Atmospheric and Solar Neutrinos with a Heavy Singlet

We follow a minimalistic approach to neutrino masses, by introducing a single heavy singlet $N$ into the standard model (or supersymmetric standard model) with a heavy Majorana mass $M$, which couples as a single right-handed neutrino in a Dirac fashion to leptons, and induces a single light see-saw mass $m_{\nu}\sim 5\times 10^{-2} eV$, leaving two neutrinos massless. This trivial extension to the standard model may account for the atomospheric neutrino data via $\nu_{\mu}\to \nu_{\tau}$ oscillations with near maximal mixing angle $\theta_{23}\sim \pi/4$ and $\Delta m_{\mu \tau}^2 \sim 2.5\times 10^{-3} eV^2$. In order to account for the solar neutrino data the model is extended to SUSY GUT/ string-inspired type models which can naturally yield an additional light tau neutrino mass $m_{\nu_{\tau}}\sim few \times 10^{-3} eV$ leading to $\nu_{e L}\to (\cos \theta_{23}{\nu}_{\mu L} -\sin \theta_{23}{\nu}_{\tau L})$ oscillations with $\Delta m_{e1}^2\sim 10^{-5} eV^2$ and a mixing angle $\sin^2 2 \theta_1 \approx 10^{-2}$ in the correct range for the small angle MSW solution to the solar neutrino problem. The model predicts $\nu_{e L}\to (\sin \theta_{23}{\nu}_{\mu L} +\cos \theta_{23}{\nu}_{\tau L})$ oscillations with a similar angle but a larger splitting $\Delta m_{e2}^2 \sim 2.5\times 10^{-3} eV^2$.Comment: 10 pages, Latex. Expanded discussion of mixing angles mainly in an Appendi

Flavour from the Planck scale to the electroweak scale

We discuss a theory of flavour in which Higgs Yukawa couplings are related to those of the new scalar triplet leptoquark and/or $Z'$ responsible for $R_{K^{(*)}}$, with all couplings arising effectively from mixing with a vector-like fourth family, whose mass may be anywhere from the Planck scale to the electroweak scale for the leptoquarks explanation, but is pinned down to the TeV scale if the $Z'$ exchange plays a role. However, in this particular model, only leptoquark exchange can contribute significantly to $R_{K^{(*)}}$, since $Z'$ exchange is too constrained from $B_s$ mixing and $\tau \rightarrow 3 \mu$, although other Higgs Yukawa matrix structures may allow it.Comment: 6 pages, 11 figures. Contribution to the 2019 EW session of the 54th Rencontres de Morion

Minimal see-saw model predicting best fit lepton mixing angles

We discuss a minimal predictive see-saw model in which the right-handed neutrino mainly responsible for the atmospheric neutrino mass has couplings to (nu_e, nu_mu, nu_tau) proportional to (0,1,1) and the right-handed neutrino mainly responsible for the solar neutrino mass has couplings to (nu_e, nu_mu, nu_tau) proportional to (1,4,2), with a relative phase eta = -2pi/5. We show how these patterns of couplings could arise from an A_4 family symmetry model of leptons, together with Z_3 and Z_5 symmetries which fix eta = -2pi/5 up to a discrete phase choice. The PMNS matrix is then completely determined by one remaining parameter which is used to fix the neutrino mass ratio m_2/m_3. The model predicts the lepton mixing angles theta12=34 degrees, theta23=41 degrees, theta13=9.5 degrees, which exactly coincide with the current best fit values for a normal neutrino mass hierarchy, together with the distinctive prediction for the CP violating oscillation phase delta =106 degrees.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1304.626

Jason L. Powell, Social Theory and Aging, Rowman and Littlefield, Lanham, Maryland, 2005, 157 pp., pbk $16.95, ISBN 0 7425 1954 6.

We construct a realistic Supersymmetric Grand Unified Theory of Flavour based on PSL(7)×SO(10), where the quarks and leptons in the 16 of SO(10) are assigned to the complex triplet representation of PSL(7), while the flavons are assigned to a combination of sextets and anti-triplets of PSL(7). Using a D-term vacuum alignment mechanism, we require the flavon sextets of PSL(7) to be aligned along the 3-3 direction leading to the third family Yukawa couplings, while the flavon anti-triplets describe the remaining Yukawa couplings. Other sextets are aligned along the neutrino flavour symmetry preserving directions leading to tri-bimaximal neutrino mixing via a type II see-saw mechanism, with predictions for neutrinoless double beta decay and cosmology. <br/

750 GeV Diphoton Resonance from Singlets in an Exceptional Supersymmetric Standard Model

The 750-760 GeV diphoton resonance may be identified as one or two scalars and/or one or two pseudoscalars contained in the two singlet superfields S_{1,2} arising from the three 27-dimensional representations of E_6 . The three 27s also contain three copies of colour-triplet charge \mp 1/3 vector-like fermions D,\bar{D} and two copies of charged inert Higgsinos \tilde{H}^{+},\tilde{H}^{-} to which the singlets S_{1,2} may couple. We propose a variant of the E_6SSM where the third singlet S_3 breaks a gauged U(1)_N above the TeV scale, predicting Z'_N, D,\bar{D}, \tilde{H}^{+},\tilde{H}^{-} at LHC Run 2, leaving the two lighter singlets S_{1,2} with masses around 750 GeV. We calculate the branching ratios and cross-sections for the two scalar and two pseudoscalar states associated with the S_{1,2} singlets, including possible degeneracies and maximal mixing, subject to the constraint that their couplings remain perturbative up to the unification scale.Comment: 22 pages, 4 figures, some minor changes to the text, references adde

LHC Signatures of the Constrained Exceptional Supersymmetric Standard Model

We discuss two striking Large Hadron Collider (LHC) signatures of the constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m_0, soft trilinear coupling A_0 and soft gaugino mass M_{1/2}. The first signature we discuss is that of light exotic colour triplet charge 1/3 fermions, which we refer to as D-fermions. We calculate the LHC production cross section of D-fermions, and discuss their decay patterns. Secondly we discuss the E6 type U(1)_N spin-1 Z' gauge boson and show how it may decay into exotic states, increasing its width and modifying the line shape of the dilepton final state. We illustrate these features using two representative cE6SSM benchmark points, including an "early LHC discovery" point, giving the Feynman rules and numerical values for the relevant couplings in order to facilitate further studies.Comment: 30 pages, 5 figures, corrections to figure caption

Spectrum of Higgs particles in the Exceptional Supersymmetric Standard Model

We discuss the spectrum of Higgs bosons in the framework of the exceptional supersymmetric standard model. The presence of a $Z'$ and exotic particles predicted by the exceptional SUSY model allows the lightest Higgs particle to be significantly heavier than in the MSSM and NMSSM. When the mass of the lightest Higgs boson is larger than $135-140 {GeV}$ the heaviest scalar, pseudoscalar and charged Higgs states lie beyond the ${TeV}$ range.Comment: Presented at 12th Lomonosov Conference on Elementary Particle Physics, Moscow, Russia, 25-31 August 2005, some minor changes to the text, references adde