Dual Lie Bialgebra Structures of Poisson Types

Let $A=F[x,y]$ be the polynomial algebra on two variables $x,y$ over an algebraically closed field $F$ of characteristic zero. Under the Poisson bracket, $A$ is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of $A^*$ induced from the multiplication of the associative commutative algebra $A$ coincides with the maximal good subspace of $A^*$ induced from the Poisson bracket of the Poisson Lie algebra $A$. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products, five classes of new infinite dimensional Lie algebras are obtained.Comment: accepted for publication in SCIENCE CHINA Mathematic

Quarkonium-Hadron Interactions in Perturbative QCD

The next to leading order (NLO) quarkonium-hadron cross section is calculated in perturbative QCD. The corresponding leading order (LO) result was performed by Peskin more than 20 years ago using the operator product expansion (OPE). In this work, the calculation is performed using the Bethe-Salpeter amplitude and the factorization formula. The soft divergence appearing in the intermediate stages of the calculations are shown to vanish after adding all possible crossed terms, while the collinear divergences are eliminated by mass factorization. Applying the result to the Upsilon system, one finds that there are large higher order correction near the threshold. The relevance of the present result to the charmonium case is also discussed.Comment: Yonsei University. to be published in PR

Thermodynamics of Spin-1/2 AF-AF-F and F-F-AF Trimerized Quantum Heisenberg Chains

The magnetization process, the susceptibility and the specific heat of the spin-1/2 AF-AF-F and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at $m=1/6$ for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.Comment: 11 pages, 10 figure

Probing Exotic Charged Higgs Decays in the Type-II 2HDM through Top Rich Signal at a Future 100 TeV pp Collider

The exotic decay modes of non-Standard Model Higgs bosons are efficient in probing the hierarchical Two Higgs Doublet Models (2HDM). In particular, the decay mode $H^\pm\to HW^\pm$ serves as a powerful channel in searching for charged Higgses. In this paper, we analyzed the reach for $H^\pm\to HW^\pm \to t\bar{t}W$ at a 100 TeV $pp$ collider, and showed that it extends the reach of the previously studied $\tau\tau W$ final states once above the top threshold. Top tagging technique is used, in combination with the boosted decision tree classifier. Almost the entire hierarchical Type-II 2HDM parameter space can be probed via the combination of all channels at low $\tan\beta$ region.Comment: 17 page