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

Invariance of generalized wordlength patterns

The generalized wordlength pattern (GWLP) introduced by Xu and Wu (2001) for an arbitrary fractional factorial design allows one to extend the use of the minimum aberration criterion to such designs. Ai and Zhang (2004) defined the $J$-characteristics of a design and showed that they uniquely determine the design. While both the GWLP and the $J$-characteristics require indexing the levels of each factor by a cyclic group, we see that the definitions carry over with appropriate changes if instead one uses an arbitrary abelian group. This means that the original definitions rest on an arbitrary choice of group structure. We show that the GWLP of a design is independent of this choice, but that the $J$-characteristics are not. We briefly discuss some implications of these results.Comment: To appear in: Journal of Statistical Planning and Inferenc

Radiative and non radiative muon capture on the proton in heavy baryon chiral perturbation theory

We have evaluated the amplitude for muon capture by a proton, mu + p --> n + nu, to O(p^3) within the context of heavy baryon chiral perturbation theory (HBChPT) using the new O(p^3) Lagrangian of Ecker and Mojzis (E&M). We obtain expressions for the standard muon capture form factors and determine three of the coefficients of the E&M Lagrangian, namely, b_7, b_{19}, and b_{23}. We describe progress on the next step, a calculation of the radiative muon capture process, mu + p --> n + nu + gamma.Comment: Talk at the 15th Int. Conf. on Few-Body Problems in Physics, 22-26 July, 1997, Groningen, The Netherlands, to be published in the proceedings; 5 pages, LaTeX, using espcrc1.st

Ordinary and radiative muon capture on the proton and the pseudoscalar form factor of the nucleon

We calculate ordinary and radiative muon capture on the proton in an effective field theory of pions, nucleons and delta isobars, working to third and second order in the small scale expansion respectively. Preceding calculations in chiral effective field theories only employed pion and nucleon degrees of freedom and were not able to reproduce the photon spectrum in the pioneering experiment of radiative muon capture on the proton from TRIUMF. For the past few years it has been speculated that the discrepancy between theory and experiment might be due to Delta(1232) related effects, which are only included via higher order contact interactions in the standard chiral approach. In this report we demonstrate that this speculation does not hold true. We show that contrary to expectations from naive dimensional analysis isobar effects on the photon spectrum and the total rate in radiative muon capture are of the order of a few percent, consistent with earlier findings in a more phenomenological approach. We further demonstrate that both ordinary and radiative muon capture constitute systems with a very well behaved chiral expansion, both in standard chiral perturbation theory and in the small scale expansion, and present some new ideas that might be at the bottom of the still unresolved discrepancy between theory and experiment in radiative muon capture. Finally we comment upon the procedure employed by the TRIUMF group to extract new information from their radiative muon capture experiment on the pseudoscalar form factor of the nucleon. We show that it is inconsistent with the ordinary muon capture data.Comment: 22 pp, RevTeX, uses epsf, 8 figs, enlarged version, discussion of ordinary muon capture on protons substantially enlarged, accepted for publication in Nucl.Phys.A, FZJ-IKP(TH)-2000-0

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