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

Anisotropic power-law inflation for a conformal-violating Maxwell model

A set of power-law solutions of a conformal-violating Maxwell model with a non-standard scalar-vector coupling will be shown in this paper. In particular, we are interested in a coupling term of the form $X^{2n} F^{\mu\nu}F_{\mu\nu}$ with $X$ denoting the kinetic term of the scalar field. Stability analysis indicates that the new set of anisotropic power-law solutions is unstable during the inflationary phase. The result is consistent with the cosmic no-hair conjecture. We show, however, that a set of stable slowly expanding solutions does exist for a small range of parameters $\lambda$ and $n$. Hence a small anisotropy can survive during the slowly expanding phase.Comment: 13 pages with 3 figure

Secular non-secular master equation

Redfield non-secular master equation governing relaxation of a spin in weak interaction with a thermal bath is studied. Using the fact that the relaxation follows the exponential law, we prove that in most cases the semi-secular approximation is sufficient to find the system relaxation rate. Based on this, a "secular" form of the non-secular master equation is for the first time developed which correctly set up one of most fundamental equations in relaxation investigation. This key secular form allows us to derive a general formula of the phonon-induced quantum tunneling rate which is valid for the entire range of temperature regardless of the basis. In incoherent tunneling regime and localized basis, this formula reduces to the ubiquitous incoherent tunneling rate. Meanwhile, in eigenstates basis, this tunneling rate is demonstrated to be equal to zero. From this secular form, we end the controversy surrounding the selection of basis for the secular approximation by figuring out the conditions for using this approximation in localized and eigenstates basis. Particularly, secular approximation in localized basis is justified in the regime of high temperature and small tunnel splittings. In contrast, a large ground doublet's tunnel splitting is required for the secular approximation in eigenstates basis. With these findings, this research lays a sound foundation for any treatments of the spin-phonon relaxation under any conditions provided that the non-secular master equation is relevant.Comment: 9 pages, 0 figure