Chiral color symmetry and possible G′G'-boson effects at the Tevatron and LHC

A gauge model with chiral color symmetry is considered and possible effects of the color $G'$-boson octet predicted by this symmetry are investigated in dependence on two free parameters, the mixing angle $\theta_G$ and $G'$ mass $m_{G'}$. The allowed region in the $m_{G'} - \theta_G$ plane is found from the Tevatron data on the cross section $\sigma_{t\bar{t}}$ and forward-backward asymmetry $A_{\rm FB}^{p \bar p}$ of the $t\bar{t}$ production. The mass limits for the $G'$-boson are shown to be stronger than those for the axigluon. A possible effect of the $G'$-boson on the $t\bar{t}$ production at the LHC is discussed and the mass limits providing for the $G'$-boson evidence at the LHC are estimated in dependence on $\theta_G$.Comment: 11 pages, 2 figures, accepted for publication in Modern Physics Letters

On Remoteness Functions of Exact Slow kk-NIM with k+1k+1 Piles

Given integer $n$ and $k$ such that $0 < k \leq n$ and $n$ piles of stones, two player alternate turns. By one move it is allowed to choose any $k$ piles and remove exactly one stone from each. The player who has to move but cannot is the loser. Cases $k=1$ and $k = n$ are trivial. For $k=2$ the game was solved for $n \leq 6$. For $n \leq 4$ the Sprague-Grundy function was efficiently computed (for both the normal and mis\`ere versions). For $n = 5,6$ a polynomial algorithm computing P-positions was obtained. Here we consider the case $2 \leq k = n-1$ and compute Smith's remoteness function, whose even values define the P-positions. In fact, an optimal move is always defined by the following simple rule: if all piles are odd, keep a largest one and reduce all other; if there exist even piles, keep a smallest one of them and reduce all other. Such strategy is optimal for both players, moreover, it allows to win as fast as possible from an N-position and to resist as long as possible from a P-position.Comment: 20 page

Quantum correlation measurements in interferometric gravitational wave detectors

Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational-wave detectors, such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer