A Majorana Fermion t-J Model in One Dimension

We study a rotation invariant Majorana fermion model in one dimension using diagrammatic perturbation theory and numerical diagonalization of small systems. The model is inspired by a Majorana representation of the antiferromagnetic spin-1/2 chain, and it is similar in form to the t-J model of electrons, except that the Majorana fermions carry spin-1 and Z_2 charge. We discuss the implications of our results for the low-energy excitations of the spin-1/2 chain. We also discuss a generalization of our model from 3 species of Majorana fermions to N species; the SO(4) symmetric model is particularly interesting.Comment: 29 LaTeX pages, 11 postscript figure

The Equivalence Theorem and Effective Lagrangians

We point out that the equivalence theorem, which relates the amplitude for a process with external longitudinally polarized vector bosons to the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a more general formulation of this theorem also holds for effective interactions. The generalized theorem can be utilized to determine the high-energy behaviour of scattering processes just by power counting and to simplify the calculation of the corresponding amplitudes. We apply this method to the phenomenologically most interesting terms describing effective interactions of the electroweak vector and Higgs bosons in order to examine their effects on vector-boson scattering and on vector-boson-pair production in $f\bar{f}$ annihilation. The use of the equivalence theorem in the literature is examined.Comment: 20 pages LaTeX, BI-TP 94/1

Constraints on the minimal supergravity model from the b->s+\gamma decay

The constraints on the minimal supergravity model from the b->s+\gamma decay are studied. A large domain in the parameter space for the model satisfies the CLEO bound, BR(b->s+\gamma)<5.4X10^{-4}. However, the allowed domain is expected to diminish significantly with an improved bound on this decay. The dependence of the b->s+\gamma branching ratio on various parameters is studied in detail. It is found that, for A_t<0 and the top quark mass within the vicinity of the center of the CDF value, m_t^{pole}=174\pm17 GeV, there exists only a small allowed domain because the light stop is tachyonic for most of the parameter space. A similar phenomenon exists for a lighter top and A_t negative when the GUT coupling constant is slightly reduced. For A_t>0, however, the branching ratio is much less sensitive to small changes in m_t, and \alpha_G.Comment: 12 pages, plain tex file, three figures avaliable upon request, CTP-TAMU-03/94, NUB-TH.7316/94, and CERN-TH.3092/9

The Nonresonant Cabibbo Suppressed Decay B±→π+π−π±B^\pm\to \pi^+\pi^-\pi^\pm and Signal for CP Violation

We consider various contributions to the nonresonant decay $B^\pm\rightarrow \pi^+\pi^-\pi^\pm$, both of the long-distance and short-distance types with the former providing for most of the branching ratio, predicted to be $BR(B^\pm\rightarrow \pi^+\pi^-\pi^\pm) = (1.5 - 8.4 )\times 10^{-5}$. We also discuss an application to CP violation resulting from the interference of that nonresonant background (with $m(\pi^+\pi^-)\approx 3.4$ GeV) and $B^\pm\rightarrow \chi_{c0} \pi^\pm$ followed by $\chi_{c0}\rightarrow \pi^+\pi^-$. The resulting value of the partial rate asymmetry is (0.40\sim 0.48)\mbox{sin}\gamma, where \gamma = \mbox{arg}(V_{ub}^*).Comment: 10 pages, Revte

A real space auxiliary field approach to the BCS-BEC crossover

The BCS to BEC crossover in attractive Fermi systems is a prototype of weak to strong coupling evolution in many body physics. While extensive numerical results are available, and several approximate methods have been developed, most of these schemes are unsuccessful in the presence of spatial inhomogeneity. Such situations call for a real space approach that can handle large spatial scales and retain the crucial thermal fluctuations. With this in mind, we present comprehensive results of a real space auxiliary field approach to the BCS to BEC crossover in the attractive Hubbard model in two dimensions. The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a $T_c$ scale that agrees with quantum Monte Carlo estimates to within a few percent. We provide results on the $T_c$, amplitude and phase fluctuations, density of states, and the momentum resolved spectral function over the entire interaction and temperature window. We suggest how the method generalises successfully to the presence of disorder, trapping, and population imbalance.Comment: This article supersedes arXiv:1105.115