Golden Ratio Prediction for Solar Neutrino Mixing

It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio phi. Two such proposals have been made, cot theta_{12} = phi and cos theta_{12} = phi/2. We compare these Ansatze and discuss a model leading to cos theta_{12} = phi/2 based on the dihedral group D_{10}. This symmetry is a natural candidate because the angle in the expression cos theta_{12} = phi/2 is simply pi/5, or 36 degrees. This is the exterior angle of a decagon and D_{10} is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions.Comment: 15 pages, 1 figure. Matches published versio

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.Comment: 32 page

Non-Abelian Discrete Flavor Symmetries on Orbifolds

We study non-Abelian flavor symmetries on orbifolds, $S^1/Z_2$ and $T^2/Z_3$. Our extra dimensional models realize $D_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$ and $\Delta(6N^2)$ including $A_4$ and $S_4$. In addition, one can also realize their subgroups such as $Q_N$, $T_7$, etc. The $S_3$ flavor symmetry can be realized on both $S^1/Z_2$ and $T^2/Z_3$ orbifolds.Comment: 16 page

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}.Comment: 19 pages, 4 figure

The Cabibbo Angle in a Supersymmetric D14 Model

We construct a supersymmetric model with the flavor symmetry D14 in which the CKM matrix element |V_{ud}| can take the value |V_{ud}| =cos (pi/14) = 0.97493 implying that the Cabibbo angle theta_C is sin (theta_C) = |V_{us}| = sin (pi/14) = 0.2225. These values are very close to those observed in experiments. The value of |V_{ud}| (theta_C) is based on the fact that different Z2 subgroups of D14 are conserved in the up and down quark sector. In order to achieve this, D14 is accompanied by a Z3 symmetry. The spontaneous breaking of D14 is induced by flavons, which are scalar gauge singlets. The quark mass hierarchy is partly due to the flavor group D14 and partly due to a Froggatt-Nielsen symmetry U(1)_{FN} under which only the right-handed quarks transform. The model is completely natural in the sense that the hierarchies among the quark masses and mixing angles are generated with the help of symmetries. The issue of the vacuum alignment of the flavons is solved up to a small number of degeneracies, leaving four different possible values for |V_{ud}|. Out of these, only one of them leads to a phenomenological viable model. A study of the Z2 subgroup breaking terms shows that the results achieved in the symmetry limit are only slightly perturbed. At the same time they allow |V_{ud}| (theta_C) to be well inside the small experimental error bars.Comment: 1+24 page

Finite flavour groups of fermions

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. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U(3) and finite subgroups of SU(3). Though in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects.Comment: 89 pages, 6 figures, some references added, rearrangement of part of the material, section on SU(3) subgroups substantially extended, some minor revisions. Version for publication in J. Phys. A. Table 12 corrected to match eq.(256), table 14 and eq.(314) corrected to match the 2-dimensional irreps defined on p.6

Direct and Indirect Detection of Dark Matter in D6 Flavor Symmetric Model

We study a fermionic dark matter in a non-supersymmetric extension of the standard model with a family symmetry based on D6xZ2xZ2. In our model, the final state of the dark matter annihilation is determined to be e+ e- by the flavor symmetry, which is consistent with the PAMELA result. At first, we show that our dark matter mass should be within the range of 230 GeV - 750 GeV in the WMAP analysis combined with mu to e gamma constraint. Moreover we simultaneously explain the experiments of direct and indirect detection, by simply adding a gauge and D6 singlet real scalar field. In the direct detection experiments, we show that the lighter dark matter mass ~ 230 GeV and the lighter standard model Higgs boson ~ 115 GeV is in favor of the observed bounds reported by CDMS II and XENON100. In the indirect detection experiments, we explain the positron excess reported by PAMELA through the Breit-Wigner enhancement mechanism. We also show that our model is consistent with no antiproton excess suggested by PAMELA.Comment: 20 pages, 9 figures, 2 tables, accepted version for publication in European Physical Journal

Non-Abelian Discrete Flavor Symmetries from T^2/Z_N Orbifolds

In [1] it was shown how the flavor symmetry A4 (or S4) can arise if the three fermion generations are taken to live on the fixed points of a specific 2-dimensional orbifold. The flavor symmetry is a remnant of the 6-dimensional Poincare symmetry, after it is broken down to the 4-dimensional Poincare symmetry through compactification via orbifolding. This raises the question if there are further non-abelian discrete symmetries that can arise in a similar setup. To this end, we generalize the discussion by considering all possible 2-dimensional orbifolds and the flavor symmetries that arise from them. The symmetries we obtain from these orbifolds are, in addition to S4 and A4, the groups D3, D4 and D6 \simeq D3 x Z2 which are all popular groups for flavored model building.Comment: 12 pages, 4 figure

Hydrodynamical Description of 200 A GeV/c S+Au Collisions: Hadron and Electromagnetic Spectra

We study relativistic S+Au collisions at 200 A GeV/c using a hydrodynamical approach. We test various equations of state (EOSs), which are used to describe the strongly interacting matter at densities attainable in the CERN-SPS heavy ion experiments. For each EOS, suitable initial conditions can be determined to reproduce the experimental hadron spectra; this emphasizes the ambiguity between the initial conditions and the EOS in such an approach. Simultaneously, we calculate the resulting thermal photon and dielectron spectra, and compare with experiments. If one allows the excitation of resonance states with increasing temperature, the electro-magnetic signals from scenarios with and without phase transition are very similar and are not resolvable within the current experimental resolution. With regard to the CERES dilepton data, none of the EOSs considered, in conjunction with the standard leading order dilepton rates, succeed in reproducing the observed excess of dileptons below the rho peak. Our work, however, suggests that an improved measurement of the photon and dilepton spectra has the potential to strongly constrain the EOS.Comment: Uses REVTeX, 48 pages, 13 Postscript figure

Probing the equation of state in the AGS energy range with 3-d hydrodynamics

The effect of (i) the phase transition between a quark gluon plasma (QGP) and a hadron gas and (ii) the number of resonance degrees of freedom in the hadronic phase on the single inclusive distributions of 16 different types of produced hadrons for Au+Au collisions at AGS energies is studied. We have used an exact numerical solution of the relativistic hydrodynamical equations without free parameters which, because of its 3-d character, constitutes a considerable improvement over the classical Landau solution. Using two different equations of state (eos) - one containing a phase transition from QGP to the Hadronic Phase and two versions of a purely hadronic eos - we find that the first one gives an overall better description of the Au+Au experimental data at $AGS$ energies. We reproduce and analyse measured meson and proton spectra and also make predictions for anti-protons, deltas, anti-deltas and hyperons. The low m_t enhancement in pi- spectra is explained by baryon number conservation and strangeness equilibration. We also find that negative kaon data are more sensitive to the eos, as well as the K-/pi- ratio. All hyperons and deltas are sensitive to the presence of a phase transition in the forward rapidity region. Anti-protons, Omegas and heavy anti-baryons are sensitive in the whole rapidity range.Comment: 25 pages (.tex) and 9 figures (.ps