Search for double charmonium decays of the P-wave spin-triplet bottomonium states

Using a sample of 158 million $\Upsilon(2S)$ events collected with the Belle detector, we search for the first time for double charmonium decays of the $P$-wave spin-triplet bottomonium states ($\Upsilon(2S) \to \gamma \chi_{bJ}$, \chi_{bJ} \to \jpsi \jpsi, \jpsi \psp, \psp \psp for J=0, 1, and 2). No significant $\chi_{bJ}$ signal is observed in the double charmonium mass spectra, and we obtain the following upper limits, \BR(\chi_{bJ} \to \jpsi \jpsi)<7.1\times 10^{-5}, $2.7\times 10^{-5}$, $4.5\times 10^{-5}$, \BR(\chi_{bJ} \to \jpsi \psp)<1.2\times 10^{-4}, $1.7\times 10^{-5}$, $4.9\times 10^{-5}$, \BR(\chi_{bJ} \to \psp \psp)<3.1\times 10^{-5}, $6.2\times 10^{-5}$, $1.6\times 10^{-5}$ for J=0, 1, and 2, respectively, at the 90% confidence level. These limits are significantly lower than the central values (with uncertainties of 50% to 70%) predicted using the light cone formalism but are consistent with calculations using the NRQCD factorization approach.Comment: 7 pages, 4 figures, 1 tabl

The Fornax Spectroscopic Survey: The Number of Unresolved Compact Galaxies

We describe a sample of thirteen bright (18.5<Bj<20.1) compact galaxies at low redshift (0.05<z<0.21) behind the Fornax Cluster. These galaxies are unresolved on UK Schmidt sky survey plates, so would be missing from most galaxy catalogs compiled from this material. The objects were found during initial observations of The Fornax Spectroscopic Survey. This project is using the Two-degree Field spectrograph on the Anglo-Australian Telescope to obtain spectra for a complete sample of all 14000 objects, stellar and non-stellar, with 16.5<Bj<19.7, in a 12 square degree area centered on the Fornax cluster of galaxies. The surface density of compact galaxies with magnitudes 16.5<Bj<19.7 is 7+/-3 /sq.deg., representing 2.8+/-1.6% of all local (z<0.2) galaxies to this limit. There are 12+/-3 /sq.deg. with 16.5<Bj<20.2. They are luminous (-21.5<Mb<-18.0, for H0=50 km/s/mpc) and most have strong emission lines (H alpha equivalent widths of 40-200 A) and small sizes typical of luminous HII galaxies and compact narrow emission line galaxies. Four out of thirteen have red colors and early-type spectra, so are unlikely to have been detected in any previous surveys.Comment: LaTeX source; 5 pages including 3 figures; uses emulateapj.st

The quasisuperminimizing constant for the minimum of two quasisuperminimizers in R^n

It was shown in Bj\"orn--Bj\"orn--Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), 264-284) that $u:=\min\{u_1,u_2\}$ is a $\overline{Q}$-quasisuperminimizer if $u_1$ and $u_2$ are $Q$-quasisuperminimizers and $\overline{Q}=2Q^2/(Q+1)$. Moreover, one-dimensional examples therein show that $\overline{Q}$ is close to optimal. In this paper we give similar examples in higher dimensions. The case when $u_1$ and $u_2$ have different quasisuperminimizing constants is considered as well

Confirming the molecular nature of the Zb(10610)Z_b(10610) and the Zb(10650)Z_b(10650)

The decays of the $Z_b(10610)$ and the $Z_b(10650)$ to $\Upsilon(nS)\pi$, $h_b(mP)\pi$ and $\chi_{bJ}(mP)\gamma$ ($n=1,2,3$, $m=1,2$ and $J=0,1,2$) are investigated within a nonrelativistic effective field theory. It is argued that, while the decays to $\Upsilon(nS) \pi$ suffer from potentially large higher order corrections, the $P$-wave transitions of the $Z_b$ states offer the best possibility to confirm the nature of the $Z_b$ states as molecular states and to further study their properties. We give nontrivial and parameter-free predictions for the ratios of various partial widths for final states with $h_b(mP)\pi$ and $\chi_{bJ}(mP)\gamma$. In addition, the branching fractions for the neutral $Z_b$-states to $\chi_{bJ}\gamma$ are predicted to be of order $10^{-4}$--$10^{-3}$. This provides a fine test of the molecular nature in future high-luminosity experiments.Comment: 18 pages, 2 figure