arXiv subjects

Stephen F. King

Publications and source records attributed to Stephen F. King.

At least 55 records · Page 3Linked to original sources

arXiv2023

Quantum Gravity Effects on Dark Matter and Gravitational Waves

We explore how quantum gravity effects, manifested through the breaking of discrete symmetry responsible for both Dark Matter and Domain Walls, can have observational effects through CMB observations and gravitational waves. To illustrate the idea we consider a simple model with two scalar fields and two $\mathcal{Z}_2$ symmetries, one being responsible for Dark Matter stability, and the other spontaneously broken and responsible for Domain Walls, where both symmetries are assumed to be explicitly broken by quantum gravity effects. We show the recent gravitational wave spectrum observed by several pulsar timing array projects can help constrain such effects.

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arXiv2023

Neutrino Mass and Mixing with Modular Symmetry

This is a review article about neutrino mass and mixing and flavour model building strategies based on modular symmetry. After an introduction to neutrino mass and lepton mixing, we then turn to the main subject of this review, namely a pedagogical introduction to modular symmetry as a candidate for family symmetry, from the bottom-up point of view. After an informal introduction to modular symmetry, we introduce the modular group, and discuss its fixed points and residual symmetry, assuming supersymmetry throughout. We then introduce finite modular groups of level $N$ and modular forms with integer or rational modular weights, corresponding to simple geometric groups or their double or metaplectic covers, including the most general finite modular groups and vector-valued modular forms, with detailed results for $N=2, 3, 4, 5$. The interplay between modular symmetry and generalized CP symmetry is discussed, deriving CP transformations on matter multiplets and modular forms, highlighting the CP fixed points and their implications. In general, compactification of extra dimensions generally leads to a number of moduli, and modular invariance with factorizable and non-factorizable multiple moduli based on symplectic modular invariance and automorphic forms is reviewed. Modular strategies for understanding fermion mass hierarchies are discussed, including the weighton mechanism, small deviations from fixed points, and texture zeroes. Then examples of modular models are discussed based on single modulus $A_4$ models, a minimal $S'_4$ model of leptons (and quarks), and a multiple moduli model based on three $S_4$ groups capable of reproducing the Littlest Seesaw model. We then extend the discussion to include Grand Unified Theories (GUTs) based on modular (flipped) $SU(5)$ and $SO(10)$. Finally we discuss top-down approaches, including eclectic flavour symmetry and moduli stabilisation.

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arXiv2023

Gravitational Waves and Gravitino Mass in No-Scale Supergravity Inflation with Polonyi Term

We study a No-Scale supergravity inflation model which has a non-minimal deformation of the Kähler potential and a Wess-Zumino superpotential extended by the inclusion of a Polonyi mass term. The non-minimal structure of the Kähler potential is responsible for an inflexion point that can lead to the production of gravitational waves at late stages of inflation, while the Polonyi term breaks supersymmetry at the end of inflation, generating a non-vanishing gravitino mass. After a thorough parameter space scan, we identify promising points for gravitational wave production. We then study the resulting gravitational wave energy density for this set of points, and we observe that the gravitational waves should be observable in the next generation of both space-based and ground-based interferometers. Finally, we show how the presence of the Polonyi term can be used to further boost the gravitational wave energy density, which is correlated with the gravitino mass.

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arXiv2023

$B$-anomalies in a twin Pati-Salam theory of flavour including the 2022 LHCb $R_{K^{(*)}}$ analysis

We perform a comprehensive phenomenological analysis of the twin Pati-Salam theory of flavour, focussing on the parameter space relevant for interpreting the $B$-anomalies via vector leptoquark $U_1$ exchange. This model provides a very predictive framework in which the $U_1$ couplings and the Yukawa couplings find a common origin via mixing of chiral quarks and leptons with vector-like fermions, providing a direct link between the $B$-anomalies and the fermion masses and mixing. We propose and study a simplified model with three vector-like fermion families, in the massless first family approximation, and show that the second and third family charged fermion masses and mixings and the $B$-anomalies can be simultaneously explained and related. The model has the proper flavour structure to be compatible with all low-energy observables, and leads to predictions in promising observables such as $τ\rightarrow3μ$, $τ\rightarrowμγ$ and $B\rightarrow K^{(*)}ν\barν$ at Belle II and LHCb. The model also predicts a rich spectrum of TeV scale gauge bosons and vector-like fermions, all accessible to the LHC. In this updated version we have included an extended analysis considering the new 2022 LHCb data on $R_{K^{(*)}}$, which has slightly shifted the preferred parameter space with respect to the 2021 case. The model can still explain the $R_{D^{(*)}}$ anomalies at 1$σ$ in a narrow window, however we expect small deviations from the SM on the $R_{K^{(*)}}$ ratios, to be tested in the future via more precise measurements by the LHCb collaboration. We also predict $ΔR_{D}= ΔR_{D^{*}}$, with future measurements shifting the world averages to slightly smaller central values.

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arXiv2023

Modular flavour symmetry and orbifolds

We develop a bottom-up approach to flavour models which combine modular symmetry with orbifold constructions. We first consider a 6d orbifold $\mathbb{T}^2/\mathbb{Z}_N$, with a single torus defined by one complex coordinate $z$ and a single modulus field $τ$, playing the role of a flavon transforming under a finite modular symmetry. We then consider 10d orbifolds with three factorizable tori, each defined by one complex coordinate $z_i$ and involving the three moduli fields $τ_1, τ_2, τ_3$ transforming under three finite modular groups. Assuming supersymmetry, consistent with the holomorphicity requirement, we consider all 10d orbifolds of the form $(\mathbb{T}^2)^3/(\mathbb{Z}_N\times\mathbb{Z}_M)$, and list those which have fixed values of the moduli fields (up to an integer). The key advantage of such 10d orbifold models over 4d models is that the values of the moduli are not completely free but are constrained by geometry and symmetry. To illustrate the approach we discuss a 10d modular seesaw model with $S_4^3$ modular symmetry based on $(\mathbb{T}^2)^3/(\mathbb{Z}_4\times\mathbb{Z}_2)$ where $τ_1=i,\ τ_2=i+2$ are constrained by the orbifold, while $τ_3=ω$ is determined by imposing a further remnant $S_4$ flavour symmetry, leading to a highly predictive example in the class CSD$(n)$ with $n=1-\sqrt{6}$.

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arXiv2023

Gravitational wave signals from leptoquark-induced first order electroweak phase transitions

We consider the extension of the Standard Model (SM) with scalar leptoquarks in $SU(2)$ singlet, doublet and triplet representations. Through the coupling between leptoquark and the SM Higgs field, the electroweak phase transition (EWPT) can turn into first order and consequently produce gravitational wave signals. We compute the required value of the leptoquark-Higgs for first order EWPT to happen and discuss about the possible constraint from Higgs phenomenology. Choosing some benchmarks, we present the strength of the gravitational waves produced during the leptoquark-induced first order EWPT and compare them to detector sensitivities. We find that the $SU(2)$ representations of the leptoquark can be distinguished by gravitational waves in the parameter space where first order EWPT can happen as a function of the Higgs portal coupling.

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arXiv2023

Neutrino Mass and Mixing Models with Eclectic Flavor Symmetry $Δ(27) \rtimes T'$

The Kähler potentials of modular symmetry models receive unsuppressed contributions which may be controlled by a flavor symmetry, where the combination of the two symmetry types is referred to as eclectic flavor symmetry. After briefly reviewing the consistency conditions of eclectic flavor symmetry models, including with generalised (g)CP, we perform a comprehensive bottom-up study of eclectic flavor symmetry models based on $Ω(1)\cong Δ(27)\rtimes T^\prime$, consisting of the flavor symmetry $Δ(27)$ in a semi-direct product with the modular symmetry $T^\prime$. The modular transformations of different $Δ(27)$ multiplets are given by solving the consistency condition. The eight nontrivial singlets of $Δ(27)$ are related by $T'$ modular symmetry, and they have to be present or absent simultaneously in any $Ω(1)$ model. The most general forms of the superpotential and Kähler potential invariant under $Ω(1)$ are discussed, and the corresponding fermion mass matrices are presented. Based on the eclectic flavor group $Ω(1)$, two concrete lepton models which can successfully describe the experimental data of lepton masses and mixing parameters are constructed. For the two models without gCP, all six mixing parameters vary in small regions. A nearly maximal atmospheric mixing angle $θ_{23}$ and Dirac CP phase $δ_{CP}$ are obtained in the first model. After considering the compatible gCP symmetry and the assumption of $\Re τ=0$ in the first model, the $μ-τ$ reflection symmetry is preserved in the charged lepton diagonal basis. As a consequence, the atmospheric mixing angle and Dirac CP phase are predicted to be maximal, and two Majorana CP phases are predicted to be $π$.

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arXiv2023

A Predictive and Testable Unified Theory of Fermion Masses, Mixing and Leptogenesis

We consider a minimal non-supersymmetric $SO(10)$ Grand Unified Theory (GUT) model that can reproduce the observed fermionic masses and mixing parameters of the Standard Model. We calculate the scales of spontaneous symmetry breaking from the GUT to the Standard Model gauge group using two-loop renormalisation group equations. This procedure determines the proton decay rate and the scale of $U(1)_{B-L}$ breaking, which generates cosmic strings and the right-handed neutrino mass scales. Consequently, the regions of parameter space where thermal leptogenesis is viable are identified and correlated with the fermion masses and mixing, the neutrinoless double beta decay rate, the proton decay rate, and the gravitational wave signal resulting from the network of cosmic strings. We demonstrate that this framework, which can explain the Standard Model fermion masses and mixing and the observed baryon asymmetry, will be highly constrained by the next generation of gravitational wave detectors and neutrino oscillation experiments which will also constrain the proton lifetime.

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arXiv2022

Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry

We study the prediction for leptogenesis in two renormalizable supersymmetric $SO(10)\times A_4$ modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fermion masses and mixing parameters as well as the baryon asymmetry of the Universe. The predictions for the light neutrino masses, the effective mass in neutrinoless doble beta decay and the leptonic CP violation phases are discussed.

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arXiv2022

Data-driven analysis of a SUSY GUT of flavour

We present a data-driven analysis of a concrete Supersymmetric (SUSY) Grand Unified Theory (GUT) of flavour, based on $SU(5)\times S_4$, which predicts charged fermion and neutrino mass and mixing, and where the mass matrices of both the Standard Model and the Supersymmetric particles are controlled by a common symmetry at the GUT scale. This framework also predicts non-vanishing non-minimal flavour violating effects, motivating a sophisticated data-driven parameter analysis to uncover the signatures and viability of the model. This computer-intensive Markov-Chain-Monte-Carlo (MCMC) based analysis includes a large range of flavour as well as dark matter and SUSY observables, predicts distributions for a range of physical quantities which may be used to test the model. The predictions include maximally mixed sfermions, $μ\rightarrow e γ$ close to its experimental limit and successful bino-like dark matter with nearby winos (making direct detection unlikely), implying good prospects for discovering winos and gluinos at forthcoming collider runs. The results also demonstrate that the Georgi-Jarlskog mechanism does not provide a good description of the splitting of down type quark masses and charged leptons, while neutrinoless double beta decay is predicted at observable rates.

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arXiv2022

Leptogenesis in Type Ib seesaw models

We study leptogenesis in three different realisations of the type Ib seesaw mechanism, where the effective masses of the neutrinos are obtained by the spontaneous symmetry breaking of two different Higgs doublets. In the minimal type Ib seesaw model, where two right-handed neutrinos form a Dirac mass, we show that it is impossible to produce the correct baryon asymmetry, even including a pseudo-Dirac mass splitting. In an extended type Ib seesaw model, with a third very heavy Majorana right-handed neutrino, together with the low scale Dirac pair of right-handed (RH) neutrinos and an extra singlet Higgs boson, we find that the imbalance of matter and antimatter can be explained by resonant leptogenesis. In the resulting low scale effective type Ib seesaw mechanism, we derive the allowed range of the seesaw couplings consistent with resonant leptogenesis. Dark matter may also be included via the right-handed neutrino portal. The Dirac RH neutrino masses may lie in the 1-100 GeV mass range, accessible to the future experiments SHiP and FCC-$ee$, allowing the type Ib seesaw mechanism with leptogenesis and dark matter to be tested.

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arXiv2022

A Simplified Twin Pati-Salam Theory of Flavour with a TeV Scale Vector Leptoquark

In this talk, we discuss a simplified version of a recently proposed twin Pati-Salam (PS) theory of flavour broken to the $G_{4321}$ gauge group at high energies, then to the Standard Model at low energies, yielding a TeV scale vector leptoquark $U^μ_1(3,1,2/3)$ which may be used to address the lepton universality anomalies $R_{K^{(*)}}$ and $R_{D^{(*)}}$ in $B$ decays. The model also accounts for quark and lepton mass hierarchies, providing a link between the flavour anomalies and a theory of flavour.

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arXiv2021

Flipped SU(5) with modular $A_4$ symmetry

We study Flipped $SU(5)\times U(1)$ Grand Unified Theories (GUTs) with $Γ_3\simeq A_4$ modular symmetry. We propose two models with different modular weights assignments, where the fermion mass hierarchy can arise from weighton fields. In order to relax the constraint on the Dirac neutrino Yukawa matrix we appeal to mechanisms which allow incomplete GUT representations, allowing a good fit to quark and charged lepton masses and quark mixing for a single modulus field $τ$, with the neutrino masses and lepton mixing well determined by the type I seesaw mechanism, at the expense of some tuning. We also discuss the double seesaw possibility allowed by the extra singlets generically predicted in such string inspired theories.

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arXiv2021

Spontaneously stabilised dark matter from a fermiophobic $U(1)'$ gauge symmetry

We consider the possibility that dark matter is stabilised by a discrete $Z_2$ symmetry which arises from a subgroup of a $U(1)'$ gauge symmetry, spontaneously broken by integer charged scalars, and under which the chiral quarks and leptons do not carry any charges. A chiral fermion $χ$ with half-integer charge is odd under the preserved $Z_2$, and hence becomes a stable dark matter candidate, being produced through couplings to right-handed neutrinos with vector-like $U(1)'$ charges, as in the type Ib seesaw mechanism. We calculate the relic abundance in such a low energy effective seesaw model containing few parameters, then consider a high energy renormalisable model with a complete fourth family of vector-like fermions, where the chiral quark and lepton masses arise from a seesaw-like mechanism. With the inclusion of the fourth family, the lightest vector-like quark can contribute to the dark matter production, enlarging the allowed parameter space that we explore.

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arXiv2021

Fermiophobic $Z'$ model for simultaneously explaining the muon anomalies $R_{K^{(*)}}$ and $(g-2)_μ$

We discuss a simple renormalisable, gauge invariant model with a fermiophobic $Z'$ boson: it has no couplings to the three Standard Model (SM) chiral families, but does couple to a fourth vector-like (VL) family. The SM Higgs couples to the fourth VL lepton, leading to an enhanced contribution to the muon anomalous magnetic moment $\left(g-2\right)_μ$. The latter contribution requires a non-vanishing coupling of $Z'$ to right-handed muons, which arises within this model due to mixing effects between the SM and VL fermions, along with $Z'$ couplings to the second generation SM lepton doublet and third generation SM quark doublet. This model can simultaneously account for the measured $B$-decay ratios $R_{K^{(*)}}$ and $\left(g-2\right)_μ$. We identify the parameter space where this explanation is consistent with existing experimental constraints coming from $B_{s}-\bar{B}_{s}$ mixing, neutrino trident production and collider searches. We also check that the SM Higgs coupling to the fourth VL lepton does not produce a dangerous contribution to the Higgs diphoton decay.

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arXiv2021

Twin Pati-Salam theory of flavour with a TeV scale vector leptoquark

We propose a twin Pati-Salam (PS) theory of flavour broken to the $G_{4321}$ gauge group at high energies, then to the Standard Model at low energies, yielding a TeV scale vector leptoquark $U^μ_1(3,1,2/3)$ which has been suggested to address the lepton universality anomalies $R_{K^{(*)}}$ and $R_{D^{(*)}}$ in $B$ decays. Quark and lepton masses are mediated by vector-like fermions, with personal Higgs doublets for the second and third families, which may be replaced by a two Higgs doublet model (2HDM). The twin PS theory of flavour successfully accounts for all quark and lepton (including neutrino) masses and mixings, and predicts a dominant coupling of $U^μ_1(3,1,2/3)$ to the third family left-handed doublets. However the predicted mass matrices, assuming natural values of the parameters, are not consistent with the single vector leptoquark solution to the $R_{D^{(*)}}$ anomaly, given its current value.

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arXiv2021

Confronting SO(10) GUTs with proton decay and gravitational waves

Grand Unified Theories (GUT) predict proton decay as well as the formation of cosmic strings which can generate gravitational waves. We determine which non-supersymmetric $SO(10)$ breaking chains provide gauge unification in addition to a gravitational signal from cosmic string decay. We calculate the GUT and intermediate scales for these $SO(10)$ breaking chains by solving the renormalisation group equations at the two-loop level. This analysis predicts the GUT scale, hence the proton lifetime, in addition to the scale of cosmic string generation and thus the associated gravitational wave signal. We determine which $SO(10)$ breaking chains survive in the event of the null results of the next generation of gravitational waves and proton decay searches and determine the correlations between proton decay and gravitational waves scales if these observables are measured.

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arXiv2021

Modular $S_4\times SU(5)$ GUT

Modular symmetry offers the possibility to provide an origin of discrete flavour symmetry and to break it along particular symmetry preserving directions without introducing flavons or driving fields. It is also possible to use a weighton field to account for charged fermion mass hierarchies rather than a Froggatt-Nielsen mechanism. Such an approach can be applied to flavoured Grand Unified Theories (GUTs) which can be greatly simplified using modular forms. As an example, we consider a modular version of a previously proposed $S_4\times SU(5)$ GUT, with Gatto-Sartori-Tonin and Georgi-Jarlskog relations, in which all flavons and driving fields are removed, with their effect replaced by modular forms with moduli assumed to be at various fixed points, rendering the theory much simpler. In the neutrino sector there are two right-handed neutrinos constituting a Littlest Seesaw model satisfying Constrained Sequential Dominance (CSD) where the two columns of the Dirac neutrino mass matrix are proportional to $(0,1, -1)$ and $(1, n, 2-n)$ respectively, and $n=1+\sqrt{6}\approx 3.45$ is prescribed by the modular symmetry, with predictions subject to charged lepton mixing corrections. We perform a numerical analysis, showing quark and lepton mass and mixing correlations around the best fit points.

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