How to Put a Heavier Higgs on the Lattice

Lattice work, exploring the Higgs mass triviality bound, seems to indicate that a strongly interacting scalar sector in the minimal standard model cannot exist while low energy QCD phenomenology seems to indicate that it could. We attack this puzzle using the 1/N expansion and discover a simple criterion for selecting a lattice action that is more likely to produce a heavy Higgs particle. Our large $N$ calculation suggests that the Higgs mass bound might be around $850 GeV$, which is about 30% higher than previously obtained

Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the χ2\chi^2-method

We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$ of critical exponents of the deconfinement transition in $SU(2)$ gauge theory by applying the $\chi^2$-method to Monte Carlo data of the modulus and the square of the Polyakov loop. With the same technique we find from the Binder cumulant $g_r$ its universal value at the critical point in the thermodynamical limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in complete agreement with that of the $3d$ Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te

Specific Heat Exponent for the 3-d Ising Model from a 24-th Order High Temperature Series

We compute high temperature expansions of the 3-d Ising model using a recursive transfer-matrix algorithm and extend the expansion of the free energy to 24th order. Using ID-Pade and ratio methods, we extract the critical exponent of the specific heat to be alpha=0.104(4).Comment: 10 pages, LaTeX with 5 eps-figures using epsf.sty, IASSNS-93/83 and WUB-93-4

“Stock PIKs”- Taking a firm by its tails

Payment-in-kind bonds (PIKs) make interest payments in the form of an issue of additional bonds rather than cash. This research provides a rationale for the recent PIK issuance by firms with low credit ratings. PIKs offer a financially constrained firm in need of restructuring both an immediate automatic stay and a prepackaged bankruptcy procedure, features that make PIKs better than alternative debt instruments. In many instances PIKs are structured to facilitate a contingent transfer of control to PIK holders, and provide an avenue of obtaining equity in the firm whether the firm value is high or low in the future. The barbell strategy of acquisition that involves a deal with the equity holders (if the firm prospects improve), and a deal with the debt holders (if the firm defaults) dominates the cost of acquisition before the firm defaults, or after the firm goes bankrupt.Monetary Policy, Stock Market, Economic Development

Large Nc Continuum Reduction and the Thermodynamics of QCD

It is noted that if large Nc continuum reduction applies to an observable, then that observable is independent of temperature for all temperatures below some critical value. This fact, plus the fact that mesons and glueballs are weakly interacting at large Nc is used as the basis for a derivation of large Nc continuum reduction for the chiral condensate. The structure of this derivation is quite general and can be extended to a wide class of observables

Thermostatistics of extensive and non-extensive systems using generalized entropies

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short-range and long-range interactions. The first method is quite general and it is based on the numerical evaluation of the density of states with a given energy. The second method is more specific for Tsallis thermostatistics and it is based on a standard Monte Carlo Metropolis algorithm along with a numerical integration procedure. We show here that both methods are robust and efficient. We present results of the application of the methods to the one-dimensional Ising model both in a short-range case and in a long-range (non-extensive) case. We show that the thermodynamic potentials for different values of the system size N and different values of the non-extensivity parameter q can be described by scaling relations which are an extension of the ones holding for the Boltzmann-Gibbs statistics (q=1). Finally, we discuss the differences in using standard or non-standard mean value definitions in the Tsallis thermostatistics formalism and present a microcanonical ensemble calculation approach of the averages.Comment: Submitted to Physica A. LaTeX format, 38 pages, 17 EPS figures. IMEDEA-UIB, 07071 Palma de Mallorca, Spain, http://www.imedea.uib.e

Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

We study the pure gauge model on a lattice manifold with trivial fundamental homotopy group, homotopically equivalent to an $S_4$. Monopole loops may fluctuate freely on that lattice without restrictions due to the boundary conditions. For the original Wilson action on the hypertorus there is an established two-state signal in energy distribution functions which disappears for the new geometry. Our finite size scaling analysis suggests stringent upper bounds on possible discontinuities in the plaquette action. However, no consistent asymptotic finite size scaling behaviour is observed.Comment: 18 pages (3 figures), LaTeX + POSTSCRIPT (287 KB), preprint BI-TP 94/3

Status of the Higgs Mass Bound

The status of the triviality bound of the Higgs mass in the Minimal Standard Model is reviewed. It is emphasized that the bound is obtained, in the scalar sector, by limiting cutoff effects on physical processes. Results from several regularization schemes, including actions that allow a parameterization and tuning of the leading cutoff effects, are presented. They lead to the conclusion that the Minimal Standard Model will describe physics to an accuracy of a few percent up to energies of the order 2 to 4 times the Higgs mass, $M_H$, only if $M_H \le 710 \pm 60 ~ GeV$. The status of Higgs and fermion mass bounds in Higgs-fermion models is also briefly reviewed.Comment: To appear in the proceedings of Lattice '93, Dallas, Oct. 12--16, 1993. 6 pages, uuencoded compressed postscript file. Preprint FSU-SCRI-93-14

Low temperature expansion for the 3-d Ising Model

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767