QCD phase diagram for small densities from simulations at imaginary mu

We present results on the QCD phase diagram for small densities without reweighting. Our simulations are performed with an imaginary chemical potential mu_I for which the fermion determinant is positive. On an 8^3x4 lattice with 2 flavors of staggered quarks, we map out the pseudo-critical temperature T_c(mu_I). For mu_I/T < pi/3, this is an analytic function whose Taylor expansion converges rapidly, with truncation errors smaller than statistical ones. The result is analytically continued to give the location of the pseudo-critical line for real mu_B<500 MeV.Comment: Lattice2002(nonzerot), 3 pp, 5 figure

Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

We present unambiguous evidence from lattice simulations of QCD with three degenerate quark species for two tricritical points in the (T,m) phase diagram at fixed imaginary \mu/T=i\pi/3 mod 2\pi/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary chemical potential, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to non-degenerate and light quark masses is discussed.Comment: 4 pages, 5 figure

Mapping the phase diagram of strongly interacting matter

We employ a conformal mapping to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$. This method allows us to identify the singularity corresponding to the critical point of a second-order phase transition at finite $\mu$, given information only at $\mu=0$. The scheme is potentially useful for computing thermodynamic properties of strongly interacting hot and dense matter in lattice gauge theory. The technique is illustrated by an application to a chiral effective model.Comment: 5 pages, 3 figures; published versio

The Quantum Effective Action, Wave Functions and Yang-Mills (2+1)

We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the effective action from the ground state wave function previously obtained in the Hamiltonian formalism by solving the Schrodinger equation.Comment: 16 pages, expanded discussion section, added references, version accepted for Phys. Rev.

WIMP Dark Matter and the QCD Equation of State

Weakly Interacting Massive Particles (WIMPs) of mass m freeze out at a temperature T_f ~ m/25, i.e. in the range 400 MeV -- 40 GeV for a particle in the typical mass range 10 -- 1000 GeV. The WIMP relic density, which depends on the effective number of relativistic degrees of freedom at T_f, may be measured to better than 1% by Planck, warranting comparable theoretical precision. Recent theoretical and experimental advances in the understanding of high temperature QCD show that the quark gluon plasma departs significantly from ideal behaviour up to temperatures of several GeV, necessitating an improvement of the cosmological equation of state over those currently used. We discuss how this increases the relic density by approximately 1.5 -- 3.5% in benchmark mSUGRA models, with an uncertainly in the QCD corrections of 0.5 -- 1 %. We point out what further work is required to achieve a theoretical accuracy comparable with the expected observational precision, and speculate that the effective number of degrees of freedom at T_f may become measurable in the foreseeable future.Comment: 4pp, 2figs. More info including Matlab scripts used to generate equation of state curves at http://www.pact.cpes.sussex.ac.uk/arXiv/hep-ph/0501232

Towards a controlled study of the QCD critical point

The phase diagram of QCD, as a function of temperature T and quark chemical potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative nature makes it a natural object of lattice studies. However, the sign problem prevents the application of standard Monte Carlo techniques at non-zero baryon density. We have been pursuing an approach free of the sign problem, where the chemical potential is taken as imaginary and the results are Taylor-expanded in mu/T about mu=0, then analytically continued to real mu. Within this approach we have determined the sensitivity of the critical chemical potential mu_E to the quark mass, d(\mu_E)^2/dm_q|_{\mu_E=0}. Our study indicates that the critical point moves to {\em smaller} chemical potential as the quark mass {\em increases}. This finding, contrary to common wisdom, implies that the deconfinement crossover, which takes place in QCD at mu=0 when the temperature is raised, will remain a crossover in the mu-region where our Taylor expansion can be trusted. If this result, obtained on a coarse lattice, is confirmed by simulations on finer lattices now in progress, then we predict that no {\em chiral} critical point will be found for mu_B \lesssim 500 MeV, unless the phase diagram contains additional transitions.Comment: 4 pages, 6 figures, proceedings of Quark Matter 2008, Jaipur (India), Feb. 2008, to appear in J. Phys.

Speech Codes Theory

Rooted in the ethnography of communication and based on empirical research, speech codes theory is a theoretical/methodological tool for studying situated communication practices. Two important applications of speech codes theory are to reveal local cultures and to examine the ways in which people make use of communication to accomplish important goals pertaining to communal life. Speech codes theory offers researchers a systematic approach to describing, interpreting, analyzing, and comparing local communicative practices and the cultures which they instantiate

The confining string and its breaking in QCD

We point out that the world sheet swept by the confining string in presence of dynamical quarks can belong to two different phases, depending on the number of charge species and the quark masses. When it lies in the normal phase (as opposed to the tearing one) the string breaking is invisible in the Wilson loop, while is manifest in operators composed of disjoint sources, as observed in many numerical experiments. We work out an explicit formula for the correlator of Polyakov loops at finite temperature, which is then compared with recent lattice data, both in the quenched case and in presence of dynamical quarks. The analysis in the quenched case shows that the free bosonic string model describes accurately the data for distances larger than ~ 0.75 fm. In the unquenched case we derive predictions on the dependence of the static potential on the temperature which are compatible with the lattice data.Comment: 15 pages, LaTeX with 4 eps figures (included

Model analysis of thermal UV-cutoff effects on the chiral critical surface at finite temperature and chemical potential

We study the effects of temporal UV-cutoff on the chiral critical surface in hot and dense QCD using a chiral effective model. Recent lattice QCD simulations indicate that the curvature of the critical surface might change toward the direction in which the first order phase transition becomes stronger on increasing the number of lattice sites. To investigate this effect on the critical surface in an effective model approach, we use the Nambu-Jona-Lasinio model with finite Matsubara frequency summation. We find that qualitative feature of the critical surface does not alter appreciably as we decrease the summation number, which is unlike the case what is observed in the recent lattice QCD studies. This may either suggest the dependence of chemical potential on the coupling strength or due to some additional interacting terms such as vector interactions which could play an important role at finite density.Comment: 7 pages, 8 figure