Lattice Gluon Propagator in the Landau Gauge: A Study Using Anisotropic Lattices

Lattice gluon propagators are studied using tadpole and Symanzik improved gauge action in Landau gauge. The study is performed using anisotropic lattices with asymmetric volumes. The Landau gauge dressing function for the gluon propagator measured on the lattice is fitted according to a leading power behavior: $Z(q^2)\simeq (q^2)^{2\kappa}$ with an exponent $\kappa$ at small momenta. The gluon propagators are also fitted using other models and the results are compared. Our result is compatible with a finite gluon propagator at zero momentum in Landau gauge.Comment: 14 pages, 4 figure

Effective generation of Ising interaction and cluster states in coupled microcavities

We propose a scheme for realizing the Ising spin-spin interaction and atomic cluster states utilizing trapped atoms in coupled microcavities. It is shown that the atoms can interact with each other via the exchange of virtual photons of the cavities. Through suitably tuning the parameters, an effective Ising spin-spin interaction can be generated in this optical system, which is used to produce the cluster states. This scheme does not need the preparation of initial states of atoms and cavity modes, and is insensitive to cavity decay.Comment: 11pages, 2 figures, Revtex

QCD corrections to polarization of J/\psi and \Upsilon at Fermilab Tevatron and CERN LHC

In this work, we present more detail of the calculation on the NLO QCD corrections to polarization of direct J/psi production via color singlet at Tevatron and LHC, as well as the results for Upsilon for the first time. Our results show that the J/psi polarization status drastically changes from transverse polarization dominant at LO into longitudinal polarization dominant in the whole range of the transverse momentum $p_t$ of J/psi when the NLO corrections are counted. For Upsilon production, the p_t distribution of the polarization status behaves almost the same as that for J/psi except that the NLO result is transverse polarization at small p_t range. Although the theoretical evaluation predicts a larger longitudinal polarization than the measured value at Tevatron, it may provide a solution towards the previous large discrepancy for J/psi and Upsilon polarization between theoretical predication and experimental measurement, and suggests that the next important step is to calculate the NLO corrections to hadronproduction of color octet state J/psi^(8) and Upsilon^(8). Our calculations are performed in two ways, namely we do and do not analytically sum over the polarizations, and then check them with each other.Comment: 12 pages, 12 figures, two columns, use revtex4; to appear in PR

The Sorting Index and Permutation Codes

In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced a new Mahonian statistic $sor$, called the sorting index. Petersen proved that the pairs of statistics $(sor,cyc)$ and $(inv,rl\textrm{-}min)$ have the same joint distribution over the symmetric group, and asked for a combinatorial proof of this fact. In answer to the question of Petersen, we observe a connection between the sorting index and the B-code of a permutation defined by Foata and Han, and we show that the bijection of Foata and Han serves the purpose of mapping $(inv,rl\textrm{-}min)$ to $(sor,cyc)$. We also give a type $B$ analogue of the Foata-Han bijection, and we derive the quidistribution of $(inv_B,{\rm Lmap_B},{\rm Rmil_B})$ and $(sor_B,{\rm Lmap_B},{\rm Cyc_B})$ over signed permutations. So we get a combinatorial interpretation of Petersen's equidistribution of $(inv_B,nmin_B)$ and $(sor_B,l_B')$. Moreover, we show that the six pairs of set-valued statistics $\rm (Cyc_B,Rmil_B)$, $\rm(Cyc_B,Lmap_B)$, $\rm(Rmil_B,Lmap_B)$, $\rm(Lmap_B,Rmil_B)$, $\rm(Lmap_B,Cyc_B)$ and $\rm(Rmil_B,Cyc_B)$ are equidistributed over signed permutations. For Coxeter groups of type $D$, Petersen showed that the two statistics $inv_D$ and $sor_D$ are equidistributed. We introduce two statistics $nmin_D$ and $\tilde{l}_D'$ for elements of $D_n$ and we prove that the two pairs of statistics $(inv_D,nmin_D)$ and $(sor_D,\tilde{l}_D')$ are equidistributed.Comment: 25 page