Lattice QCD at finite temperature and density

We study the phase structure of QCD at finite temperature and density by numerical simulations on a lattice. The most important point for the numerical study at finite density is treatment of the sign problem. We propose a method to avoid the sign problem, which is based on a cumulant expansion of the complex phase in the density of state method combined with the reweighting method. Using the method, we study the critical point terminating a first order phase transition line in lattice QCD at high temperature and density.Comment: 6 pages, 4 figures, talk presented at the YITP workshop on "New Frontiers in QCD 2010", March 1-19, 2010, Kyoto, Japa

Solubility, Light Output and Energy Resolution Studies of Molybdenum-Loaded Liquid Scintillators

The search for neutrinoless double-beta decay is an important part of the global neutrino physics program. One double-beta decay isotope currently under investigation is 100Mo. In this article, we discuss the results of a feasibility study investigating the use of molybdenum-loaded liquid scintillator. A large, molybdenum-loaded liquid scintillator detector is one potential design for a low-background, internal-source neutrinoless double-beta decay search with 100Mo. The program outlined in this article included the selection of a solute containing molybdenum, a scintillating solvent and the evaluation of the mixture's performance as a radiation detector.Comment: 8 pages, 3 figure

Lee-Yang zero analysis for the study of QCD phase structure

We comment on the Lee-Yang zero analysis for the study of the phase structure of QCD at high temperature and baryon number density by Monte-Carlo simulations. We find that the sign problem for non-zero density QCD induces a serious problem in the finite volume scaling analysis of the Lee-Yang zeros for the investigation of the order of the phase transition. If the sign problem occurs at large volume, the Lee-Yang zeros will always approach the real axis of the complex parameter plane in the thermodynamic limit. This implies that a scaling behavior which would suggest a crossover transition will not be obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for SU(3) pure gauge theory as a simple example without the sign problem, and then consider the case of non-zero density QCD. It is suggested that the distribution of the Lee-Yang zeros in the complex parameter space obtained by each simulation could be more important information for the investigation of the critical endpoint in the $(T, \mu_q)$ plane than the finite volume scaling behavior.Comment: 16 pages, 3 figures, 2 tables, minor change

Critical point in finite density lattice QCD by canonical approach

We propose a method to find the QCD critical point at finite density calculating the canonical partition function ${\cal Z}_{\rm C} (T,N)$ by Monte-Carlo simulations of lattice QCD, and analyze data obtained by a simulation with two-flavor p4-improved staggered quarks with pion mass $m_{\pi} \approx 770 {\rm MeV}$. It is found that the shape of an effective potential changes gradually as the temperature decreases and a first order phase transition appears in the low temperature and high density region. This result strongly suggests the existence of the critical point in the $(T, \mu_q)$ phase diagram.Comment: 4 pages, 2 figures, To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

Study of the critical point in lattice QCD at high temperature and density

We propose a method to probe the nature of phase transitions in lattice QCD at finite temperature and density, which is based on the investigation of an effective potential as a function of the average plaquette. We analyze data obtained in a simulation of two-flavor QCD using p4-improved staggered quarks with bare quark mass $m/T = 0.4$, and find that a first order phase transition line appears in the high density regime for $\mu_q/T \sim 2.5$. The effective potential as a function of the quark number density is also studied. We calculate the chemical potential as a function of the density from the canonical partition function and discuss the existence of the first order phase transition line.Comment: 7 pages, 7 figures, talk presented at Lattice 200

Phase structure of hot dense QCD by a histogram method

We study the phase structure of QCD at high temperature and density by lattice QCD simulations adopting a histogram method. The quark mass dependence and the chemical potential dependence of the nature of phase transition are investigated focusing on the probability distribution function (histogram). The shape of the distribution function changes with the quark mass and chemical potential. Through the shape of the distribution, the critical surface which separates the first order transition and crossover regions in the heavy quark region is determined for the (2+1)-flavor case. Moreover, we determined the critical point at finite density for two-flavor QCD with an intermediate quark mass, using a Gaussian approximation of the complex phase distribution of the quark determinant. The chemical potential dependence of the critical quark mass is also evaluated in the situation where two light quarks and many massive quarks exist. We find that the first order transition region becomes wider with the chemical potential in the many-flavor QCD.Comment: 16 pages, 20 figures, mini-revie

Remarks on the reweighting method in the chemical potential direction

We comment on the reweighting method in the chemical potential $(\mu_{\rm q})$ direction. We study the fluctuation of the reweighting factor during Monte-Carlo steps. We find that it is the absolute value of the reweighting factor that mainly contributes to the shift of the phase transition line $(\beta_c)$ by the presence of $\mu_{\rm q}$. The phase fluctuation is a cause of the sign problem, but the effect on $\beta_c$ seems to be small. We also discuss $\beta_c$ for Iso-vector chemical potential and $\beta_c$ determined from simulations with imaginary chemical potential.Comment: 5pages, 2 figures, Contribution to SEWM 2002 (Heidelberg, 2-5 October 2002