Long distance contribution to K+→π+ννˉK^+ \to \pi^+ \nu {\bar \nu} decay and O(p4)O(p^4) terms in CHPT

The long distance contribution to $K^+ \to \pi^+ \nu {\bar \nu}$ is calculated using chiral perturbation theory. The leading contribution comes from $O(p^4)$ tree terms. The branching ratio of the $O(p^4)$ long distance contribution is found to be of order $10_{-3}$ smaller than the short distance contributions.Comment: 12 pages, 1 figure (available upon request

Role of Scalar Meson Resonances in $K_{L}^{0} \rightarrow \pi^{0} \gamma \gamma Decay

Corrections to $K_{L}^{0}\rightarrow \pi^{0} \gamma \gamma$ decay induced by scalar meson exchange are studied within chiral perturbation theory. In spite of bad knowledge of scalar-mesons parameters, the calculated branching ratio can be changed by a few percent.Comment: 18 pages of text, 2 figures (available upon request); preprint IJS-TP-16-94 , TUM-T31-63-94

Radiative Kaon Decays K±→π±π0γK^\pm\to\pi^\pm\pi^0\gamma and Direct CP Violation

It is stressed that a measurement of the electric dipole amplitude for direct photon emission in \kpm decays through its interference with inner bremsstrahlung is important for differentiating among various models. Effects of amplitude CP violation in the radiative decays of the charged kaon are analyzed in the Standard Model in conjunction with the large $N_c$ approach. We point out that gluon and electromagnetic penguin contributions to the CP-violating asymmetry between the Dalitz plots of \kpm are of equal weight. The magnitude of CP asymmetry ranges from $2\times 10^{-6}$ to $1\times 10^{-5}$ when the photon energy in the kaon rest frame varies from 50 MeV to 170 MeV.Comment: Latex, 11 pages, ITP-SB-93-36, IP-ASTP-22-9

A perturbative treatment for the energy levels of neutral atoms

Energy levels of neutral atoms have been re-examined by applying an alternative perturbative scheme in solving the Schrodinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number $Z$ up to 84 and compare very well with those obtained within the framework of hyper-virial-Pade scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.Comment: 18 page

Running mass of the rho0 meson's implication for the dilepton mass spectrum and the mu+mu-/e+e- branching ratio in the K+ --> pi+l+l- decays

We make an attempt to resolve the discrepancy of the observed e+e- mass spectrum in the K+ --> pi+e+e- decay with that predicted by meson dominance. To this end we investigate the properties of the rho0 propagator. We use dispersion relations to evaluate the running mass squared m_rho^2(t) of the rho0 resonance without adjustable parameters. To improve the convergence of the dispersion integral, the momentum dependence of strong vertices is taken from the flux-tube-breaking model of Kokoski and Isgur. The obtained behavior of m_rho^2(t) at small momentum squared t makes the K+ --> pi+e+e- form factor rise faster with increasing $t$ than in the original meson-dominance calculation and more in agreement with the published data. As a consequence, the meson-dominance prediction of the mu+mu-/e+e- branching ratio changes slightly, from 0.224 to 0.236. We do not see any possibility to accommodate into the meson-dominance approach an even steeper e+e- spectrum, indicated by the preliminary data of the E865 collaboration at BNL AGS.Comment: 13 pages, RevTeX, epsf.sty, 4 embedded figure

QCD chiral Lagrangian on the lattice, strong coupling expansion and Ward identities with Wilson fermions

We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the consequences of the chiral symmetry breaking induced by the Wilson term, we study the lattice chiral Lagrangian at the leading order of the strong coupling and large $N$ expansion. We show that the effects of the Wilson term can be conveniently taken into account, in the lattice effective theory, by a suitable renormalization procedure. In particular, we show that, at the leading order of the strong coupling and large N expansion, the chiral symmetry is exactly recovered on the lattice provided that the bare quark mass and the lattice operators are properly renormalized.Comment: 45 pages, no figures. Latex fil

The standard model at low energies

The hadronic sector of the standard model at low energies is described by a non--decoupling effective field theory, chiral perturbation theory. An introduction is given to the construction of effective chiral Lagrangians, both in the purely mesonic sector and with inclusion of baryons. The connection between the relativistic formulation and the heavy baryon approach to chiral perturbation theory with baryons is reviewed.Comment: Lectures given at the 6th Indian-Summer School on Intermediate Energy Physics, Prague, Aug. 1993, Latex, 26 pages (with a4.sty), UWThPh-1993-3

Vector-meson contributions do not explain the rate and spectrum in K_L -> pi0 gamma gamma

We analyze the recent NA48 data for the reaction K_L -> pi0 gamma gamma with and without the assumption of vector meson dominance (VMD). We find that the data is well described by a three-parameter expression inspired by O(p^6) chiral perturbation theory. We also find that it is impossible to fit the shape of the decay distribution and the overall rate simultaneously if one imposes the VMD constraints on the three parameters. We comment on the different fits and their implications for the CP-conserving component of the decay K_L -> pi0 e+ e-.Comment: Version accepted for publication on Phys. Rev. D. 19 pages, LaTeX, 8 figures, uses epsf.st

On the Corrections to Dashen's Theorem

The electromagnetic corrections to the masses of the pseudoscalar mesons $\pi$ and $K$ are considered. We calculate in chiral perturbation theory the contributions which arise from resonances within a photon loop at order $O(e^2 m_q)$. Within this approach we find rather moderate deviations to Dashen's theorem.Comment: 14 pages, sligthly enlarged version; a numerical error is corrected and the embedding of the figures is improved. The complete paper, including figures, is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/; to be published in Phys.Rev.

Ultra-violet Behavior of Bosonic Quantum Membranes

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $\beta = 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.Comment: 25 pages, Latex, no figure