arXiv subjects

W. Grimus

Publications and source records attributed to W. Grimus.

At least 55 records · Page 3Linked to original sources

arXiv2005

S3 x Z2 model for neutrino mass matrices

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 $μ$--$τ$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3} = 0$. A partial and less predictive form of $μ$--$τ$ interchange symmetry is obtained when the symmetry $S_3$ is softly broken in the scalar potential. Enlarging the symmetry group $S_3 \times \mathbbm{Z}_2$ by an additional discrete electron-number symmetry $\mathbbm{Z}_2^{(e)}$, a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group $D_4$.

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arXiv2005

On a model with two zeros in the neutrino mass matrix

We consider a Majorana neutrino mass matrix $\mathcal{M}_ν$ with $(\mathcal{M}_ν)_{μμ} = (\mathcal{M}_ν)_{ττ} = 0$, in the basis where the charged-lepton mass matrix is diagonal. We show that this pattern for the lepton mass matrices can be enforced by extending the Standard Model with three scalar SU(2) triplets and by using a horizontal symmetry group $\mathbbm{Z}_4$. The Ma--Sarkar (type-II seesaw) mechanism leads to very small vacuum expectation values for the triplets, thus explaining the smallness of the neutrino masses; at the same time, that mechanism renders the physical scalars originating in the triplets very heavy. We show that the conditions $(\mathcal{M}_ν)_{μμ} = (\mathcal{M}_ν)_{ττ} = 0$ allow both for a normal neutrino mass spectrum and for an inverted one. In the first case, the neutrino masses must be larger than $0.1 {eV}$ and the atmospheric mixing angle $θ_{23}$ must be practically equal to $45^\circ$. In the second case, the product $\sin{θ_{13}} | \tan{2 θ_{23}} |$ must be of order one or larger, thus correlating the large or maximal atmospheric neutrino mixing with the smallness of the mixing angle $θ_{13}$.

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arXiv2004

Softly broken lepton number L_e - L_μ- L_τwith non-maximal solar neutrino mixing

We consider the most general neutrino mass matrix which leads to $θ_{13} = 0$, and present the formulae needed for obtaining the neutrino masses and mixing parameters in that case. We apply this formalism to a model based on the lepton number $\bar L = L_e - L_μ- L_τ$ and on the seesaw mechanism. This model needs only one Higgs doublet and has only two right-handed neutrino singlets. Soft $\bar L$ breaking is accomplished by the Majorana mass terms of the right-handed neutrinos; if the $\bar L$-conserving and $\bar L$-breaking mass terms are of the same order of magnitude, then it is possible to obtain a consistent $\bar L$ model with a solar mixing angle significantly smaller than $45^\circ$. We show that the predictions of this model, $m_3 = 0$ and $θ_{13} = 0$, are invariant under the renormalization-group running of the neutrino mass matrix.

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arXiv2004

Renormalization of the neutrino mass operators in the multi-Higgs-doublet Standard Model

We derive the renormalization group equations (RGE) for the flavour coupling matrices of the effective dimension-five operators which yield Majorana neutrino masses in the multi-Higgs-doublet Standard Model; in particular, we consider the case where two different scalar doublets occur in those operators. We also write down the RGE for the scalar-potential quartic couplings and for the Yukawa couplings of that model, in the absence of quarks. As an application of the RGE, we consider two models which, based on a mu-tau interchange symmetry, predict maximal atmospheric neutrino mixing, together with U_{e3} = 0, at the seesaw scale. We estimate the change of those predictions due to the evolution of the coupling matrices of the effective mass operators from the seesaw scale down to the electroweak scale. We derive an upper bound on that change, thereby finding that the radiative corrections to those predictions are in general negligible.

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arXiv2004

Lepton mixing angle $θ_{13} = 0$ with a horizontal symmetry $D_4$

We discuss a model for the lepton sector based on the seesaw mechanism and on a $D_4$ family symmetry. The model predicts the mixing angle $θ_{13}$ to vanish. The solar mixing angle $θ_{12}$ is free--it will in general be large if one does not invoke finetuning. The model has an enlarged scalar sector with three Higgs doublets, together with two real scalar gauge singlets $χ_i$ ($ i = 1, 2$) which have vacuum expectation values < χ_i >_0$ at the seesaw scale. The atmospheric mixing angle $θ_{23}$ is given by $\tan θ_{23} = <χ_2>_0$ /<χ_1>_0$, and it is maximal if the Lagrangian is $D_4$-invariant; but $D_4$ may be broken softly, by a term of dimension two in the scalar potential, and then < χ_2_0$ becomes different from < χ_1_0$. Thus, the strength of the soft $D_4$ breaking controls the deviation of $θ_{23}$ from $π/ 4$. The model predicts a normal neutrino mass spectrum ($m_3 > m_2 > m_1$) and allows successful leptogenesis if $m_1 \sim 4 \times 10^{-3} \mathrm{eV}$; these properties of the model are independent of the presence and strength of the soft $D_4$ breaking.

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arXiv2004

Symmetry realization of texture zeros

We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in Grand Unified Theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture.

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arXiv2004

Models of maximal atmospheric neutrino mixing and leptogenesis

We discuss two extensions of the Standard Model based on the seesaw mechanism and on non-abelian family symmetry groups O(2) and $D_4$, respectively. Both models have a twofold-degenerate neutrino Dirac mass matrix $M_D$, a Majorana mass matrix invariant under a $μ$--$τ$ interchange symmetry and the predictions of maximal atmospheric neutrino mixing and vanishing mixing angle $θ_{13}$. Leptogenesis can naturally be incorporated if $10^{-3} \lesssim m_1 \lesssim 10^{-2}$ eV where $m_1$ the mass of the lightest neutrino and if the relevant heavy neutrinos are in the range $10^{11}$ to $10^{12}$ GeV. The $D_4$ model is more constrained and leptogenesis requires $m_1$ to be in the vicinity of $4 \times 10^{-3}$ eV.

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arXiv2004

Leptogenesis in seesaw models with a twofold-degenerate neutrino Dirac mass matrix

We study leptogenesis in two seesaw models where maximal atmospheric neutrino mixing and $U_{e3} = 0$ result from symmetries. Salient features of those models are the existence of three Higgs doublets and a twofold degeneracy of the neutrino Dirac mass matrix. We find that in those models both leptogenesis and neutrinoless double beta decay depend on the same unique Majorana phase. Leptogenesis can produce a baryon asymmetry of the universe of the right size provided the mass of the heavy neutrino whose decays generate the lepton asymmetry is in the range $10^{11}$--$10^{12} \mathrm{GeV}$. Moreover, in these models, leptogenesis precludes an inverted neutrino mass spectrum since it requires the mass of the lightest neutrino to be in the range $10^{-3}$--$10^{-2} \mathrm{eV}$.

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arXiv2003

Quark mixing from softly broken symmetries

Quark flavor mixing may originate in the soft breaking of horizontal symmetries. Those symmetries, which in the simplest case are three family U(1) groups, are obeyed only by the dimension-4 Yukawa couplings and lead, when unbroken, to the absence of mixing. Their breaking may arise from the dimension-3 mass terms of SU(2)-singlet vector-like quarks. Those gauge-singlet mass terms break the horizontal symmetries at a scale much higher than the Fermi scale, yet softly, leading to quark mixing while the quark masses remain unsuppressed.

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arXiv2003

Maximal atmospheric neutrino mixing and the small ratio of muon to tau mass

We discuss the problem of the small ratio of muon mass to tau mass in a class of seesaw models where maximal atmospheric neutrino mixing is enforced through a $μ$--$τ$ interchange symmetry. We introduce into those models an additional symmetry $T$ such that $m_μ= 0$ in the case of exact $T$ invariance. The symmetry $T$ may be softly broken in the Higgs potential, and one thus achieves $m_μ\ll m_τ$ in a technically natural way. We speculate on a wider applicability of this mechanism.

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arXiv2003

A non-standard CP transformation leading to maximal atmospheric neutrino mixing

We discuss a neutrino mass matrix $\mathcal{M}_ν$ originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle $θ_{13}$ of the lepton mixing matrix $U$ is allowed and--in the usual phase convention--CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a simple seesaw extension of the Standard Model where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard $CP$ symmetry.

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arXiv2003

Models of maximal atmospheric neutrino mixing

We discuss two types of neutrino mass matrices which both give $θ_{23} = 45^\circ$, i.e., a maximal atmospheric mixing angle. We review three models, based on the seesaw mechanism and on simple extensions of the scalar sector of the Standard Model, where those mass matrices are obtained from symmetries.

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arXiv2003

A discrete symmetry group for maximal atmospheric neutrino mixing

We propose a discrete non-abelian symmetry group which enforces maximal atmospheric neutrino mixing, while $θ_{13} = 0$ and the solar mixing angle $θ_{12}$ remains undetermined; without finetuning, $θ_{12}$ will be large but non-maximal. Our extension of the Standard Model has three right-handed neutrino singlets $ν_R$ and implements the seesaw mechanism. Furthermore, we have an enlarged scalar sector with three Higgs doublets and two scalar gauge singlets; the latter have masses and vacuum expectation values of the order of the seesaw scale. Lepton mixing stems exclusively from the $ν_R$ Majorana mass matrix, where non-diagonal elements are generated by the vacuum expectation values of the scalar singlets. The model predicts a neutrino mass spectrum with $m_3 > m_2 > m_1$ and the effective Majorana mass of neutrinoless $ββ$ decay is equal to $m_1 m_2 / m_3$.

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arXiv2003

Neutrino Physics - Theory

We discuss recent developments in neutrino physics and focus, in particular, on neutrino oscillations and matter effects of three light active neutrinos. Moreover, we discuss the difference between Dirac and Majorana neutrinos, neutrinoless $ββ$-decay, absolute neutrino masses and electromagnetic moments. Basic mechanisms and a few models for neutrino masses and mixing are also presented.

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arXiv2003

The solar LMA neutrino oscillation solution in the Zee model

We examine the neutrino mass matrix in the version of Zee model where both Higgs doublets couple to the leptons. We show that in this case one can accommodate the large mixing angle (LMA) MSW solution of the solar neutrino problem, while avoiding maximal solar mixing and conflicts with constraints on lepton family number-violating interactions. In the simplified scenario we consider, we have the neutrino mass spectrum characterized by $m_1 \simeq m_2 \simeq \sqrt{Δm^2_\mathrm{atm}}/\sin 2θ$ and $m_3/m_1 \simeq \cos 2θ$, where $θ$ is the solar mixing angle.

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arXiv2002

On the Orthogonality of Independently Propagating States as Occurring in the Lee-Oehme-Yang Theory

We generalize a theorem by Khalfin, originally derived for the states $| F_1 > = | M^0>$, $| F_2 > = |\bar M^0>$, where $M^0$ is a neutral flavoured meson (e.g., $K^0$ or $B_d^0$), by assuming CPT invariance. Dispensing with CPT invariance and allowing for an arbitrary pair of orthogonal states $| F_{1,2}>$, we show that any linear combinations $| P_a > = p_a | F_1 > + q_a | F_2>$ and $| P_b > = p_b | F_1 > - q_b | F_2>$, if postulated to be independently propagating in time, as in the Lee--Oehme--Yang Theory, must be mutually orthogonal. This implies a reciprocity relation: equality of the probabilities of the transitions $| F_1 > \leftrightarrow | F_2>$. Also implied is another relation involving the coefficients $p_{a,b}$, $q_{a,b}$, which can be interpreted as $\mathrm{Im} θ= 0$, where $θ$ is the rephasing-invariant parameter describing CPT violation in $M^0 \bar M^0$ mixing for Khalfin's choice of $| F_{1,2}>$. The states $| F_{1,2}>$ of \emph{our} theorem need not form a particle-antiparticle pair, nor even be restricted to particle physics.

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arXiv2002

Maximal atmospheric neutrino mixing in an SU(5) model

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the $U(1)_F$ symmetry associated with a suitably defined family number $F$, together with a $\mathbbm{Z}_2$ symmetry which does not commute with $F$. $U(1)_F$ is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in addition, $U(1)_F$ is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale $10^{16} \mathrm{GeV} < m_U < 10^{19} \mathrm{GeV}$; indeed, we have found a particular solution to this problem which yields results almost identical to the ones of the Minimal Supersymmetric Standard Model.

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arXiv2002

One-loop corrections to the seesaw mechanism in the multi-Higgs-doublet Standard Model

We consider the lepton sector of the Standard Model and allow for an arbitrary number of Higgs doublets and, moreover, for the presence of right-handed neutrino singlets which enable the seesaw mechanism. In this framework, we identify and calculate the dominant one-loop radiative corrections to the tree-level mass matrix of the light neutrinos. The interesting feature is that both the tree-level and the one-loop contributions to the light-neutrino mass matrix are quadratic in the Yukawa couplings, with the effect that the one-loop contribution is smaller than the tree-level one mainly because of the one-loop factor $(16π^2)^{-1}$. We also point out the possibility of generating radiatively--in this framework--the ratio of solar over atmospheric neutrino mass-squared differences, as needed for the large-mixing-angle MSW solution of the solar-neutrino problem.

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