arXiv subjects
Publications and source records attributed to Paul H. Frampton.
By studying symmetric mass textures for the up and down quark sectors, and expanding in a small parameter $λ\sim sinθ_C$, bounds are set on entries commonly assumed to vanish. Consequences of a 2 + 1 family structure which can result from horizontal symmetry are examined. Generalizing to squarks, we study suppression of Flavor Changing Neutral Currents by mass degeneracy and/or small mixing angles.
We study the production of scalar and vector leptoquarks in $e^-e^-$ scattering. We use the most general couplings to the known fermions which are dimensionless, baryon and lepton number conserving, and $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ invariant. Expressions are presented for production cross sections and predictions are given for future linear colliders.
Recent interest in horizontal symmetry model building has been driven mainly by the large top mass and hence strong hierarchy in quark masses, and the possibility of appropriately constrained soft squark mass matrices, in place of an assumed universality condition, for satisfying the relevant FCNC constraints. Here we present the first successful SUSY-$SU(5)$ model that has such a feature. The horizontal symmetry is a gauged $(Q_{12} \times U(1))_H$ ($\subset (SU(2) \times U(1))_H$). All nonrenormalizable terms compatible with the symmetry are allowed in the mass matrix constructions. Charged lepton masses can also be accommodated.
By extending the standard gauge group to SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)_X with X charges carried only by the third family we accommodate the LEP measurement of R_b and predict a potentially measurable discrepancy in A_{FB}^{b} in e^+e^- scattering and that D^0\bar{D}^0 mixing may be near its experimental limit. The Z', which explicitly violates the GIM mechanism, can nevertheless be naturally consistent with FCNC constraints. Direct detection of the Z' is possible but challenging.
Using effective Lagrangians, we argue that any time-reversal-violating but parity-conserving effects are too small to be observed in flavor-conserving nuclear processes without dramatic improvement in experimental accuracy. In the process we discuss other arguments that have appeared in the literature.
By including the effects of superstring thresholds, we reconsider minimal string unification together with the requirement of producing a supersymmetry-breaking gluino condensate in the hidden sector. This gives, for examples of phenomenologically-viable $Z_8'$ and other related orbifolds, the constraint that $0.1215 \leq α_s(M_Z) \leq 0.1270$. In such models, a hidden photino can be a source of cosmological dark matter detectable by gravitational microlensing.
It is shown how to use as horizontal symmetry the dicyclic group $Q_6 \subset SU(2)$ in a supersymmetric unification $SU(5)\otimes SU(5)\otimes SU(2)$ where one $SU(5)$ acts on the first and second families, in a horizontal doublet, and the other acts on the third. This can lead to acceptable quark masses and mixings, with an economic choice of matter supermultiplets, and charged lepton masses can be accommodated.
Using as a flavor symmetry a finite nonabelian dicyclic $Q_{2N}$ group, we show how to derive quark mass matrices with two arrangements of symmetric texture zeros which are phenomenologically viable. Three other such acceptable textures in the recent literature are unattainable in this approach and hence disfavored. We assume massive vector-like fermions and Higgs singlets transforming as judiciously-chosen $Q_{2N}$ doublets and use the tree-level mass generation mechanism of Froggatt and Nielsen.
The CP violation parameter $Re(ε'/ε)$ has previously been calculated in the standard model and the result depends on the top quark mass in an exciting way. We consider how the result is modified in two specific extensions of the standard model. The first adds only fermions, an extra vector-like quark doublet, and tends to reduce $Re(ε'/ε)$. The second contains three extended families with the third family treated differently and additional gauge bosons - the 331 model - and can accommodate larger values of $Re(ε'/ε)$ for a given $m_t$. When the experimental values of $m_t$ and $Re(ε'/ ε)$ are known more accurately, it will allow discrimination between theories. If the lower experimental number $Re(ε'/ε) = (0.74 \pm 0.60) \times 10^{-3}$ (Fermilab, E731) is confirmed and $m_t$ is near the value 175GeV the standard model is acceptable. But, if the higher value $Re(ε'/ε) = (2.3 \pm 0.65) \times 10^{-3}$ (CERN, NA31) persists, a dynamics like the 331 model where the third family is treated differently from the first two and there exist additional gauge bosons seems to be favored.
After a brief introduction to what are the basic flavor questions to be addressed, I introduce the underlying ideas of horizontal symmetries, with group $G_H$. For the purposes of specific model building, it is useful to classify models according to the scale at which $G_H$ is broken. I consider the three cases: below $m_t$; somewhat above $m_t$; and at $M_{GUT}$. After a discussion of the shadow sector in the $E_6 \times E_8'$ superstring, there is a summary.
It now appears phenomenologically that the third family may be essentially different from the first two. Particularly the high value of the top quark mass suggests a special role. In the standard model all three families are treated similarly [becoming exactly the same at asymptotically high energies] so I need to extend the model to accommodate the goal of a really different third family. In this article I describe not one but two such viable extensions, quite different one from another. The first is the 331 model which predicts dileptonic gauge bosons. In the second, using as a flavor symmetry a finite nonabelian dicyclic $Q_{2N}$ group, I show how to derive quark mass matrices with two arrangements of symmetric texture zeros which are phenomenologically viable. Three other such acceptable textures in the recent literature are unattainable in this approach and hence disfavored. I assume massive vector-like fermions and Higgs singlets transforming as judiciously-chosen $Q_{2N}$ doublets and use the tree-level mass generation mechanism of Froggatt and Nielsen.
We consider the production of a 300GeV dilepton in very intense 4GeV electron scattering off of a lead target. The production cross-section and angular distribution of the resulting muons are calculated. There occur several such events per year, and their detection is rendered feasible by measurement of $e^+μ^-μ^-$ angular correlations.
The 3-3-1 model, based on the gauge group $SU(3)_c\times SU(3)_L\times U(1)_X$, makes a natural prediction of three generations based on anomaly cancellation. Since this is accomplished by incorporating the third family of quarks differently from the other two, it leads to potentially large flavor changing neutral currents. A sensitive place to look for such effects is the flavor changing $b\to sγ$ decay, which has recently been measured at CLEO. We compute this decay rate in the 3-3-1 model and compare it with that of the two-Higgs-doublet model, a subset of the full 3-3-1 model. We find that the additional 3-3-1 physics weakens the bound on the charged Higgs mass from $M_{H^+}>290$~GeV to $M_{H^+}\agt120$~GeV.
It now appears phenomenologically that the third family of fundamental fermions may be essentially different fron the first two. Particularly the high value (174GeV?) of the top quark mass suggests a special role. In the standard model all three families are treated similarly [becoming exactly the same at asymptotically high energies] so we need to extend the model to accommodate the goal of a really different third family. In this article I describe not one but two such viable extensions, quite different one from another. The first is the 331 model which predicts dileptonic gauge bosons. The second is the $Q_6$ model which predicts additional leptons between 50 and 200 GeV. One expects there are many other models of this general type characterized by the prediction of new particles at accessible masses. Supersymmetrization will not be discussed here.
Absract It is proposed that there exist, within a new $SU(2)^{'}$, a gauged discrete group $Q_6$ (the order 12 double dihedral group) acting as a family symmetry. This nonabelian finite group can explain hierarchical features of families, using an assignment for quarks and leptons dictated by the requirements of anomaly cancellation and of no additional quarks.
We argue that it is inconsistent to ignore the gravitational backreaction for on-shell superstring states at the Planck mass and beyond, and that these quantum states become Kerr black holes in the classical limit. Consequences are discussed.
The use of nonabelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g = 31, the most appealing candidates are two subgroups of SU(2): the dicyclic [double dihedral] group G = $Q_6 ={ }^{(d)}D_3$ ( g = 12 ) and the double tetrahedral group $^{(d)}T = Q_4\tilde{\times}Z_3$ ( g = 24 ). Both can allow a hierarchy $t > b, τ> c > s, μ> u, d, e$. The top quark is uniquely allowed to have a G symmetric mass. Sequential breaking of G and radiative corrections give the smaller masses. Anomaly freedom for gauging $G \subset SU(2)$ is a strong constraint in assignment of fermions to representations of G.
Under the assumptions that $SU(3)_c\times U(1)_Y \times G^{\prime}$ with $G^{\prime}$ simple is a local symmetry group at high energies, that color is parity-conserving, and the Y-charges are irreducible, we show that anomaly constraints imply the minimal set of fermions is fifteen in number. Given this minimal set, we further show that $G^{\prime}$ must be $SU(2)$ and the unbroken gauge symmetry is {\it either} color {\it or} the product of color with electric charge.