arXiv subjects
Publications and source records attributed to I. Horvath.
We report our calculation of the pion decay constant $f_π$, the axial renormalization constant $Z_A$, and the quenched chiral logarithms from the overlap fermions. The calculation is done on a quenched $20^4$ lattice at $a=0.148$ fm using tree level tadpole improved gauge action. The smallest pion mass we reach is about 280 MeV. The lattice size is about 4 times the Compton wavelength of the lowest mass pion.
We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in disagreement with the assumptions of the Instanton Liquid Model. We conclude that the fluctuations of topological charge in the QCD vacuum are not locally quantized.
We argue that the distributions of both the intrinsic fluence and the intrinsic duration of the gamma-ray emission in gamma-ray bursts from the BATSE sample are well represented by log-normal distributions, in which the intrinsic dispersion is much larger than the cosmological time dilatation and redshift effects. We perform separate bivariate log-normal distribution fits to the BATSE short and long burst samples. The bivariate log-normal behavior results in an ellipsoidal distribution, whose major axis determines an overall statistical relation between the fluence and the duration. We show that this fit provides evidence for a power-law dependence between the fluence and the duration, with a statistically significant different index for the long and short groups. We discuss possible biases which might affect this result, and argue that the effect is probably real. This may provide a potentially useful constraint for models of long and short bursts.
In the article a test is developed, which allows to test the null-hypothesis of the intrinsic randomness in the angular distribution of gamma-ray bursts collected at the Current BATSE Catalog. The method is a modified version of the well-known counts-in-cells test, and fully eliminates the non-uniform sky-exposure function of BATSE instrument. Applying this method to the case of all gamma-ray bursts no intrinsic non-randomness is found. The test also did not find intrinsic non-randomnesses for the short and long gamma-ray bursts, respectively. On the other hand, using the method to the new intermediate subclass of gamma-ray bursts, the null-hypothesis of the intrinsic randomness for 181 intermediate gamma-ray bursts is rejected on the 96.4% confidence level. Taking 92 dimmer bursts from this subclass itself, we obtain the surprising result: This "dim" subclass of the intermediate subclass has an intrinsic non-randomness on the 99.3% confidence level. On the other hand, the 89 "bright" bursts show no intrinsic non-randomness.
The counts-in-cells and the two-point angular correlation function method are used to test the randomnesses in the angular distributions of both the all gamma-ray bursts collected at BATSE Catalog, and also their three subclasses ("short", "intermediate", "long"). The methods elimate the non-zero sky-exposure function of BATSE instrument. Both tests suggest intrinsic non-randomnesses for the intermediate subclass; for the remaining three cases only the correlation function method. The confidence levels are between 95% and 99.9%. Separating the GRBs into two parts ("dim half" and "bright half", respectively) we obtain the result that the "dim" half shows a non-randomness on the 99.3% confidence level from the counts-in-cells test.
The anisotropy of the sky distribution of 2025 gamma-ray bursts (GRBs) collected in Current BATSE catalog is confirmed. It is shown that the quadrupole term being proportional to $\sim \sin 2b \sin l$ is non-zero with a probability 99.9%. The occurrence of this anisotropy term is then supported by the binomial test even with the probability 99.97%. It is also argued that this anisotropy cannot be caused exclusively by instrumental effects due to the non-uniform sky exposure of BATSE instrument; there should exist also some intrinsic anisotropy in the angular distribution of GRBs. Separating GRBs into short and long subclasses, it is shown that the 251 short ones are distributed anisotropically, but the 681 long ones seem to be distributed still isotropically. The 2-sample Kolmogorov-Smirnov test shows that they are distributed differently with a 98.7% probability. The character of anisotropy suggests that the cosmological origin of short GRBs further holds, and there is no evidence for their Galactical origin. The work in essence contains the key ideas and results of a recently published paper (\cite{balazs}), to which the new result following from the 2-sample Kolmogorov-Smirnov test is added, too.
The isotropy of gamma-ray bursts collected in Current BATSE catalog is studied. It is shown that the quadrupole term being proportional to $\sim \sin 2b \sin l$ is non-zero with a probability 99.9%. The occurrence of this anisotropy term is then confirmed by the binomial test even with the probability 99.97 %. Hence, the sky distribution of all known gamma-ray bursts is anisotropic. It is also argued that this anisotropy cannot be caused exclusively by instrumental effects due to the nonuniform sky exposure of BATSE instrument. Separating the GRBs into short and long subclasses, it is shown that the short ones are distributed anisotropically, but the long ones seem to be distributed still isotropically. The character of anisotropy suggests that the cosmological origin of short GRBs further holds, and there is no evidence for their Galactical origin.
Two classes of Gamma Ray Bursts have been identified so far, characterized by T_90 durations shorter and longer than approximately 2 seconds. We show here that the BATSE 3B data allow a good fit with three Gaussian distributions in log T_90. The chi^2 statistic indicates a 40 % probability for two Gaussians, whereas the three-Gaussian fit probability is 98 %. Using another statistical method, it is argued that the probability that the third class is a random fluctuation is less than 0.02 %.
We have carried out a principal component analysis for 625 gamma-ray bursts in the BATSE 3B catalog for which non-zero values exist for the nine measured variables. This shows that only two out of the three basic quantities of duration, peak flux and fluence are independent, even if this relation is strongly affected by instrumental effects, and these two account for 91.6% of the total information content. The next most important variable is the fluence in the fourth energy channel (at energies above 320 keV). This has a larger variance and is less correlated with the fluences in the remaining three channels than the latter correlate among themselves. Thus a separate consideration of the fourth channel, and increased attention on the related hardness ratio $H43$ appears useful for future studies. The analysis gives the weights for the individual measurements needed to define a single duration, peak flux and fluence. It also shows that, in logarithmic variables, the hardness ratio $H32$ is significantly correlated with peak flux, while $H43$ is significantly anticorrelated with peak flux. The principal component analysis provides a potentially useful tool for estimating the improvement in information content to be achieved by considering alternative variables or performing various corrections on available measurements
We discuss detailed fits of the BATSE and PVO gamma-ray burst peak-flux distributions with Friedman models taking into account possible density evolution and standard candle or power law luminosity functions. A chi-square analysis is used to estimate the goodness of the fits and we derive the significance level of limits on the density evolution and luminosity function parameters. Cosmological models provide a good fit over a range of parameter space which is physically reasonable.
After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations.
On simple cubic lattices, we compute low temperature series expansions for the energy, magnetization and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds respectively, and the eight-state Potts model in D=2 to 25 excited bonds. We use a recursive procedure which enumerates states explicitly. We analyze the series using Dlog Pade analysis and inhomogeneous differential approximants.
We propose a bilocal field theory for mesons in two dimensions obtained as a kind of non local bosonization of two dimensional QCD. Its semi-classical expansion is equivalent to the $1/N_c$ expansion of QCD. Using an ansatz we reduce the classical equation of motion of this theory in the baryon number one sector to a relativistic Hartree equation and solve it numerically. This (non topological) soliton is identified with the baryon.