Causality and the effective range expansion

We derive the generalization of Wigner's causality bounds and Bethe's integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.Comment: 27 pages, 5 figures, explicit examples added, typos corrected, final versio

Improved Effective Range Expansion for Casimir-Polder potential

We study the effective range expansion of scattering on a real Casimir-Polder potential. We use Liouville transformations which transform the potential landscape while preserving the reflection and transmission amplitudes. We decompose the scattering calculation in two more elementary problems, one for the homogeneous 1/z^4 potential and the other one for the correction to this idealization. We use the symmetries of the transformed problem and the properties of the scattering matrices to derive an improved effective range expansion leading to a more accurate expansion of scattering amplitudes at low energy

Cooperative secretions facilitate host range expansion in bacteria

The majority of emergent human pathogens are zoonotic in origin, that is, they can transmit to humans from other animals. Understanding the factors underlying the evolution of pathogen host range is therefore of critical importance in protecting human health. There are two main evolutionary routes to generalism: organisms can tolerate multiple environments or they can modify their environments to forms to which they are adapted. Here we use a combination of theory and a phylogenetic comparative analysis of 191 pathogenic bacterial species to show that bacteria use cooperative secretions that modify their environment to extend their host range and infect multiple host species. Our results suggest that cooperative secretions are key determinants of host range in bacteria, and that monitoring for the acquisition of secreted proteins by horizontal gene transfer can help predict emerging zoonoses

Effective range expansion in various scenarios of EFT(\notpi)

Using rigorous solutions, we compare the ERE parameters obtained in three different scenarios of EFT(\notpi) in nonperturbative regime. A scenario with unconventional power counting (like KSW) is shown to be disfavored by the PSA data, while the one with elaborate prescription of renormalization but keeping conventional power counting intact seems more promising.Comment: 6 pages, 3 tables, no figure, revtex4-1, minor revisions, to appear in EP

Phase shift effective range expansion from supersymmetric quantum mechanics

Supersymmetric or Darboux transformations are used to construct local phase equivalent deep and shallow potentials for $\ell \neq 0$ partial waves. We associate the value of the orbital angular momentum with the asymptotic form of the potential at infinity which allows us to introduce adequate long-distance transformations. The approach is shown to be effective in getting the correct phase shift effective range expansion. Applications are considered for the $^1P_1$ and $^1D_2$ partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical Review

Effective Range Expansion for the Interaction Defined on the Lattice

The relation between the interaction parameters for fermions on the spatial lattice and the two-body $T$ matrix is discussed. The presented method allows determination of the interaction parameters through the relatively simple computational scheme which include the effect of finite lattice spacing. In particular the relation between the interaction parameters and the effective range expansion parameters is derived in the limit of large lattices.Comment: Proceedings from XVI Nuclear Physics Workshop in Kazimierz Dolny, Poland. Accepted to publish in the International Journal of Modern Physics E, vol. 1