Quarkonium Mass Splitting Revisited: Effects of Closed Mesonic Channels

Modifications of the mass spectrum the quarkonium induced by its virtual dissociation into a pair of heavy mesons is considered. Coupling between quark and mesonic channels results in noticeable corrections to spin-dependent mass splitting. In particular, the observable hierarchy of mass splittings in the $\chi_c, \chi_b$ and $\chi'_b$ multiplets is reproduced.Comment: 9 pages, plain LaTe

Measurement of tan beta in associated t H^\pm Production in gamma gamma Collisions

The ratio of neutral Higgs field vacuum expectation values, tan beta, is one of the most important parameters to determine in type-II Two-Higgs Doublet Models (2HDM), specifically the Minimal Supersymmetric Standard Model (MSSM). Assuming the energies and integrated luminosity of a future high energy e^+e^- linear collider of sqrt{s}=500, 800, 1000, and 1500 GeV and L=1 ab^{-1} we show that associated t H^+/- production in gamma gamma collisions can be used to make an accurate determination of tan beta for low and high tan beta by precision measurements of the gamma gamma -> H^+/- t + X cross section.Comment: 7 pages, 11 figures, uses REVTEX

On the population of remnant FRII radio galaxies and implications for radio source dynamics

The purpose of this work is two-fold: (1) to quantify the occurrence of ultra-steep spectrum remnant FRII radio galaxies in a 74 MHz flux limited sample, and (2) perform Monte-Carlo simulations of the population of active and remnant FRII radio galaxies to confront models of remnant lobe evolution, and provide guidance for further investigation of remnant radio galaxies. We find that fewer than 2$\%$ of FRII radio galaxies with S$_{ \rm74~MHz} > 1.5$ Jy are candidate ultra-steep spectrum remnants, where we define ultra-steep spectrum as $\alpha_{\rm 74~MHz}^{\rm 1400~MHz} > 1.2$. Our Monte-Carlo simulations demonstrate that models involving Sedov-like expansion in the remnant phase, resulting in rapid adiabatic energy losses, are consistent with this upper limit, and predict the existence of nearly twice as many remnants with normal (not ultra-steep) spectra in the observed frequency range as there are ultra-steep spectrum remnants. This model also predicts an ultra-steep remnant fraction approaching 10$\%$ at redshifts $z < 0.5$. Importantly, this model implies the lobes remain over-pressured with respect to the ambient medium well after their active lifetime, in contrast with existing observational evidence that many FRII radio galaxy lobes reach pressure equilibrium with the external medium whilst still in the active phase. The predicted age distribution of remnants is a steeply decreasing function of age. In other words young remnants are expected to be much more common than old remnants in flux limited samples. For this reason, incorporating higher frequency data $\gtrsim 5$ GHz will be of great benefit to future studies of the remnant population.Comment: 19 pages, 8 figures, 4 table

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter $\sigma$ confined to a two-dimensional channel of width $1.95\,\sigma$ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction $\phi_K$ that is less than the maximum possible $\phi_{\rm max}$, the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any \emph{real} divergence of the pressure at $\phi_K$. We give arguments that this avoided phase transition is a structural feature -- the remnant in our narrow channel system of the hexatic to crystal transition -- but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale $\tilde{\xi}_3$ as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around $15\,\sigma$ at $\phi_K$, which is larger than the penetration lengths that have been reported for three dimensional systems. It is argued that the $\alpha$-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches $\phi_K$.Comment: 17 pages, 16 figure

Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity

We relate the structure factor $S(\mathbf{k} \to \mathbf{0})$ in a system of jammed hard spheres of number density $\rho$ to its complexity per particle $\Sigma(\rho)$ by the formula $S(\mathbf{k} \to \mathbf{0})=-1/ [\rho^2\Sigma''(\rho)+2\rho\Sigma'(\rho)]$. We have verified this formula for the case of jammed disks in a narrow channel, for which it is possible to find $\Sigma(\rho)$ and $S(\mathbf{k})$ analytically. Hyperuniformity, which is the vanishing of $S(\mathbf{k} \to \mathbf{0})$, will therefore not occur if the complexity is nonzero. An example is given of a jammed state of hard disks in a narrow channel which is hyperuniform when generated by dynamical rules that produce a non-extensive complexity.Comment: 5 pages, 3 figure