Considerations on the Schmid theorem for triangle singularities

We investigate the Schmid theorem, which states that if one has a tree level mechanism with a particle decaying to two particles and one of them decaying posteriorly to two other particles, the possible triangle singularity developed by the mechanism of elastic rescattering of two of the three decay particles does not change the cross section provided by the tree level. We investigate the process in terms of the width of the unstable particle produced in the first decay and determine the limits of validity and violation of the theorem. One of the conclusions is that the theorem holds in the strict limit of zero width of that resonance, in which case the strength of the triangle diagram becomes negligible compared to the tree level. Another conclusion, on the practical side, is that for realistic values of the width, the triangle singularity can provide a strength comparable or even bigger than the tree level, which indicates that invoking the Schmid theorem to neglect the triangle diagram stemming from elastic rescattering of the tree level should not be done. Even then, we observe that the realistic case keeps some memory of the Schmid theorem, which is visible in a peculiar interference pattern with the tree level.Comment: 13 pages, 13 figure

Has Blending Compromised Cepheid-Based Determinations of the Extragalactic Distance Scale?

We examine the suggestion that half of the HST Key Project- and Sandage/Saha-observed galaxies have had their distances systematically underestimated, by 0.1-0.3 mag in the distance modulus, due to the underappreciated influence of stellar profile blending on the WFC chips. The signature of such an effect would be a systematic trend in (i) the Type Ia supernovae corrected peak luminosity and (ii) the Tully-Fisher residuals, with increasing calibrator distance, and (iii) a differential offset between PC and WFC distance moduli, within the same galaxy. The absence of a trend would be expected if blending were negligible (as has been inherently assumed in the analyses of the aforementioned teams). We adopt a functional form for the predicted influence of blending that is consistent with the models of Mochejska et al. and Stanek & Udalski, and demonstrate that the expected correlation with distance predicted by these studies is not supported by the data. We conclude that the Cepheid-based extragalactic distance scale has not been severely compromised by the neglect of blending.Comment: 14 pages, 2 figures, 1 table, LaTeX, accepted for publication in Astrophysical Journal Letters, also available at http://casa.colorado.edu/~bgibson/publications.htm

Gap formation and soft phonon mode in the Holstein model

We investigate electron-phonon coupling in many-electron systems using dynamical mean-field theory in combination with the numerical renormalization group. This non-perturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions

Three-nucleon interactions: dynamics

A discussion is presented of the dynamics underlying three-body nuclear forces, with emphasis on changes which occurred over several decades.Comment: Talk given at the FM50 symposium, Tokyo, October 200

Peculiar Velocities of Nonlinear Structure: Voids in McVittie Spacetime

As a study of peculiar velocities of nonlinear structure, we analyze the model of a relativistic thin-shell void in the expanding universe. (1) Adopting McVittie (MV) spacetime as a background universe, we investigate the dynamics of an uncompensated void with negative MV mass. Although the motion itself is quite different from that of a compensated void, as shown by Haines & Harris (1993), the present peculiar velocities are not affected by MV mass. (2) We discuss how precisely the formula in the linear perturbation theory applies to nonlinear relativistic voids, using the results in (1) as well as the previous results for the homogeneous background (Sakai, Maeda, & Sato 1993). (3) We re-examine the effect of the cosmic microwave background radiation. Contrary to the results of Pim & Lake (1986, 1988), we find that the effect is negligible. We show that their results are due to inappropriate initial conditions. Our results (1)-(3) suggest that the formula in the linear perturbation theory is approximately valid even for nonlinear voids.Comment: 12 pages, aastex, 4 ps figures separate, Fig.2 added, to appear in Ap