W. Grimus - Univ. of Vienna

W. Grimus
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W. Grimus
Univ. of Vienna

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High Energy Physics - Phenomenology (49)
High Energy Physics - Theory (2)
Mathematics - Mathematical Physics (2)
Mathematical Physics (2)
Quantum Physics (2)
Physics - History of Physics (1)
Physics - Statistical Mechanics (1)

Publications Authored By W. Grimus

We consider a two-Higgs-doublet extension of the Standard Model, with three right-handed neutrino singlets and the seesaw mechanism, wherein all the Yukawa-coupling matrices are lepton flavour-diagonal and lepton flavour violation is soft, originating solely in the non-flavour-diagonal Majorana mass matrix of the right-handed neutrinos. We consider the limit $m_R \to \infty$ of this model, where $m_R$ is the seesaw scale. We demonstrate that there is a region in parameter space where the branching ratios of all five charged-lepton decays $\ell_1^- \to \ell_2^- \ell_3^+ \ell_3^-$ are close to their experimental upper bounds, while the radiative decays $\ell_1^- \to \ell_2^- \gamma$ are invisible because their branching ratios are suppressed by $m_R^{-4}$. Read More

In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are non-singular in $\varepsilon = p^2 - m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. Read More

We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet $\eta$, which has symmetries that lead to co-bimaximal mixing, i. Read More

In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a $\mathbf{10} \oplus \mathbf{120} \oplus \bar{\mathbf{126}}$ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by $Z_n$ symmetries, with suitable $n$, and one case is generated by a $Z_2 \times Z_2$ symmetry. Read More

The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem. Read More

We perform a systematic analysis of all possible texture zeros in general and symmetric quark mass matrices. Using the values of masses and mixing parameters at the electroweak scale, we identify for both cases the maximally restrictive viable textures. Furthermore, we investigate the predictive power of these textures by applying a numerical predictivity measure recently defined by us. Read More

Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have derived the complete list of mixing patterns achievable in this way, as well as the symmetry groups associated to each case. Read More

We discuss renormalization in a toy model with one fermion field and one real scalar field phi, featuring a spontaneously broken discrete symmetry which forbids a fermion mass term and a phi^3 term in the Lagrangian. We employ a renormalization scheme which uses the MSbar scheme for the Yukawa and quartic scalar couplings and renormalizes the vacuum expectation value of phi by requiring that the one-point function of the shifted field is zero. In this scheme, the tadpole contributions to the fermion and scalar selfenergies are canceled by choice of the renormalization parameter delta_v of the vacuum expectation value. Read More

We perform a systematic and complete analysis of texture zeros in the lepton mass matrices and identify all viable and maximally restrictive cases of pairs (M_\ell, M_D) and (M_\ell, M_L), where M_\ell, M_D and M_L are the charged-lepton, Dirac neutrino and Majorana neutrino mass matrices, respectively. To this end, we perform a thorough analysis of textures which are equivalent through weak-basis permutations. Furthermore, we introduce numerical measures for the predictivity of textures and apply them to the viable and maximally restrictive texture zero models. Read More

Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. Read More

It has been suggested that residual symmetries in the charged-lepton and neutrino mass matrices can possibly reveal the flavour symmetry group of the lepton sector. We review the basic ideas of this purely group-theoretical approach and discuss some of its results. Finally, we also list its shortcomings. Read More

We investigate the two classes of finite subgroups of SU(3) that are called type C and D in the book of Miller, Blichfeldt and Dickson. We present two theorems which fully determine the form of the generators in a suitable basis. After exploring further properties of these groups, we are able to construct a complete list of infinite series in which these groups are arranged. Read More

The recent enormous improvement of our knowledge of the neutrino oscillation parameters has motivated us to reinvestigate the allowed ranges of the elements of the neutrino mass matrix in the basis where the charged-lepton mass mass matrix is diagonal. Moreover, we have studied the correlations of the elements of the neutrino mass matrix. The result of this analysis is useful for finding textures in the neutrino mass matrix and, therefore, for model building in the lepton sector. Read More

We present a general framework for models in which the lepton mixing matrix is the product of the maximal mixing matrix U_\omega\ times a matrix constrained by a well-defined Z_2 symmetry. Our framework relies on neither supersymmetry nor non-renormalizable Lagrangians nor higher dimensions; it relies instead on the double seesaw mechanism and on the soft breaking of symmetries. The framework may be used to construct models for virtually all the lepton mixing matrices of the type mentioned above which have been proposed in the literature. Read More

The type II seesaw mechanism for neutrino mass generation usually makes use of one complex scalar triplet. The collider signature of the doubly-charged scalar, the most striking feature of this scenario,consists mostly in decays into same-sign dileptons or same-sign $W$ boson pairs. However, certain scenarios of neutrino mass generation, such as those imposing texture zeros by a symmetry mechanism, require at least two triplets in order to be consistent with type-II the seesaw mechanism. Read More

We investigate the possibility that the first column of the lepton mixing matrix U is given by u_1 = (2,-1,-1)^T/sqrt{6}. 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 Z_q x S_4 where the cyclic factor Z_q with q = 1,2,3,. Read More

Assuming Majorana nature of neutrinos, we re-investigate, in the light of the recent measurement of the reactor mixing angle, the allowed ranges for the absolute values of the elements of the neutrino mass matrix in the basis where the charged-lepton mass matrix is diagonal. Apart from the derivation of upper and lower bounds on the values of the matrix elements, we also study their correlations. Moreover, we analyse the sensitivity of bounds and correlations to the global fit results of the neutrino oscillation parameters which are available in the literature. Read More

We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by searching for viable hybrid textures in which the non-zero matrix elements of M_nu have simple ratios. Referring to the classification scheme of Frampton, Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu tau} = 1:2. There are analogous ratios for texture A2. Read More

We focus on the use of a mu-tau interchange symmetry to explain features of lepton mixing, especially maximal atmospheric neutrino mixing. We review two models which achieve this goal and are based on the seesaw mechanism and on the soft breaking of the family-lepton-number symmetries. We also note that that symmetry may be embedded in a generalized CP symmetry. Read More

We propose a simple mechanism which enforces |U_{mu j}| = | U_{tau j}| forall j = 1,2,3 in the lepton mixing matrix U. This implies maximal atmospheric neutrino mixing and a maximal CP-violating phase but does not constrain the reactor mixing angle theta_{13}. We implement the proposed mechanism in two renormalizable seesaw models which have features strongly resembling those of models based on a flavour symmetry group Delta(27). Read More

In 1912, Otto Sackur and Hugo Tetrode independently put forward an equation for the absolute entropy of a monoatomic ideal gas and published it in "Annalen der Physik." The grand achievement in the derivation of this equation was the discretization of phase space for massive particles, expressed as \delta q \delta p = h, where q and p are conjugate variables and h is Planck's constant. Due to the dependence of the absolute entropy on Planck's constant, Sackur and Tetrode were able to devise a test of their equation by applying it to the monoatomic vapor of mercury; from the satisfactory numerical comparison of h obtained from thermodynamic data on mercury with Planck's value from black-body radiation, they inferred the correctness of their equation. Read More

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which we apply and illustrate the general theory. Read More

It is well-known that, in the basis where the charged-lepton mass matrix is diagonal, there are seven cases of two texture zeros in Majorana neutrino mass matrices that are compatible with all experimental data. We show that two of these cases, namely B3 and B4 in the classification of Frampton, Glashow and Marfatia, are special in the sense that they automatically lead to near-maximal atmospheric neutrino mixing in the limit of a quasi-degenerate neutrino mass spectrum. This property holds true irrespective of the values of the solar and reactor mixing angles because, for these two cases, in the limit of a quasi-degenerate spectrum, the second and third row of the lepton mixing matrix are, up to signs, approximately complex-conjugate to each other. Read More

We motivate the usage of finite groups as symmetries of the Lagrangian. After a presentation of basic group-theoretical concepts, we introduce the notion of characters and character tables in the context of irreducible representations and discuss their applications. We exemplify these theoretical concepts with the groups S_4 and A_4. Read More

We attempt to give a complete description of the "exceptional" finite subgroups Sigma(36x3), Sigma(72x3) and Sigma(216x3) of SU(3), with the aim to make them amenable to model building for fermion masses and mixing. The information on these groups which we derive contains conjugacy classes, proper normal subgroups, irreducible representations, character tables and tensor products of their three-dimensional irreducible representations. We show that, for these three exceptional groups, usage of their principal series, i. Read More

The Large Hadron Collider presents an unprecedented opportunity to probe the realm of new physics in the TeV region and shed light on some of the core unresolved issues of particle physics. These include the nature of electroweak symmetry breaking, the origin of mass, the possible constituent of cold dark matter, new sources of CP violation needed to explain the baryon excess in the universe, the possible existence of extra gauge groups and extra matter, and importantly the path Nature chooses to resolve the hierarchy problem - is it supersymmetry or extra dimensions. Many models of new physics beyond the standard model contain a hidden sector which can be probed at the LHC. Read More

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 p \bar p colliders. Read More

We present a model which employs the seesaw mechanism with five right-handed neutrinos, leading to trimaximal and CP-conserving lepton mixing. Tri-bimaximal mixing is a natural limiting case of our model which occurs when one particular vacuum expectation value is real and preserves the mu-tau interchange symmetry of the Lagrangian. Our model allows for leptogenesis even in the case of exact tri-bimaximal mixing. Read More

We determine the symmetry groups under which the charged-lepton and the Majorana-neutrino mass terms are invariant. We note that those two groups always exist trivially, i.e. Read More

We elaborate on an earlier proposal by Ernest Ma of a type II seesaw mechanism for suppressing the vacuum expectation values of some Higgs doublets. We emphasize that, by nesting this form of seesaw mechanism into various other seesaw mechanisms, one may obtain light neutrino masses in such a way that the new-physics scale present in the seesaw mechanism - the masses of scalar gauge-SU(2) triplets, scalar SU(2) doublets, or right-handed neutrinos - does not need to be higher than a few 10 TeV. We also investigate other usages of the type II seesaw mechanism for Higgs doublets. Read More

We construct a model for tri-bimaximal lepton mixing which employs only family symmetries and their soft breaking; neither vacuum alignment nor supersymmetry, extra dimensions, or non-renormalizable terms are used in our model. It is an extension of the Standard Model making use of the seesaw mechanism with five right-handed neutrino singlets. The scalar sector comprises four Higgs doublets and one complex gauge singlet. Read More

Using the seesaw mechanism, we construct a model for the light-neutrino Majorana mass matrix which yields trimaximal lepton mixing together with maximal CP violation and maximal atmospheric-neutrino mixing. We demonstrate that, in our model, the light-neutrino mass matrix retains its form under the one-loop renormalization-group evolution. With our neutrino mass matrix, the absolute neutrino mass scale is a function of |U_e3| and of the atmospheric mass-squared difference. Read More

We consider trimaximal lepton mixing, defined by |U_{alpha 2}|^2 = 1/3 for all alpha = e, mu, tau. This corresponds to a two-parameter lepton mixing matrix U. We present a model for the lepton sector in which trimaximal mixing is enforced by softly broken discrete symmetries; one version of the model is based on the group Delta(27). Read More

We discuss a realization of the non-abelian group O(2) as a family symmetry for the lepton sector. The reflection contained in O(2) acts as a mu-tau interchange symmetry, enforcing--at tree level--maximal atmospheric neutrino mixing and a vanishing mixing angle theta_13. The small ratio m_mu/m_tau (muon over tau mass) gives rise to a suppression factor in the mass of one of the pseudoscalars of the model. Read More

We present general expressions for the oblique parameters S, T, U, V, W, and X in the SU(2)xU(1) electroweak model with an arbitrary number of scalar SU(2) doublets, with hypercharge 1/2, and an arbitrary number of scalar SU(2) singlets. Read More

We derive a general expression for Delta rho (or, equivalently, for the oblique parameter T) in the SU(2) x U(1) electroweak model with an arbitrary number of scalar SU(2) doublets, with hypercharge +-1/2, and an arbitrary number of scalar SU(2) singlets. The experimental bound on Delta rho constitutes a strong constraint on the masses and mixings of the scalar particles in that model. Read More

We discuss some recent developments in SUSY Grand Unified Theories based on the gauge group SO(10). Considering renormalisable Yukawa couplings, we present ways to accommodate quark and lepton masses and and mixings. Read More

We consider renormalizable SO(10) Yukawa interactions and put the three fermionic 16-plets into the 3-dimensional irreducible A_4 representation. Scanning the possible A_4 representation assignments to the scalars, we find a unique case which allows to accommodate the down-quark and charged-lepton masses. Assuming type II seesaw dominance, we obtain a viable scenario with the Zee-Wolfenstein neutrino mass matrix, i. Read More

In these lecture notes we present mechanisms for the generation of Majorana neutrino masses and lepton mixing. We consider simple extensions of the Standard Model. Apart from a section about radiative mass generation, we put special emphasis on the seesaw mechanism and mu-tau interchange symmetry. Read More

We consider fermion masses and mixings in a renormalizable SUSY SO(10) GUT with Yukawa couplings of scalar fields in the representation 10 + 120 + 126 bar. We investigate a scenario defined by the following assumptions: i) A single large scale in the theory, the GUT scale. ii) Small neutrino masses generated by the type I seesaw mechanism with negligible type II contributions. Read More

Using the type-II seesaw mechanism with three Higgs doublets phi_alpha (alpha = e, mu, tau) and four Higgs triplets, we build a model for lepton mixing based on a 384-element horizontal symmetry group, generated by the permutation group S_3 and by six Z_2 transformations. The charged-lepton mass matrix is diagonal; the symmetries of the model would require all the three masses m_alpha to be equal, but different vacuum expectation values of the phi_alpha allow the m_alpha to split. The number of parameters in the Majorana neutrino mass matrix m_nu depends on two options: full breaking of the permutation group S_3, or leaving a mu--tau interchange symmetry intact; and hard or spontaneous violation of CP. Read More

Some models for the lepton sector, based on seesaw extensions of the Standard Model, are discussed in which the mu-tau interchange symmetry is realized in various ways. The symmetries defining such models and their characteristic predictions for lepton mixing are presented. Read More

We investigate a scenario in a supersymmetric SO(10) Grand Unified Theory in which the fermion mass matrices are generated by renormalizable Yukawa couplings of the $\mathbf{10} \oplus \mathbf{120} \oplus \bar{\mathbf{126}}$ representation of scalars. We reduce the number of parameters by assuming spontaneous CP violation and a $\mathbbm{Z}_2$ family symmetry, leading to nine real Yukawa coupling constants for three families. Since in the ``minimal SUSY SO(10) GUT'' an intermediate seesaw scale is ruled out and our scenario lives in the natural extension of this theory by the $\mathbf{120}$, we identify the vacuum expectation value (VEV) $w_R$ of $(\mathbf{10}, \mathbf{1}, \mathbf{3}) \in \bar{\mathbf{126}}$ with the GUT scale of $2 \times 10^{16}$ GeV. Read More

We consider the scenario in which the mass matrices of the charged fermions in the SO(10) Grand Unified Theory are generated exclusively by renormalizable Yukawa couplings to one $\mathbf{10} \oplus \mathbf{120}$ representation of scalars. We analyze, partly analytically and partly numerically, this scenario in the three-generations case. We demonstrate that it leads to unification of the $b$ and $\tau$ masses at the GUT scale. Read More

We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional term of the Lindblad form, the socalled dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-hermitian part of H_{eff} --the ``particle decay''-- can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Read More

We demonstrate that Abelian family symmetries allow one to enforce texture zeros in arbitrary entries of the fermion mass matrices. Placing zeros in any number of elements of all occurring mass matrices can be done with two alternative methods; one of them utilizes the group Z_n with n sufficiently high. Concentrating on the lepton sector and on neutrino masses, we discuss the methods in the case of seesaw models and scalar triplet models. Read More

Using the seesaw mechanism and a discrete symmetry, we construct a class of models for the neutrino mass matrix where the inverse of that matrix is the sum of a mu-tau antisymmetric background and a perturbation. We consider various possibilities for that perturbation. The simplest possible perturbations lead to four-parameter neutrino mass matrices which are unable to fit the experimental data. Read More

We present a supersymmetric model in which the lepton mixing matrix $U$ obeys, at the seesaw scale, the Harrison--Perkins--Scott \textit{Ansatz}--vanishing $U_{e3}$, maximal atmospheric neutrino mixing, and $\sin^2{\theta_\odot} = 1/3$ ($\theta_\odot$ is the solar mixing angle). The model features a permutation symmetry $S_3$ among the three lepton multiplets of each type--left-handed doublets, right-handed charged leptons, and right-handed neutrinos--and among three Higgs doublets and three zero-hypercharge scalar singlets; a fourth right-handed neutrino, a fourth Higgs doublet, and a fourth scalar singlet are invariant under $S_3$. In addition, the model has seven $\mathbbm{Z}_2$ symmetries, out of which six do not commute with $S_3$. Read More

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry $S_3 \times \mathbbm{Z}_2$. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry $S_3$ is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys $\mu$--$\tau$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3} = 0$. Read More