We extend the littlest modular seesaw to a Grand Unified scenario based on SU (5) endowed with three modular S 4 symmetries. We leverage symmetry protected zeroes in the leptonic and down quark sectors to suppress deviations to the littlest modular seesaw predictions, but not contributions to the quark mixing. The model is supplemented by two weighton fields, such that the hierarchical nature of the charged-lepton masses, as well as the quark masses and mixing, stem from the content and symmetries of the model, rather than a hierarchical nature of the Yukawa coefficients.

Portugal

Ivo Medeiros Varzielas

United Kingdom

Steve King

Miguel Levy

A modular SU (5) littlest seesaw

We revisit the phenomenological predictions of the Universal Texture Zero (UTZ) model of flavour originally presented in [1], and update them in light of both improved experimental constraints and numerical analysis techniques. In particular, we have developed an in-house Markov Chain Monte Carlo (MCMC) algorithm to exhaustively explore the UTZ’s viable parameter space, considering both leading- and next-to-leading contributions in the model’s effective operator product expansion. We also extract – for the first time – reliable UTZ predictions for the (poorly constrained) leptonic CP-violating phases, and ratio observables that characterize neutrino masses probed by (e.g.) oscillation,  $$\beta $$  <math> <mi>β</mi> </math>  -decay, and cosmological processes. We therefore dramatically improve on the proof-in-principle phenomenological analysis originally presented in [1], and ultimately show that the UTZ remains a minimal, viable, and appealing theory of flavour. Our results also further demonstrate the potential of robustly examining multi-parameter flavour models with MCMC routines.

Germany

Jordan Bernigaud

Jim Talbert

Revisiting the universal texture zero of flavour: a Markov chain Monte Carlo analysis

We present the first complete model of the Littlest Modular Seesaw, based on two right-handed neutrinos, within the framework of multiple modular symmetries, justifying the use of multiple moduli fields which take their values at 3 specific stabilizers of Γ4 ≃ S 4, including a new phenomenological possibility. Using a semi-analytical approach, we perform a χ 2 analysis of each case and show that good agreement with neutrino oscillation data is obtained, including predictive relations between the leptonic mixing angles and the ratio of light neutrino masses, which non-trivially agree with the experimental values. It is noteworthy that in this very predictive setup, the models fit the global fits of the experimental data remarkably well, both with and without the Super-Kamiokande atmospheric data, for both models presented here. By extending the model to include a weighton and the double cover group   <math> <msubsup> <mi>Γ</mi> <mn>4</mn> <mo>′</mo> </msubsup> <mo>≃</mo> <msubsup> <mi>S</mi> <mn>4</mn> <mo>′</mo> </msubsup> </math>  $$ {\Gamma}_4^{\prime}\simeq {S}_4^{\prime } $$ , we are able to also account for the hierarchy of the charged leptons using modular symmetries, without altering the neutrino predictions.

Littlest modular seesaw

We consider the phenomenological signatures of Simplified Models of Flavourful Leptoquarks, whose Beyond-the-Standard Model (SM) couplings to fermion generations occur via textures that are well motivated from a broad class of ultraviolet flavour models (which we briefly review). We place particular emphasis on the study of the vector leptoquark ∆ μ  with assignments (3 , 1 , 2/3) under the SM’s gauge symmetry, SU(3) C  × SU(2) L  × U(1) Y , which has the tantalising possibility of explaining both   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$  and   <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> </msub> </math>  $$ {\mathcal{R}}_{D^{\left(\ast \right)}} $$  anomalies. Upon performing global likelihood scans of the leptoquark’s coupling parameter space, focusing in particular on models with tree-level couplings to a single charged lepton species, we then provide confidence intervals and benchmark points preferred by low (er)-energy flavour data. Finally, we use these constraints to further evaluate the (promising) Large Hadron Collider (LHC) detection prospects of pairs of τ-flavoured ∆ μ , through their distinct (a)symmetric decay channels. Namely, we consider direct third-generation leptoquark and jets plus missing-energy searches at the LHC, which we find to be complementary. Depending on the simplified model under consideration, the direct searches constrain the ∆ μ  mass up to 1500-1770 GeV when the branching fraction of ∆ μ  is entirely to third-generation quarks (but are significantly reduced with decreased branching ratios to the third generation), whereas the missing-energy searches constrain the mass up to 1150-1700 GeV while being largely insensitive to the third-generation branching fraction.

Monika Blanke

Denmark

Spain

José Zurita

LHC signatures of τ-flavoured vector leptoquarks

We study multi-Higgs models with a triplet of  $$A_4$$  <math> <msub> <mi>A</mi> <mn>4</mn> </msub> </math>   or  $$S_4$$  <math> <msub> <mi>S</mi> <mn>4</mn> </msub> </math>   symmetry that is softly-broken. Focusing on parameters that softly break the respective symmetries but preserve the directions of the vacuum expectation values of the triplet we analyse the masses of physical states and discuss their decays. In contrast with previously studied symmetries, we find some cases with stable states that are protected by residual symmetries left unbroken by both the soft-breaking parameters and by the vacuum.

Diogo Ivo

Softly-broken  $$A_4$$  <math> <msub> <mi>A</mi> <mn>4</mn> </msub> </math>   or  $$S_4$$  <math> <msub> <mi>S</mi> <mn>4</mn> </msub> </math>   3HDMs with stable states

We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically, proliferation of quadratic couplings in the most general softly broken case makes the analysis cumbersome. We identify two sets of soft breaking terms which play different roles: those which preserve the symmetric vacuum expectation value alignment, and the remaining terms which shift it. Focusing on alignment preserving terms, we check which structural features of the symmetric parent model are conserved and which are modified. We find remarkable examples of structural features which are inherited from the parent symmetric model and which persist even when no exact symmetry is left. The general procedure is illustrated with the example of the three-Higgs-doublet model with the softly broken symmetry group  $$\Sigma (36)$$  <math> <mrow> <mi>Σ</mi> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </math>  .

China

Igor Ivanov

Exploring multi-Higgs models with softly broken large discrete symmetry groups

We propose a 3+1 Higgs Doublet Model based on the ∆(27) family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings. The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields. The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved   <math> <msubsup> <mi>Z</mi> <mn>2</mn> <mfenced> <mn>1</mn> </mfenced> </msubsup> </math>  $$ {Z}_2^{(1)} $$  discrete symmetry, which also leads to stable scalar and fermionic dark matter candidates. The leptonic sector features the predictive cobimaximal mixing pattern, consistent with the experimental data from neutrino oscillations. For the scenario of normal neutrino mass hierarchy, the model predicts an effective Majorana neutrino mass parameter in the range 3 meV ≲ m  ββ  ≲ 18 meV, which is within the declared range of sensitivity of modern experiments. The model predicts Flavour Changing Neutral Currents which constrain the model, for instance, μ → e nuclear conversion processes and Kaon mixing are found to be within the reach of the forthcoming experiments.

Chile

A. Cárcamo Hernández

M. López-Ibáñez

Estonia

Aurora Melis

Controlled fermion mixing and FCNCs in a ∆(27) 3+1 Higgs Doublet Model

We consider effective Lagrangians which, after electroweak- and family-symmetry breaking, yield fermionic mass matrices and/or other flavoured couplings exhibiting residual family symmetries (RFS). Thinking from the bottom up, these RFS intimately link ultraviolet (UV) Beyond-the-Standard Model (BSM) physics to infrared flavour phenomenology without direct reference to any (potentially unfalsifiable) UV dynamics. While this discussion is typically performed at the level of RFS group generators and the UV flavour groups they can close, we now also focus on the RFS-implied shape of the low-energy mass/coupling matrices. We then show how this information can be used to algorithmically guide the reconstruction of an effective Lagrangian, thereby forming top-down models realizing the typical bottom-up phenomenological conclusions. As a first application we take results from scans of finite groups capable of controlling (through their RFS) CKM or PMNS mixing within the SM alone. We then extend this to recently studied scenarios where RFS also control special patterns of leptoquark couplings, thus providing proof-in-principle completions for such ‘Simplified Models of Flavourful Leptoquarks.’

Reconstructing effective Lagrangians embedding residual family symmetries

The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries Γ N  and for a given element γ ∈ Γ N , we present an algorithm for finding stabilisers (specific values for moduli fields τ  γ  which remain unchanged under the action associated to γ). We then employ this algorithm to find all stabilisers for each element of finite modular groups for N = 2 to 5, namely, Γ2 ≃ S 3, Γ3 ≃ A 4, Γ4 ≃ S 4 and Γ5 ≃ A 5. These stabilisers then leave preserved a specific cyclic subgroup of Γ N . This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry.

Ye-Ling Zhou

Symmetries and stabilisers in modular invariant flavour models

We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns de- rived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these ‘simplified models’ can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$ . Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous $$ {\mathcal{R}}_{K^{\left(\ast \right)}} $$ measurements withstand further experimental scrutiny.