We exploit a recent advance in the study of topological superconductors to propose a solution to the family puzzle of particle physics in the context of SO(18) (or more correctly, Spin(18)) grand unification. We argue that Yukawa couplings of interme
diate strength may allow the mirror matter and extra families to decouple at arbitrarily high energies. As was clear from the existing literature, we have to go beyond the Higgs mechanism in order to solve the family puzzle. A pattern of symmetry breaking which results in the SU(5) grand unified theory with horizontal or family symmetry USp(4) = Spin(5) (or more loosely, SO(5)) leaves exactly three light families of matter and seems particularly appealing. We comment briefly on an alternative scheme involving discrete non-abelian family symmetries. In a few lengthy appendices we review some of the pertinent condensed matter theory.
Learned et. al. proposed that a sufficiently advanced extra-terrestrial civilization may tickle Cepheid and RR Lyrae variable stars with a neutrino beam at the right time, thus causing them to trigger early and jogging the otherwise very regular phas
e of their expansion and contraction. This would turn these stars into beacons to transmit information throughout the galaxy and beyond. The idea is to search for signs of phase modulation (in the regime of short pulse duration) and patterns, which could be indicative of intentional, omnidirectional signaling. We have performed such a search among variable stars using photometric data from the Kepler space telescope. In the RRc Lyrae star KIC 5520878, we have found two such regimes of long and short pulse durations. The sequence of period lengths, expressed as time series data, is strongly auto correlated, with correlation coefficients of prime numbers being significantly higher ($p=99.8$%). Our analysis of this candidate star shows that the prime number oddity originates from two simultaneous pulsation periods and is likely of natural origin. Simple physical models elucidate the frequency content and asymmetries of the KIC 5520878 light curve. Despite this SETI null result, we encourage testing other archival and future time-series photometry for signs of modulated stars. This can be done as a by-product to the standard analysis, and even partly automated.
We document the presence of a few Cepheid and RR Lyrae variable stars with previously unrecognized characteristics. These stars exhibit the property of a period ratio of main pulsation divided by secondary pulsation P1/P2 very close to sqrt(2). Other
stars of these types have period ratios which do not show clustering with a close association and a single remarkable non-harmonic number. Close examination reveals a deviation of multiples of a few times ~0.06% for these stars. This deviation seems to be present in discrete steps on the order of ~0.000390(4), indicating the possible presence of a sort of fine structure in this oscillation.
We study the LHC phenomenology of a general class of Private Higgs (PH) models, in which fermions obtain their masses from their own Higgs doublets with $op(1)$ Yukawa couplings, and the mass hierarchy is translated into a dynamical chain of vacuum e
xpectation values. This is accomplished by introducing a number of light gauge-singlet scalars, the darkons, some of which could play the role of dark matter. These models allow for substantial modifications to the decays of the lightest Higgs boson, for instance through mixing with TeV-scale PH fields and light darkons: the simplest version of the model predicts the ratios of partial widths to satisfy $G(h to VV^*)_{text{PH}}/G(h to VV^*)_{text{SM}} approx G(h to gg)_{text{PH}}/G(h to gg)_{text{SM}} leq 1$ and $G(h to bbar b)_{text{PH}}/G(h to bbar b)_{text{SM}} sim op(1)$, where the inequalities are saturated only in the absence of Higgs mixing with light darkons. An extension of the model proposed previously for generating nonzero neutrino masses can also contribute substantially to $h to gg$ without violating electroweak precision constraints. If the Higgs coupling to fermions is found to deviate from the Standard Model (SM) expectation, then the PH model may be a viable candidate for extending the SM.
It is consistent with the measurement of theta_13 ~ 0.15 by Daya Bay to suppose that, in addition to being unitary, the neutrino mixing matrix is also almost hermitian, and thereby only a small perturbation from diag(+1,-1,-1) in a suitable basis. We
suggest this possibility simply as an easily falsifiable ansatz that has not already been studied, as well as to offer a potentially useful means of organizing the experimental data. We explore the phenomenological implications of this ansatz and parametrize one type of deviation from the leading order relation |V_e3| approx |V_tau 1|. We also emphasize the group-invariant angle between orthogonal matrices as a means of comparing to data. The discussion is purely phenomenological, without any attempt to derive the condition V{dag} approx V from a fundamental theory.
We use the discrete group Sigma(81) = (Z_3 x Z_3 x Z_3)rtimes Z_3 to explore a particular region of parameter space in the Private Higgs model. In doing so we suggest a relation among the off-diagonal entries of the neutrino mass matrix and a possibl
e explanation for the muon magnetic moment anomaly, a_mu^{exp}-a_mu^{SM} ~ 10^{-9}. We predict three new nearly degenerate Higgs doublets with masses of order ~ 500 GeV to ~ 1 TeV, and three nearly degenerate SM-singlet TeV-scale neutrinos. The largest scale in the model is ~ 10 TeV, so there is no severe hierarchy problem. The appendix is devoted to the group theory of Sigma(81).
Motivated by the possibility that the amplitude for neutrinoless double beta decay may be much smaller than the planned sensitivity of future experiments, we study ansatze for the neutrino mass matrix with $M_{ee} = 0$. For the case in which CP is co
nserved, we consider two classes of real-valued mass matrices: Class I defined by $|M_{emu}| = |M_{etau}|$, and Class II defined by $|M_{mumu}| = |M_{tautau}|$. The important phenomenological distinction between the two is that Class I permits only small values of $V_{e3}$ up to $sim 0.03$, while Class II admits large values of $V_{e3}$ up to its empirical upper limit of 0.22. Then we introduce CP-violating complex phases into the mass matrix. We show that it is possible to have tribimaximal mixing with $M_{ee} = 0$ and $|M_{mutau}| = |M_{mumu}| = |M_{tautau}|$ if the Majorana phase angles are $pmpi/4$. Alternatively, for smaller values of $|M_{mutau}| = |M_{mumu}| = |M_{tautau}|$ it is possible to obtain $|V_{e3}| sim 0.2$ and generate relatively large CP-violating amplitudes. To eliminate phase redundancy, we emphasize rephasing any mass matrix with $M_{ee} = 0$ into a standard form with two complex phases. The discussion alternates between analytical and numerical but remains purely phenomenological, without any attempt to derive mass matrices from a fundamental theory.
