The time-of-propagation counter for Belle II

The Belle II detector operating at the future upgrade to the KEKB accelerator will perform high-statistics precision investigations into the flavor sector of the Standard Model. As charged hadron identification is a vital element of the experiment's success, the time-of-propagation (TOP) counter has been chosen as the primary particle identification device in the barrel region of Belle II. The TOP counter is a compact variant of the detection of internally reflected Cherenkov light (DIRC) technique and relies heavily on exquisite single photon timing resolution with micro-channel plate photomultiplier tubes. We discuss the general principles of TOP operation and optimization of the Belle II TOP configuration, which is expected to provide 4 sigma or better separation of kaons and pions up to momenta of approximately 4 GeV/c.Comment: 5 pages, 5 figures, 2 tables; Submitted to special edition of NIMA, Proceedings of RICH201

Implications of the non-universal Z boson in FCNC mediated rare decays

We analyze the effect of the non-universal $Z$ boson in the rare decays $B_s \to l^+ l^-$, $B_s \to l^+ l^- \gamma$ and $Z \to b \bar s$ decays. These decays involve the FCNC mediated $b \to s$ transitions, and are found to be very small in the standard model. The smallness of these decays in the standard model makes them sensitive probe for new physics. We find an enhancement of at least an order in these branching ratios because of the non-universal $Zbs$ coupling.Comment: 15 pages, 4 figures, minor changes in the text, references added, to appear in PR

The Buy Price in Auctions with Discrete Type Distributions

This paper considers second-price, sealed-bid auctions with a buy price where bidders' types are discretely distributed. We characterize all equilibria, restricting our attention to equilibria where bidders whose types are less than a buy price bid their own valuations. Budish and Takeyama (2001) analyzed the two-bidder, two-type framework, and showed that if bidders are risk-averse, a seller can obtain a higher expected revenue from the auction with a certain buy price than from the auction without a buy price. We extend their revenue improvement result to the n-bidder, two-type framework. However, in case of three or more types, bidders' risk aversion is not a sufficient condition for the revenue improvement. Our example illustrates that even if bidders are risk-averse, a seller cannot always obtain a higher expected revenue from the auction with a buy price.Auction; Buy price; Risk aversion

Finite Size Effects and Conformal Symmetry of O(N)O(N) Nonlinear σ\sigma Model in Three Dimensions

We study the $O(N)$ nonlinear $\sigma$ model on a three-dimensional compact space $S^1 \times S^2$ (of radii $L$ and $R$ respectively) by means of large $N$ expansion, focusing on the finite size effects and conformal symmetries of this model at the critical point. We evaluate the correlation length and the Casimir energy of this model and study their dependence on $L$ and $R$. We examine the modular transformation properties of the partition function, and study the dependence of the specific heat on the mass gap in view of possible extension of the $C-$theorem to three dimensions.Comment: 12 pages uuencoded compressed PostScript file including 1 figur

Ultraviolet Property of Noncommutative Wess-Zumino-Witten Model

We construct noncommutative extension of the Wess-Zumino-Witten (WZW) model and study its ultraviolet property. The \beta-function of the U(N) noncommutative WZW model resembles that of the ordinary WZW model. The U(1) noncommutative model has also a nontrivial fixed point.Comment: 7 pages, 1 figur

Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms

We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with $U_q(\widehat{sl_2})$. Integrable $XXZ$ spin-1 chain hamiltonian with general boundary interactions is also obtained.Comment: 14 pages, LaTeX, no figur