QCD phase diagram and charge fluctuations

We discuss the phase structure and fluctuations of conserved charges in two flavor QCD. The importance of the density fluctuations to probe the existence of the critical end point is summarized. The role of these fluctuations to identify the first order phase transition in the presence of spinodal phase separation is also discussed.Comment: 8 pages, 8 figures, plenary talk given at the 19th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions: Quark Matter 2006 (QM 2006), Shanghai, China, 14-20 Nov 200

The alphaalphas2alpha alpha_s^2 corrections to the first moment of the polarized virtual photon structure function g1gamma(x,Q2,P2)g_1^gamma(x,Q^2,P^2)

We present the next-to-next-to-leading order ($alpha alpha_s^2$) corrections to the first moment of the polarized virtual photon structure function $g_1^gamma(x,Q^2,P^2)$ in the kinematical region $Lambda^2 ll P^2 ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The $alpha alpha_s^2$ corrections are found to be about 3% of the sum of the leading order ($alpha$) andthe next-to-leading order ($alpha alpha_s$) contributions, when $Q^2=30 sim 100 {rm GeV}^2$and $P^2=3{rm GeV}^2$, and the number of active quark flavors $n_f$ is three to five.Comment: 21 page

Virtual photon structure functions and positivity constraints

We study the three positivity constraints among the eight virtual photon structure functions, derived from the Cauchy-Schwarz inequality and which are hence model-independent. The photon structure functions obtained from the simple parton model show quite different behaviors in a massive quark or a massless quark case, but they satisfy, in both cases, the three positivity constraints. We then discuss an inequality which holds among the unpolarized and polarized photon structure functions $F_1^\gamma$, $g_1^\gamma$ and $W_{TT}^\tau$, in the kinematic region $\Lambda^2\ll P^2 \ll Q^2$, where $-Q^2 (-P^2)$ is the mass squared of the probe (target) photon, and we examine whether this inequality is satisfied by the perturbative QCD results.Comment: 24 pages, 13 eps figure

Gauge field for edge state in graphene

By considering the continuous model for graphene, we analytically study a special gauge field for the edge state. The gauge field explains the properties of the edge state such as the existence only on the zigzag edge, the partial appearance in the $k$-space, and the energy position around the Fermi energy. It is demonstrated utilizing the gauge field that the edge state is robust for surface reconstruction, and the next nearest-neighbor interaction which breaks the particle-hole symmetry stabilizes the edge state.Comment: 9 pages, 5 figure

New Constraints on the Variable Equation of State Parameter from X-Ray Gas Mass Fractions and SNe Ia

Recent measurements are suggesting that we live in a flat Universe and that its present accelerating stage is driven by a dark energy component whose equation of state may evolve in time. Assuming two different parameterizations for the function $\omega(z)$, we constrain their free parameters from a joint analysis involving measurements from X-Ray luminosity of galaxy clusters and SNe type Ia data.Comment: paper, 6 pages, 1 figure Accepted by Int. Journal of Modern Physics D (IJPMD