Numerical analysis of the Higgs mass triviality bound

Previous large $N$ calculations are combined with numerical work at $N=4$ to show 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 $M_H \le 710\pm60 ~ GeV$. This bound is the result of a systematic search in the space of dimension six operators and is expected to hold in the {\it continuum}. Given that studying the scalar sector in isolation is already an approximation, we believe that our result is sufficiently accurate and that further refinements would be of progressively diminishing interest to particle physics. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called num_hig.ps (to get it type: get num_hig.ps)Comment: 22 pages with 10 ps figures included. Tex file. FSU-SCRI-93-29, CU-TP-590, RU-93-0

K^0--\bar{K}^0 mixing in full lattice QCD

There are at least two methods to calculate $B_K$ with staggered fermions: one is the two spin trace formalism and the other is the one spin trace formalism. We have performed numerical simulations on a $16^3 \times 40$ lattice in full QCD with $\beta = 5.7$ and a dynamical quark mass 0.01 in lattice units. We try various sources to select only the pseudo-Goldstone bosons and compare the various results.Comment: Contribution to Lattice 94, 3 pages, Compressed, uuenocded postscript file of the complete pape

Miscellanies of K0−Kˉ0 K^0 - \bar{K}^0 mixing and BK B_K

We have computed $B_K$, using two different methods with staggered fermions on a $16^3 \times 40$ lattice at $\beta = 5.7$ with two dynamical flavors of a mass 0.01. % Using an improved wall source method, we have studied a series of non-degenerate quark antiquark pairs and observed no effect on $B_K$, although effects were seen on the individual terms making up $B_K$.Comment: 4 pages (latex, including 8 postscript figures, uuencoded gzip-compressed tar files), Nucl. Phys. B (Proc. Suppl.) Lattice 9

Semi-Analytical Solution of the ϕ4\phi^4 Theory on an F4F_4 Lattice

Investigating the cutoff dependence of the Higgs mass triviality bound, the $\phi^4$ theory is formulated on an $F_4$ lattice which preserves Lorentz invariance to a higher degree than the commonly used hypercubic lattice. I solve this model non-perturbatively by evaluating the high temperature expansion through 13th order following the approach of L\"uscher and Weisz. The results are continued across the transition line into the broken phase by integrating the perturbative RG equations. In the broken phase, the renormalized coupling never exceeds 2/3 of the tree level unitarity bound when $\Lambda/m_R \geq 2$. The results confirm recent Monte Carlo data and I obtain as an upper bound for the Higgs mass $m_R/f_\pi \leq 2.46 \pm 0.02_{\rm HTE} \pm 0.08_{\rm PT}$ at $\Lambda/m_R=2$.Comment: 36 pages, CU-TP-603, Latex, 3 PS figures included, uuencoded compressed shar fil

Regularization dependence of the Higgs mass triviality bound

We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff effects at four percent in several regularized models with tunable couplings in the bare action yield triviality bounds displaying a large degree of universality. Extrapolating from $N=\infty$ to $N=4$ we conservatively estimate that a Higgs particle with mass up to $0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff effects, indicating that strong scalar self interactions in the standard model are not ruled out. We also present preliminary numerical results of the physical $N=4$ case for the $F_4$ lattice that are in agreement with the large $N$ expectations. Note: The full ps file is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called lat92_proc.ps (to get it type: get lat92_proc.ps)Comment: 5 pages with 5 ps figures included. LaTex file. Contribution to the LAT92 proceedings. Preprint, FSU-SCRI-92-150, RU-92-4

One Spin Trace Formalism for BK B_K

It has been known for some time that there are two methods to calculate $B_K$ with staggered fermions: one is the two spin trace formalism and the other is the one spin trace formalism. Until now, the two spin trace formalism has been exclusively used for weak matrix element calculations with staggered fermions. Here, the one spin trace formalism to calculate $B_K$ with staggered fermions is explained. It is shown that the one spin trace operators require additional chiral partner operators in order to keep the continuum chiral behavior. The renormalization of the one spin trace operators is described and compared with the two spin trace formalism.Comment: 47 pages, latex, 4 figures are available on reques