Eigenvalues of Ruijsenaars-Schneider models associated with An−1A_{n-1} root system in Bethe ansatz formalism

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].Comment: Latex file, 25 page

q-deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy.Comment: LaTex file 18 page

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

Free boson representation of DY_{\hbar}(gl_N)_k

We construct a realization of the Yangian double DY_\hbar(gl_N) and DY_\hbar(sl_N) of an arbitrary level k in terms of free boson fields with a continuous parameter. In the \hbar \to 0 limit this realization becomes the Wakimoto realization of kac-Moody algebra gl_N and sl_N, respectively. The vertex operators and the screening currents are also constructed with the same spirits; the screening currents commute with DY_\hbar(sl_N) modulo total difference.Comment: 19pages, Latex, no figure

Four Statements about the Fourth Generation

This summary of the Workshop "Beyond the 3-generation SM in the LHC era" presents a brief discussion of the following four statements about the fourth generation: 1) It is not excluded by EW precision data; 2) It addresses some of the currently open questions; 3) It can accommodate emerging possible hints of new physics; 4) LHC has the potential to discover or fully exclude it.Comment: Summary of the "Beyond the 3-generation SM in the LHC era" Workshop, CERN, September 4-5, 2008; 7 pages. V2: updated bibliography and minor typos fixed. To appear in PMC Physics

Singlet Charge 2/32/3 Quark hiding the Top: Tevatron and LEP Implications

If $c$ and $t$ quarks are strongly mixed with a weak singlet charge $2/3$ quark, $BR(t\to \ell\nu + X)$ could be suppressed via the $t\to cH^0$ mode, thereby the top quark could still hide below $M_W$, whereas the heavy quark signal observed at the Tevatron is due to the dominantly singlet quark $Q$. This may occur without affecting the small $m_c$ value. Demanding $m_Q \simeq 175$ GeV and m_t \ltap M_W, we find that $BR(t\to \ell\nu + X)$ cannot be too suppressed. The heavy quark $Q$ decays via $W,\ H$, and $Z$ bosons. The latter can lead to $b$-tagged $Z + 4$ jet events, while the strong $c$--$Q$ mixing is reflected in sizable $Q\to sW$ fraction. $Z\to t\bar c$ decay occurs at tree level and may be at the $10^{-3}$ order, leading to the signature of $Z\to \ell\nu b\bar c$, all isolated and with large $p_T$, at $10^{-5}$ order.Comment: 10 pages + 3 Figures (not included), ReVTeX, NTUTH-94-1

Enhanced b→sgb\to sg Decay, Inclusive η′\eta^\prime Production, and the Gluon Anomaly

The experimental hint of large $B\to \eta^\prime + X_s$ is linked to the $b\to s$ penguins via the gluon anomaly. Using running $\alpha_s$ in the $\eta^\prime$-$g$-$g$ coupling, the standard $b\to sg^*$ penguin alone seems insufficient, calling for the need of dipole $b\to sg$ at 10% level from new physics, which could also resolve the ${\cal B}_{s.l.}$ and charm counting problems. The intereference of standard and new physics contributions may result in direct CP asymmetries at 10% level, which could be observed soon at B Factories.Comment: 12 pages, revtex, 3 figs. (version to appear in Phys. Rev. Lett.

On the Classical W4(2)W_{4}^{(2)} Algebra

We consider the classical \w42 algebra from the integrable system viewpoint. The integrable evolution equations associated with the \w42 algebra are constructed and the Miura maps , consequently modifications, are presented. Modifying the Miura maps, we give a free field realization the classical \w42 algebra. We also construct the Toda type integrable systems for it.Comment: 14 pages, latex, no figure

Window on Higgs Boson: Fourth Generation b′b^\prime Decays Revisited

Direct and indirect searches of the Higgs boson suggest that 113 GeV $\lesssim m_H \lesssim$ 170 GeV is likely. With the LEP era over and the Tevatron Run II search via $p\bar p \to WH+X$ arduous, we revisit a case where $WH$ or $ZH +$ jets could arise via strong $b^\prime\bar b^\prime$ pair production. In contrast to 10 years ago, the tight electroweak constraint on $t^\prime$--$b^\prime$ (hence $t^\prime$--$t$) splitting reduces FCNC $b^\prime\to bZ$, $bH$ rates, making $b^\prime\to cW$ naturally competitive. Such a "cocktail solution" is precisely the mix that could evade the CDF search for $b^\prime\to bZ$, and the $b^\prime$ may well be lurking below the top. In light of the Higgs program, this two-in-one strategy should be pursued.Comment: 4 pages, RevTex, 4 eps figures, One more figure, version to be published in Phys. Rev.