T' and the Cabibbo Angle
The use of the binary tetrahedral group ($T^{'}$) as flavor symmetry is discussed. I emphasize the CKM quark and PMNS neutrino mixings. I present a novel formula for the Cabibbo angle.
hep-ph↗
arXiv subjects
Paul H. Frampton
Publications and source records attributed to Paul H. Frampton.
Past Eras In Cyclic Cosmological Models
In infinitely cyclic cosmology past eras are discussed using set theory and transfinite numbers. One consistent scenario, already in the literature, is where there is always a countably infinite number, $\aleph_0$, of universes and no big bang. I describe here an alternative where the present number of universes is $\aleph_0$ and in the infinite past there was only a finite number of universes. In this alternative model it is also possible that there was no big bang.
hep-th↗
Cosmological Entropy and Black Holes in Galactic Halos
In this talk we discuss intermediate mass black holes (IMBHs) by their amplilification of distant sources; MACHO searches have studied event times $2 h \lesssim t_0 \lesssim 2 y$ corresponding masses in the range $10^{-6} M_{\odot} \lesssim M \lesssim 100 M_{\odot}$. We suggest that larger masses up to $10^6 M_{\odot}$ are also of considerable interest by arguments about the entropy of the universe. One percent by mass of dark energy can provide ninety-nine percent of total entropy.
astro-ph.CO↗
High Longevity Microlensing Events and Dark Matter Black Holes
Gravitational microlensing has been employed to identify massive halo objects by their amplification of distant sources; MACHO searches have studied event times $2 h \lesssim t_0 \lesssim 2 y$ corresponding masses in the range $10^{-6} M_{\odot} \lesssim M \lesssim 100 M_{\odot}$. We suggest that larger masses up to $10^6 M_{\odot}$ are also of considerable interest. It has not been excluded that there is a significant number of halo black holes with such high masses as suggested by cosmological entropy considerations and potentially detectable by high longevity microlensing events.
gr-qc↗
Doubly-Charged Boson Production in $p \bar{p}$ Collisions at $\sqrt{s} = 1.96$ TeV
It is suggested that the observed excess of muons in studies of $p \bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV arises from the decay of doubly-charged bosons. Such particles are predicted in the 3-3-1 model where the electroweak gauge group is extended to $SU(3) \times U(1)$.
hep-ph↗
Predictions of Neutrino Mixing Angles in a T'Model
Flavor symmetry ($T^{'} \times Z_2$) where $T^{'}$ is the binary tetrahedral group predicts for neutrino mixing angles $θ_{13} = \sqrt{2} (\fracπ{4} - θ_{23})$ and, with one phenomenological input, provides upper and lower bounds on both $θ_{13}$ and $θ_{23}$. The predictions arise from the deviation of the Cabibbo angle $Θ_{12}$ from its lowest-order value $\tan 2Θ_{12} = (\sqrt{2})/3$ and from the $T^{'}$ mechanism which relates mixing of $(ν_τ, ν_μ, ν_e)$ neutrinos to mixing of $(s, d)$ quarks.
hep-ph↗
Renormalizable $A_4$ Model for Lepton Sector
We revisit $A_4$ flavor symmetry for the lepton sector with minimal Higgs sector, namely just one $A_4-$triplet SU(2)-doublet scalar. To increase predictivity even further, we impose the constraint of renormalizability. A geometric interpretation of an $A_4-$triplet aids our understanding of tribimaximal mixing. To increase predictivity even further, we impose the constraint of renormalizability. We investigate the neutrino mass hierarchy in such a minimal $A_4$ model and find there are two solutions: one with $m_2 \gg m_1 = m_3$ is phenomenologically unacceptable; the other with $m_3 \gg m_1 = m_2$ is a normal hierarchy. An inverted hierarchy is impossible without addition of more parameters by either more Higgs scalars or higher-order irrelevant operators.
hep-ph↗
Innocuous Implications of a Minimum Length in Quantum Gravity
A modification to the time-energy uncertainty relation in quantum gravity has been interpreted as increasing the duration of fluctuations producing virtual black holes with masses greater than the Planck mass. I point out that such virtual black holes have an exponential factor arising from the action such that their contribution to proton decay is suppressed, rather than enhanced, relative to Planck-mass black holes.
hep-th↗
Simplified Renormalizable $T^{'}$ Model for Tribimaximal Mixing and Cabibbo Angle
In a simplified renormalizable model where the neutrinos have PMNS (Pontecorvo-Maki-Nakagawa-Sakata) mixings tan$^{2} θ_{12} = {1/2}, θ_{13}=0, θ_{23} = π/4$ and with flavor symmetry $T^{'}$ there is a corresponding prediction where the quarks have CKM (Cabibbo-Kobayashi-Maskawa) mixings tan$2 Θ_{12} = \frac{\sqrt{2}}{3}, Θ_{13}=0, Θ_{23} =0$.
hep-ph↗
Strong Incompatability of Tribimaximal Mixing with Quark-Lepton Complementarity
Although tribimaximal mixing (TBM) and quark-lepton complementarity (QLC) are both compatible with experimental data within one standard deviation ($ 1 σ$), the TBM and QLC assumptions are mutually exclusive by $56 σ$.
hep-ph↗
Relations Between Standard Model Parameters from $T^{'}$ Flavor Symmetry
Spontaneously broken flavor symmetry involving the binary tetrahedral group $T^{'}$ relates parameters in the standard model. In one example the CP violating Pontecorvo-Maki-Nakagawa-Sakata phase $δ_{PMNS}$ and atmospheric mixing angle $θ_{23}$ of neutrinos are related to the Cabibbo mixing angle $Θ_C$ for quarks. A second formula relates a ratio of neutrino mass eigenvalues to the Cabibbo angle.
hep-ph↗
Study of $T'$ Flavor Symmetry
A systematic study of the flavor group $T^{'}$ is presented in terms of a specific model which extends the standard model symmetry to $[SU(3) \times SU(2) \times U(1)]_{(local)} \times [T^{'} \times Z_2 \times Z_2^{'} \times Z_2^{''}]_{(global)}$. In the model, approximate tribimaximal mixing occurs in the neutrino sector. There is also one new formula relating a quark mixing parameter to quark masses. Most exciting are new formulas relating lepton and quark mixing parameters of the type usually associated with grand unification but here relying only on the group structure of $T^{'}$. Flavor-changing neutral currents in the model lead to lower bounds on scalar masses.
hep-ph↗
Particle phenomenology and Maldacena
A brief review is offered of employing Maldacena's AdS/CFT correspondence in attempting to identify a model which extends to higher energy the standard model of particle phenomenology.
hep-th↗
Multifluid Models for Cyclic Cosmology
Inspired by the Landau two-fluid model of superfluidity, we consider a similar multifluid description for cosmology where two normal fluids occur for matter and radiation respectively. For cyclic cosmology, two dark energy superfluid components turn out to be insufficient but three superfluids can lead to a sensible five-fluid model which in a certain limit becomes indistinguishable from the brane-world cyclic model proposed earlier (Baum and Frampton). Distinguishing more general five-fluid models from brane-world models for cyclic cosmology could be feasible with more accurate observational data.
hep-th↗
Upper and Lower Bounds on Gravitational Entropy
The entropy in the interior of the Universe has many contributions including well understood ones from radiation and relic neutrinos. The gravitational entropy is larger and more subtle. One contribution which provides our lower bound is from supermassive black holes at the centers of galaxies. The remainder is harder to pin down. We suggest an upper bound which is many orders of magnitude below the holographic bound yet above that of the supermassive black holes. We propose that gravitational entropy in dark matter halos is the largest contributor to the present entropy of the universe.
gr-qc↗
Constraints on Deflation from the Equation of State of Dark Energy
In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE-condition ({\it Comes Back Empty}) imposes a lower bound on the number $N_{\rm cp}$ of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state $w = p/ρ= -1 - ϕ$ with $ϕ> 0$. More accurate measurement of $ϕ$ will constrain $N_{\rm cp}$. The critical density $ρ_c$ in the model has a lower bound $ρ_c \ge (10^9 {\rm GeV})^4$ or $ρ_c \ge (10^{18} {\rm GeV})^4$ when the smallest bound state has size $10^{-15}$m, or $10^{-35}$m, respectively.
hep-th↗
Flavor Symmetry for Quarks and Leptons
Present data on neutrino masses and mixing favor the highly symmetric tribimaximal neutrino mixing matrix which suggests an underlying flavor symmetry. A systematic study of non-abelian finite groups of order $g \leq 31$ reveals that tribimaximal mixing can be derived not only from the well known tetrahedral flavor symmetry $T \equiv A_4$, but also by using the binary tetrahedral symmetry $T^{'} \equiv SL_2(F_3)$ which does not contain the tetrahedral group as a subgroup. $T^{'}$ has the further advantage that it can also neatly accommodate the quark masses including a heavy top quark.
hep-ph↗
Quiver Gauge Theory and Conformality at the TeV Scale
This review describes the conformality approach to extending the standard model of particle phenomenology using an assumption of no conformal anomaly at high energy. Topics include quiver gauge theory, the conformality approach to phenomenology, strong-electroweak unification at 4 TeV, cancellation of quadratic divergences, cancellation of U(1) anomalies, and a dark matter candidate.
hep-ph↗