Vacuum Alignment Research Articles

Towards a complete A4 × 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 $\mu$ 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 $2\pi/3$ from a choice of the nine complex roots of unity, providing a direct link between neutrino oscillations and leptogenesis.

Novel constraint on the parameter space of the Georgi-Machacek model with current LHC data

The same-sign diboson process $pp\to W^\pm W^\pm jj$ has been measured at the LHC using leptonic decay channels of the $W$ bosons, with production cross sections of two fiducial regions reported to be consistent with the standard model expectations within 1 sigma. These results constrain new physics models with a modified $W^+W^+W^-W^-$ vertex. We consider in particular the Georgi-Machacek model in which the quartic $W$ boson vertex is effectively modified due to mediations of new Higgs bosons in the model. The relevant gauge-gauge-scalar couplings are all proportional to the vacuum expectation value of the isospin triplets, which can be of $\mathcal{O}(10)$ GeV because of custodial vacuum alignment. Using the current 8-TeV data at the LHC, we exclude parameter space on the plane of the triplet vacuum expectation value and the new Higgs boson mass. The expected discovery reach at the 14-TeV LHC is also studied.

Phenomenology of the inert (2+1) and (4+2) Higgs doublet models

We make a phenomenological study of a model with two inert doublets plus one Higgs doublet (I(2+1)HDM) which is symmetric under a Z$_2$ group, preserved after Electro-Weak Symmetry Breaking (EWSB) by the vacuum alignment $(0,0,v)$. This model may be regarded as an extension to the model with one inert doublet plus one Higgs doublet (I(1+1)HDM), by the addition of an extra inert scalar doublet. The neutral fields from the two inert doublets provide a viable Dark Matter (DM) candidate which is stabilised by the conserved $Z_2$ symmetry. We study the new Higgs decay channels offered by the scalar fields from the extra doublets and their effect on the Standard Model (SM) Higgs couplings, including a new decay channel into photon(s) plus missing energy, which distinguishes the I(2+1)HDM from the I(1+1)HDM. Motivated by Supersymmetry, which requires an even number of doublets, we then extend this model into a model with four inert doublets plus two Higgs doublets (I(4+2)HDM) and study the phenomenology of the model with the vacuum alignment $(0,0,0,0,v,v)$. This scenario offers a wealth of Higgs signals, the most distinctive ones being cascade decays of heavy Higgs states into inert ones. Finally, we also remark that the smoking-gun signature of all the considered models is represented by invisible Higgs decays into the lightest inert Higgs bosons responsible for DM.

Higgs boson as a top-mode pseudo-Nambu-Goldstone boson

In the spirit of the top-quark condensation, we propose a model which has a naturally light composite Higgs boson, ``tHiggs'' (${h}_{t}^{0}$), to be identified with the 126 GeV Higgs discovered at the LHC. The tHiggs, a bound state of the top quark and its flavor (vectorlike) partner, emerges as a pseudo-Nambu--Goldstone boson (NGB), ``top-mode pseudo-Nambu-Goldstone boson,'' together with the exact NGBs to be absorbed into the $W$ and $Z$ bosons as well as another (heavier) top-mode pseudo-Nambu-Goldstone bosons ($CP$-odd composite scalar, ${A}_{t}^{0}$). Those five composite (exact/pseudo-) NGBs are dynamically produced simultaneously by a single supercritical four-fermion interaction having $U(3)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry which includes the electroweak symmetry, where the vacuum is aligned by a small explicit breaking term so as to break the symmetry down to a subgroup, $U(2)\ifmmode\times\else\texttimes\fi{}U(1{)}^{\ensuremath{'}}$, in a way not to retain the electroweak symmetry, in sharp contrast to the little Higgs models. The explicit breaking term for the vacuum alignment gives rise to a mass of the tHiggs, which is protected by the symmetry and hence naturally controlled against radiative corrections. Realistic top-quark mass is easily realized similarly to the top-seesaw mechanism by introducing an extra (subcritical) four-fermion coupling which explicitly breaks the residual $U(2{)}^{\ensuremath{'}}\ifmmode\times\else\texttimes\fi{}U(1{)}^{\ensuremath{'}}$ symmetry with $U(2{)}^{\ensuremath{'}}$ being an extra symmetry besides the above $U(3{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1)$. We present a phenomenological Lagrangian of the top-mode pseudo-Nambu-Goldstone bosons along with the Standard Model particles, which will be useful for the study of the collider phenomenology. The coupling property of the tHiggs is shown to be consistent with the currently available data reported from the LHC. Several phenomenological consequences and constraints from experiments are also addressed.

A to Z of Flavour with Pati-Salam

We propose an elegant theory of flavour based on A 4 × Z 5 family symmetry with Pati-Salam unification which provides an excellent description of quark and lepton masses, mixing and CP violation. The A 4 symmetry unifies the left-handed families and its vacuum alignment determines the columns of Yukawa matrices. The Z 5 symmetry distinguishes the right-handed families and its breaking controls CP violation in both the quark and lepton sectors. The Pati-Salam symmetry relates the quark and lepton Yukawa matrices, with Y u = Y ν and Y d ~ Y e . Using the see-saw mechanism with very hierarchical right-handed neutrinos and CSD4 vacuum alignment, the model predicts the entire PMNS mixing matrix and gives a Cabibbo angle θ C ≈ 1/4. In particular, for a discrete choice of Z 5 phases, it predicts maximal atmospheric mixing, θ 23 = 45° ± 0.5° and leptonic CP violating phase δ l = 260° ± 5°. The reactor angle prediction is θ 13 = 9° ± 0.5°, while the solar angle is 34° ≳ θ 12 ≳ 31°, for a lightest neutrino mass in the range 0 ≲ m 1 ≲ 0.5 meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.

Vacuum alignment with more flavors

We study the alignment of the vacuum in gauge theories with ${N}_{f}$ Dirac fermions transforming according to a complex representation of the gauge group. The alignment of the vacuum is produced by adding a small mass perturbation to the theory. We study in detail the ${N}_{f}=2,3$, and 4 case. For ${N}_{f}=2$ and ${N}_{f}=3$ we reproduce earlier known results including the Dashen phase with spontaneous violation of the combined charge conjugation and parity symmetry, $CP$. For ${N}_{f}=4$ we find regions with and without spontaneous $CP$ violation. We then generalize to an arbitrary number of flavors. Here it is shown that at the point where ${N}_{f}\ensuremath{-}1$ flavors are degenerate with positive mass $m>0$ and the mass of the ${N}_{f}$th flavor becomes negative and equal to $\ensuremath{-}m$, $CP$ breaks spontaneously.

Vacuum alignment and lattice artifacts: Staggered fermions

In confining lattice gauge theories in which part of the flavor group is coupled weakly to additional gauge fields, both the dynamics of the weak gauge fields as well as lattice artifacts may have non-trivial effects on the orientation of the vacuum in flavor space. Here we discuss this issue for lattice gauge theories employing staggered fermions. Staggered fermions break flavor symmetries to a much smaller group on the lattice, and orientations in flavor space that are equivalent in the continuum may be distinct on the lattice. Assuming universality, we show that in the continuum limit the weakly gauged flavor symmetries are always vector-like, disproving a recent claim in the literature.

Vacuum alignment and lattice artifacts: Wilson fermions

Confinement in asymptotically free gauge theories is accompanied by the spontaneous breaking of the global flavor symmetry. If a subgroup of the flavor symmetry group is coupled weakly to additional gauge fields, the vacuum state tends to align such that the gauged subgroup is unbroken. Independently, a lattice discretization of the continuum theory typically reduces the manifest flavor symmetry, and, in addition, can give rise to new lattice-artifact phases with spontaneously broken symmetries. Here, we study the interplay of these two phenomena for Wilson fermions, using chiral lagrangian techniques. We consider two examples: electromagnetic corrections to QCD, and a prototype composite-Higgs model.

TFT-LCD中的液晶扩散研究

In order to improve the process and defect in ODF,the relationship between diffusion time and distance of liquid crystal in TFT-LCD(after vacuum alignment)is researched in this paper.A liquid crystal diffusion model of tilted state has been proposed by the assumption of newton fluid. Mathematical derivations prove that the flat state diffusion equation is a special case of tilted angle 0. The gravity effect becomes more significant by longer diffusion distance in titled state.That is why the diffusion time has difference between the two states.Panel size and LC pattern design have an effect on the final pattern of liquid crystal diffusion.Cell gap and photo spacer will affect the diffusion velocity.The effect can be reduced by more uniform gap and smaller density of spacer.Experimental studies show that the theoretical data calculated by the model is close to the experiment data.The model can make a good flow prediction for the diffusion of liquid crystal in TFT-LCD.

Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses

We catalogue and study three-Higgs-doublet models in terms of all possible allowed symmetries (continuous and discrete, Abelian and non-Abelian), where such symmetries may be identified as flavour symmetries of quarks and leptons. We analyse the potential in each case, and derive the conditions under which the vacuum alignments (0,0,v), (0,v,v) and (v,v,v) are minima of the potential. For the alignment (0,0,v), relevant for dark matter models, we calculate the corresponding physical Higgs boson mass spectrum. Motivated by supersymmetry, we extend the analysis to the case of three up-type Higgs doublets and three down- type Higgs doublets (six doublets in total). Many of the results are also applicable to flavon models where the three Higgs doublets are replaced by three electroweak singlets.

Vacuum alignment and phase structure of holographic bi-layers

We study the D3/probe D5 system with two domain wall hypermultiplets. The conformal symmetry can be broken by a magnetic field, B (or running coupling), which promotes condensation of the fermions on each individual domain wall. Separation of the domain walls promotes condensation of the fermions between one wall and the other. We study the competition between these two effects showing a first order phase transition when the separation is ∼0.56λ1/4B−1/2. We identify extremal brane configurations which exhibit both condensations simultaneously but they are not the preferred ground state.

Neutrino mass textures from F-theory

Experimental data on the neutrino mixing and masses strongly suggest an underlying approximate symmetry of the relevant Yukawa superpotential terms. Intensive phenomenological explorations during the last decade indicate that permutation symmetries such as S_4, A_4 and their subgroups, under certain assumptions and vacuum alignments, predict neutrino mass textures compatible with such data. Motivated by these findings, in the present work we analyse the neutrino properties in F-theory GUT models derived in the framework of the maximal underlying E_8 symmetry in the elliptic fibration. More specifically, we consider local F-SU(5) GUT models and study in detail spectral cover geometries with monodromies associated to the finite symmetries S_4, A_4 and their transitive subgroups, including the dihedral group D_4 and Z_2 X Z_2. We discuss various issues that emerge in the implementation of S_4, A_4 neutrino models in the F-theory context and suggest how these can be resolved. Realistic models are presented for the case of monodromies based on their transitive subgroups. We exemplify this procedure with a detailed analysis performed for the case of Z_2 X Z_2 model.

Flavour models for TM1 lepton mixing

We present a framework for lepton flavour models such that the first column of the lepton mixing matrix is . We show that the flavour symmetry group adequate for this purpose is S4. Our models are based on a vacuum alignment that can be obtained in a supersymmetric framework.

Discrete symmetries, roots of unity, and lepton mixing

We investigate the possibility that the first column of the lepton mixing matrix U is given by . In a purely group-theoretical approach, based on residual symmetries in the charged-lepton and neutrino sectors and on a theorem on vanishing sums of roots of unity, we discuss the finite groups which can enforce this. Assuming that there is only one residual symmetry in the Majorana neutrino mass matrix, we find the almost unique solution where the cyclic factor with q = 1, 2, 3, … is irrelevant for obtaining u1 in U. Our discussion also provides a natural mechanism for achieving this goal. Finally, barring vacuum alignment, we realize this mechanism in a class of renormalizable models.

SpontaneousCPviolation inA4×SU(5)with constrained sequential dominance 2

We revisit a two right-handed neutrino model with two texture zeros, namely an indirect model based on ${A}_{4}$ with the recently proposed new type of constrained sequential dominance (CSD2), involving vacuum alignments along the $(0,1,\ensuremath{-}1{)}^{T}$ and $(1,0,2{)}^{T}$ directions in flavor space, which are proportional to the neutrino Dirac mass matrix columns. In this paper we construct a renormalizable and unified indirect ${A}_{4}\ifmmode\times\else\texttimes\fi{}SU(5)$ model along these lines and show that, with spontaneous $CP$ violation and a suitable vacuum alignment of the phases, the charged lepton corrections lead to a reactor angle in good agreement with results from Daya Bay and RENO. The model predicts a right-angled unitarity triangle in the quark sector and a Dirac $CP$ violating oscillation phase in the lepton sector of $\ensuremath{\delta}\ensuremath{\approx}130\ifmmode^\circ\else\textdegree\fi{}$, while providing a good fit to all quark and lepton masses and mixing angles.

Spontaneous CP violation from vacuum alignment in S 4 models of leptons

We construct models of leptons based on S 4 family symmetry combined with a generalised CP symmetry H CP . We show how the flavon potential can spontaneously break the symmetry S 4 ⋊ H CP down to $ {Z_2}\times H_{CP}^v $ in the neutrino sector, where the choice of preserved CP symmetry $ H_{CP}^v $ is controlled by free (real) parameters in the flavon potential. We propose two realistic models of this kind, one at the effective level and one at the renormalisable level. Both models predict trimaximal lepton mixing with CP being either fully preserved or maximally broken, with the intermediate possibility forbidden by the structure of the models.

Predictivity of models with spontaneously broken non-Abelian discrete flavor symmetries

In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can also be applied to non-supersymmetric flavor models.

On the terms violating the custodial symmetry in multi-Higgs-doublet models

We prove that a generic multi-Higgs-doublet model (NHDM) must generally contain terms in the potential that violate custodial symmetry. This is done by showing that the O(4) violating terms of the NHDM potential cannot be excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect higher-order corrections to necessarily introduce such terms. We also note, in the case of custodially symmetric Higgs–quark couplings, that vacuum alignment will lead to up–down mass degeneration; this is not true if the vacua are not aligned.

Lepton flavor at the electroweak scale: A completeA4model

Apparent regularities in fermion masses and mixings are often associated with physics at a high flavor scale, especially in the context of discrete flavor symmetries. One of the main reasons for that is that the correct vacuum alignment requires usually some high scale mechanism to be phenomenologically acceptable. Contrary to this expectation, we present in this paper a renormalizable radiative neutrino mass model with an ${A}_{4}$ flavor symmetry in the lepton sector, which is broken at the electroweak scale. For that we use a novel way to achieve the vacuum expectation value alignment via an extended symmetry in the flavon potential proposed before by two of the authors. We discuss various phenomenological consequences for the lepton sector and show how the remnants of the flavor symmetry suppress large lepton flavor violating processes. The model naturally includes a dark matter candidate, whose phenomenology we outline. Finally, we sketch possible extensions to the quark sector and discuss its implications for the LHC, especially how an enhanced diphoton rate for the resonance at 125 GeV can be explained within this model.

Discrete family symmetry, Higgs mediators and θ 13

We present a new (supersymmetric) framework for obtaining an excellent description of quark, charged lepton and neutrino masses and mixings from a Delta(6n^2) family symmetry with multiplet assignments consistent with an underlying SO(10) Grand Unification. It employs a Higgs mediator sector in place of the usual Froggatt-Nielsen messengers, with quark and lepton messengers, and provides significant improvements over existing models of this type having unsuppressed Yukawa couplings to the third generation and a simplified vacuum alignment mechanism. The neutrino mass differences are naturally less hierarchical than those of the quarks and charged leptons. Similarly the lepton mixing angles are much larger than those in the quark sector and have an approximate tri-bi-maximal (TB) mixing form for theta_{12} and theta_{23}. However the mixing angle theta_{13} is naturally much larger than in pure TB mixing and can be consistent with the value found in recent experiments. The magnitude of theta_{13} is correlated with a the predicted deviation of theta_{23} from bi-maximal mixing. The model has light familon fields that can significantly modify the associated SUSY phenomenology.