arXiv subjects

Stephen F. King

Publications and source records attributed to Stephen F. King.

At least 109 records · Page 6Linked to original sources

arXiv2018

Lepton Mixing Predictions from $S_4$ in the Tri-Direct CP approach to Two Right-handed Neutrino Models

We perform an exhaustive analysis of all possible breaking patterns arising from $S_4\rtimes H_{CP}$ in a new {\it tri-direct CP approach} to the minimal seesaw model with two right-handed neutrinos, and construct a realistic flavour model along these lines. According to this approach, separate residual flavour and CP symmetries persist in the charged lepton, `atmospheric' and `solar' right-handed neutrino sectors, i.e. we have {\it three} symmetry sectors rather than the usual two of the {\it semi-direct CP approach} (charged leptons and neutrinos). Following the {\it tri-direct CP approach}, we find twenty-six kinds of independent phenomenologically interesting mixing patterns. Eight of them predict a normal ordering (NO) neutrino mass spectrum and the other eighteen predict an inverted ordering (IO) neutrino mass spectrum. For each phenomenologically interesting mixing pattern, the corresponding predictions for the PMNS matrix, the lepton mixing parameters, the neutrino masses and the effective mass in neutrinoless double beta decay are given in a model independent way. One breaking pattern with NO spectrum and two breaking patterns with IO spectrum corresponds to form dominance. We find that the lepton mixing matrices of three kinds of breaking patterns with NO spectrum and one form dominance breaking pattern with IO spectrum preserve the first column of the tri-bimaximal (TB) mixing matrix, i.e. yield a TM1 mixing matrix.

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arXiv2018

$R_{K^{(*)}}$ with leptoquarks and the origin of Yukawa couplings

We construct a model where the Yukawa couplings of the Standard Model (SM) fermions arise from the breaking of a $Z_2$ symmetry and through mixing with a fourth family of vector-like fermions. By adding a scalar leptoquark, which is an electroweak triplet and odd under the $Z_2$ symmetry, we obtain an explanation for $R_{K^{(*)}}$ that is linked to the origin of the Yukawa couplings. The coupling of SM fermions to the leptoquark is mediated by the fourth family fermions, and is predicted to be related to CKM entries and mass ratios of SM fermions.

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arXiv2018

Flavourful $Z'$ portal for vector-like neutrino Dark Matter and $R_{K^{(*)}}$

We discuss a flavourful $Z'$ portal model with a coupling to fourth-family singlet Dirac neutrino dark matter. In the absence of mixing, the $Z'$ is fermiophobic, having no couplings to the three chiral families, but does couple to a fourth vector-like family. Due to mixing effects, the $Z'$ gets induced couplings to second family left-handed lepton doublets and third family left-handed quark doublets. This model can simultaneously account for the measured $B$-decay ratios $R_{K}$ and $R_{K^*}$ and for the observed relic abundance of dark matter. We identify the parameter space where this explanation is consistent with existing experimental constraints from dark matter direct and indirect detection, LHC searches, and precision measurements of flavour mixing and neutrino processes.

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arXiv2018

$SU(3) \times SO(10)$ in 6d

We discuss a simple and elegant $SU(3)\times SO(10)$ family unified gauge theory in 6d compactified on a torus with the orbifold $T_2/Z_2^3$ and supplemented by a $Z_6\times Z_3$ discrete symmetry. The orbifold boundary conditions generate all the desired $SU(3)$ breaking vacuum alignments, including the $(0,1,-1)$ and $(1,3,-1)$ alignments of the Littlest Seesaw model for atmospheric and solar neutrino mixing, as well as the usual $SO(10)$ breaking with doublet-triplet splitting. The absence of driving and messenger fields considerably simplifies the field content of the model. It naturally explains why there are three families of quarks and leptons, and accounts for all their masses, mixing angles and CP phases via rather elegant looking Yukawa and Majorana matrices in the theory basis. The resulting model controls proton decay and allows successful Leptogenesis.

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arXiv2018

$R_{K^{(*)}}$ and the origin of Yukawa couplings

We explore the possibility that the semi-leptonic $B$ decay ratios $R_{K^{(*)}}$ which violate $μ- e$ universality are related to the origin of the fermion Yukawa couplings in the Standard Model. Some time ago, a vector-like fourth family (without a $Z'$) was used to generate fermion mass hierarchies and mixing patterns without introducing any family symmetry. Recently the idea of inducing flavourful $Z'$ couplings via mixing with a vector-like fourth family which carries gauged $U(1)'$ charges has been proposed as a simple way of producing controlled flavour universality violation while elegantly cancelling anomalies. We show that the fusion of these two ideas provides a nice connection between $R_{K^{(*)}}$ and the origin of Yukawa couplings in the quark sector. However the lepton sector requires some tuning of Yukawa couplings to obtain the desired coupling of $Z'$ to muons.

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arXiv2018

The Dark Side of the Littlest Seesaw: freeze-in, the two right-handed neutrino portal and leptogenesis-friendly fimpzillas

We propose a minimal model to simultaneously account for a realistic neutrino spectrum through a type-I seesaw mechanism and a viable dark matter relic density. The model is an extension of the Littlest Seesaw model in which the two right-handed neutrinos of the model are coupled to a $Z_2$-odd dark sector via right-handed neutrino portal couplings. In this model, a highly constrained and direct link between dark matter and neutrino physics is achieved by considering the freeze-in production mechanism of dark matter. We show that the neutrino Yukawa couplings which describe neutrino mass and mixing may also play a dominant role in the dark matter production. We investigate the allowed regions in the parameter space of the model that provide the correct neutrino masses and mixing and simultaneously give the correct dark matter relic abundance. In certain cases the right-handed neutrino mass may be arbitrarily large, for example in the range $10^{10}-10^{11}$ GeV required for vanilla leptogenesis, with a successful relic density arising from frozen-in dark matter particles with masses around this scale, which we refer to as "fimpzillas".

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arXiv2018

Mu-tau symmetry and the Littlest Seesaw

Motivated by the latest neutrino oscillation data which is consistent with maximal atmospheric mixing and maximal leptonic CP violation, we review various results in $μτ$ symmetry, then include several new observations and clarifications, including identifying a new general form of neutrino mass matrix with $μτ$ symmetry. We then apply the new results to the neutrino mass matrix associated with the Littlest Seesaw model, and show that it approximately satisfies the new general form with $μτ$ symmetry, and that this is responsible for its approximate predictions of maximal atmospheric mixing and maximal CP violation in the lepton sector.

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arXiv2018

Flavourful Axion Phenomenology

We present a comprehensive discussion of the phenomenology of flavourful axions, including both standard Peccei-Quinn (PQ) axions, associated with the solution to the strong $CP$ problem, and non-standard axion-like particles (ALPs). We give the flavourful axion-fermion and axion-photon couplings and calculate the branching ratios of heavy meson ($K$, $D$, $B$) decays involving a flavourful axion. We also calculate the mixing between axions and heavy mesons $ K^0 $, $ D^0 $, $ B^0 $ and $ B_s^0 $, which affects the meson oscillation probability and mass difference. Mixing also contributes to meson decays into axions and axion decays into two photons, and may be relevant for ALPs. We discuss charged lepton flavour-violating decays involving final state axions of the form $\ell_1 \to \ell_2 a (γ) $, as well as $ μ\to eee $ and $ μ-e $ conversion. Finally we describe the phenomenology of a particular "A to Z" Pati-Salam model, in which PQ symmetry arises accidentally due to discrete flavour symmetry. Here all axion couplings are fixed by a fit to flavour data, leading to sharp predictions and correlations between flavour-dependent observables.

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arXiv2018

Fitting high-energy Littlest Seesaw parameters using low-energy neutrino data and leptogenesis

We show that the four high-energy Littlest Seesaw parameters in the flavour basis,namely two real Yukawa couplings plus the two right-handed neutrino masses, can be determined by an excellent fit to the seven currently constrained observables of low-energy neutrino data and leptogenesis. Taking into account renormalisation group corrections, we estimate $χ^2 \simeq 1.5-2.6$ for the three d.o.f., depending on the high-energy scale and the type of non supersymmetric Littlest Seesaw model. We extract allowed ranges of neutrino parameters from our fit data, including the approximate mu-tau symmetric predictions $θ_{23}=45^o\pm 1^o$ and $δ= -90^o \pm 5^o $, which, together with a normal mass ordering with $m_1=0$, will enable Littlest Seesaw models to be tested in future neutrino experiments.

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arXiv2018

An $S_4 \times SU(5)$ SUSY GUT of flavour in 6d

We propose a 6d model with a SUSY $SU(5)$ gauge symmetry. After compactification, it explains the origin of the $S_4$ Family Symmetry with CSD3 vacuum alignment, as well as $SU(5)$ breaking with doublet-triplet splitting. The model naturally accounts for all quark and lepton (including neutrino) masses and mixings, incorporating the highly predictive Littlest Seesaw structure. It spontaneously breaks CP symmetry, resulting in successful CP violation in the quark and lepton sectors, while solving the Strong CP problem. It also explains the Baryon Asymmetry of the Universe (BAU) through leptogenesis, with the leptogenesis phase directly linked to the Dirac and Majorana phases.

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arXiv2018

${SO(10)}$ inspired $Z'$ models at the LHC

We study and compare various $Z'$ models arising from $SO(10)$, focussing in particular on the Abelian subgroup $U(1)_{R} \times U(1)_{B-L}$, broken at the TeV scale to Standard Model hypercharge $U(1)_{Y}$. The gauge group $U(1)_{R} \times U(1)_{B-L}$, which is equivalent to the $U(1)_{Y}\times U(1)_χ$ in a different basis, is well motivated from $SO(10)$ breaking and allows neutrino mass via the linear seesaw mechanism. Assuming supersymmetry, we consider single step gauge unification to predict the gauge couplings, then consider the detection and characterisation prospects of the resulting $Z'$ at the LHC by studying its possible decay modes into di-leptons as well as into Higgs bosons. The main new result here is to analyse in detail the expected leptonic forward-backward asymmetry at the high luminosity LHC and show that it may be used to discriminate the $U(1)_{R} \times U(1)_{B-L}$ model from the usual $B-L$ model based on $U(1)_{Y}\times U(1)_{B-L}$.

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arXiv2017

$\mathbf{SO(10)}\times \mathbf{S_4} $ Grand Unified Theory of Flavour and Leptogenesis

We propose a Grand Unified Theory of Flavour, based on $SO(10)$ together with a non-Abelian discrete group $S_4$, under which the unified three quark and lepton 16-plets are unified into a single triplet $3'$. The model involves a further discrete group $ \mathbb{Z}_4^R\times \mathbb{Z}_4^3$ which controls the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum alignment is discussed, along with the GUT breaking potential and the doublet-triplet splitting, and proton decay is shown to be under control. The Yukawa matrices are derived in detail, from renormalisable diagrams, and neutrino masses emerge from the type I seesaw mechanism. A full numerical fit is performed with 15 input parameters generating 19 presently constrained observables, taking into account supersymmetry threshold corrections. The model predicts a normal neutrino mass ordering with a CP oscillation phase of $260^{\circ}$, an atmospheric angle in the first octant and neutrinoless double beta decay with $m_{ββ}= 11$ meV. We discuss $N_2$ leptogenesis, which fixes the second right-handed neutrino mass to be $M_2\simeq 2\times 10^{11}$ GeV, in the natural range predicted by the model.

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arXiv2017

Accidental Peccei-Quinn Symmetry from Discrete Flavour Symmetry and Pati-Salam

We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a discrete $A_4$ family symmetry combined with a discrete flavour symmetry $ \mathbb{Z}_3 \times \mathbb{Z}_5^2 $, in a realistic Pati-Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong $ CP $ problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of $ A_4 $ triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of an accidental PQ symmetry arising from a discrete flavour symmetry constrains the form of the Yukawa matrices, providing a link between flavour and the strong $ CP $ problem. Our model predicts specific flavour-violating couplings of the flavourful axion and thus puts a strong limit on the axion scale from kaon decays.

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arXiv2017

A natural $ S_4 \times SO(10) $ model of flavour

We propose a natural $ S_4 \times SO(10) $ supersymmetric grand unified theory of flavour with an auxiliary $\mathbb{Z}_4^2 \times \mathbb{Z}_4^R$ symmetry, based on small Higgs representations (nothing larger than an adjoint) and hence a type-I seesaw mechanism. The Yukawa structure of all fermions is determined by the hierarchical vacuum expectation values of three $ S_4 $ triplet flavons, with CSD3 vacuum alignments, where up-type quarks and neutrinos couple to one Higgs $\mathbf{10}$, and the down-type quarks and charged leptons couple to a second Higgs $\mathbf{10}$. The Yukawa matrices are obtained from sums of low-rank matrices, where each matrix in the sum naturally accounts for the mass of a particular family, as in sequential dominance in the neutrino sector, which predicts a normal neutrino mass hierarchy. The model accurately fits all available quark and lepton data, with predictions for the leptonic $CP$ phase in 95$\%$ credible intervals given by $ 281^\circ < δ^\ell < 308^\circ $ and $ 225^\circ < δ^\ell < 253^\circ $. The model reduces to the MSSM, with the two Higgs doublets emerging from the two Higgs $\mathbf{10}$s without mixing, and we demonstrate how a $μ$ term of $\mathcal{O}$(TeV) can be realised, as well as doublet-triplet splitting, with Planck scale operators controlled by symmetry, leading to acceptable proton decay.

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arXiv2017

Non-universal $Z'$ from Fluxed GUTs

We make a first systematic study of non-universal TeV scale neutral gauge bosons $Z'$ arising naturally from a class of F-theory inspired models broken via $SU(5)$ by flux. The phenomenological models we consider may originate from semi-local F-theory GUTs arising from a single $E_8$ point of local enhancement, assuming the minimal ${\cal Z}_2$ monodromy in order to allow for a renormalisable top quark Yukawa coupling. We classify such non-universal anomaly-free $U(1)'$ models requiring a minimal low energy spectrum and also allowing for a vector-like family. We discuss to what extent such models can account for the anomalous $B$-decay ratios $R_{K}$ and $R_{K^*}$.

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arXiv2017

A Comprehensive Renormalisation Group Analysis of the Littlest Seesaw Model

We present a comprehensive renormalisation group analysis of the Littlest Seesaw model involving two right-handed neutrinos and a very constrained Dirac neutrino Yukawa coupling matrix. We perform the first $χ^2$ analysis of the low energy masses and mixing angles, in the presence of renormalisation group corrections, for various right-handed neutrino masses and mass orderings, both with and without supersymmetry. We find that the atmospheric angle, which is predicted to be near maximal in the absence of renormalisation group corrections, may receive significant corrections for some non-supersymmetric cases, bringing it into close agreement with the current best fit value in the first octant. By contrast, in the presence of supersymmetry, the renormalisation group corrections are relatively small, and the prediction of a near maximal atmospheric mixing angle is maintained, for the studied cases. Forthcoming results from T2K and NOvA will decisively test these models at a precision comparable to the renormalisation group corrections we have calculated.

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arXiv2017

Flavourful $Z'$ models for $R_{K^{(*)}}$

We show how any flavour conserving $Z'$ model can be made flavour violating and non-universal by introducing mass mixing of quarks and leptons with a fourth family of vector-like fermions with non-universal $Z'$ couplings. After developing a general formalism, we focus on two concrete examples, namely a fermiophobic model, and an $SO(10)$ GUT model, and show how they can account for the anomalous $B$ decay ratios $R_K$ and $R_{K^*}$. A similar analysis could be performed for $B-L$ models, $E_6$ models, composite models, and so on.

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arXiv2017

Sensitivities and synergies of DUNE and T2HK

Long-baseline neutrino oscillation experiments, in particular Deep Underground Neutrino Experiment (DUNE) and Tokai to Hyper-Kamiokande (T2HK), will lead the effort in the precision determination of the as yet unknown parameters of the leptonic mixing matrix. In this article, we revisit the potential of DUNE, T2HK and their combination in light of the most recent experimental information. As well as addressing more conventional questions, we pay particular attention to the attainable precision on δ, which is playing an increasingly important role in the physics case of the long-baseline programme. We analyse the complementarity of the two designs, identify the benefit of a programme comprising distinct experiments and consider how best to optimise the global oscillation programme. This latter question is particularly pertinent in light of a number of alternative design options which have recently been mooted: a Korean second detector for T2HK and different beams options at DUNE. We study the impact of these options and quantify the synergies between alternative proposals, identifying the best means of furthering our knowledge of the fundamental physics of neutrino oscillation.

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