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

Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is \C_+. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C^{m,\al}, $m\ge4$.Comment: 9 pages, v2:final version, to be publishe

The Design of Mechanically Compatible Fasteners for Human Mandible Reconstruction

Mechanically compatible fasteners for use with thin or weakened bone sections in the human mandible are being developed to help reduce large strain discontinuities across the bone/implant interface. Materials being considered for these fasteners are a polyetherertherketone (PEEK) resin with continuous quartz or carbon fiber for the screw. The screws were designed to have a shear strength equivalent to that of compact/trabecular bone and to be used with a conventional nut, nut plate, or an expandable shank/blind nut made of a ceramic filled polymer. Physical and finite element models of the mandible were developed in order to help select the best material fastener design. The models replicate the softer inner core of trabecular bone and the hard outer shell of compact bone. The inner core of the physical model consisted of an expanding foam and the hard outer shell consisted of ceramic particles in an epoxy matrix. This model has some of the cutting and drilling attributes of bone and may be appropriate as an educational tool for surgeons and medical students. The finite element model was exercised to establish boundary conditions consistent with the stress profiles associated with mandible bite forces and muscle loads. Work is continuing to compare stress/strain profiles of a reconstructed mandible with the results from the finite element model. When optimized, these design and fastening techniques may be applicable, not only to other skeletal structures, but to any composite structure

Development of a systematic approach to conversion of the ileoanal pouch into continent ileostomy

Based on practical experience, a systematic approach to conversion of ileal J-pouches into continent ileostomies is developed by defining three types of conversion surgery, each with two subtypes. Type 1 refers to conversion without pouch reconstruction, type 2 to partial pouch reconstruction, and type 3 to complete pouch reconstruction. The subdivisions (a and b) take into account whether the afferent loop of the former pelvic pouch (a) or a higher ileal/jejunal segment of the small intestine (b) is used in conversion and/or reconstruction. The six resulting surgical variants are shown in schematic illustrations with accompanying descriptions of technical details to provide the specialized surgeon with comprehensive technical guidance

Comment on soft-pion emission in DVCS

The soft-pion theorem for pion production in deeply virtual Compton scattering, derived by Guichon, Mosse and Vanderhaegen, is shown to be consistent with chiral perturbation theory. Chiral symmetry requires that the nonsinglet operators corresponding to spin-independent and spin-dependent parton distributions have the same anomalous dimensions in cases where those operators are related by chiral transformations. In chiral perturbation theory, their scale-dependences can thus be absorbed in the coefficents of the corresponding effective operators, without affecting their chiral structures.Comment: 2 pages, RevTe

Rare Kaon Decays in the 1/Nc1/N_c-Expansion

We study the unknown coupling constants that appear at order $p^4$ in the Chiral Perturbation Theory analysis of $K \to \pi \gamma^* \to \pi l^+ l^-$, $K^{+-} \to \pi^{+-} \gamma \gamma$ and $K \to \pi \pi \gamma$ decays. To that end, we compute the chiral realization of the $\Delta S \, = \, 1$ Hamiltonian in the framework of the $1/N_c$-expansion of the low-energy action. The phenomenological implications are also discussed.Comment: 18 pages, LaTeX, CPT-92/P.279

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

On the absence of fifth-order contributions to the nucleon mass in heavy-baryon chiral perturbation theory

(New version with some expanded discussion; figures and minor typos corrected.) We have calculated the contribution proportional to the fifth power of the pion mass in the chiral expansion of the nucleon mass in two flavour HBCPT. Only one irreducible two-loop integral enters, and this vanishes. All other corrections in the heavy-baryon limit can be absorbed in the physical pion-nucleon coupling constant which enters in the third order term, and so there are no contributions at fifth order. Including finite nucleon mass corrections, the only contribution agrees with the expansion of the relativistic one-loop graph in powers of the ration of the pion and nucleon masses, and is only 0.3% of the third order term. This is an encouraging result for the convergence of two-flavour heavy-baryon chiral perturbation theory.Comment: 4 pages RevTex, 4 eps figure