CORE and the Haldane Conjecture

The Contractor Renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper\cite{QGAF} I showed that the Contractor Renormalization group (CORE) method could be used to map a theory of free quarks, and quarks interacting with gluons, into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple Contractor Renormalization group (CORE) computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.Comment: 36 pages, 4 figures, 5 tables, latex; extensive additions to conten

Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

Probing New Physics From CP Violation in Radiative B Decays

When new CP-violating interactions are dominated by flavor changing neutral particle exchanges, that may occur in many extensions of the standard model. We examine a type 3 two Higgs doublet model and find that direct CP asymmetries can be as large as about 25% . Time-dependent and time-integrated mixing-induced CP asymmetries up to 85 and 40 %, respectively, are possible without conflict with other constraints. It mainly requirs an enhanced chromo-magnetic dipole $b\to sg$ decay to be close to the present experimental bound.Comment: 7 pages, latex, no figure

Is the ground state of Yang-Mills theory Coulombic?

We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.Comment: 10 pages, 9 .eps figure

Model independent properties of two-photon exchange in elastic electron proton scattering

We derive from first principles, as the C-invariance of the electromagnetic interaction and the crossing symmetry, the general properties of two-photon exchange in electron-proton elastic scattering. We show that the presence of this mechanism destroys the linearity of the Rosenbluth separation.Comment: 12 pages, no figures- Corrected misprints, changes in P. 7. No changes in conclusion

Higher Twist Effects in the Drell-Yan Angular Distribution

We study the Drell-Yan process $\pi N \rightarrow \mu^+ \mu^- X$ at large $x_F$ using perturbative QCD. A higher-twist mechanism suggested by Berger and Brodsky is known to qualitatively explain the observed $x_F$ dependence of the muon angular distribution, but the predicted large $x_F$ behavior differs quantitatively from observations. We have repeated the model calculation taking into account the effects of nonasymptotic kinematics. At fixed-target energies we find important corrections which improve the agreement with data. The asymptotic result of Berger and Brodsky is recovered only at much higher energies. We discuss the generic reasons for the large corrections at high $x_F$. A proper understanding of the $x_F \to 1$ data would give important information on the pion distribution amplitude and exclusive form factor.Comment: 8 pages in Latex with 3 figures appended as Postscript files, HU-TFT-94-12, LBL-35430. (The introductory part has been slightly altered and three references have been added

Flavor Changing Scalar Interactions

The smallness of fermion masses and mixing angles has recently been been attributed to approximate global $U(1)$ symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor changing reaction rates may be acceptably small in electroweak theories with several scalar doublets without imposing any special symmetries on the scalars themselves, such theories generically yield too much CP violation in the neutral kaon mass matrix. Hence in these theories CP must also be a good approximate symmetry. Such models provide an alternative mechanism for CP violation and have various interesting phenomenological features.Comment: 18 pages. UTTG-22-92; LBL 33016; UCB 92/3

On the Gerasimov-Drell-Hearn sum rule for the deuteron

The Gerasimov-Drell-Hearn sum rule is evaluated for the deuteron by explicit integration up to 550 MeV including contributions from the photodisintegration channel and from coherent and incoherent single pion production as well. The photodisintegration channel converges fast enough in this energy range and gives a large negative contribution, essentially from the $^1S_0$ resonant state near threshold. Its absolute value is about the same size as the sum of proton and neutron GDH values. It is only partially cancelled by the single pion production contribution. But the incoherent channel has not reached convergence at 550 MeV.Comment: 6 pages latex including 3 postscript figures, talk at the 15th Int. Conf. on Few-Body Problems in Physics, Groningen, Netherlands, 22-26 July 1997. To be published in Nucl. Phys.

A Perturbative/Variational Approach to Quantum Lattice Hamiltonians

We propose a method to construct the ground state $\psi(\lambda)$ of local lattice hamiltonians with the generic form $H_0 + \lambda H_1$, where $\lambda$ is a coupling constant and $H_0$ is a hamiltonian with a non degenerate ground state $\psi_0$. The method is based on the choice of an exponential ansatz $\psi(\lambda) = {\rm exp}(U(\lambda)) \psi_0$, which is a sort of generalized lattice version of a Jastrow wave function. We combine perturbative and variational techniques to get succesive approximations of the operator $U(\lambda)$. Perturbation theory is used to set up a variational method which in turn produces non perturbative results. The computation with this kind of ansatzs leads to associate to the original quantum mechanical problem a statistical mechanical system defined in the same spatial dimension. In some cases these statistical mechanical systems turn out to be integrable, which allow us to obtain exact upper bounds to the energy. The general ideas of our method are illustrated in the example of the Ising model in a transverse field.Comment: 27 pages, three .ps figures appended, DFTUZ 94-2