Flavon Fields Research Articles

T′ models with high quality flaxions

The "gauged'' Peccei-Quinn (PQ) mechanism of Fukuda, Ibe, Suzuki and Yanagida is implemented in the flavorful axion model of Carone and Merchand. This model of flavor is similar to other successful ones based on the double tetrahedral group, but the flavor symmetry includes a global U(1) factor that leads to the presence of a flavorful axion. Here we gauge that U(1) symmetry and introduce a heavy sector that includes (1) the fermions necessary to cancel anomalies and (2) a second scalar flavon field that spontaneously breaks the U(1) symmetry. The full theory has an accidental U(1)$\times$U(1)$'$ global symmetry, anomalous with respect to QCD; U(1)$_\text{PQ}$ emerges as a linear combination. The gauged flavor symmetry restricts the possible PQ symmetry-breaking higher-dimension operators so that sufficient axion quality is preserved. We provide a model of the quark sector, as a proof of principle, and then a model which incorporates the standard model charged leptons as well. In both cases, the charge assignments that lead to acceptable axion quality also lead to a multiplicity of some of the heavy sector states; we check that the Landau pole for hypercharge remains above the cut off of the effective theory. We consider relevant phenomenological constraints on these models including those on the predicted axion couplings.

Flavon alignments from orbifolding: SU(5) \xd7 SU(3) model with \U0001d54b6/\u2206(54)

We systematically develop the formalism necessary for ensuring that boundary conditions of flavon fields in extra dimensions are consistent with heterotic string theory. Having developed a set of consistency conditions on the boundary conditions, we explore a series of examples of orbifolds in various dimensions to see which ones can satisfy them. In addition we impose the further phenomenological requirements of having non-trivial flavon vacuum alignments and also of having quarks and leptons located appropriately in extra dimensions. The minimal successful case seems to be a 10d theory with a SU(3)fl gauged flavour symmetry, where the six-dimensional torus is compactified on a \U0001d54b6/∆(54) orbifold. We construct a realistic SU(5) grand unified theory along these lines, leading to tribimaximal-reactor lepton mixing, which we show to be consistent with current neutrino data.

Modular A4 symmetry models of neutrinos and charged leptons

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with A4 modular symmetry, where the only flavon field is the single modulus field τ, and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of A4. Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of 1, 1′ and 1′′ representations of A4, using the simplest different modular weights to break the degeneracy, leading to ten different charged lepton Yukawa matrices, instead of the usual one. This implies ten different Weinberg models and thirty different type I seesaw models, which we analyse in detail. We find that fourteen models for both NO and IO neutrino mass ordering can accommodate the data, as compared to one in previous analyses, providing many new possibilities.

Effective alignments and the landscape of S4 flavor models

We explore the concept of effective alignments: contractions of multiple flavour symmetry breaking flavon fields. These contractions give rise to directions that are hard or impossible to obtain directly by breaking the flavour symmetry. Within this context, and using $S_4$ as the flavour symmetry to exemplify, we perform a phenomenological check of lepton flavour models built from pairing any two effective alignments up to order 2 (in flavon contractions). The check is performed for each pair of effective alignments in a framework with models of constrained sequential dominance type, in a basis where the charged leptons are diagonal. We thus obtain an indication of which effective alignments are interesting for model building, within this so-called $S_4$ landscape. We find three types of viable topologies and provide examples of models realizing this strategy for each topology.

Baryogenesis from flavon decays

Many popular attempts to explain the observed patterns of fermion masses involve a flavon field. Such weakly coupled scalar fields tend to dominate the energy density of the Universe before they decay. If the flavon decay happens close to the electroweak transition, the right-handed electrons stay out of equilibrium until the sphalerons shut off. We show that an asymmetry in the right-handed charged leptons produced in the decay of a flavon can explain the baryon asymmetry of the Universe.

Cosmological constraints on light flavons

The Froggatt-Nielsen mechanism is a well-motivated framework for generating the fermion mass hierarchy. This mechanism introduces flavons, complex scalars which are singlet under the Standard Model gauge symmetry and charged under a new global family symmetry. We make use of a leptophilic flavon to produce the charged lepton Yukawa matrix. The real part of the flavon mixes with the Higgs boson and introduces lepton flavour violating interactions which are bounded by experiment. The imaginary part of the flavon, η, is a long-lived light particle, whose abundance is restricted by cosmological observations. For mη< 2me where the decay of η to charged leptons is kinematically forbidden, we identify allowed regions of mη with respect to the vacuum expectation value of the flavon field where all experimental and cosmological constraints are satisfied.

Modular S4 models of lepton masses and mixing

We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group Γ4 ≃ S4. We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter sin2θ23 and i) the Dirac CPV phase δ, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries ℤ3ST and ℤ2S respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus.

Flavon stabilization in models with discrete flavor symmetry

We propose a simple mechanism for stabilizing flavon fields with aligned vacuum structure in models with discrete flavor symmetry. The basic idea is that flavons are stabilized by the balance between the negative soft mass and non-renormalizable terms in the potential. We explicitly discuss how our mechanism works in A4 flavor model, and show that the field content is significantly simplified. It also works as a natural solution to the cosmological domain wall problem.

A_4 realization of linear seesaw and neutrino phenomenology

Motivated by the crucial role played by the discrete flavor symmetry groups in explaining the observed neutrino oscillation data, we consider the A_4 realization of linear seesaw by extending the standard model (SM) particle content with two types of right-handed (RH) neutrinos along with the flavon fields, and the SM symmetry with A_4times Z_4times Z_3 and a global symmetry U(1)_X, which is broken explicitly by the Higgs potential. We scrutinize this model to see if it can explain the recent results from neutrino oscillation experiments, by searching for parameter space that can accommodate the observables such as the reactor mixing angle theta _{13}, the CP violating phase delta _text {CP}, sum of active neutrino masses Sigma _{i} m_i, solar and atmospheric mass-squared differences, and the lepton number violating parameter called the effective Majorana mass parameter, in line with recent experimental results. We also discuss the scope of this model to explain the baryon asymmetry of the Universe through leptogenesis. We also investigate the possibility of probing the non-unitarity effect in this scenario, but it is found to be rather small.

Common origin of dirac neutrino mass and freeze-in massive particle dark matter

Motivated by the fact that the origin of tiny Dirac neutrino masses via the standard model Higgs field and non-thermal dark matter populating the Universe via freeze-in mechanism require tiny dimensionless couplings of similar order of magnitudes (∼ 10−12), we propose a framework that can dynamically generate such couplings in a unified manner. Adopting a flavour symmetric approach based on A4 group, we construct a model where Dirac neutrino coupling to the standard model Higgs and dark matter coupling to its mother particle occur at dimension six level involving the same flavon fields, thereby generating the effective Yukawa coupling of same order of magnitudes. The mother particle for dark matter, a complex scalar singlet, gets thermally produced in the early Universe through Higgs portal couplings followed by its thermal freeze-out and then decay into the dark matter candidates giving rise to the freeze-in dark matter scenario. Some parts of the Higgs portal couplings of the mother particle can also be excluded by collider constraints on invisible decay rate of the standard model like Higgs boson. We show that the correct neutrino oscillation data can be successfully produced in the model which predicts normal hierarchical neutrino mass. The model also predicts the atmospheric angle to be in the lower octant if the Dirac CP phase lies close to the presently preferred maximal value.

Fully constrained Majorana neutrino mass matrices using varvec{varSigma (72times 3)}

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (nu _2) columns, namely tri-chi-maximal mixing (text {T}chi text {M}) and tri-phi-maximal mixing (text {T}phi text {M}), were proposed. In 2012, it was shown that text {T}chi text {M} with chi =pm ,frac{pi }{16} as well as text {T}phi text {M} with phi = pm ,frac{pi }{16} leads to the solution, sin ^2 theta _{13} = frac{2}{3} sin ^2 frac{pi }{16}, consistent with the latest measurements of the reactor mixing angle, theta _{13}. To obtain text {T}chi text {M}_{(chi =pm ,frac{pi }{16})} and text {T}phi text {M}_{(phi =pm ,frac{pi }{16})}, the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, m_1:m_2:m_3=frac{left( 2+sqrt{2}right) }{1+sqrt{2(2+sqrt{2})}}:1:frac{left( 2+sqrt{2}right) }{-1+sqrt{2(2+sqrt{2})}}. In this paper we construct a flavour model based on the discrete group varSigma (72times 3) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric 3times 3 matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of varSigma (72times 3). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.

Connecting nonzero θ13, Dirac CP phase and leptogenesis through spontaneous CP violation

We have analyzed a Type-I+II seesaw scenario to generate neutrino masses and mixing in a A4 based flavor symmetric framework. The Standard Model (SM) particle content is extended by three singlet right handed neutrinos, an additional higgs triplet along with few SM singlet flavon fields. In this set-up, the pure type-I contribution to the neutrino mass matrix exhibits a tribimaximal (TBM) of lepton mixing where the triplet contribution generates θ13. Complex vev of one flavon provides a unique source of spontaneous CP violation. Here it turns out that the triplet contribution provides a common source for θ13, Dirac CP phase (δ) and CP violation required for leptogenesis.

Flavon-induced lepton flavour violation

ATLAS and CMS have observed a flavor violating decay of the Higgs to muon and tau. The fact that flavour violating couplings of the Higgs boson are exactly zero in the Standard Model suggests the mixing of the Higgs with another scalar with flavour violating couplings. We use the flavon field from the Froggatt-Nielsen mechanism, responsible for generating the lepton Yukawa matrices, for this purpose. The parameter space is constrained from experimental bounds on charged lepton flavor violation in other processes, however, we show that a substantial region of parameter space survives these bounds while producing a large enough Br(h → μτ).

Higgs couplings and new signals from Flavon–Higgs mixing effects within multi-scalar models

Testing the properties of the Higgs particle discovered at the LHC and searching for new physics signals, are some of the most important tasks of Particle Physics today. Current measurements of the Higgs couplings to fermions and gauge bosons, seem consistent with the Standard Model, and when taken as a function of the particle mass, should lay on a single line. However, in models with an extended Higgs sector the diagonal Higgs couplings to up-quarks, down-quarks and charged leptons, could lay on different lines, while non-diagonal flavor-violating Higgs couplings could appear too. We describe these possibilities within the context of multi-Higgs doublet models that employ the Froggatt–Nielsen (FN) mechanism to generate the Yukawa hierarchies. Furthermore, one of the doublets can be chosen to be of the inert type, which provides a viable dark matter candidate. The mixing of the Higgs doublets with the flavon field, can provide plenty of interesting signals, including: i) small corrections to the couplings of the SM-like Higgs, ii) exotic signals from the flavon fields, iii) new signatures from the heavy Higgs bosons. These aspects are studied within a specific model with 3+1 Higgs doublets and a singlet FN field. Constraints on the model are derived from the study of K and D mixing and the Higgs search at the LHC. For last, the implications from the latter aforementioned constraints to the FCNC top decay t→ch are presented too.

Hunting the flavon

The next generation of experiments in particle physics will for the first time systematically test flavor physics models based on flavon fields. Starting from the current quark-flavor constraints on such models we show how the new generation of lepton flavor experiments will dominate indirect searches in the coming decades. A future 100 TeV hadron collider will then be the first experiment to probe flavons as propagating degrees of freedom. Our estimate of the collider reach relies on a proper treatment of backgrounds and detector effects. Complementary searches for indirect effects in lepton flavor experiments and propagating degrees of freedom at colliders are very limited at the LHC, but will be a new feature at a 100 TeV hadron collider.

SUSY SU(5)×S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS

We propose an $S_{4}$ flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of \textbf{10} dimensional representations in SU(5) are all assigned to be $1_{1}$ of $S_{4}$. The second generation of \textbf{10} is to be $1_{2}$ of $S_{4}$. Right-handed neutrinos of singlet \textbf{1} and three generations of $\bar{\textbf{5}}$ are all assigned to be $3_{1}$ of $S_{4}$. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is $\langle\Phi^{\nu}\rangle \sim \lambda_{c}\langle\Phi^{e}\rangle$. Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification $m_{\tau}=m_{b}$ and the popular Georgi-Jarlskog relation $m_{\mu}=3m_{s}$ as well as a new mass relation $m_{e}=\frac{8}{27}m_{d}$ in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field $H_{24}$. The GUT relation leads to a sizable mixing angle $\theta^{e}_{12} \sim \theta_{c}$ and the correct quark mixing matrix $V_{CKM}$ can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing $\theta^{\nu}_{13}$ in TBM mixing to a large $\theta^{PMNS}_{13}\simeq\theta_{c}/\sqrt{2}$, in excellent agreement with experimental results. A Dirac CP violation phase $\phi_{12}\simeq\pm\pi/2$ is required to make the deviation from $\theta^{\nu}_{12}$ small. We also present some phenomenological numerical results predicted by the model.

Warped flavor symmetry predictions for neutrino physics

A realistic five-dimensional warped scenario with all standard model fields propagating in the bulk is proposed. Mass hierarchies would in principle be accounted for by judicious choices of the bulk mass parameters, while fermion mixing angles are restricted by a $\Delta(27)$ flavor symmetry broken on the branes by flavon fields. The latter gives stringent predictions for the neutrino mixing parameters, and the Dirac CP violation phase, all described in terms of only two independent parameters at leading order. The scheme also gives an adequate CKM fit and should be testable within upcoming oscillation experiments.

Combining Pati-Salam and flavour symmetries

We construct an extension of the Standard Model (SM) which is based on grand unification with Pati-Salam symmetry. The setup is supplemented with the idea of spontaneous flavour symmetry breaking which is mediated through flavon fields with renormalizable couplings to new heavy fermions. While we argue that the new gauge bosons in this approach can be sufficiently heavy to be irrelevant at low energies, the fermionic partners of the SM quarks, in particular those for the third generation, can be relatively light and provide new sources of flavour violation. The size of the effects is constrained by the observed values of the SM Yukawa matrices, but in a way that is different from the standard minimal-flavour violation approach. We determine characteristic deviations from the SM that could eventually be observed in future precision measurements.

Constraining a type I seesaw model withA4flavor symmetry from neutrino data and leptogenesis

We study a type I seesaw model of neutrino masses within the framework of $A_4$ flavor symmetry. Incorporating the presence of both singlet and triplet flavons under $A_4$ symmetry, we construct the leptonic mass matrices involved in type I seesaw mechanism. We then construct the light neutrino mass matrix using the $3\sigma$ values of neutrino oscillation parameters keeping the presently undetermined parameters namely, the lightest neutrino mass $m_{\text{lightest}}$, one Dirac CP phase $\delta$ and two Majorana phases $\alpha, \beta$ as free parameters. Comparing the mass matrices derived using $A_4$ parameters as well as light neutrino parameters, we then evaluate all the $A_4$ parameters in terms of light neutrino parameters. Assuming some specific vacuum alignments of $A_4$ triplet flavon field, we then numerically evaluate all the free parameters in the light neutrino sector, using which we also find out the remaining $A_4$ parameters. We then use the numerical values of these parameters to calculate baryon asymmetry through the mechanism of leptogenesis. We not only constrain the $A_4$ vacuum alignments from the requirement of successful leptogenesis, but also constrain the free parameters in the light neutrino sector $(m_{\text{lightest}}, \delta, \alpha, \beta)$ to certain range of values. These values can be tested in ongoing and future neutrino experiments providing a way to discriminate between different possible $A_4$ vacuum alignments discussed in this work.

Flavored Peccei-Quinn symmetry

In an attempt to uncover any underlying physics in the standard model (SM), we suggest a $\mu$--$\tau$ power law in the lepton sector, such that relatively large 13 mixing angle with bi-large ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong CP problem, in a way that no domain wall problem occurs, based on $A_{4}\times U(1)_{X}$ symmetry in a supersymmetric framework. Here we refer to the global $U(1)_X$ symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry". In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under $U(1)_X$, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected each other. So, the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around $10^{12}$ GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay and axion. We examine the model predictions, arisen from the $\mu$--$\tau$ power law, on leptonic $CP$ violation, neutrinoless double beta decay and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass $m_a\simeq2.53\times10^{-5}$ eV and the axion coupling to photon $g_{a\gamma\gamma}\simeq1.33\times10^{-15}~{\rm GeV}^{-1}$. And subsequently the square of the ratio between them is shown to be 1 or 2 orders of magnitude lower than that of the conventional axion model.