Equation of state from lattice QCD

Recent results on the equation of state from lattice QCD are reviewed. The lattice technique and previous results are shortly discussed. New results for physical quark masses and two sets of lattice spacings are presented. The pressure, energy density, entropy density, speed of sound and quark number susceptibilities are determined.Comment: 10 pages, 11figures. Plenary talk presented at the Quark Matter 2005 conferenc

Finite temperature and chemical potential in lattice QCD and its critical point

We propose a method to study lattice QCD at finite temperature (T) and chemical potential (\mu). We compare the method with direct results and with the Glasgow method by using n_f=4 QCD at Im(\mu)\neq0. We locate the critical endpoint (E) of QCD on the Re(\mu)-T plane. We use n_f=2+1 dynamical staggered quarks with semi-realistic masses on L_t=4 lattices. Our results are based on {\cal{O}}(10^3-10^4) configurations.Comment: 8 pages, 4 figures. Talk given at the XXX. Hirschegg Workshop on Ultrarelativistic Heavy-Ion Collisions, January 13-19, 200

Propagation of ultrahigh energy cosmic rays and compact sources

The clustering of ultrahigh energy (>10^{20} eV) cosmic rays (UHECR) suggests that they might be emitted by compact sources. Statistical analysis (Dubovsky et al., 2000) estimated the source density. We extend their analysis to give also the confidence intervals (CI) for the source density using a.) no assumptions on the relationship between clustered and unclustered events; b.) nontrivial distributions for the source luminosities and energies; c.) the energy dependence of the propagation. We also determine the probability that a proton created at a distance r with energy E arrives at earth above a threshold E_c. Using this function one can determine the observed spectrum just by one numerical integration for any injection spectrum. The observed 14 UHECR events above 10^{20} eV with one doublet gives for the source densities 180_{-165}^{+2730}\cdot 10^{-3} Mpc^{-3} (on the 68% confidence level).Comment: 4 pages, 1 figure, talk to be presented at the 27th International Cosmic Ray Conference, Hamburg, Germany, August 7-15, 200

Lattice QCD results at finite T and \mu

We propose a method to study lattice QCD at finite temperature (T) and chemical potential (\mu). We test the method and compare it with the Glasgow method using n_f=4 staggered QCD with imaginary \mu. The critical endpoint (E) of QCD on the Re(\mu)-T plane is located. We use n_f=2+1 dynamical staggered quarks with semi-realistic masses on L_t=4 lattices. Our results are based on {\cal{O}}(10^3-10^4) configurations.Comment: 9 pages, 4 figures. Talk given at Budapest'02 Workshop on Quark and Hadron Dynamics, Budapest, March 3-7, 200

Ultrahigh energy cosmic rays as a Grand Unification signal

We analyze the spectrum of the ultrahigh energy (above \approx 10^{9} GeV) cosmic rays. With a maximum likelihood analysis we show that the observed spectrum is consistent with the decay of extragalactic GUT scale particles. The predicted mass for these superheavy particles is m_X=10^b GeV, where b=14.6_{-1.7}^{+1.6}.Comment: 4 pages, 3 figures, talk to be presented at the 27th International Cosmic Ray Conference, Hamburg, Germany, August 7-15, 200

The critical point of lattice QCD on the \mu-T plane

We propose a method to study lattice QCD at finite temperature and chemical potential. We compare it with direct results and with the Glasgow method by using n_f=4 QCD at Im(\mu)\neq 0. We locate the critical endpoint (E) of QCD on the Re(\mu)-T plane. In this study we use n_f=2+1 dynamical staggered quarks with semi-realistic masses on L_t=4 lattices.Comment: 5 pages, 3 Figures. Talk given at EPS HEP2001, July 12-18,2001 Budapes