2,054 research outputs found
Implementing the three-particle quantization condition including higher partial waves
We present an implementation of the relativistic three-particle quantization
condition including both - and -wave two-particle channels. For this, we
develop a systematic expansion about threshold of the three-particle
divergence-free K matrix, , which is a
generalization of the effective range expansion of the two-particle K matrix,
. Relativistic invariance plays an important role in this
expansion. We find that -wave two-particle channels enter first at quadratic
order. We explain how to implement the resulting multichannel quantization
condition, and present several examples of its application. We derive the
leading dependence of the threshold three-particle state on the two-particle
-wave scattering amplitude, and use this to test our implementation. We show
how strong two-particle -wave interactions can lead to significant effects
on the finite-volume three-particle spectrum, including the possibility of a
generalized three-particle Efimov-like bound state. We also explore the
application to the system, which is accessible to lattice QCD
simulations, where we study the sensitivity of the spectrum to the components
of . Finally, we investigate the circumstances
under which the quantization condition has unphysical solutions.Comment: 57 pages, 12 figures, 3 tables (v2: Made minor clarifications,
updated a reference, fixed typos
Counts-in-Cylinders in the Sloan Digital Sky Survey with Comparisons to N-body Simulations
Environmental statistics provide a necessary means of comparing the
properties of galaxies in different environments and a vital test of models of
galaxy formation within the prevailing, hierarchical cosmological model. We
explore counts-in-cylinders, a common statistic defined as the number of
companions of a particular galaxy found within a given projected radius and
redshift interval. Galaxy distributions with the same two-point correlation
functions do not necessarily have the same companion count distributions. We
use this statistic to examine the environments of galaxies in the Sloan Digital
Sky Survey, Data Release 4. We also make preliminary comparisons to four models
for the spatial distributions of galaxies, based on N-body simulations, and
data from SDSS DR4 to study the utility of the counts-in-cylinders statistic.
There is a very large scatter between the number of companions a galaxy has and
the mass of its parent dark matter halo and the halo occupation, limiting the
utility of this statistic for certain kinds of environmental studies. We also
show that prevalent, empirical models of galaxy clustering that match observed
two- and three-point clustering statistics well fail to reproduce some aspects
of the observed distribution of counts-in-cylinders on 1, 3 and 6-Mpc/h scales.
All models that we explore underpredict the fraction of galaxies with few or no
companions in 3 and 6-Mpc/h cylinders. Roughly 7% of galaxies in the real
universe are significantly more isolated within a 6 Mpc/h cylinder than the
galaxies in any of the models we use. Simple, phenomenological models that map
galaxies to dark matter halos fail to reproduce high-order clustering
statistics in low-density environments.Comment: 17 pages, 10 figures. Accepted, Ap
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