arXiv subjects
Publications and source records attributed to Paul H. Frampton.
For the three family quark flavor mixing, the best parametrization is the original Kobayashi-Maskawa matrix, $V_{KM}$, with four real parameters: three rotation angles $θ_{1,2,3}$ and one phase $δ$. A popular way of presentation is by the unitarity triangle which, however, explicitly displays only three, not four, independent parameters. Here we propose an alternative presentation which displays simultaneously all four parameters: the unitarity boomerang.
Although the unitarity triangles ($UTs$) carry information about the Kobayashi-Maskawa (KM) quark mixing matrix, it explicitly contains just three parameters which is one short to completely fix the KM matrix. It has been shown recently, by us, that the unitarity boomerangs ($UB$) formed using two $UTs$, with a common inner angle, can completely determine the KM matrix and, therefore, better represents, quark mixing. Here, we study detailed properties of the $UBs$, of which there are a total 18 possible. Among them, there is only one which does not involve very small angles and is the ideal one for practical uses. Although the $UBs$ have different areas, there is an invariant quantity, for all $UBs$, which is equal to a quarter of the Jarlskog parameter $J$ squared. Hunting new physics, with a unitarity boomerang, can reveal more information, than just using a unitarity triangle.
We argue that a primordial black hole is a natural and unique candidate for all dark matter. We show that, in a smooth-hybrid new double inflation model, a right amount of the primordial black holes, with a sharply-defined mass, can be produced at the end of the smooth-hybrid regime, through preheating. We first consider masses < 10^(-7)M_sun which are allowed by all the previous constraints. We next discuss much heavier mass 10^5 M_sun hinted at by entropy, and galactic size evolution, arguments. Effects on the running of the scalar spectral index are computed.
The dimensionless entropy, ${\cal S} \equiv S/k$, of the visible universe, taken as a sphere of radius 50 billion light years with the Earth at its "center", is discussed. An upper limit ($10^{112}$), and a lower limit ($10^{102}$), for ${\cal S}$ are introduced. It is suggested that intermediate-mass black holes (IMBHs) constitute all dark matter, and that they dominate ${\cal S}$.
A flavor-nonuniversal chiral color model is introduced. It is used for comparison to the recent data on $\bar{p} p \to \bar{t} t$. We concluded that the data are consistent with interpretation as an axigluon exchange within 1$σ$ and a unique rise and fall behavior is predicated with regard to the asymmetry $A^t_{FB}$ as a function of $t \bar{t}$ invariant mass, which can distinguish our model from others before one discovers the axigluon resonance. Further aspects of the model are discussed.
In a variant of chiral color with the electroweak gauge group generalized to $SU(3)_L \times U(1)$ anomaly cancellation occurs more readily than in the $SU(2)_L \times U(1)$ case. Three families are required by anomaly cancellation and the top family appears non-sequentially.
Based on constraints from microlensing and disk stability, both with and without limitations from wide binary surveys, we estimate the total number and entropy of intermediate mass black holes. Given the visible universe comprises $10^{11}$ halos each of mass $\sim 10^{12} M_{\odot}$, typical core black holes of mean mass $\sim 10^7 M_{\odot}$ set the dimensionless entropy ($S/k$) of the universe at a thousand googols. Identification of all dark matter as black holes sets the dimensionless entropy of the universe at ten million googols, implying that dark matter can contribute over 99% of entropy, which favors all dark matter as black holes in the mass regime of $ \sim 10^{5} M_{\odot}$.
For the universe I use dimensionless entropy $S/k = \ln Ω$ for which the most convenient unit is the googol ($10^{100}$) and identify all dark matter as black holes whereupon the present entropy is about a thousand googols. While the energy of the universe has been established to be about 0.04 baryons, 0.24 dark matter and 0.72 dark energy, the cosmological entropy is almost entirely, about $(1 - 10^{-15})$, from black holes and only $10^{-15}$ from everything else. This identification of all dark matter as black holes is natural in statistical mechanics.
Using the binary tetrahedral group $T^{'}$, the three angles and phase of the quark CKM mixing matrix are pursued by symmetry-breaking which involves $T^{'}$-doublet VEVs and the Chen-Mahanthappa CP-violation mechanism. The NMRT$^{'}$M, Next-to-Minimal-Renormalizable -T$^{'}$-Model is described, and its one parameter comparison to experimental data is explored.
While the energy of the universe has been established to be about 0.04 baryons, 0.24 dark matter and 0.72 dark energy, the cosmological entropy is almost entirely, about $(1 - 10^{-15})$, from black holes and only $10^{-15}$ from everything else. This identification of all dark matter as black holes is natural in statistical mechanics. Cosmological history of dark matter is discussed.
A discussion of the entropy of the universe leads to the suggestion of very many intermediate-mass black holes between thirty and three hundred thousand solar masses in the halo. It is consistent with observations on wide binaries as well as microlensing and considerations of disk stability that such IMBHs constitute all cold dark matter
Generalizing a previous model to accommodate the third quark family and CP violation, we present a $T^{'}$ model which predicts tribimaximal neutrino (PMNS) mixings while the central predictions for quark mixings are $|V_{td}/V_{ts}| = 0.245$ and $|V_{ub}/V_{cb}| = 0.237$ with a predicted CP violating KM phase $δ_{KM} = 65.8^{0}$. All these are acceptably close to experiment, including the KM phase for which the allowed values are $63^{0} < δ_{KM} < 72^{0}$, and depend only on use of symmetry $T^{'} \times Z_2$ to define the model and no additional parameters.
A nonabelian finite flavor group $G \subset SO(3)$ can have double covering $G^{'} \subset SU(2)$ such that $G \not\subset G^{'}$. This situation is not contradictory, but quite natural, and we give explicit examples such as $G=D_n, G^{'}=Q_{2n}$ and $G=T, G^{'}=T^{'}$. This observation can be crucial in particle theory model building.
In an SU(9) model of gauged family unification, we propose an explanation for why angles observed in the lepton flavor ({\it PMNS}) mixing matrix are significantly larger than those measured for any analagous quark flavor ({\it KM}) mixing angle. It is directly related to a see-saw mechanism that we assume to be responsible for the generation of neutrino masses. Our model is more constrained and therefore even more predictive than a model previously proposed by Barr.
It is shown that the ratio of branching ratios in Higgs boson decay $r = Γ(H \to τ^+τ^-)/Γ(H\to μ^+μ^-)$ in a simplified ($T^{'} \times Z_2$) model is $(r)_{T^{'} \times Z_2} \simeq 0.001$. This prediction is on a footing with the successful one in $(s, d)$ mixing, $\tan 2 Θ_{12} = {1/3}(\sqrt{2})$. This value for $r$ differs from that of the minimal standard model by a very large factor (over 250,000) and can provide a smoking gun for ($T^{'} \times Z_2$) flavor symmetry.
Observational searches for Intermediate-Mass Black Holes (IMBHs), defined to have masses between 30 and 300,000 solar masses, provide limits which allow up to ten percent of what is presently identified as halo dark matter to be in the form of IMBHs. These concentrate entropy so efficiently that the halo contribution can be bigger than the core supermassive black hole. Formation of IMBHs is briefly discussed.
Observational searches for Intermediate Mass Black Holes (IMBHs), defined to have masses between 30 and 300,000 solar masses, provide limits which allow up to ten percent of what is presently identified as halo dark matter to be in the form of IMBHs. These concentrate entropy so efficiently that the halo contribution can be bigger than the core supermassive black hole. Formation of IMBHs is briefly discussed.
It is commonly assumed that dark matter may be composed of one or at most a few elementary particles. PAMELA data present a window of opportunity into a possible relationship between luminous and dark matter. Along with ATIC data the two positron excesses are interpreted as a reflection of dark matter family structure. In a unified model it is predicted that at least a third enhancement might show up at a different energy. The strength of the enhancements however depends on interfamily mixing angles.