Chiral Symmetry and Scalars

The suggestion by Jaffe that if $\sigma$ is a light $q^{2}\bar{q}^{2}$ state $0^{++}$ then even the fundamental chiral transformation properties of the $\sigma$ becomes {\bf unclear}, has stimulated much interest. Adler pointed out that in fact the seminal work on chiral symmetry via PCAC consistency, is really quite consistent with the $\sigma$ being predominantly $q^{2}\bar{q}^{2}$. This interpretation was actually backed by subsequent work on effective Lagrangian methods for linear and non linear realizations. More recent work of Achasov suggests that intermediate four-quark states determine amplitudes involving other scalars $a_{0}(980)$ and $f_{0}(980)$ below 1 GeV, and the report by Ning Wu that study on $\sigma$ meson in $J/\psi \to \omega\pi^{+}\pi^{-}$ continue to support a non $q\bar{q}$ $\sigma$ with mass as low as 390 MeV. It is also noted that more recent re-analysis of $\pi K$ scattering by S. Ishida {\em et al.} together with the work of the E791 Collaboration, support the existence of the scalar $\kappa$ particle with comparatively light mass as well.Comment: 4 pages, aipproc style file. Parallel session talk at Hadron 2001-Protvin

The ρ−π\rho - \pi Puzzle of J/\psi and \psi' Decays

The recent BES Collaboration data on \psi' \ra PV, particularly the isospin violating mode \psi' \ra \pi^0 \omega^0 and finding of a finite number for B(\psi' \ra K^{*0}\bar{K}^0), enable us now to deal more precisely about the challenges to theory concerning this extraordinary and remarkable so called $\rho - \pi$ Puzzle of $J/\psi$ and $\psi'$ Decays. In terms of existing data, and deploying the simplest phenomenology, measurement of \psi' \ra \pi^+\pi^- and whether a finite number for the $K^{*+} K^-$ mode might require a significantly larger accumulation of data, remain interesting questions.Comment: 9pages, added reference, typos, and very slight change in text, LATEX forma

Aspects of Charmonium Physics

I review possible resolution of the $J/\psi (\psi^{\prime}) \to \rho-\pi$ puzzle based on two inputs: the relative phase between the one- photon and the gluonic decay amplitudes, and a possible hadronic excess in the inclusive nonelectromagnetic decay rate of $\psi^{\prime}$. The status of a universal large phase here is examined for its meaning and implications (including those for B-physics). Since the future of tau/charm facility(s) are again under consideration together with a future anti-proton facility at GSI, I propose to extend my review to include a broader discussion of charmonium physics. Outstanding questions like the status of the $^{1}P_{1}$ state of charmonium, measuring $D^{0}-\bar D^{0}$ mixing and relative strong phases, status of molecular P(S) - wave charmonia will also be discussed amongst others.Comment: 7 pages, aipproc style file. Plenary session talk at Hadron 2001-Protvin

Improvement of uncoupled Hartree-Fock expectation values for physical properties

Hartree-Fock calculation method as zero-order approximation for determining atomic and molecular second-order propertie

One-loop effective potential for SO(10) GUT theories in de Sitter space

Zeta-function regularization is applied to evaluate the one-loop effective potential for SO(10) grand-unified theories in de Sitter cosmologies. When the Higgs scalar field belongs to the 210-dimensional irreducible representation of SO(10), attention is focused on the mass matrix relevant for the SU(3)xSU(2)xU(1) symmetry-breaking direction, to agree with low-energy phenomenology of the particle-physics standard model. The analysis is restricted to those values of the tree-level-potential parameters for which the absolute minima of the classical potential have been evaluated. As shown in the recent literature, such minima turn out to be SO(6)xSO(4)- or SU(3)xSU(2)xSU(2)xU(1)-invariant. Electroweak phenomenology is more naturally derived, however, from the former minima. Hence the values of the parameters leading to the alternative set of minima have been discarded. Within this framework, flat-space limit and general form of the one-loop effective potential are studied in detail by using analytic and numerical methods. It turns out that, as far as the absolute-minimum direction is concerned, the flat-space limit of the one-loop calculation about a de Sitter background does not change the results previously obtained in the literature, where the tree-level potential in flat space-time was studied. Moreover, when curvature effects are no longer negligible in the one-loop potential, it is found that the early universe remains bound to reach only the SO(6)xSO(4) absolute minimum.Comment: 25 pages, plain Tex, plus Latex file of the tables appended at the end. Published in Classical and Quantum Gravity, Vol. 11, pp. 2031-2044, August 199

Elusive vector glueball

If the vector glueball exists in the mass range that theory suggests, its resonance production cross section can be seen in e+e- annihilation only if the decay width is very narrow (< a few MeV). Otherwise it willbe observed only indirectly through its mixing with psi(2S). A few tests of the glueball-psi' mixing are proposed for future charm factories.Comment: One misleading short sentence delete

A one-phase interior point method for nonconvex optimization

The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty method. We propose an IPM that, by careful initialization and updates of the slack variables, is guaranteed to find a first-order certificate of local infeasibility, local optimality or unboundedness of the (shifted) feasible region. Our proposed algorithm differs from other IPM methods for nonconvex programming because we reduce primal feasibility at the same rate as the barrier parameter. This gives an algorithm with more robust convergence properties and closely resembles successful algorithms from linear programming. We implement the algorithm and compare with IPOPT on a subset of CUTEst problems. Our algorithm requires a similar median number of iterations, but fails on only 9% of the problems compared with 16% for IPOPT. Experiments on infeasible variants of the CUTEst problems indicate superior performance for detecting infeasibility. The code for our implementation can be found at https://github.com/ohinder/OnePhase .Comment: fixed typo in sign of dual multiplier in KKT syste