Siegert pseudostate perturbation theory: one- and two-threshold cases

Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relationship of the Siegert Pseudostates. We apply the theory to a 2-channel model problem, and find the rate of convergence of the perturbation expansion should be examined with the aide of the variance $D= ||E-\sum_{n}\lambda^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually

A Rich Cluster of Galaxies Near the Quasar B2 1335+28 at z=1.1: Color Distribution and Star-Formation Properties

We previously reported a significant clustering of red galaxies (R-K=3.5--6) around the radio-loud quasar B2 1335+28 at z=1.086. In this paper, we establish the existence of a rich cluster at the quasar redshift, and study the properties of the cluster galaxies through further detailed analysis of the photometric data. The color distribution of the galaxies in the cluster is quite broad and the fraction of blue galaxies (\sim 70%) is much larger than in intermediate-redshift clusters. Using evolutionary synthesis models, we show that this color distribution can be explained by galaxies with various amounts of star-formation activity mixed with the old stellar populations. Notably, there are about a dozen galaxies which show very red optical-NIR colors but also show significant UV excess with respect to passive-evolution models. They can be interpreted as old early-type galaxies with a small amount of star formation. The fact that the UV-excess red galaxies are more abundant than the quiescent red ones suggests that a large fraction of old galaxies in this cluster are still forming stars to some extent. However, a sequence of quiescent red galaxies is clearly identified on the R-K versus K color-magnitude (C-M) diagram. The slope and zero point of their C-M relation appear to be consistent with those expected for the precursors of the C-M relation of present-day cluster ellipticals when observed at z=1.1. We estimate the Abell richness class of the cluster to be R \sim 1. New X-ray data presented here place an upper limit of L_x < 2 10^{44} erg s^{-1} for the cluster luminosity. Inspections of the wider optical images reveal some lumpy structure, suggesting that the whole system is still dynamically young.Comment: 54 pages including 13 Postscript figures, 1 jpg figure, and 1 table, uses aasms4.sty and epsf.sty. Accepted for publication in ApJ: Replaced as the older verison was missed to include the figure 2c, 2d, and figure

A New Constraint on the Lyα\alpha Fraction of UV Very Bright Galaxies at Redshift 7

We study the extent to which very bright (-23.0 < MUV < -21.75) Lyman-break selected galaxies at redshifts z~7 display detectable Lya emission. To explore this issue, we have obtained follow-up optical spectroscopy of 9 z~7 galaxies from a parent sample of 24 z~7 galaxy candidates selected from the 1.65 sq.deg COSMOS-UltraVISTA and SXDS-UDS survey fields using the latest near-infrared public survey data, and new ultra-deep Subaru z'-band imaging (which we also present and describe in this paper). Our spectroscopy has yielded only one possible detection of Lya at z=7.168 with a rest-frame equivalent width EW_0 = 3.7 (+1.7/-1.1) Angstrom. The relative weakness of this line, combined with our failure to detect Lya emission from the other spectroscopic targets allows us to place a new upper limit on the prevalence of strong Lya emission at these redshifts. For conservative calculation and to facilitate comparison with previous studies at lower redshifts, we derive a 1-sigma upper limit on the fraction of UV bright galaxies at z~7 that display EW_0 > 50 Angstrom, which we estimate to be < 0.23. This result may indicate a weak trend where the fraction of strong Lya emitters ceases to rise, and possibly falls between z~6 and z~7. Our results also leave open the possibility that strong Lya may still be more prevalent in the brightest galaxies in the reionization era than their fainter counterparts. A larger spectroscopic sample of galaxies is required to derive a more reliable constraint on the neutral hydrogen fraction at z~7 based on the Lya fraction in the bright galaxies.Comment: 20 pages, 7 figures, accepted for publication in Ap

Resonance between Noise and Delay

We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise'' and ``delay''. We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Lett Expanded and Added Reference

Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates

We calculate the energies of three-quark states with definite permutation symmetry (i.e. of SU(6) multiplets) in the N=0,1,2 shells, confined by the Y-string three-quark potential. The exact Y-string potential consists of one, so-called three-string term, and three angle-dependent two-string terms. Due to this technical complication we treat the problem at three increasingly accurate levels of approximation: 1) the (approximate) three-string potential expanded to first order in trigonometric functions of hyper-spherical angles; 2) the (approximate) three-string potential to all orders in the power expansion in hyper-spherical harmonics, but without taking into account the transition(s) to two-string potentials; 3) the exact minimal-length string potential to all orders in power expansion in hyper-spherical harmonics, and taking into account the transition(s) to two-string potentials. We show the general trend of improvement %convergence of these approximations: The exact non-perturbative corrections to the total energy are of the order of one per cent, as compared with approximation 2), yet the exact energy differences between the $[20,1^{+}], [70,2^{+}], [56,2^{+}], [70,0^{+}]$-plets are shifted to 2:2:0.9, from the Bowler and Tynemouth separation rule 2:2:1, which is obeyed by approximation 2) at the one per cent level. The precise value of the energy separation of the first radial excitation ("Roper") $[56^{\prime},0^{+}]$-plet from the $[70,1^{-}]$-plet depends on the approximation, but does not become negative, i.e. the "Roper" remains heavier than the odd-parity $[70,1^{-}]$-plet in all of our approximations.Comment: 19 pages, 6 figure

Dissipative Field Theory with Caldeira-Leggett Method and its Application to Disoriented Chiral Condensation

The effective field theory including the dissipative effect is developed based on the Caldeira-Leggett theory at the classical level. After the integration of the small field fluctuations considered as the field radiation, the integro-differential field equation is given and shown to include the dissipative effects. In that derivation, special cares should be taken for the boundary condition of the integration. Application to the linear sigma model is given, and the decay process of the chiral condensate is calculated with it, both analytically in the linear approximation and numerically. With these results, we discuss the stability of chiral condensates within the quenched approximation.Comment: 16pages, ReV-Te

Flavor mixing in the gluino coupling and the nucleon decay

Flavor mixing in the quark-squark-gluino coupling is studied for the minimal SU(5) SUGRA-GUT model and applied to evaluation of the nucleon lifetime. All off-diagonal (generation mixing) elements of Yukawa coupling matrices and of squark/slepton mass matrices are included in solving numerically one-loop renormalization group equations for MSSM parameters, and the parameter region consistent with the radiative electroweak symmetry breaking condition is searched. It is shown that the flavor mixing in the gluino coupling for a large $\tan\beta$ is of the same order of magnitude as the corresponding Kobayashi-Maskawa matrix element in both up-type and down-type sector. There exist parameter regions where the nucleon decay amplitudes for charged lepton modes are dominated by the gluino dressing process, while for all the examined regions the neutrino mode amplitudes are dominated by the wino dressing over the gluino dressing.Comment: 24 pages, LaTeX, figures are available upon request. ICRR-Report-317-94-1

Performance confirmation of the Belle II imaging Time Of Propogation (iTOP) prototype counter

The Bell Detector at the KEKB asymmetric-energy e{sup +}e{sup -} collider performed extremely well, logging an integrated luminosity an order of magnitude higher than the design baseline. With this inverse attobarn of integrated luminosity, time-dependent CP-violation inn the 3rd generation beauty quarks was firmly established, and is now a precision measurement. Going beyond this to explore if the Kobayashi-Maskawa mechanism is the only contributor to quark-mixing, and to interrogate the flavor sector for non-standard model enhancements, requires a detector and accelerator capable of topping this world-record luminosity by more than an order of magnitude. The Belle II detector at the upgraded Super-KEKB accelerator has been designed to meet this highly ambitious goal of operating at a luminosity approaching 10{sup 36} cm{sup -2} s{sup -1}. Such higher event rates and backgrounds require upgrade of essentially all detector subsystems, as well as their readout. Comparing the Belle composite (threshold Aerogel + Time of Flight) particle identification (PID) system with the DIRC employed by BaBar, quartz radiator internal Cherenkov photon detection proved to have higher kaon efficiency and lower pion fake rates. However, because the detector structure and CsI calorimeter will be retained, an improved barrel PID must fit within a very narrow envelope, as indicated in Figure 1. To effectively utilize this space, a more compact detector concept based on the same quartz radiators, but primarily using photon arrival time was proposed. This Time Of Propagation (TOP) counter was studied in a number of earlier prototype tests. Key to the necessary 10's of picosecond single-photon timing has been the development of the so-called SL-10 Micro-Channel Plate Photo-Multiplier Tube (MCP-PMT), which has demonstrated sub-40 ps single photon Transit Time Spread TTS. Further simulation study of this detector concept indicated that a focusing mirror in the forward direction, as well as a modest image expansion volume and more highly pixelated image plane improve the theoretical detector performance, since timing alone is limited by chromatic dispersion of the Cherenkov photons. This imaging-TOP (or iTOP) counter is the basis of Belle II barrel PID upgrade. However, a number of critical performance parameters must be demonstrated prior to releasing this prototype design for production manufacture

Muon anomalous magnetic moment, lepton flavor violation, and flavor changing neutral current processes in SUSY GUT with right-handed neutrino

Motivated by the large mixing angle solutions for the atmospheric and solar neutrino anomalies, flavor changing neutral current processes and lepton flavor violating processes as well as the muon anomalous magnetic moment are analyzed in the framework of SU(5) SUSY GUT with right-handed neutrino. In order to explain realistic mass relations for quarks and leptons, we take into account effects of higher dimensional operators above the GUT scale. It is shown that the supersymmetric (SUSY) contributions to the CP violation parameter in $K^0-\bar{K}^0$ mixing, $\epsilon_K$, the $\mu \to e \gamma$ branching ratio, and the muon anomalous magnetic moment become large in a wide range of parameter space. We also investigate correlations among these quantities. Within the current experimental bound of $\text{B}(\mu \to e \gamma)$, large SUSY contributions are possible either in the muon anomalous magnetic moment or in $\epsilon_K$. In the former case, the favorable value of the recent muon anomalous magnetic moment measurement at the BNL E821 experiment can be accommodated. In the latter case, the allowed region of the Kobayashi-Maskawa phase can be different from the prediction within the Standard Model (SM) and therefore the measurements of the CP asymmetry of $B\to J/\psi K_S$ mode and $\Delta m_{B_s}$ could discriminate this case from the SM. We also show that the $\tau \to \mu \gamma$ branching ratio can be close to the current experimental upperbound and the mixing induced CP asymmetry of the radiative B decay can be enhanced in the case where the neutrino parameters correspond to the Mikheyev-Smirnov-Wolfenstein small mixing angle solution.Comment: 70 pages, 14 figure