Triplet Fermions Research Articles

One-loop matching of the type-III seesaw model onto the Standard Model Effective Field Theory

In previous works [1, 2], we have performed the one-loop matching of both type-I and type-II seesaw models for neutrino masses onto the Standard Model Effective Field Theories (SMEFT). In the present paper, by matching the type-III seesaw model onto the SMEFT at the one-loop level, we complete this series of studies on the construction of low-energy effective field theories (EFTs) for the canonical seesaw models. After integrating out the heavy fermionic triplets in the type-III seesaw model via both functional and diagrammatic approaches, we find 33 dimension-six (dim-6) operators in the Warsaw basis and their Wilson coefficients, while the number of dim-6 operators is 31 (or 41) for the EFT of type-I (or type-II) seesaw model. Furthermore, we calculate the branching ratios of radiative decays of charged leptons in the EFT. Then, the relationship between the beta function of the quartic Higgs coupling λ in the full theory and that of λEFT in the EFT is clarified. Finally, we briefly discuss the phenomenological implications of three types of seesaw EFTs and propose working observables that are sensitive to the four-fermion operators, which could be used to distinguish among different seesaw models in collider experiments.

Anomaly-free dark matter models with one-loop neutrino masses and a gauged U(1) symmetry

We systematically study and classify scotogenic models with a local U(1) gauge symmetry. These models give rise to radiative neutrino masses and a stable dark matter candidate, but avoid the theoretical problems of global and discrete symmetries. We restrict the dark sector particle content to up to four scalar or fermionic SU(2) singlets, doublets or triplets and use theoretical arguments based on anomaly freedom, Lorentz and gauge symmetry to find all possible charge assignments of these particles. The U(1) symmetry can be broken by a new Higgs boson to a residual discrete symmetry, that still stabilizes the dark matter candidate. We list the particle content and charge assignments of all non-equivalent models. Specific examples in our class of models that have been studied previously in the literature are the U(1)D scotogenic and singlet-triplet scalar models breaking to Z2. We also briefly discuss the new phenomenological aspects of our model arising from the presence of a new massless dark photon or massive Z′ boson as well as the additional Higgs boson.

Probing Pauli susceptibility of [formula omitted]-borophene in the presence of gas molecules

Monolayer β12-borophene hosts two different Dirac and triplet fermions. Due to the large number of atoms in its unit cell, a description of their perturbed models leads to interesting phenomena. In this paper, we focus on an analytical tight-binding framework to describe the effect of adsorbed gas molecules on the magnetic properties of β12-borophene. We employ the Green’s function approach to calculate the Pauli spin paramagnetic susceptibility of the system. With this, we explain the peculiar characteristics of magnetic responses of the system depending on the position of gas molecules on the host boron atoms. From a wider perspective, these results can be useful for practical applications based on low-dimensional gas sensors.

Parallel seesaw mechanisms for neutrinos and freeze-in long-lived dark matter

If dark matter is light, it may be due to a seesaw mechanism just as neutrinos are. It is postulated that both originate from the same type of heavy fermion anchors, either singlets or triplets. In the latter case, a shift of the W mass is predicted, as suggested by the CDF precision measurement. A spontaneously broken dark U(1) gauge symmetry is assumed, resulting in freeze-in long-lived light dark matter.

Hadronic Isospin Helicity and the Consequent SU(4) Gauge Theory

A new approach to the Dirac equation and the associated hadronic symmetries is proposed. In this approach, we linearize the second Casimir operator of the Lorentz Group, which is defined by the energy–momentum four-vector and the fermion spin, thereby using the spinor-helicity representation instead of the three-vector representation of the particle momentum and spin vector. We then expand the so-obtained standard Dirac equation by employing an inner abstract “hadronic” isospin, initially describing a SU(2) fermion doublet. Application of the spin-helicity representation of that isospin leads to the occurrence of a quadruplet of inner states, revealing the SU(4) symmetry via the isospin helicity operator. This further leads to two independent fermion state spaces, specifically, singlet and triplet states, which we interpret as U(1) symmetry of the leptons and SU(3) symmetry of the three quarks, respectively. These results indicate the genuinely very different physical nature of the strong SU(4) symmetry in comparison to the chiral SU(2) symmetry. While our approach does not require the a priori concept of grand unification, such a notion arises naturally from the formulation with the isospin helicity. We then apply the powerful procedures developed for the electroweak interactions in the SM, in order to break the SU(4) symmetry by means of the Higgs mechanism involving a scalar Higgs field as an SU(4) quadruplet. Its finite vacuum creates the masses of the three vector bosons involved, which can change the three quarks into a lepton and vice versa. Finally, we consider a toy model for calculation of the strong coupling constant of a Yukawa potential.

Reviewing the prospect of fermion triplets as dark matter and source of baryon asymmetry in non-standard cosmology

Indirect searches of Dark Matter (DM), in conjugation with 'missing track searches' at the collider seem to confine SU(2) L fermion triplet DM (FTDM) mass within a narrow range around 1 TeV. The canonical picture of the pure FTDM is in tension since it is under-abundant for the said mass range. Several preceding studies have reported that an extra species (ϕ), redshifts faster than the radiation (∼ a (4+n) where n > 0), leads to a faster expanding early Universe by dominating in the energy density with an enhanced Hubble parameter. This has the potential to revive the under-abundant FTDM (ℤ2 odd, lightest generation) by causing freeze-out earlier without modifying the interaction strength between DM and thermal bath. On the other hand, although the CP asymmetry produced due to the decay of ℤ2 even heavier generations of the triplet remains unaffected, its evolution is greatly affected by the non-standard cosmology. It has been observed through numerical estimations that the minimum mass of the triplet, required to produce sufficient baryon asymmetry of the Universe (BAU), can be lowered up to two orders (compared to the standard cosmology) in this fast expansion scenario. The non-standard parameters n and Tr (a reference temperature below which radiation dominance prevails), which simultaneously control DM abundance as well as the frozen value of BAU, are tightly constrained from the observed experimental values. We have found that n is strictly bounded within the interval 0.4 ≲ n ≲ 1.8 where the upper bound is imposed by the BAU constraint whereas the lower bound arises to satisfy the correct DM abundance. It has been noticed that the restriction on Tr is not so stringent as it can vary from sub GeV to a few tens of GeV.

Neutrino phenomenology, W -mass anomaly, and muon ( g−2 ) in a minimal type-III seesaw model using a T′ modular symmetry

In this study, we attempt to introduce a model to illustrate neutrino phenomenology by incorporating two right-handed fermion triplet superfields, i.e., $\Sigma_{R_j}$, in the presence of the modular symmetry $\Gamma_3^\prime \simeq A_4^\prime$, a double cover of the $A_4$ modular symmetry. The motivation in utilizing double cover is, so far only even modular forms were considered for constructing modular invariant models, but, in this case, it is possible to extend the modular invariance approach to general integral weight modular forms, i.e., the odd weight modular forms. Hence, this type of amalgamation between $T^\prime$ modular symmetry and minimally extending the seesaw can correctly explain the neutrino phenomenology. Additionally, we have made an attempt to accommodate the most recent measurement of the $W$ boson mass, published by the CDF-II collaboration and shed some light on the recent results of muon $(g-2)$. Finally, we have discussed lepton flavor violation in order to establish a constraint on the mass of right-handed fermion.

Strain engineering of multi-interband optical transitions in β12-borophene

The optical conductivity of strained monolayer β12-borophene is investigated via the Kubo formula and the five-band tight-binding method. In our model, the hopping energy of electrons is modified by strain following the Harrison rule. We investigate the effect of these modifications on the electronic dispersion and optical conductivity. Our results indicate that inherent massless Dirac fermions become massive with tensile strain and that inherent triplet fermions are doubled with compressive strain. Moreover, the strain-induced longitudinal optical conductivity was found to show a redshift spectrum with both tensile and compressive strains, while a blueshift spectrum was appeared for the transverse/Hall optical conductivity. These results show that strain can tune both electronic properties of β12-borophene and relevant practical optoelectronic applications.

Origin of neutrino masses, dark matter, leptogenesis, and inflation in a seesaw model with triplets

We consider a new physics model, where the Standard Model (SM) is extended by hyperchargeless $Y=0$ triplet fermions and a Higgs triplet with hypercharge $Y=2$. The first two generation fermion triplets are even under the ${Z}_{2}$ transformation. In contrast, the third fermion triplet and scalar triplet are odd under the same ${Z}_{2}$ transformation. It is a unifying framework for the simultaneous explanation of neutrino mass and mixing, dark matter, baryogenesis, inflation, and reheating temperature of the Universe. The two ${Z}_{2}$ even neutral fermions explain the neutrino low energy variables, whereas the third one can serve as a viable dark matter candidate, explaining the exact relic density. The scalar triplet is coupled nonminimally to gravity and forms the inflaton. We calculate the inflationary parameters and find them consistent with the new Planck-2018 constraints. We also do the reheating analysis for the inflaton decays/annihilations to relativistic SM particles. The triplet fermions associated with ${Z}_{2}$ even sector can provide the observed baryon asymmetry of the Universe at the TeV scale.

The triplet Dirac seesaw in the view of the recent CDF-II W mass anomaly

In the present letter, a Dirac neutrino mass model is presented in the view of the new result on W boson mass of mWCDF−II=80.4335±0.0094 GeV, recently reported by the CDF-II experimental collaboration. The newly measured value of the W mass anomaly shows a 7-σ deviation from that predicted by the standard model. The model explains the CDF-II W boson mass anomaly by extending the standard model with hypercharge zero vector-like fermion triplet. Symmetry is amended with a global U(1)B−L which is broken with an hypercharge zero electroweak triplet. It is demonstrated that the model can successfully explain CDF-II result, Dirac neutrino mass origin, while satisfying standard model precision constraints and collider constraints with scalar and fermion triplet masses in the ranger 1.4 TeV−5.2 TeV and 100 TeV −1013 GeV, respectively.

Lowering the scale of fermion triplet leptogenesis with two Higgs doublets

In this paper, we consider the possibility of generating the observed baryon asymmetry of the Universe via leptogenesis in the context of triplet fermion mediated type-III seesaw model of neutrino mass. With a hierarchical spectrum of the additional fermions, the lower bound on the lightest triplet mass is $\sim 10^{10} {\rm~GeV}$ for successful leptogenesis, a couple of orders higher than that of the type-I case. We investigate the possibility of lowering this bound in the framework of two-Higgs-doublet models. We find that the bounds can be lowered down to $10^7$ GeV for a hierarchical spectrum. If we include the flavor effects, then a further lowering by one order of magnitude is possible. We also discuss if such lowering can be compatible with the naturalness bounds on the triplet mass.

A New Route to Symmetries through the Extended Dirac Equation

A new route to the Dirac equation and its symmetries is outlined on the basis of the four-vector representation of the Lorentz group (LG). This way permits one to linearize the first Casimir operator of the LG in terms of the energy–momentum four-vector and enables one to derive an extended Dirac equation that naturally reveals the SU(2) symmetry in connection with an isospin associated with the LG. The procedure gives a spin-one-half fermion doublet, which we interpret as the electron and neutrino or the up-and-down quark doublet. Similarly, the second Casimir operator can be linearized by invoking an abstract isospin that is not connected with the LG, but with the two basic empirical fermion types. Application of the spinor helicity formalism yields two independent singlet and triplet fermion states—which we interpret as being related to U(1) and the lepton, respectively—to the SU(3) symmetry group of the three colors of the quarks. The way in which we obtain these results indicates the genuine yet very different physical natures of these basic symmetries. This new notion does not need the idea of grand unification. However, by still combining them in the product group SU(4)=SU(3)⊗U(1) and then further combining all groups into SU(2)⊗SU(4), one may get a symmetry scheme that perhaps supports the notion of unification by the group SU(8). We also argue that the simpler SO(4) group—instead of SU(4)—seems more appropriate for achieving unification.

Far-field thermal properties of β12 borophene under an external electric field.

Borophene has been reported as the latest very promising 2D material. We theoretically investigate the thermal radiation of β12 borophene. β12 borophene has been composited on Ag substrate. Theoretical research frequently mentions three types of model of β12 borophene. The energy bands of the three models are different. Homogeneous and inversion symmetric models have a gapless Dirac cone near the K(K') point, while they are gapped in the inversion non-symmetric model. The homogeneous model has gapless triplet fermions and three-band touching points at high-symmetry points. The optical conductivity exhibits peaks due to the energy transition of high-symmetry points. The radiation spectrum follows Wien's displacement law in homogeneous and inversion symmetric models, while it is broken in the inversion non-symmetric model. The total energy radiation changes as the voltage increases for the three β12 borophene models. The radiation of energy can be controlled by applying a suitable voltage.

SU(5) grand unification and W-boson mass

A realistic extension of the minimal SU(5) theory consisting of the addition of an adjoint fermion is known to predict light real fermion and scalar weak triplets, potentially accessible at the LHC. These particles, in addition to playing a key role in gauge coupling unification, have profound phenomenological implications. The fermion triplet, that through the seesaw mechanism offers a testable origin of neutrino mass, has been already extensively discussed. The scalar triplet develops a vacuum expectation value that modifies the W-boson mass. We show that its low-energy effective theory is remarkably predictive: in the leading approximation, all the relevant physical processes involving the scalar triplet depend only on its mass and the deviation from the Standard Model W-mass value.

Type III seesaw under A_4 modular symmetry with leptogenesis

We make an attempt to study neutrino phenomenology in the framework of type-III seesaw by considering A_4 modular symmetry in the super-symmetric context. In addition, we have included a local U(1)_{B-L} symmetry which eventually helps us to avoid certain unwanted terms in the superpotential. Hitherto, the seesaw being type-III, it involves three fermion triplet superfields Sigma _R, along with which, we have included a singlet weighton field (rho ). In here, modular symmetry plays a crucial role by avoiding the usage of excess flavon (weighton) fields. Also, the Yukawa couplings acquire modular forms which are expressed in terms of Dedekind eta function eta (tau ). However, for numerical analysis we use q expansion expressions of these couplings. Therefore, the model discussed here is triumphant enough to accommodate the observed neutrino oscillation data and also successfully explains observed baryon asymmetry of the universe through leptogenesis.

WIMP and FIMP dark matter in singlet-triplet fermionic model

We present an extension of the SM involving three triplet fermions, one triplet scalar and one singlet fermion, which can explain both neutrino masses and dark matter. One triplet of fermions and the singlet are odd under a Z2 symmetry, thus the model features two possible dark matter candidates. The two remaining Z2-even triplet fermions can reproduce the neutrino masses and oscillation parameters consistent with observations. We consider the case where the singlet has feeble couplings while the triplet is weakly interacting and investigate the different possibilities for reproducing the observed dark matter relic density. This includes production of the triplet WIMP from freeze-out and from decay of the singlet as well as freeze-in production of the singlet from decay of particles that belong to the thermal bath or are thermally decoupled. While freeze-in production is usually dominated by decay processes, we also show cases where the annihilation of bath particles give substantial contribution to the final relic density. This occurs when the new scalars are below the TeV scale, thus in the reach of the LHC. The next-to-lightest odd particle can be long-lived and can alter the successful BBN predictions for the abundance of light elements, these constraints are relevant in both the scenarios where the singlet or the triplet are the long-lived particle. In the case where the triplet is the DM, the model is subject to constraints from ongoing direct, indirect and collider experiments. When the singlet is the DM, the triplet which is the next-to-lightest odd particle can be long-lived and can be probed at the proposed MATHUSLA detector. Finally we also address the detection prospects of triplet fermions and scalars at the LHC.

Optical redshift and blueshift spectra in monolayer β12 -borophene: Inversion symmetry breaking effects

We have calculated the optical conductivity of monolayer ${\ensuremath{\beta}}_{12}$-borophene in the presence of an inversion symmetry breaking (ISB) field. We theoretically formulate such a field to effectively be induced by a substrate through an orbital hybridization effect in the experimental growth process. In the electronic band structure, the effect of the ISB field on the anisotropic dispersion appears as a perturbed manipulation of the energy scale. Different orientations of dispersion of triplet and Dirac fermions in ${\ensuremath{\beta}}_{12}$-borophene cause anisotropic optical interband transitions. Simulated ISB-induced optical conductivity using the Kubo formula produces various optical redshift and blueshift spectra. The longitudinal (Hall) component of optical conductivity presents a pure redshift (blueshift) spectrum with the ISB field, whereas the coexistence of both redshift and blueshift spectra emerge for the transverse component. This paper is a handful for practical applications in two-dimensional-based optoelectronic devices.

Flavour anomalies and dark matter assisted unification in SO(10) GUT

With the recent experimental hint of new physics from flavor physics anomalies, combined with the evidence from neutrino masses and dark matter, we consider a minimal extension of SM with a scalar leptoquark and a fermion triplet. The scalar leptoquark with couplings to leptons and quarks can explain lepton flavor non-universality observables RK, {R}_{K^{left(ast right)}} , {R}_{D^{left(ast right)}} and RJ/ψ. Neutral component of fermion triplet provides current abundance of dark matter in the Universe. The interesting feature of the proposal is that the minimal addition of these phenomenologically rich particles (scalar leptoquark and fermion triplet) assist in realizing the unification of the gauge couplings associated with the strong and electroweak forces of standard model when embedded in the non-supersymmetric SO(10) grand unified theory. We discuss on unification mass scale and the corresponding proton decay constraints while taking into account the GUT threshold corrections.

S.M.A.S.H.E.D.: Standard Model Axion Seesaw Higgs inflation Extended for Dirac neutrinos

Inspired by the S.M.A.S.H. framework we construct a model that addresses the strong CP problem, axion dark matter, inflation and Dirac neutrino masses as well as leptogenesis. The model possesses only two dynamical scales, namely the SM breaking scale vH and the Peccei Quinn (PQ) breaking scale v .We introduce heavy vector-like quarks in the usual KSVZ fashion to implement the PQ mechanism for the strong CP problem. To generate neutrino masses via a dimension six operator scaling as mν ∼ v 3 H / v 2 σ we add heavy triplet and doublet leptons, which are vector-like under the SM but chiral under PQ symmetry. The model is free from the cosmological domain wall problem and predicts an axion to photon coupling which is about an order of magnitude larger than in conventional DFSZ and KSVZ models. Thus our scenario can be probed and potentially excluded by current and next generation axion experiments such as ORGAN or MADMAX.In addition we numerically demonstrate that our construction can generate the observed baryon asymmetry by realizing a version of the Dirac-Leptogenesis scenario. As a consequence of our neutrino mass mechanism we find that the asymmetry in triplet fermion decays can also be significantly enhanced by up to six orders of magnitude when compared to typical Seesaw scenarios without needing to invoke a resonant enhancement.In passing we note that a decaying Dirac fermion with multiple decay modes contains all the necessary ingredients required for the “quasi optimal efficiency”-scenario previously encountered in the context decaying scalar triplets. The impact of the right handed neutrinos and the axion on ΔN eff is estimated and lies within current bounds.

Displaced vertex and disappearing track signatures in type-III seesaw

We investigate a prospect of probing the type-III seesaw neutrino mass generation mechanism at various collider experiments by searching for a disappearing track and a displaced vertex signature originating from the decay of SU(2)_L triplet fermion (Sigma ). Since Sigma is primarily produced at colliders through the electroweak gauge interactions, its production rate is uniquely determined by its mass. We find that a Sigma particle produces a disappearing track signature from the decay of its charged component, which can be searched at the HL-LHC. Furthermore, we show that if the lightest observed neutrino has a mass of around 10^{-9} eV, the neutral component of {Sigma } can be discovered at the proposed MATHUSLA detector. We also show that the charged component of {Sigma } can be potentially be observed at FCC-he as a displaced vertex signature.