Modular invariance has recently paved the way for promising new directions in flavor model building. Motivated by this development, we present in this work the first implementation of the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$S_3$</tex-math></inline-formula> modular symmetry within the Pati&#8211;Salam unification framework, addressing the flavor structure of quarks and leptons. Assigning left- and right-handed matter fields as <inline-formula><tex-math id='TM0003' notation='LaTeX'>$S_3$</tex-math></inline-formula> doublets or singlets, we propose three benchmark models that achieve compelling fits to 16 observables including charged fermion mass ratios and flavor mixing parameters. Light neutrino masses arise via the type-I seesaw mechanism, and neutrino oscillation parameters are explored in light of the latest NuFIT v6.0 results. All models favor a normal neutrino mass ordering, with the atmospheric mixing angle lying in the lower octant. For models I and III, the effective Majorana mass <inline-formula><tex-math id='TM0004' notation='LaTeX'>$m_{\beta \beta }$</tex-math></inline-formula> is within the reach of upcoming neutrinoless double-beta decay experiments, while it is too small to be detected in model II. Predicted leptonic <italic>CP</italic>-violating phases and the sum of the active neutrino masses span wide but distinctive ranges, enabling future experiments to test and differentiate the proposed models.

not found

Mohamed Belfkir

Mohamed Amin Loualidi

Salah Nasri

Fermion Masses and Mixing in Pati–Salam Unification with <italic>S</italic> <sub>3</sub> Modular Symmetry

The Zee-Babu model is a minimal realization of radiative neutrino mass generation mechanism at the two-loop level. We study the phenomenology of this model at future multi-TeV muon colliders. After imposing all theoretical and low-energy experimental constraints on the model parameters, we find that the Zee-Babu states are expected not to reside below the TeV scale, making it challenging to probe them at the LHC. We first analyze the production rates for various channels, including multi singly charged and/or doubly charged scalars at muon colliders. For concreteness, we study several benchmark points that satisfy neutrino oscillation data and other constraints and find that most channels have large production rates. We then analyze the discovery reach of the model using two specific channels: the pair production of singly and doubly charged scalars. For the phenomenologically viable scenarios considered in this study, charged scalars with masses up to <math><mrow><mi>O</mi><mo>(</mo><mn>3</mn><mi>–</mi><mn>4</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math> can be probed for the center-of-mass energy of 10 TeV and total luminosity of <math><mrow><mn>10</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>.

South Korea

Adil Jueid

Bangladesh

Talal Ahmed Chowdhury

Italy

Switzerland

Shaikh Saad

Probing Zee-Babu states at muon colliders

In this work, we delve into the often overlooked cosmological implications of the spontaneous breaking of the non-Abelian discrete groups, specifically focusing on the formation of domain walls in the case of <math><msub><mi>S</mi><mn>4</mn></msub></math> flavor symmetry. In particular, we investigate three interesting breaking patterns of the <math><msub><mi>S</mi><mn>4</mn></msub></math> group and study the structure of the domain walls in the broken phase for three possible residual symmetries. The presentation of domain walls in the case of multiple vacua is usually complicated, which therefore implies that most of the analyses only approximate their presentation. Here, we propose a subtle way to represent the <math><msub><mi>S</mi><mn>4</mn></msub></math> domain wall networks by presenting the vacua in each breaking pattern as vectors with their components corresponding to their coordinates in the flavon space. Then, through the properties of the obtained vectors, we find that the domain wall networks can be represented by Platonic or Archimedean solids where the vertices represent the degenerate vacua while the edges correspond to the domain walls that separate them. As an illustration, we propose a type-II seesaw model that is based on the <math><msub><mi>S</mi><mn>4</mn></msub></math> flavor symmetry, and study its phenomenological implications on the neutrino sector. To solve the domain wall problem within this toy model, we consider an approach based on high-dimensional effective operators induced by gravity that explicitly break the structure of the induced vacua favoring one vacuum over the others.

United Arab Emirates

Morocco

Mohamed Amine Ouahid

Cosmological domain walls from the breaking of <math><msub><mi>S</mi><mn>4</mn></msub></math> flavor symmetry

We investigate the prospects of probing the doubly-charged scalars of the minimal Left-Right Symmetric model (MLRSM) at a muon collider. We assess its capability by studying the production of doubly-charged scalars and their subsequent decay into four charged lepton final states containing the same-charge lepton pairs. We find that the channels with same-charge electron and muon pairs, i.e., (<math><msup><mrow><mi>e</mi></mrow><mrow><mo>±</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>±</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>∓</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>∓</mo></mrow></msup></math> and its charge conjugated pairs), have the largest sensitivity due to the lowest Standard Model background. Besides, we show that the possibility of using fully polarized initial muon beams in the muon collider can enhance the detection sensitivity of doubly-charged scalars of the MLRSM. Furthermore, we show that one can put exclusion limits on the magnitudes of triplet Yukawa couplings that are directly related to the neutrino sector of the MLRSM for the mass range <math><mn>1.1</mn><mo>−</mo><mn>5</mn></math> TeV of the doubly-charged scalars.

United States

Doubly-charged scalars of the minimal left-right symmetric model at muon colliders

A series of pulsar timing arrays (PTAs) recently observed gravitational waves at the nanohertz frequencies. Motivated by this remarkable result, we present a novel class of Pati-Salam models that give rise to a network of metastable cosmic strings, offering a plausible explanation for the observed PTA data. Additionally, we introduce a hybrid inflationary scenario to eliminate magnetic monopoles that arise during the subsequent phase transitions from the Pati-Salam symmetry to the Standard Model gauge group. The resulting scalar spectral index is compatible with Planck data, and the tensor-to-scalar ratio is anticipated to be extremely small. Moreover, we incorporate a nonthermal leptogenesis to generate the required baryon asymmetry in our framework. Finally, the gravitational wave spectra generated by the metastable cosmic strings not only correspond to signals observed in recent PTAs, including NANOGrav, but are also within the exploration capacity of both present and future ground- and space-based experiments.

China

Waqas Ahmed

Gravitational waves from metastable cosmic strings in the Pati-Salam model in light of new pulsar timing array data

Abstract The search for dark matter (DM) candidates at high-energy colliders is one of the most promising avenues to understand the nature of this elusive component of the universe. Several searches at the Large Hadron Collider (LHC) have strongly constrained a wide range of simplified models. The combination of the bounds from the LHC with direct-detection experiments exclude the most minimal scalar-singlet DM model. To address this, lepton portal DM models are suitable candidates where DM is predominantly produced at lepton colliders since the DM candidate only interacts with the lepton sector through a mediator that carries a lepton number. In this work, we analyze the production of DM pairs in association with a Higgs boson decaying into two bottom quarks at future muon colliders in the framework of the minimal lepton portal DM model. It is found that the usual cut-based analysis methods fail to probe heavy DM masses for both the resolved (where the decay products of the Higgs boson can be resolved as two well-separated small-R jets) and the merged (where the Higgs boson is clustered as one large-R jet) regimes. We have then built a search strategy based on boosted-decision trees (BDTs). We have optimized the hyperparameters of the BDT model to both have a high signal-to-background ratio and to avoid overtraining effects. We have found very important enhancements of the signal significance with respect to the cut-based analysis by factors of 8–50 depending on the regime (resolved or merged) and the benchmark points. Using this BDT model on a 1D parameter space scan, we found that future muon colliders with  TeV and  can exclude DM masses up to 1 TeV at the 95% confidence level.

Boosting dark matter searches at muon colliders with machine learning: The mono-Higgs channel as a case study

We revisit the bottom and <math><mi>τ</mi></math> Yukawa coupling unification in the supersymmetric 4-2-2 model and present for the first time the sbottom-neutralino coannihilation scenario consistent with the bottom and <math><mi>τ</mi></math> Yukawa coupling unification. In addition, we present gluino-neutralino, stop-neutralino, stau-neutralino, chargino-neutralino, and A-resonance scenario and show that all such solutions are consistent with existing experimental collider constraints, Planck 2018 dark matter relic density bounds as well as direct and indirect bounds on neutralino-nucleons scattering cross sections. It is shown that in the sbottom-neutralino coannihilation scenario, the sbottom mass is between 1.2 to 3.5 TeV, whereas in the case of gluino-neutralino, stop-neutralino, the gluino mass can be between 1 to 3 TeV and the stop mass in the range of 1 to 3.5 TeV. Moreover, in the case of a coannihilation scenario, the stau and chargino masses can be as heavy as 3.5 TeV, while the A-resonance solutions are in the range of 0.5 to 3.5 TeV. We anticipate that some part of the parameter space will be accessible in the supersymmetry searches at LHC run 3 and beyond.

Pakistan

Shabbar Raza

Umer Zubair

LHC run 3, <math><mrow><mi>b</mi><mtext>−</mtext><mi>τ</mi></mrow></math> Yukawa unification, and dark matter implications in a SUSY 4-2-2 model

Lepton portal dark matter (DM) models are a class of models where the DM candidates solely couple to charged leptons through a mediator carrying a lepton number. These models are very interesting since they avoid constraints from direct detection experiments even for coupling of order <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>, they have small annihilation cross sections, and can be probed efficiently at lepton colliders. In this work, we consider a minimal lepton portal DM model that consists of extending the standard model with two <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math> singlets: a charged scalar singlet and an electrically neutral right-handed fermion. We systematically study the production mechanisms of DM at multi-TeV muon colliders. After considering all the possible theoretical and experimental constraints and studying the phenomenology of lepton flavor violation and DM in the muonphilic scenario, we analyze the production rates of 54 channels (26 channels for prompt DM production and 28 channels for charged scalar production) at multi-TeV muon colliders. Finally, we discuss the possible collider signatures of some channels and the corresponding backgrounds. We find that at least nine channels for DM production can be very efficient in testing DM with masses up to about 1 TeV.

Lepton portal dark matter at muon colliders: Total rates and generic features for phenomenologically viable scenarios

Determinants of the second rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function <math><mi>f</mi><mo>(</mo><mi>D</mi><mo>)</mo></math> of the determinants of their energy-momentum, and the metric, <math><mi>D</mi><mo>=</mo><mo>|</mo><mtext>det</mtext><mo>.</mo><mi>T</mi><mo>|</mo><mo>/</mo><mo>|</mo><mtext>det</mtext><mo>.</mo><mi>g</mi><mo>|</mo></math>. We derive the gravitational field equations and examine the nonlinear terms induced by the determinant, specifically, the inverse of the energy-momentum tensor. We also show that these extensions require a nonzero stress-energy tensor for the vacuum. We propose a scale-free model, <math><mi>f</mi><mo>(</mo><mi>D</mi><mo>)</mo><mo>=</mo><mi>λ</mi><msup><mrow><mi>D</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup></math>, and show how it induces the familiar invariant terms formed by the trace of the energy-momentum tensor by expanding the action around the stress-energy of the vacuum. We study the hydrostatic equilibrium equations for a neutron star by providing relevant values of the dimensionless constant λ. We show that the differences from the predictions of general relativity, in the mass-radius relations, which are sensitive to the equations of state, are conspicuous for <math><mi>λ</mi><mo>∼</mo><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></math>. We also show that the model does not affect the predictions on the primordial nucleosynthesis when it is applied to the early radiation era. This novel and unfamiliar type of the gravity-matter coupling can lead to a rich phenomenology in gravitational physics.

Hemza Azri

Gravity from the determinant of the energy-momentum: Astrophysical implications

We revisit the hybrid inflation model gauged by <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> extension of the minimal supersymmetric standard model in a no-scale background. Considering a single predictive framework, we study inflation, leptogenesis, gavitino cosmology, and the stochastic background of gravitational waves produced by metastable cosmic strings. The spontaneous breaking of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> at the end of inflation produces a network of metastable cosmic strings, while the interaction between the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> Higgs field and the neutrinos generate heavy Majorana masses for the right-handed neutrinos. The heavy Majorana masses explain the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and nonthermal leptogenesis. We show that a successful nonthermal leptogenesis and a stable gravitino as a dark matter candidate can be achieved for a wide range of reheating temperatures and <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> symmetry breaking scales. The possibility of realizing metastable cosmic strings in a grand unified theory setup is briefly discussed. We find that a successful reheating with nonthermal leptogenesis and gravitino dark matter restricts the allowed values of string tension to a narrow range <math><msup><mn>10</mn><mrow><mo>−</mo><mn>9</mn></mrow></msup><mo>≲</mo><mi>G</mi><msub><mi>μ</mi><mrow><mi>C</mi><mi>S</mi></mrow></msub><mo>≲</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, predicting a stochastic gravitational-wave background that lies within the <math><mrow><mn>1</mn><mi>σ</mi></mrow></math> bounds of the recent NANOGrav 12.5-yr data, as well as within the sensitivity bounds of future GW experiments.