cosmic strings can naturally emerge. We show that the interplay between multiple scalar fields can amplify the phase transition signal, potentially leading to double peaks over the wideband sloped spectrum from cosmic strings. We also underscore the possibility of observing such a gravitational wave background to provide insights into the reheating temperature of the universe. We conclude highlighting how the model can be naturally combined with scenarios addressing the origin of matter of the universe, where baryogenesis occurs via leptogenesis and a right-handed neutrino plays the role of dark matter.

Pasquale Bari

Gravitational waves from phase transitions and cosmic strings in neutrino mass models with multiple majorons

United States

Henry Tye

Remembering Stephen Weinberg

We study supersymmetric (SUSY) flipped SU(5) × U(1) unification, focussing on its predictions for proton decay, fermion masses and gravitational waves. We performed a two-loop renormalisation group analysis and showed that the SUSY flipped SU(5) model predicts a high GUT scale M GUT &gt; 1016 GeV. We also investigated the restrictions on the M  B−L  scale which is associated with the U(1) χ  breaking scale. We found that the M  B−L  scale can vary in a broad region with negligible or little effect on the value of M GUT. Proton decay in this model is induced by dimension-6 operators only. The dimension-5 operator induced by SUSY contribution is suppressed due to the missing partner mechanism. We found that the partial decay width p → π 0 e + is high suppressed, being at least one order of magnitude lower than the future Hyper-K sensitivity. We also studied fermion (including neutrino) masses and mixings which can also influence proton decay. We presented two scenarios of flavour textures to check the consistency of the results with fermion masses and mixing. The B − L gauge breaking leads to the generation of cosmic strings. The B − L scale here is not constrained by gauge coupling unification. If this scale is very close that of GUT breaking, strings can be unstable due to the decay to monopole-antimonople pair. Such metastable strings can be used to explain the NANOGrav signals of stochastic gravitational wave background, which may be interpreted here as resulting from the decay of metastable cosmic strings.

Flipped SU(5): unification, proton decay, fermion masses and gravitational waves