arXiv subjects

Stephen F. King

Publications and source records attributed to Stephen F. King.

At least 145 records · Page 8Linked to original sources

arXiv2016

Littlest Seesaw

We propose the Littlest Seesaw (LS) model consisting of just two right-handed neutrinos, where one of them, dominantly responsible for the atmospheric neutrino mass, has couplings to $(ν_e,ν_μ,ν_τ)$ proportional to $(0,1,1)$, while the subdominant right-handed neutrino, mainly responsible for the solar neutrino mass, has couplings to $(ν_e,ν_μ,ν_τ)$ proportional to $(1,n,n-2)$. This constrained sequential dominance (CSD) model preserves the first column of the tri-bimaximal (TB) mixing matrix (TM1) and has a reactor angle $θ_{13} \sim (n-1) \frac{\sqrt{2}}{3} \frac{m_2}{m_3}$. This is a generalisation of CSD ($n=1$) which led to TB mixing and arises almost as easily if $n\geq 1$ is a real number. We derive exact analytic formulas for the neutrino masses, lepton mixing angles and CP phases in terms of the four input parameters and discuss exact sum rules. We show how CSD ($n=3$) may arise from vacuum alignment due to residual symmetries of $S_4$. We propose a benchmark model based on $S_4\times Z_3\times Z'_3$, which fixes $n=3$ and the leptogenesis phase $η= 2π/3$, leaving only two inputs $m_a$ and $m_b=m_{ee}$ describing $Δm^2_{31}$, $Δm^2_{21}$ and $U_{PMNS}$. The LS model predicts a normal mass hierarchy with a massless neutrino $m_1=0$ and TM1 atmospheric sum rules. The benchmark LS model additionally predicts: solar angle $θ_{12}=34^\circ$, reactor angle $θ_{13}=8.7^\circ$, atmospheric angle $θ_{23}=46^\circ$, and Dirac phase $δ_{CP}=-87^{\circ}$.

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arXiv2016

Neutrino Mass and Mixing with Discrete Symmetry

This is a review article about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Delta(96).

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arXiv2016

Approaching Minimal Flavour Violation from an SU(5) x S4 x U(1) SUSY GUT

We show how approximate Minimal Flavour Violation (MFV) can emerge from an SU(5) Supersymmetric Grand Unified Theory (SUSY GUT) supplemented by an S4 x U(1) family symmetry, which provides a good description of all quark and lepton (including neutrino) masses, mixings and CP violation. Assuming a SUSY breaking mechanism which respects the family symmetry, we calculate in full explicit detail the low energy mass insertion parameters in the super-CKM basis, including the effects of canonical normalisation and renormalisation group running. We find that the very simple family symmetry S4 x U(1) is sufficient to approximately reproduce the effects of low energy MFV.

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arXiv2016

Leptogenesis and residual CP symmetry

We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved $Z_2$ in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the $R$-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy $S_4$ flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.

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arXiv2016

750 GeV Diphoton excess from $E_6$ in F-theory GUTs

We interpret the 750-760 GeV diphoton resonance as one or more of the spinless components of a singlet superfield arising from the three 27-dimensional representations of $E_6$ in F-theory, which also contain three copies of colour-triplet charge $\mp 1/3$ vector-like fermions $D_i,\bar{D}_i$ and inert Higgs doublets to which the singlets may couple. For definiteness we consider (without change) a model that was proposed some time ago which contains such states, as well as bulk exotics, leading to gauge coupling unification. The smoking gun prediction of the model is the existence of other similar spinless resonances, possibly close in mass to 750-760 GeV, decaying into diphotons, as well as the three families of vector-like fermions $D_i,\bar{D}_i$.

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arXiv2015

MSSM from F-theory SU(5) with Klein Monodromy

We revisit a class of $SU(5)$ SUSY GUT models which arise in the context of the spectral cover with Klein Group monodromy $V_4=Z_2\times Z_2$. We show that $Z_2$ matter parities can be realised via new geometric symmetries respected by the spectral cover. We discuss a particular example of this kind, where the low energy effective theory below the GUT scale is just the MSSM with no exotics and standard matter parity, extended by the seesaw mechanism with two right-handed neutrinos.

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arXiv2015

SO(10) Grand Unification in M theory on a G2 manifold

We consider Grand Unified Theories based on $SO(10)$ which originate from string/$M$ theory on $G_2$ manifolds or Calabi-Yau spaces with discrete symmetries. In this framework we are naturally led to a novel solution of the doublet-triplet splitting problem previously considered by Dvali which involves an extra vector-like Standard Model family and light, but weakly coupled colour triplets. These additional states are predicted to be accessible at the LHC and also induce R-parity violation. Gauge coupling unification occurs with a larger GUT coupling.

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arXiv2015

Neutrino Mass and Mixing in the Seesaw Playground

We discuss neutrino mass and mixing in the framework of the classic seesaw mechanism, involving right-handed neutrinos with large Majorana masses, which provides an appealing way to understand the smallness of neutrino masses. However, with many input parameters, the seesaw mechanism is in general not predictive. We focus on natural implementations of the seesaw mechanism, in which large cancellations do not occur, where one of the right handed neutrinos is dominantly responsible for the atmospheric neutrino mass, while a second right-handed neutrino accounts for the solar neutrino mass, leading to an effective two right-handed neutrino model. We discuss recent attempts to predict lepton mixing and CP violation within such natural frameworks, focussing on the Littlest Seesaw and its distinctive predictions.

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arXiv2015

Models of Neutrino Mass, Mixing and CP Violation

In this topical review we argue that neutrino mass and mixing data motivates extending the Standard Model to include a non-Abelian discrete flavour symmetry in order to accurately predict the large leptonic mixing angles and CP violation. We begin with an overview of the Standard Model puzzles, followed by a description of some classic lepton mixing patterns. Lepton mixing may be regarded as a deviation from tri-bimaximal mixing, with charged lepton corrections leading to solar mixing sum rules, or tri-maximal lepton mixing leading to atmospheric mixing rules. We survey neutrino mass models, using a roadmap based on the open questions in neutrino physics. We then focus on the seesaw mechanism with right-handed neutrinos, where sequential dominance (SD) can account for large lepton mixing angles and CP violation, with precise predictions emerging from constrained SD (CSD). We define the flavour problem and discuss progress towards a theory of flavour using GUTs and discrete family symmetry. We classify models as direct, semidirect or indirect, according to the relation between the Klein symmetry of the mass matrices and the discrete family symmetry, in all cases focussing on spontaneous CP violation. Finally we give two examples of realistic and highly predictive indirect models with CSD, namely an A to Z of flavour with Pati-Salam and a fairly complete $A_4\times SU(5)$ SUSY GUT of flavour, where both models have interesting implications for leptogenesis.

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arXiv2015

Testing constrained sequential dominance models of neutrinos

Constrained sequential dominance (CSD) is a natural framework for implementing the see-saw mechanism of neutrino masses which allows the mixing angles and phases to be accurately predicted in terms of relatively few input parameters. We analyze a class of CSD($n$) models where, in the flavour basis, two right-handed neutrinos are dominantly responsible for the "atmospheric" and "solar" neutrino masses with Yukawa couplings to $(ν_e, ν_μ, ν_τ)$ proportional to $(0,1,1)$ and $(1,n,n-2)$, respectively, where $n$ is a positive integer. These coupling patterns may arise in indirect family symmetry models based on $A_4$. With two right-handed neutrinos, using a $χ^2$ test, we find a good agreement with data for CSD(3) and CSD(4) where the entire PMNS mixing matrix is controlled by a single phase $η$, which takes simple values, leading to accurate predictions for mixing angles and the magnitude of the oscillation phase $|δ_{CP}|$. We carefully study the perturbing effect of a third "decoupled" right-handed neutrino, leading to a bound on the lightest physical neutrino mass $m_1 \lesssim 1$ meV for the viable cases, corresponding to a normal neutrino mass hierarchy. We also discuss a direct link between the oscillation phase $δ_{CP} $ and leptogenesis in CSD($n$) due to the same see-saw phase $η$ appearing in both the neutrino mass matrix and leptogenesis.

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arXiv2015

Generalized CP and $Δ(3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix

The generalized CP transformations can only be consistently defined in the context of $Δ(3n^2)$ lepton symmetry if a certain subset of irreducible representations are present in a model. We perform a comprehensive analysis of the possible automorphisms and the corresponding CP transformations of the $Δ(3n^2)$ group. It is sufficient to only consider three automorphisms if $n$ is not divisible by 3 while additional eight types of CP transformations could be imposed for the case of $n$ divisible by 3. We study the lepton mixing patterns which can be derived from the $Δ(3n^2)$ family symmetry and generalized CP in the semi-direct approach. The PMNS matrix is determined to be the trimaximal pattern for all the possible CP transformations, and it can only take two distinct forms.

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arXiv2015

Successful $N_2$ leptogenesis with flavour coupling effects in realistic unified models

In realistic unified models involving an $SO(10)$-like pattern of Dirac and heavy right-handed (RH) neutrino masses, the lightest right-handed neutrino $N_1$ is too light to yield successful thermal leptogenesis, barring highly fine tuned solutions, while the second heaviest right-handed neutrino $N_2$ is typically in the correct mass range. We show that flavour coupling effects in the Boltzmann equations may be crucial to the success of such $N_2$ dominated leptogenesis, by helping to ensure that the flavour asymmetries produced at the $N_2$ scale survive $N_1$ washout. To illustrate these effects we focus on $N_2$ dominated leptogenesis in an existing model, the A to Z of flavour with Pati-Salam, where the neutrino Dirac mass matrix may be equal to an up-type quark mass matrix and has a particular constrained structure. The numerical results, supported by analytical insight, show that in order to achieve successful $N_2$ leptogenesis, consistent with neutrino phenomenology, requires a "flavour swap scenario" together with a less hierarchical pattern of RH neutrino masses than naively expected, at the expense of some mild fine-tuning. These results may be relevant for other $SO(10)$-like unified models where $N_2$ leptogenesis is necessary.

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arXiv2015

Phenomenological implications of a minimal F-theory GUT with discrete symmetry

We discuss the origin of both non-Abelian discrete family symmetry and Abelian continuous family symmetry, as well as matter parity, from F-theory SUSY GUTs. We propose a minimal model based on the smallest GUT group $SU(5)$, together with the non-Abelian family symmetry $D_4$ plus an Abelian family symmetry, where fluxes are responsible for doublet-triplet splitting, leading to a realistic low energy spectrum with phenomenologically acceptable quark and lepton masses and mixing. We show how a $Z_2$ matter parity emerging from F-theory can suppress proton decay while allowing neutron-antineutron oscillations, providing a distinctive signature of the set-up.

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arXiv2015

Leptogenesis in minimal predictive seesaw models

We estimate the Baryon Asymmetry of the Universe (BAU) arising from leptogenesis within a class of minimal predictive seesaw models involving two right-handed neutrinos and simple Yukawa structures with one texture zero. The two right-handed neutrinos are dominantly responsible for the "atmospheric" and "solar" neutrino masses with Yukawa couplings to $(ν_e, ν_μ, ν_τ)$ proportional to $(0,1,1)$ and $(1,n,n-2)$, respectively, where $n$ is a positive integer. The neutrino Yukawa matrix is therefore characterised by two proportionality constants with their relative phase providing a leptogenesis-PMNS link, enabling the lightest right-handed neutrino mass to be determined from neutrino data and the observed BAU. We discuss an $SU(5)$ SUSY GUT example, where $A_4$ vacuum alignment provides the required Yukawa structures with $n=3$, while a $\mathbb{Z}_9$ symmetry fixes the relatives phase to be a ninth root of unity.

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arXiv2015

Invariant approach to CP in unbroken $Δ(27)$

The invariant approach is a powerful method for studying CP violation for specific Lagrangians. The method is particularly useful for dealing with discrete family symmetries. We focus on the CP properties of unbroken $Δ(27)$ invariant Lagrangians with Yukawa-like terms, which proves to be a rich framework, with distinct aspects of CP, making it an ideal group to investigate with the invariant approach. We classify Lagrangians depending on the number of fields transforming as irreducible triplet representations of $Δ(27)$. For each case, we construct CP-odd weak basis invariants and use them to discuss the respective CP properties. We find that CP violation is sensitive to the number and type of $Δ(27)$ representations.

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arXiv2015

Observable Heavy Higgs Dark Matter

Dark Matter (DM), arising from an Inert Higgs Doublet, may either be light, below the $W$ mass, or heavy, above about 525 GeV. While the light region may soon be excluded, the heavy region is known to be very difficult to probe with either Direct Detection (DD) experiments or the Large Hadron Collider (LHC). We show that adding a second Inert Higgs Doublet helps to make the heavy DM region accessible to both DD and the LHC, by either increasing its couplings to the observed Higgs boson, or lowering its mass to $360 \gev \lesssim m_{DM}$, or both.

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arXiv2015

Towards a complete $A_4 \times SU(5)$ SUSY GUT

We propose a renormalisable model based on $A_4$ family symmetry with an $SU(5)$ grand unified theory (GUT) which leads to the minimal supersymmetric standard model (MSSM) with a two right-handed neutrino seesaw mechanism. Discrete $\mathbb{Z}_9\times \mathbb{Z}_6$ symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while $\mathbb{Z}_4^R$ symmetry is broken to $\mathbb{Z}_2^R$, identified as usual R-parity. Proton decay is highly suppressed by these symmetries. We discuss both the $A_4$ and $SU(5)$ symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing and the origin of the $μ$ term. The model provides an excellent fit (better than one sigma) to all quark and lepton (including neutrino) masses and mixing with spontaneous CP violation. With the $A_4$ vacuum alignments, $(0,1,1)$ and $(1,3,1)$, the model predicts the entire PMNS mixing matrix with no free parameters, up to a relative phase, selected to be $2π/3$ from a choice of the nine complex roots of unity, providing a direct link between neutrino oscillations and leptogenesis.

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arXiv2015

GUT predictions for quark-lepton Yukawa coupling ratios with messenger masses from non-singlets

We propose new predictions from Grand Unified Theories (GUTs) (applicable to both supersymmetric (SUSY) and non-SUSY models) for the ratios of quark and lepton Yukawa couplings. These new predictions arise from splitting the masses of the messenger fields for the GUT scale Yukawa operators by Clebsch-Gordan factors from GUT symmetry breaking. This has the effect that these factors enter inversely in the predicted quark-lepton Yukawa coupling ratios, leading to new possible GUT predictions. We systematically construct the new predictions that can be realised in this way in SU(5) GUTs and Pati-Salam unified theories and discuss model building applications.

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