arXiv subjects
Publications and source records attributed to K. M. Bitar.
We study QCD with two flavors of dynamical Wilson fermions at $β= 5.5$ and three values of $κ$. The corresponding pion masses are 0.375, 0.324 and 0.262 in lattice units, with pion to rho mass ratios of 0.76, 0.71 and 0.62, respectively. We use the configurations to compute the heavy quark potential, leading to lattice spacings of 0.110, 0.105 and 0.099 fm, and to compute spectroscopy for several different valence quark $κ$'s.
We test the asymptotic scaling behavior of state-of-the-art simulations of QCD with two flavors of light Wilson fermions. This is done by matching $π$ and $ρ$ masses on lattices of size $16^3\times32$ and $8^3\times16$. We find that at $β=6/g^2=5.3$ matching is not possible over a range extending down to $β=3.5$. The large lattice data at $β=5.5$ matches the small lattice values at $β=4.9(1)$ leading to a shift $Δβ=0.6(1)$, considerably larger than the perturbative prediction of $0.45$. In both cases we conclude that the simulations are very far from the asymptotic scaling region.
We present data for the scaling behavior of lattice QCD with two flavors of light Wilson fermions. This is done by matching $π$ n and $ρ$ masses at the two lattice sizes of $16^3\times32 $ and $8^3\times16$. We find that at $β=6/g^2\equiv5.3$ the matching does not occur over a range extending down to $β=3.5$. For $β=5.5$ matching may be achieved at $β=4.8-4.9$, leading to a $Δβ=0.6-0.7$ which is higher than the perturbative 2-loop value of 0.45. In both cases we conclude that the simulations are very far from the perturbative scaling region.
The Nambu--Jona-Lasinio model is chirally symmetric. Addition of a Wilson term explicitly breaks this symmetry and leaves the model with a remaining parity-flavor symmetry. In the approximation of a large number of colors it has been shown that there is a phase where the remaining parity-flavor symmetry is spontaneously broken and that on the phase boundary all pions become massless. Using numerical simulations we confirm the existence of this phase for the case of two flavors and two colors. We also confirm the large N prediction of the existence of large finite size effects that alter the shape of the phase boundary dramatically when periodic boundary conditions are used.
We present our full analysis of the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry on the four--dimensional hypercubic lattice with naive and Wilson fermions. We find that this model is an excellent toy field theory to investigate issues related to lattice QCD. We use the large $N$ approximation to leading order in $1/N$ to obtain non perturbative analytical results over almost the whole parameter range. By using numerical simulations we estimate that the size of the $1/N$ corrections for most of the quantities we consider are small and in this way we strengthen the validity of the leading order large $N$ calculations. We obtain results regarding the approach to the continuum chiral limit, the effects of the zero momentum fermionic modes on finite lattices and the scalar and pseudoscalar spectrum. 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 complete E-mail address. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called NJL_long.ps (to get it type: get NJL_long.ps)
The main results of our analysis of the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry on the four--dimensional hypercubic lattice with naive and Wilson fermions are presented. Large $N$ techniques and numerical simulations are used to study various properties of the model. The scalar and pseudoscalar spectrum, the approach to the continuum and chiral limits, the size of the $1/N$ corrections, and the effects of the zero momentum fermionic modes on finite lattices are studied. Also, some interesting observations are made by viewing the model as an embedding theory of the Higgs sector.
We introduce a new Monte Carlo method for pure gauge theories. It is not intended for use with dynamical fermions. It belongs to the class of Local Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the action by updating individual sites or links by following a classical mechanics trajectory in fictitious time. We choose to update a one-parameter subgroup of the gauge field on each link of the lattice, and the classical trajectory can be found in closed form in terms of elliptic functions for this case. We show that this gives an overrelaxation algorithm with a tunable parameter which, unlike some previous methods, does not require the numerical integration of the equations of motion.
In an effort to investigate some of the low energy properties of QCD, in particular those related to chiral symmetry breaking, as well as to obtain insights on the behavior of an interacting theory of fermions on the lattice, the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry is studied on the four--dimensional hypercubic lattice using large $N$ techniques and numerical simulations. Naive and Wilson fermions are considered and transparent results are obtained regarding the following: the scalar and pseudoscalar spectrum, the approach to the continuum and chiral limits, the size of the $1/N$ corrections, and the effects of the zero momentum fermionic modes on finite lattices. Also, some interesting observations are made by viewing the model as an embedding theory of the Higgs sector. 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 NJL.ps (to get it type: get NJL.ps)
We present results of a lattice simulation of quantum chromodynamics with two degenerate flavors of dynamic Wilson fermions at $6/g^2=5.3$ at each of two dynamical fermion hopping parameters, $κ=0.1670$ and 0.1675, corresponding to pion masses in lattice units of about 0.45 and 0.31. The simulations include three other values of valence quark mass, in addition to the dynamical quarks. We present calculations of masses and of the decay constants of vector mesons and of pseudoscalars, including the D-meson decay constant. The effects of sea quarks on matrix elements and spectroscopy are small.
We have measured some simple matrix elements for pseudoscalar and vector mesons made of Wilson valence quarks and staggered sea quarks at $β=5.6$ at sea quark masses $am_q=0.01$ and 0.025. Our measurements include the decay constants of pseudoscalars (including $f_D$), the wave function at the origin (or decay constant) of vector mesons, and the calculation of quark masses from current algebra. The effects of sea quarks on the simulations are small. We make comparisons to quenched simulations at similar values of the lattice spacing ($1/a \simeq 2$ GeV).
We present results from simulations of lattice QCD using two flavors of dynamical Wilson fermions at a lattice coupling $β=5.3$ on $16^3 \times 32$ lattices at two hopping parameters, $κ=0.1670$ and $0.1675$, leading to $m_π\approx 0.44$ and $0.33$ respectively. We show spectroscopy for S-wave hadrons and compare our results to other recent simulations with dynamical Wilson fermions. (Complete postscript file can be obtained by anonymous ftp from ftp.scri.fsu.edu as file "lat92.ps" from directory "pub/heller".)
We present an analysis of hadronic spectroscopy for Wilson valence quarks with dynamical staggered fermions at lattice coupling $6/g^2 = β=5.6$ at sea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched approximation at $β=5.85$ and 5.95, both on $16^3 \times 32$ lattices. We make comparisons with our previous results with dynamical staggered fermions at the same parameter values but on $16^4$ lattices doubled in the temporal direction.
We present preliminary results from the 1991 HEMCGC simulations with staggered dynamical fermions on a $16^3 \times 32$ lattice at $β= 5.6$ with sea quark masses $am_q = 0.025$ and 0.01. The spectroscopy was done both for staggered valence quarks with mass equal to the sea quark masses and for Wilson valence quarks at six different values for $κ$, 0.1320, 0.1410, 0.1525, 0.1565, 0.1585, and 0.1600. In addition to the measurements performed in our earlier work, we also measured the $Δ$ and other `extended' hadrons for staggered valence quarks and pseudo-scalar decay constants and vector meson matrix elements, the wave function at the origin, for Wilson valence quarks.