Generalized wordlength patterns and strength

Xu and Wu (2001) defined the \emph{generalized wordlength pattern} $(A_1, ..., A_k)$ of an arbitrary fractional factorial design (or orthogonal array) on $k$ factors. They gave a coding-theoretic proof of the property that the design has strength $t$ if and only if $A_1 = ... = A_t = 0$. The quantities $A_i$ are defined in terms of characters of cyclic groups, and so one might seek a direct character-theoretic proof of this result. We give such a proof, in which the specific group structure (such as cyclicity) plays essentially no role. Nonabelian groups can be used if the counting function of the design satisfies one assumption, as illustrated by a couple of examples

Experimental Restrictions on Ne'eman's Fifth Interaction

Recently, Ne'eman has proposed a "fifth interaction" between the strangeness current and a neutral vector meson χ, for the purpose of breaking SU(3) symmetry. We show that a χ mass less than 2mπ would be inconsistent with a variety of experiments, including K-mesonic atoms, the long-range pp potential, K1 regeneration from a K2 beam, the Lamb shift, modern refinements of the Cavendish "ice-bucket" experiment, and the absence of π0→γ+χ and χ→e++e-. The remaining possibility, that mχ exceeds 2mπ, is discussed briefly

Relevance of the precautionary principle in water recycling

Presented at the International Conference on Integrated Concepts on Water Recycling, Wollongong, NSW, Australia, 14–17 February 2005.In an engineering context the precautionary principle is often perceived as an excuse to do nothing or a substantial barrier to technical progress. The precautionary principle requires that remedial measures be taken in situations of scientific uncertainty where evidence of harm cannot be proven but potential damage to human or environmental health is significant. In this paper the scope of the precautionary principle in water recycling is discussed. It is clear that uncertainties and risks exist in many areas of water recycling. Those risks are closely linked to the risks of sewage discharge. Hence water recycling has two main areas of concern (i) the dilemma that minimising potential environmental harm by reducing effluent discharge may increase potential harm through reducing the water flow in receiving waters and (ii) the consequences of using recycled water of varying quality for a number of applications. The precautionary principle can be regarded as an opportunity to improve water recycling practice and in fact increase the scope of ecologically sustainable water recycling. Hence the precautionary principle has an important role to play as a guide in decision making and in dealing with the vast number of risks and uncertainties in water recycling

On the pion electroproduction amplitude

We analyze amplitudes for the pion electroproduction on proton derived from Lagrangians based on the local chiral SU(2) x SU(2) symmetries. We show that such amplitudes do contain information on the nucleon axial form factor F_A in both soft and hard pion regimes. This result invalidates recent Haberzettl's claim that the pion electroproduction at threshold cannot be used to extract any information regarding F_A.Comment: 14 pages, 6 figures, revised version, accepted for publication in Phys. Rev.

Polarized photons in radiative muon capture

We discuss the measurement of polarized photons arising from radiative muon capture. The spectrum of left circularly polarized photons or equivalently the circular polarization of the photons emitted in radiative muon capture on hydrogen is quite sensitive to the strength of the induced pseudoscalar coupling constant $g_P$. A measurement of either of these quantities, although very difficult, might be sufficient to resolve the present puzzle resulting from the disagreement between the theoretical prediction for $g_P$ and the results of a recent experiment. This sensitivity results from the absence of left-handed radiation from the muon line and from the fact that the leading parts of the radiation from the hadronic lines, as determined from the chiral power counting rules of heavy-baryon chiral perturbation theory, all contain pion poles.Comment: 10 pages, 6 figure

Observation of double radiative capture on pionic hydrogen

We report the first observation of double radiative capture on pionic hydrogen. The experiment was conducted at the TRIUMF cyclotron using the RMC spectrometer, and detected $\gamma$--ray coincidences following $\pi^-$ stops in liquid hydrogen. We found the branching ratio for double radiative capture to be $(3.05 \pm 0.27(stat.) \pm 0.31(syst.)) \times 10^{-5}$. The measured branching ratio and angle-energy distributions support the theoretical prediction of a dominant contribution from the $\pi \pi \to \gamma \gamma$ annihilation mechanism.Comment: 4 Pages, 4 Figures. accepted for publication in Phys. Rev. Let

Search for exotic baryons in double radiative capture on pionic hydrogen

We report a search for low-lying exotic baryons via double radiative capture on pionic hydrogen. The data were collected at the TRIUMF cyclotron using the RMC spectrometer by detecting gamma-ray pairs from pion stops in liquid hydrogen. No evidence was found to support an earlier claim for exotic baryons of masses 1004 and 1044 MeV/$c^2$. We obtain upper limits on the branching ratios for double radiative capture via these exotic states of $< 3 \times 10^{-6}$ and $< 4 \times 10^{-6}$ respectively.Comment: 13 pages, 4 figure

Muon capture by a proton in heavy baryon chiral perturbation theory

The matrix element for muon capture by a proton is calculated to O(p^3) within heavy baryon chiral perturbation theory using the new O(p^3) Lagrangian of Ecker and Mojzis. External nucleon fields are renormalized using the appropriate definition of the wave function renormalization factor Z_N. Our expression for Z_N differs somewhat from that found in existing literature, but is the one which is consistent with the Lagrangian we use and the one which ensures, within our approach, the nonrenormalization of the vector coupling as required by the conserved vector current. Expressions for the standard muon capture form factors are derived and compared to experimental data and we determine three of the coefficients of the Ecker - Mojzis Lagrangian, namely, b_7, b_{19}, and b_{23}.Comment: 14 pages, LaTeX, using revte