Relativistic Corrections to the Exclusive Decays of C-even Bottomonia into S-wave Charmonium Pairs

Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic corrections of the next-to-leading order in $v_c$ to the decay rate for $\chi_{b2}\to \eta_c(mS)+\eta_c(nS)$ with $m,$ $n=1$ or 2 are very large. In every case, the resummation of the relativistic corrections enhances the rate in comparison with the next-to-leading-order results. We compare our results with available predictions based on the NRQCD factorization formalism. The NRQCD predictions are significantly smaller than those based on the light-cone formalism by an or two orders of magnitudes.Comment: 20 pages, 1 figure. Typos corrected, published versio

Geometry of Houghton's Groups

Ken Brown showed finiteness properties of Houghton's groups by studying the action of those groups on infinite dimensional cell complex. We modify his proof by construction finite dimensional CAT(0) cubical complexes on which Houghton's groups act. We extendD. L. Johnson's result about finite presentation for basic case of Houghton's group to get finite presentations for all Houghton's groups beyond the base case. We also provide exponential isoperimetric inequalities for Houghton's groups

Knowledge intensive service activities (KISAs) in Korea's innovation system

노트 : This is submitted to the Korea Development Institute as the Final Report of “Analysis on Knowledge-Intensive Service Activities in Korea’s Innovation System”, in fulfillment of the Contract between KDI and STEPI. This Research is Fully Sponsored by Strategic Research Partnership of Korea Development Institute

The R∞ property for Houghton's groups

We study twisted conjugacy classes of a family of groups which are called Houghton's groups Hn (n∈N), the group of translations of n rays of discrete points at infinity. We prove that the Houghton's groups Hn have the R∞ property for all n∈N