A new signature for color octet pseudoscalars at the LHC

Color octet (pseudo)scalars, if they exist, will be copiously produced at the CERN Large Hadron Collider (LHC). However, their detection can become a very challenging task. In particular, if their decay into a pair of top quarks is kinematically forbidden, the main decay channel would be into two jets, with a very large background. In this Brief Report we explore the possibility of using anomaly-induced decays of the color octet pseudoscalars into gauge bosons to find them at the LHC.Comment: 4 pages, 2 figures. New references adde

Evolution of isolated neutron stars in globular clusters: number of Accretors

With a simple model from the point of view of population synthesis we try to verify an interesting suggestion made by Pfahl & Rappaport (2001) that dim sources in globular clusters (GCs) can be isolated accreting neutron stars (NSs). Simple estimates show, that we can expect about 0.5-1 accreting isolated NS per typical GC with $M=10^5 M_{\odot}$ in correspondence with observations. Properties of old accreting isolated NSs in GCs are briefly discussed. We suggest that accreting NSs in GCs experienced significant magnetic field decay.Comment: 6 pages, no figures. Submitted to Astronomical and Astrophysical Transactions (style included

Constrains on parameters of magnetic field decay for accreting isolated neutron stars

The influence of exponential magnetic field decay (MFD) on the spin evolution of isolated neutron stars is studied. The ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars, are used to constrain the exponential and power-law decay parameters. We show that for the exponential decay the ranges of minimum value of magnetic moment, $\mu_b$, and the characteristic decay time, $t_d$, $\sim 10^{29.5}\ge \mu_b \ge 10^{28} {\rm G} {\rm cm}^3$, $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$ are excluded assuming the standard initial magnetic moment, $\mu_0=10^{30} {\rm G} {\rm cm}^3$. For these parameters, neutron stars would never reach the stage of accretion from the interstellar medium even for a low space velocity of the stars and a high density of the ambient plasma. The range of excluded parameters increases for lower values of $\mu_0$. We also show, that, contrary to exponential MFD, no significant restrictions can be made for the parameters of power-law decay from the statistics of isolated neutron star candidates in ROSAT observations. Isolated neutron stars with constant magnetic fields and initial values of them less than $\mu_0 \sim 10^{29} {\rm G} {\rm cm}^3$ never come to the stage of accretion. We briefly discuss the fate of old magnetars with and without MFD, and describe parameters of old accreting magnetars.Comment: 18 pages, 6 PostScript figures, to be published in the Proceedings of the XXVIII ITEP Winter Schoo

ROSAT X-ray sources and exponential field decay in isolated neutron stars

In this paper we semianalyticaly evaluate influence of the exponential decay of magnetic field on the fate of isolated neutron stars. The fact of ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars gives us an opportunity to put some limits on the parameters of the exponential decay. We argue, that, if most part of neutron stars have approximately the same decay and initial parameters, then the combinations of the bottom magnetic momentum, $\mu_b$, in the range $\sim 10^{28}-10^{29.5} {\rm G} {\rm cm}^3$ and characteristic time scale, $t_d$, in the range $\sim 10^7-10^8 {\rm yrs}$ for standard initial magnetic momentum, $\mu_0=10^{30} {\rm G} {\rm cm}^3$, can be excluded, because for that sets of parameters neutron stars never come to the stage when accretion of the interstellar medium on their surfaces is possible even for low velocity of neutron stars and relatively high density of the interstellar medium. The region of excluded parameters increases with $\mu_0$ decreasing.Comment: 5 pages, 4 PostScript figures (uses A&A style

Restrictions on parameters of power-law magnetic field decay for accreting isolated neutron stars

In this short note we discuss the influence of power-law magnetic field decay on the evolution of old accreting isolated neutron stars. We show, that, contrary to exponential field decay (Popov & Prokhorov 2000), no additional restrictions can be made for the parameters of power-law decay from the statistics of isolated neutron star candidates in ROSAT observations. We also briefly discuss the fate of old magnetars with and without field decay, and describe parameters of old accreting magnetars.Comment: 8 pages including 3 PostScript figure

Geometric coupling thresholds in a two-dimensional strip

We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and simple discrete spectrum for any $a>0$. There is a sequence $0<a_1<a_2<...$ of critical values at which new eigenvalues emerge from the continuum when the Neumann window expands. We find the asymptotic behavior of these eigenvalues around the thresholds showing that the gap is in the leading order proportional to $(a-a_n)^2$ with an explicit coefficient expressed in terms of the corresponding threshold-energy resonance eigenfunction

Population synthesis of old neutron stars in the Galaxy

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin-down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, \ga 200-300 ${\rm km s^{-1}}$. The same conclusion is reached for both a constant ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to \la 1%.Comment: 8 pages, 4 PostScript figures, to appear in the proceedings of IAU Symposium 19

Two-mirror Schwarzschild aplanats. Basic relations

It is shown that the theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 leads to the unified description both the prefocal and the postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chretien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at fast focal ratio of the system.Comment: 19 page

Bound and resonant impurity states in a narrow gaped armchair graphene nanoribbon

An analytical study of discrete and resonant impurity quasi-Coulomb states in a narrow gaped armchair graphene nanoribbon (GNR) is performed. We employ the adiabatic approximation assuming that the motions parallel ("slow") and perpendicular ("fast") to the boundaries of the ribbon are separated adiabatically. The energy spectrum comprises a sequence of series of quasi-Rydberg levels relevant to the "slow" motion adjacent from the low energies to the size-quantized levels associated with the "fast" motion. Only the series attributed to the ground size-quantized sub-band is really discrete, while others corresponding to the excited sub-bands consist of quasi-discrete (Fano resonant) levels of non-zero energetic widths, caused by the coupling with the states of the continuous spectrum branching from the low lying sub-bands. In the two- and three-subband approximation the spectrum of the complex energies of the impurity electron is derived in an explicit form. Narrowing the GNR leads to an increase of the binding energy and the resonant width both induced by the finite width of the ribbon. Displacing the impurity centre from the mid-point of the GNR causes the binding energy to decrease while the resonant width of the first excited Rydberg series increases. As for the second excited series their widths become narrower with the shift of the impurity. A successful comparison of our analytical results with those obtained by other theoretical and experimental methods is presented. Estimates of the binding energies and the resonant widths taken for the parameters of typical GNRs show that not only the strictly discrete but also the some resonant states are quite stable and could be studied experimentally in doped GNRs