Excited nucleon spectrum from lattice QCD with maximum entropy method

We study excited states of the nucleon in quenched lattice QCD with the spectral analysis using the maximum entropy method. Our simulations are performed on three lattice sizes $16^3\times 32$, $24^3\times 32$ and $32^3\times 32$, at $\beta=6.0$ to address the finite volume issue. We find a significant finite volume effect on the mass of the Roper resonance for light quark masses. After removing this systematic error, its mass becomes considerably reduced toward the direction to solve the level order puzzle between the Roper resonance $N'(1440)$ and the negative-parity nucleon $N^*(1535)$.Comment: Lattice2003(spectrum), 3 pages, 4 figure

Energy Spectra for Fractional Quantum Hall States

Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q < 21 are examined and their energies are calculated. The classical Coulomb energy is evaluated among many electrons; that energy is linearly dependent on 1/nu. The residual binding energies are also evaluated. The electron pair in nearest Landau-orbitals is more affected via Coulomb transition than an electron pair in non-nearest orbitals. Each nearest electron pair can transfer to some empty orbital pair, but it cannot transfer to the other empty orbital pair because of conservation of momentum. Counting the numbers of the allowed and forbidden transitions, the binding energies are evaluated for filling factors of 126 fraction numbers. Gathering the classical Coulomb energy and the pair transition energy, we obtain the spectrum of energy versus nu. This energy spectrum elucidates the precise confinement of Hall resistance at specific fractional filling factors.Comment: 5 pages, 3 figure

Spectral Analysis of Excited Nucleons in Lattice QCD with Maximum Entropy Method

We study the mass spectra of excited baryons with the use of the lattice QCD simulations. We focus our attention on the problem of the level ordering between the positive-parity excited state N'(1440) (the Roper resonance) and the negative-parity excited state N^*(1535). Nearly perfect parity projection is accomplished by combining the quark propagators with periodic and anti-periodic boundary conditions in the temporal direction. Then we extract the spectral functions from the lattice data by utilizing the maximum entropy method. We observe that the masses of the N' and N^* states are close for wide range of the quark masses (M_pi=0.61-1.22 GeV), which is in contrast to the phenomenological prediction of the quark models. The role of the Wilson doublers in the baryonic spectral functions is also studied.Comment: 15 pages, 5 figures included, typos corrected, and references adde

Transition from real to virtual polarized photon structures

We investigate the transition of the polarized photon structure function $g_1^\gamma(x,Q^2,P^2)$ when the target photon shifts from on-shell ($P^2=0$) to far off-shell ($P^2\gg \Lambda^2$) region. The analysis is performed to the next-to-leading order in QCD. The first moment of $g_1^\gamma$ which vanishes for the real photon, turns to be a negative value when target photon becomes off-shell. The explicit $P^2$-dependence of the first moment sum rule as well as of the structure function $g_1^\gamma(x,Q^2,P^2)$ as a function of $x$ is studied in the framework of the vector meson dominance model.Comment: 16 pages, 4 eps figure

Spin structure function of the virtual photon

We investigate the spin structure of the virtual photon beyond the leading order in QCD. The first moment of the virtual photon spin structure function $g_1^\gamma(x,Q^2,P^2)$ with QCD effects turns out to be non-vanishing in contrast to the real photon case. Numerical analysis for virtual as well as real photon case is presented.Comment: 3 pages, LaTeX, 3 ps figures, uses npb.sty, Contribution to the Workshop on Deep Inelastic Scattering and QCD (DIS 99), Zeuthen, April 199

Virtual Photon Structure Functions

We discuss the perturbatively calculable virtual photon structure functions. First we present the framework for analyzing the structure functions of the virtual photon and derive a first moment of $g_1^\gamma$ of the virtual photon. We then investigate the three positivity constraints satisfied by the eight structure functions of the virtual photon.Comment: 5 pages, LaTeX, 5 eps figures, npb.sty file included Talk given at RADCOR/Loops and Legs 2002, Kloster Banz, Germany, September 8-13, 2002, to appear in the Proceeding

Parton Distributions in the Virtual Photon Target and Factorization Scheme Dependence

We investigate parton distributions in the virtual photon target, both polarized and unpolarized, up to the next-leading order (NLO) in QCD. Parton distributions can be predicted completely up to NLO, but they are factorization-scheme-dependent. We analyze parton distributions in several factorization schemes and discuss their scheme dependence. Particular attentions are paid to the axial anomaly effect on the first moments of the polarized quark parton distributions, and also to the large-$x$ behaviors of polarized and unpolarized parton distributions.Comment: 6 pages, LaTeX, 3 ps figures, uses npb.sty, Contribution to the Zeuthen Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Koenigstein-Weissig, Germany, April 200

Positivity constraints on photon structure functions

We investigate the positivity constraints for the structure functions of both virtual and real photon. From the Cauchy-Schwarz inequality we derive three positivity conditions for the general virtual photon case, which reduce, in the real photon case, to one condition relating the polarized and unpolarized structure functions.Comment: 10 pages, 1 ps figure, to appear Phys. Lett.