arXiv subjects

C. Hagedorn

Publications and source records attributed to C. Hagedorn.

15 recordsLinked to original sources

arXiv2026

Lepton mixing and charged lepton flavour violation from inverse seesaw with non-degenerate heavy states

We analyse an inverse seesaw scenario with 3+3 gauge singlets. The flavour structure is determined by a flavour symmetry, Delta (3 n^2) or Delta (6 n^2), n integer, and CP and their residual groups among charged leptons and the neutral states. For the latter, the Dirac mass matrix of the gauge singlets carries all non-trivial flavour structure. Consequently, the heavy sterile states form three pseudo-Dirac pairs which have in general distinct masses. We discuss the signal strength of different charged lepton flavour violating processes. Ensuring that the lepton mixing angles can be accommodated at the 3 sigma level or better, we find that the current bounds on the branching ratios of mu -> e gamma, mu -> 3 e, tau -> l gamma and tau -> 3 l, l=e, mu, as well as the rate of mu-e conversion in nuclei do not strongly constrain the considered parameter space, while the limits expected from the upcoming experiments Mu3E, COMET and Mu2e will have a relevant impact.

hep-ph↗

arXiv2024

Charged lepton flavour violation from inverse seesaw with flavour and CP symmetries

We study charged lepton flavour violation in a scenario in which light neutrino masses are generated via the inverse seesaw mechanism with 3+3 gauge singlet fermions, Ni and Sj, i,j=1,2,3. Lepton mixing is predicted with the help of the flavour symmetries Delta (3 n^2) and Delta (6 n^2) combined with CP. In the neutral lepton sector, the non-trivial flavour structure is only encoded in the Dirac neutrino Yukawa matrix (the coupling relating left-handed lepton doublets and gauge singlets Ni). Current experimental bounds on the processes mu -> e gamma, mu -> 3 e, mu-e conversion in nuclei and the tau lepton decays tau -> l gamma and tau -> 3 l, l=e, mu, do not constrain the considered parameter space of this scenario. Prospective limits on the decay mu -> 3 e and mu-e conversion in aluminium instead can markedly reduce the available parameter space. We also comment on the effects of the heavy sterile states on light neutrino masses and lepton mixing.

hep-ph↗

arXiv2021

Flavour and CP symmetries in the inverse seesaw

We consider an inverse seesaw mechanism of neutrino mass generation in which the Standard Model is extended by $3+3$ (heavy) sterile states, and endowed with a flavour symmetry $G_f$, $G_f=Δ(3 \, n^2)$ or $G_f=Δ(6 \, n^2)$, and a CP symmetry. These symmetries are broken in a peculiar way, so that in the charged lepton sector a residual symmetry $G_\ell$ is preserved, while the neutral fermion sector remains invariant under the residual symmetry $G_ν=Z_2 \times CP$. We study the concrete setup, where the Majorana mass term for three of the sterile states conserves $G_ν$, while the remaining mass terms (i.e. couplings of left-handed leptons and heavy sterile states, as well as the Dirac-type couplings among the latter) do not break the flavour or CP symmetry. We perform a comprehensive analysis of lepton mixing for different classes of residual symmetries, giving examples for each of these, and study in detail the impact of the additional sterile states on the predictions for lepton mixing. We further confront our results with those obtained in the model-independent scenario, in which the light neutrino mass matrix leaves the residual symmetry $G_ν$ intact. We consider the phenomenological impact of the inverse seesaw mechanism endowed with flavour and CP symmetries, in particular concerning effects of non-unitarity of the lepton mixing matrix (which strongly constrain the parameter space of the scenario), prospects for neutrinoless double beta decay and for charged lepton flavour violating processes.

hep-ph↗

arXiv2018

CP Violation in the Lepton Sector and Implications for Leptogenesis

We review the current status of the data on neutrino masses and lepton mixing and the prospects for measuring the CP-violating phases in the lepton sector. The possible connection between low energy CP violation encoded in the Dirac and Majorana phases of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix and successful leptogenesis is emphasized in the context of seesaw extensions of the Standard Model with a flavor symmetry Gf (and CP symmetry).

hep-ph↗

arXiv2014

Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP

We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Delta (3 n^2) or Gf=Delta(6 n^2) and a CP symmetry are broken to residual symmetries Ge=Z3 and Gnu=Z2 x CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z3 and Z2 generating elements, we focus on a certain set of CP transformations. The resulting lepton mixing depends on group theoretical indices and one continuous parameter. In order to study the mixing patterns comprehensively for all admitted Ge and Gnu, it is sufficient to discuss only three types of combinations. One of them requires as flavor group Delta (6 n^2). Two types of combinations lead to mixing patterns with a trimaximal column, while the third one allows for a much richer structure. For the first type of combinations the Dirac as well as one Majorana phase are trivial, whereas the other two ones predict in general all CP phases to be non-trivial and also non-maximal. Already for small values of the index n of the group, n <= 11, experimental data on lepton mixing can be accommodated well for particular choices of the parameters of the theory. We also comment on the relation of the used CP transformations to the automorphisms of Delta (3 n^2) and Delta (6 n^2).

hep-ph↗

arXiv2013

Charged lepton flavour violation in supersymmetric and holographic composite Higgs models with flavour symmetries

We discuss charged lepton flavour violating processes such as mu -> e gamma in supersymmetric extensions of the Standard Model and in models with gauge-Higgs unification and a warped extra dimension. In both classes of models the processes turn out to be compatible with present experimental bounds, but can be detected by future experiments, thanks to the presence of a flavour symmetry G_f which constrains the form of the relevant couplings. The symmetry G_f is chosen to be finite, discrete and non-abelian and also helps to predict the peculiar lepton mixing pattern.

hep-ph↗

arXiv2012

D14 - A Common Origin of the Cabibbo Angle and the Lepton Mixing Angle theta^l_13

It has been shown that the Cabibbo angle can be predicted in terms of group theoretical quantities, if the dihedral group D14 plays the role of a flavor symmetry. We extend a supersymmetric D14 model to the lepton sector and show that theta^nu_13 and the deviation of theta^nu_23 from maximal mixing in the neutrino sector originate, similar to the Cabibbo angle in the quark sector, from a mismatch of different subgroups of D14 and are of the size of the Cabibbo angle. The mixing angles in the charged lepton sector are small. Thus, the lepton mixing angle theta^l_13 is naturally in its experimentally preferred range and theta^l_23 within its 3 sigma range. The solar mixing angle is of order one and the charged lepton mass hierarchy is correctly reproduced. Leading order results are only slightly perturbed, if next-to-leading order corrections are taken into account.

hep-ph↗

arXiv2010

Charged Lepton Flavour Violating Radiative Decays $\ell_i \to \ell_j + γ$ in See-Saw Models with $A_4$ Symmetry

The charged lepton flavour violating (LFV) radiative decays, $μ\to e+γ$, $τ\to μ+γ$ and $τ\to e +γ$ are investigated in a class of supersymmetric $A_4$ models with three heavy right-handed (RH) Majorana neutrinos, in which the lepton (neutrino) mixing is predicted to leading order (LO) to be tri-bimaximal. The light neutrino masses are generated via the type I see-saw mechanism. The analysis is done within the framework of the minimal supergravity (mSUGRA) scenario, which provides flavour universal boundary conditions at the scale of grand unification $M_X \approx 2 \times 10^{16}$ GeV. Detailed predictions for the rates of the three LFV decays are obtained in two explicit realisations of the $A_4$ models due to Altarelli and Feruglio and Altarelli and Meloni, respectively.

hep-ph↗

arXiv2009

Majorana Phases and Leptogenesis in See-Saw Models with A_4 Symmetry

The related issues of Majorana CP violation in the lepton sector and leptogenesis are investigated in detail in two rather generic supersymmetric models with type I see-saw mechanism of neutrino mass generation and A_4 flavour symmetry, which naturally lead at leading order to tri-bimaximal neutrino mixing. The neutrino sector in this class of models is described at leading order by just two real parameters and one phase. This leads, in particular, to significant low energy constraints on the Majorana phases α_{21} and α_{31} in the PMNS matrix, which play the role of leptogenesis CP violating parameters in the generation of the baryon asymmetry of the Universe. We find that it is possible to generate the correct size and sign of the baryon asymmetry in both A_4 models. The sign of the baryon asymmetry is directly related to the signs of sinα_{21} and/or sinα_{31}.

hep-ph↗

arXiv2008

A Supersymmetric D4 Model for mu-tau Symmetry

We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in [1] which predicts theta_{23} maximal and theta_{13}=0 in the lepton sector. For this purpose, we extend the flavor group, which is D4 x Z2^{(aux)} in the original model, to D4 x Z5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since theta_{23} maximal and theta_{13}=0 arise through the same mismatch of D4 subgroups, D2 in the charged lepton and Z2 in the neutrino sector. In our setup D4 is solely broken by gauge singlets, the flavons. We show that their vacuum structure, which leads to the prediction of theta_{13} and theta_{23}, is a natural result of the scalar potential. We find that the neutrino mass matrix only allows for inverted hierarchy, if we assume a certain form of spontaneous CP violation. The quantity |m_{ee}|, measured in neutrinoless double beta decay, is nearly equal to the lightest neutrino mass m3. The Majorana phases phi1 and phi2 are restricted to a certain range for m3 < 0.06 eV. We discuss the next-to-leading order corrections which give rise to shifts in the vacuum expectation values of the flavons. These induce deviations from maximal atmospheric mixing and vanishing theta_{13}. It turns out that these deviations are smaller for theta_{23} than for theta_{13}.

hep-ph↗

arXiv2007

theta_C from the Dihedral Flavor Symmetries D_7 and D_14

In [1] it has been shown that the Cabibbo angle theta_C might arise from a dihedral flavor symmetry which is broken to different (directions of) subgroups in the up and the down quark sector. This leads to a prediction of theta_C in terms of group theoretical quantities only, i.e. the index n of the dihedral group D_n, the index j of the fermion representation 2_j and the preserved subgroups indicated by m_u and m_d. Here we construct a low energy model which incorporates this idea. The gauge group is the one of the Standard Model and D_7 x Z_2 ^(aux) serves as flavor symmetry. The additional Z_2 ^(aux) is necessary in order to maintain two sets of Higgs fields, one which couples only to up quarks and another one coupling only to down quarks. We assume that D_7 is broken spontaneously at the electroweak scale by vacuum expectation values of SU(2)_L doublet Higgs fields. The quark masses and mixing parameters can be accommodated well. Furthermore, the potential of the Higgs fields is studied numerically in order to show that the required configuration of the vacuum expectation values can be achieved. We also comment on more minimalist models which explain the Cabibbo angle in terms of group theoretical quantities, while theta_{13}^q and theta_{23}^q vanish at leading order. Finally, we perform a detailed numerical study of the lepton mixing matrix V_{MNS} in which one of its elements is entirely determined by the group theory of a dihedral symmetry. Thereby, we show that nearly tri-bi-maximal mixing can also be produced by a dihedral flavor group with preserved subgroups.

hep-ph↗

arXiv2007

Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups

We perform a systematic study of dihedral groups used as flavor symmetry. The key feature here is the fact that we do not allow the dihedral groups to be broken in an arbitrary way, but in all cases some (non-trivial) subgroup has to be preserved. In this way we arrive at only five possible (Dirac) mass matrix structures which can arise, if we require that the matrix has to have a non-vanishing determinant and that at least two of the three generations of left-handed (conjugate) fermions are placed into an irreducible two-dimensional representation of the flavor group. We show that there is no difference between the mass matrix structures for single- and double-valued dihedral groups. Furthermore, we comment on possible forms of Majorana mass matrices. As a first application we find a way to express the Cabibbo angle, i.e. the CKM matrix element |V_{us}|, in terms of group theory quantities only, the group index n, the representation index j and the index m_{u,d} of the different preserved subgroups in the up and down quark sector: |V_{us}|=|cos(pi(m_{u}-m_{d})j/n)| which is |cos(3 pi/7)| = 0.2225 for n=7, j=1, m_{u}=3 and m_{d}=0. We prove that two successful models which lead to maximal atmospheric mixing and vanishing theta_{13} in the lepton sector are based on the fact that the flavor symmetry is broken in the charged lepton, Dirac neutrino and Majorana neutrino sector down to different preserved subgroups whose mismatch results in the prediction of these mixing angles. This also demonstrates the power of preserved subgroups in connection with the prediction of mixing angles in the quark as well as in the lepton sector.

hep-ph↗

arXiv2006

S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor

Pursuing a bottom-up approach to explore which flavor symmetry could serve as an explanation of the observed fermion masses and mixings, we discuss an extension of the standard model (SM) where the flavor structure for both quarks and leptons is determined by a spontaneously broken S4 and the requirement that its particle content is embeddable simultaneously into the conventional SO(10) grand unified theory (GUT) and a continuous flavor symmetry G_f like SO(3)_f or SU(3)_f. We explicitly provide the Yukawa and the Higgs sector of the model and show its viability in two numerical examples which arise as small deviations from rank one matrices. In the first case, the corresponding mass matrix is democratic and in the second one only its 2-3 block is non-vanishing. We demonstrate that the Higgs potential allows for the appropriate vacuum expectation value (VEV) configurations in both cases, if CP is conserved. For the first case, the chosen Yukawa couplings can be made natural by invoking an auxiliary Z2 symmetry. The numerical study we perform shows that the best-fit values for the lepton mixing angles theta_12 and theta_23 can be accommodated for normal neutrino mass hierarchy. The results for the quark mixing angles turn out to be too small. Furthermore the CP-violating phase delta can only be reproduced correctly in one of the examples. The small mixing angle values are likely to be brought into the experimentally allowed ranges by including radiative corrections. Interestingly, due to the S4 symmetry the mass matrix of the right-handed neutrinos is proportional to the unit matrix.

hep-ph↗

arXiv2006

The discrete flavor symmetry D5

We consider the standard model (SM) extended by the flavor symmetry D5 and search for a minimal model leading to viable phenomenology. We find that it contains four Higgs fields apart from the three generations of fermions whose left- and left-handed conjugate parts do not transform in the same way under D5. We provide two numerical fits for the case of Dirac and Majorana neutrinos to show the viability of our low energy model. The fits can accommodate all data with the neutrinos being normally ordered. For Majorana neutrinos two of the right-handed neutrinos are degenerate. Concerning the Higgs sector we find that all potentials constructed with three SM-like Higgs doublets transforming as 1+2 under D5 have a further unwanted global U(1) symmetry. Therefore we consider the case of four Higgs fields forming two D5 doublets and show that this potential leads to viable solutions in general, however it does not allow spontaneous CP-violation (SCPV) for an arbitrary vacuum expectation value (VEV) configuration. Finally, we discuss extensions of our model to grand unified theories (GUTs) as well as embeddings of D5 into the continuous flavor symmetries SO(3)_f and SU(3)_f.

hep-ph↗

arXiv2005

Minimal Mass Matrices for Dirac Neutrinos

We consider the possibility of neutrinos being Dirac particles and study minimal mass matrices with as much zero entries as possible. We find that up to 5 zero entries are allowed. Those matrices predict one vanishing mass state, CP conservation and U_{e3} either zero or proportional to R, where R is the ratio of the solar and atmospheric Δm^2. Matrices containing 4 zeros can be classified in categories predicting U_{e3} = 0, U_{e3} \neq 0 but no CP violation or |U_{e3}| \neq 0 and possible CP violation. Some cases allow to set constraints on the neutrino masses. The characteristic value of U_{e3} capable of distinguishing some of the cases with non-trivial phenomenological consequences is about R/2 \sin 2 θ_{12}. Matrices containing 3 and less zero entries imply (with a few exceptions) no correlation for the observables. We outline models leading to the textures based on the Froggatt-Nielsen mechanism or the non-Abelian discrete symmetry D_4 \times Z_2.

hep-ph↗