Dirac Mass Terms Research Articles

Generalised CP and trimaximal TM1 lepton mixing in [formula omitted] family symmetry

We construct two flavor models based on S4 family symmetry and generalised CP symmetry. In both models, the S4 family symmetry is broken down to the Z2SU subgroup in the neutrino sector, as a consequence, the trimaximal TM1 lepton mixing is produced. Depending on the free parameters in the flavon potential, the Dirac CP is predicted to be either conserved or maximally broken, and the Majorana CP phases are trivial. The two models differ in the neutrino sector. The flavon fields are involved in the Dirac mass terms at leading order in the first model, and the neutrino mass matrix contains three real parameters such that the absolute neutrino masses are fixed. Nevertheless, the flavon fields enter into the Majorana mass terms at leading order in the second model. The leading order lepton mixing is of the tri-bimaximal form which is broken down to TM1 by the next to leading order contributions.

Stability of surface states of weakZ2topological insulators and superconductors

We study the stability against disorder of surface states of weak $\mathbb{Z}_2$ topological insulators (superconductors) which are stacks of strong $\mathbb{Z}_2$ topological insulators (superconductors), considering representative Dirac Hamiltonians in the Altland-Zirnbauer symmetry classes in various spatial dimensions. We show that, in the absence of disorder, surface Dirac fermions of weak $\mathbb{Z}_2$ topological insulators (superconductors) can be gapped out by a Dirac mass term which couples surface Dirac cones and leads to breaking of a translation symmetry (dimerization). The dimerization mass is a unique Dirac mass term in the surface Dirac Hamiltonian, and the two dimerized gapped phases which differ in the sign of the Dirac mass are distinguished by a $\mathbb{Z}_2$ index. In other words the dimerized surfaces can be regarded as a strong $\mathbb{Z}_2$ topological insulator (superconductor). We argue that the surface states are not localized by disorder when the ensemble average of the Dirac mass term vanishes.

Mapping Dirac gaugino masses

We investigate the mapping of Dirac gaugino masses through regions of strong coupling, focussing on SQCD with an adjoint. These models have a well-known Kutasov duality, under which a weakly coupled electric UV description can flow to a different weakly coupled magnetic IR description. We provide evidence to show that Dirac gaugino mass terms map as lim_{mu->infty} mD/(g kappa^{1/(k+1}} = lim_{mu->0} tilde{mD}/(tilde{g} tilde{kappa}^{1/(k+1}} under such a flow, where the coupling kappa appears in the superpotential of the canonically normalised theory as W \supset kappa X^{k+1}. This combination is an RG-invariant to all orders in perturbation theory, but establishing the mapping in its entirety is not straightforward because Dirac masses are not the spurions of holomorphic couplings in the N=1 theory. To circumvent this, we first demonstrate that deforming the Kutasov theory can make it flow to an N=2 theory with parametrically small N=1 deformations. Using harmonic superspace techniques we then show that the N=1 deformations can be recovered from electric and magnetic FI-terms that break N=2 -> N=1, and also show that pure Dirac mass terms can be induced by the same mechanism. We then find that the proposed RG-invariant is indeed preserved under N=2 duality, and thence along the flow to the dual N=1 Kutasov theories. Possible phenomenological applications are discussed.

Bulk Majorana mass terms and Dirac neutrinos in the Randall-Sundrum model

We present a novel scheme where Dirac neutrinos are realized even if lepton number violating Majorana mass terms are present. The setup is the Randall-Sundrum framework with bulk right handed neutrinos. Bulk mass terms of both Majorana and Dirac type are considered. It is shown that massless zero mode solutions exist when the bulk Dirac mass term is set to zero. In this limit, it is found that the effective 4D small neutrino mass is primarily of Dirac nature with the Majorana type contributions being negligible. Interestingly, this scenario is very similar to the one known with flat extra dimensions. Neutrino phenomenology is discussed by fitting both charged lepton masses and neutrino masses simultaneously. A single Higgs localised on the IR brane is highly constrained as unnaturally large Yukawa couplings are required to fit charged lepton masses. A simple extension with two Higgs doublets is presented which facilitates a proper fit for the lepton masses.

Topological classification with additional symmetries from Clifford algebras

We classify topological insulators and superconductors in the presence of additional symmetries such as reflection or mirror symmetries. For each member of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra defined by operators of the generic (time-reversal, particle-hole, or chiral) symmetries and additional symmetries, together with gamma matrices in Dirac Hamiltonians representing topological insulators and superconductors. Following Kitaev's approach, we classify gapped phases of noninteracting fermions under additional symmetries by examining all possible distinct Dirac mass terms which can be added to the set of generators of the Clifford algebra. We find that imposing additional symmetries in effect changes symmetry classes and causes shifts in the periodic table of topological insulators and superconductors. Our results are in agreement with the classification under reflection symmetry recently reported by Chiu, Yao, and Ryu [Phys. Rev. B 88, 075142 (2013)]. Several examples are discussed including a topological crystalline insulator with mirror Chern numbers and mirror superconductors.

Correction: Corrigendum: Topological crystalline insulators in the SnTe material class

Nature Communications 3: Article number: 982 (2012); Published: 31 July 2012; Updated: 21 May 2013. In the Discussion section of this Article, we incorrectly claimed that an in-plane magnetic field will generate Dirac mass terms for the surface states. Instead, the in-plane magnetic field merely shifts the location of the Dirac points.

SARAH 3.2: Dirac gauginos, UFO output, and more

SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/OMEGA. The newest version of SARAH now provides the possibility to create model files in the UFO format which is supported by MadGraph 5, MadAnalysis, GoSam, and soon by Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and one-loop corrections to the mass spectrum. This information is used to write source code for SPheno in order to create a precision spectrum generator for the given model. This spectrum-generator-generator functionality as well as the output of WHIZARD and CalcHep model files have seen further improvement in this version. Also models including Dirac Gauginos are supported with the new version of SARAH, and additional checks for the consistency of model implementations have been created.

Constraints on universal extra dimensions fromW′searches

We obtain constraints on three universal extra-dimensional models utilizing limits from the CMS Collaboration on ${W}^{\ensuremath{'}}$ production and decay into a single-top-quark final state. We find a weak constraint on the minimal universal extra-dimensional model due to small Kaluza-Klein number violating terms. In contrast, the ${W}^{\ensuremath{'}}$ search puts a strong limit on the size of the Dirac mass term of the quarks in split universal extra-dimension models. In nonminimal universal extra-dimension models, the ${W}^{\ensuremath{'}}$ search constrains the splitting between the boundary-localized kinetic terms of the gauge bosons and the quarks. Each of these bounds can be translated into constraints on the mass splitting between the Kaluza-Klein excitations of the $SU(2)$ charged quarks and the Klauza-Klein excitations of the $W$ boson.

The fermion mass hierarchy in models with warped extra dimensions and a bulk Higgs

The phenomenological implications of allowing the Higgs to propagate in both AdS${}_5$ and a class of asymptotically AdS spaces are considered. Without tuning, the vacuum expectation value (VEV) of the Higgs is peaked towards the IR tip of the space and hence such a scenario still offers a potential resolution to the gauge-hierarchy problem. When the exponent of the Higgs VEV is approximately two and one assumes order one Yukawa couplings, then the fermion Dirac mass term is found to range from $\sim 10^{-5}$ eV to $\sim 200$ GeV in approximate agreement with the observed fermion masses. However, this result is sensitive to the exponent of the Higgs VEV, which is a free parameter. This paper offers a number of phenomenological and theoretical motivations for considering an exponent of two to be the optimal value. In particular, the exponent is bounded from below by the Breitenlohner-Freedman bound and the requirement that the dual theory resolves the gauge hierarchy problem. While, in the model considered, if the exponent is too large, electroweak symmetry may not be broken. In addition, the holographic method is used to demonstrate, in generality, that the flatter the Higgs VEV, the smaller the contribution to the electroweak $T$ parameter. In addition, the constraints from a large class of gauge mediated and scalar mediated flavour changing neutral currents, will be at minimal values for flatter Higgs VEVs. Some initial steps are taken to investigate the physical scalar degrees of freedom that arise from a mixing between the $W_5/Z_5$ components and the Higgs components.

Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory

We consider Yukawa couplings in a θ-exact approach to noncommutative gauge field theory and show that both Dirac and singlet Majorana neutrino mass terms can be consistently accommodated. This shows that in fact the whole neutrino-mass extended standard model on noncommutative spacetime can be formulated in the new nonperturbative (in θ) approach which eliminates the previous restriction of Seiberg–Witten map based theories to low-energy phenomena. Spacetime noncommutativity induced couplings between neutrinos and photons as well as Z-bosons appear quite naturally in the model. We derive relevant Feynman rules for the type I seesaw mechanism.

Quantum Hall Effects in Silicene

We investigate quantum Hall effects in silicene by applying electric field E z parallel to magnetic field. Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, and shares almost every remarkable property with graphene. A new feature is its buckled structure, due to which the band structure can be controlled externally by changing E z . The low energy physics of silicene is described by massive Dirac fermions, where the mass is a function of E z and becomes zero at the critical field E cr . We show that there are no zero energy states due to the Dirac mass term except at the critical electric field E cr . Furthermore it is shown that the 4-fold degenerate zero-energy states are completely resolved even without considering Coulomb interactions. These features are highly contrasted with those in graphene, demonstrating that silicene has a richer structure. The prominent feature is that, by applying the electric field, we can control the valley degeneracy. As a function of E z , Hall plateaux appear at the filling factors ν= 0, ±1, ±2, ±3, ... except for the points where level crossings occur.

TeV-scale seesaw model with a loop-induced Dirac mass term and dark matter fromU(1)B−Lgauge symmetry breaking

We show a TeV-scale seesaw model where Majorana neutrino masses, the dark matter mass, and stability of the dark matter can be all originated from the $U(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ gauge symmetry. Dirac mass terms for neutrinos are forbidden at the tree level by $U(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$, and they are induced at the one-loop level by spontaneous $U(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ breaking. The right-handed neutrinos can be naturally at the TeV scale or below because of the induced Dirac mass terms with loop suppression. Such right-handed neutrinos would be discovered at the CERN Large Hadron Collider. On the other hand, stability of the dark matter is guaranteed without introducing an additional ${Z}_{2}$ symmetry by a remaining global $U(1)$ symmetry after the $U(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ breaking. A Dirac fermion ${\ensuremath{\Psi}}_{1}$ or a complex neutral scalar ${s}_{1}^{0}$ is the dark matter candidate in this model. Since the dark matter (${\ensuremath{\Psi}}_{1}$ or ${s}_{1}^{0}$) has its own $\mathrm{B}\ensuremath{-}\mathrm{L}$ charge, the invisible decay of the $U(1{)}_{\mathrm{B}\ensuremath{-}\mathrm{L}}$ gauge boson ${Z}^{\ensuremath{'}}$ is enhanced. Experimental constraints on the model are considered, and the collider phenomenology at the LHC as well as future linear colliders is discussed briefly.

Quantum Hall effect in a singly and doubly connected three-dimensional topological insulator

The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy spectrum is found for a singly and doubly connected geometry. This is in turn used to argue that the way to measure the quantized Hall conductivity is to perform the Laughlin's flux ramping experiment and measure the charge transferred from the inner to the outer surface, analogous to the experiment in Ref.[2]. Unlike the Hall bar setup used currently, this has the advantage of being free of the contamination from the delocalized continuum of the surface edge states. In the presence of the Zeeman coupling, and/or interaction driven Quantum Hall ferromagnetism, which translate into the Dirac mass term, the quantized charge Hall conductivity sigma_{xy}=n e^2/h, with n=0,\pm 1,\pm 3,\pm 5... Backgating of one of the surfaces leads to additional Landau level splitting and in this case n can be any integer.

Higgs quadruplet for the type III seesaw model and implications forμ→eγandμ−econversion

In Type III seesaw model the heavy neutrinos are contained in leptonic triplet representations. The Yukawa couplings of the triplet fermion and the left-handed neutrinos with the doublet Higgs field produce the Dirac mass terms. Together with the Majorana masses for the leptonic triplets, the light neutrinos obtain non-zero seesaw masses. We point out that it is also possible to have a quadruplet Higgs field to produce the Dirac mass terms to facilitate the seesaw mechanism. The vacuum expectation value of the quadruplet Higgs is constrained to be small by electroweak precision data. Therefore the Yukawa couplings of a quadruplet can be much larger than those for a doublet. We also find that unlike the usual Type III seesaw model where at least two copies of leptonic triplets are needed, with both doublet and quadruplet Higgs representations, just one leptonic triplet is possible to have a phenomenologically acceptable model because light neutrino masses can receive sizable contributions at both tree and one loop levels. Large Yukawa couplings of the quadruplet can induce observable effects for lepton flavor violating processes $\mu \to e \gamma$ and $\mu - e$ conversion. Implications of the recent $\mu \to e\gamma$ limit from MEG and also limit on $\mu - e $ conversion on Au are also given. Some interesting collider signatures for the doubly charged Higgs boson in the quadruplet are discussed.

Light neutrinos from massless texture and below TeV seesaw scale

We present general conditions on Dirac and Majorana mass terms under which a type-I seesaw mechanism can lead to three exactly massless neutrinos at the tree level. We depict several examples where the conditions are satisfied and relate some of them to an underlying U(1) symmetry. We show that higher order corrections may generate the small observed masses and this may be achieved even when the heavy Majorana neutrinos are at the electroweak scale or a little higher.

Long lived fourth generation and the Higgs

A chiral fourth generation is a simple and well motivated extension of the standard model, and has important consequences for Higgs phenomenology. Here we consider a scenario where the fourth generation neutrinos are long lived and have both a Dirac and Majorana mass term. Such neutrinos can be as light as 40 GeV and can be the dominant decay mode of the Higgs boson for Higgs masses below the W-boson threshold. We study the effect of the Majorana mass term on the Higgs branching fractions and reevaluate the Tevatron constraints on the Higgs mass. We discuss the prospects for the LHC to detect the semi-invisible Higgs decays into fourth generation neutrino pairs. Under the assumption that the lightest fourth generation neutrino is stable, it's thermal relic density can be up to 20% of the observed dark matter density in the universe. This is in agreement with current constraints on the spin dependent neutrino-neutron cross section, but can be probed by the next generation of dark matter direct detection experiments.

Inverse seesaw in supersymmetry

We study a mechanism where tiny neutrino masses arise only from radiative contribution in a supersymmetric model. Without tuning the Higgs vev or Yukawa coupling, the tree-level light neutrino mass is rotated away by introducing a new singlet neutrino sL that forms a Dirac mass term with the right-handed neutrino nR in each generation. Even with the U(1)Lep lepton number violation term as non-zero right-handed Majorana neutrino mass MRnRc¯nR, the lightest neutrino remains massless at tree level due to an approximate symmetry. Consequently, tiny neutrino masses then only arise from radiative contributions and the right-handed neutrino Majorana mass MR can be at O(keV) to give rise to the correct light neutrino mass at O(eV). Supersymmetry ensures that the Majorana neutrino masses MRnRc¯nR and MR⁎sLc¯sL are not generated simultaneously.

Schizophrenic active neutrinos and exotic sterile neutrinos

We implement a schizophrenic scenario for the active neutrinos in a model in which there are also exotic right-handed neutrinos making a model with a local U(1)B−L anomaly free. Two of right-handed neutrinos carry B−L=−4 while the third one carries B−L=5. Unlike the non-exotic version of the model, in which all right-handed neutrinos carry the same B−L=−1 charge, in this case the neutrinos have their own scalar sector and no hierarchy in the Yukawa coupling in the Dirac mass term is necessary.

Left-right symmetric model withμ↔τsymmetry

We analyze the leptonic sector in the left-right symmetric model dressed with a $(Z_{2})^{3}$ discrete symmetry which realizes, after weak spontaneous breaking, a small broken $\mu\lra\tau$ symmetry that is suggested to explain observable neutrino oscillation data. $\mu\lra\tau$ symmetry is broken at tree level in the effective neutrino mass matrix due to the mass difference $\widetilde{m}_{\tau}\neq \widetilde{m}_{\mu}$ in the diagonal Dirac mass terms, whereas all lepton mixings arise from a Majorana mass matrix. In the limit of a small breaking we determined $\theta_{13}$, and the deviation from the maximal value of $\theta_{ATM}$, in terms of the light neutrino hierarchy scale, $m_{3}$, and a single free parameter $h_{s}$ of the model.

TeV-scale seesaw mechanism catalyzed by the electron mass

We construct a model in which the neutrino Dirac mass terms are of order the electron mass and the seesaw mechanism proceeds via right-handed neutrinos with masses of order TeV. In our model the spectra of the three light and of the three heavy neutrinos are closely related. Since the mixing between light and heavy neutrinos is small, the model predicts no effects in pp and pp¯ colliders. Possible signatures of the model are the lepton-number-violating process e−e−→H−H−, where H− is a charged scalar particle, lepton-flavour-violating decays like μ−→e−e−e+, or a sizable contribution to the anomalous magnetic dipole moment of the muon.