Relativistic, model-independent, multichannel 2→22\to2 transition amplitudes in a finite volume

We derive formalism for determining $\textbf{2} + \mathcal J \to \textbf{2}$ infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $\rho$-meson form factor, in which the unstable nature of the $\rho$ is rigorously accommodated.Comment: 35 pages, 11 figure

The Mars ancient cratered terrain, smooth plains boundary: Implications of Viking color data for evolution of the Amenthes Region

The global color set compiled by the Mars Consortium was investigated. The problem of application of the martian surface color data to geologic interpretation are atmospheric contributions which increase with latitude, and the high correlation among the three color bands. In southern Amenthes the classified units show areas of possible mixing between cratered tarrain and smooth plains. It is suggested that some geologically meaningful correlation exists between surface units and the transformed color data in the Amenthes region. The knobby terrain protruding through the plains units appears to be remnants of ancient cratered terrain extending northward beneath the more youthful smooth plains

Morphologic studies of the Moon and planets

The impact, volcanic, and tectonic history of the Moon and planets were investigated over an eight year period. Research on the following topics is discussed: lunar craters, lunar basins, lunar volcanoes, correlation of Apollo geochemical data, lunar geology, Mars desert landforms, and Mars impact basins

The Martian crustal dichotomy: Product of accretion and not a specific event?

Attempts to explain the fundamental crustal dichotomy on Mars range from purely endogenic to extreme exogenic processes, but to date no satisfactory theory has evolved. What is accepted is: (1) the dichotomy is an ancient feature of the Martian crust, and (2) the boundary between the cratered highlands and northern plains which marks the dichotomy in parts of Mars has undergone significant and variable modification during the observable parts of Martian history. Some ascribe it to a single mega-impact event, essentially an instantaneous rearrangement of the crustal structures (topography and lithospheric thickness). Others prefer an internal mechanism: a period of vigorous convection subcrustally erodes the northern one third of Mars, causing foundering and isostatic lowering of that part of Mars. The evidence for each theory is reviewed, with the conclusion that there is little to recommend either. An alternative is suggested: the formation of the crustal dichotomy on Mars was not a specific tectonic event but a byproduct of the accretionary process and therefore a primordial characteristic of the Martian crust, predating the oldest recognizable landforms

Three-particle systems with resonant subprocesses in a finite volume

In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses. Here we lift this restriction, by deriving the quantization condition for identical scalar particles with a G-parity symmetry, in the case that the two-particle K matrix has a pole in the kinematic regime of interest. As in earlier work, our result involves intermediate infinite-volume quantities with no direct physical interpretation, and we show how these are related to the physical three-to-three scattering amplitude by integral equations. This work opens the door to study processes such as $a_2 \to \rho \pi \to \pi \pi \pi$, in which the $\rho$ is rigorously treated as a resonance state.Comment: 46 pages, 9 figures, JLAB-THY-18-2819, CERN-TH-2018-21

Progress in three-particle scattering from LQCD

We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes. As the finite-volume spectrum can be directly determined in LQCD, this provides a method for determining scattering observables, and associated resonance properties, from the underlying theory. In a pair of papers published over the last two years, two of us have extended this approach to apply to relativistic three-particle scattering states. In this talk we summarize recent progress in checking and further extending this result. We describe an extension of the formalism to include systems in which two-to-three transitions can occur. We then present a check of the previously published formalism, in which we reproduce the known finite-volume energy shift of a three-particle bound state.Comment: 9 pages, 3 figures, proceedings for XIIth Quark Confinement and the Hadron Spectrum (CONF12

Numerical study of the relativistic three-body quantization condition in the isotropic approximation

We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized $s$-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, $\mathcal K_{\text{df},3}$, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the $1/L$ expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wavefunctions for these bound states. We also find that certain values of $\mathcal K_{\text{df},3}$ lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.Comment: 32 pages, 21 figures, JLAB-THY-18-2657, CERN-TH-2018-046; version 2: corrected typos, updated references, minor stylistic changes---consistent with published versio

A mechanistic model of connector hubs, modularity, and cognition

The human brain network is modular--comprised of communities of tightly interconnected nodes. This network contains local hubs, which have many connections within their own communities, and connector hubs, which have connections diversely distributed across communities. A mechanistic understanding of these hubs and how they support cognition has not been demonstrated. Here, we leveraged individual differences in hub connectivity and cognition. We show that a model of hub connectivity accurately predicts the cognitive performance of 476 individuals in four distinct tasks. Moreover, there is a general optimal network structure for cognitive performance--individuals with diversely connected hubs and consequent modular brain networks exhibit increased cognitive performance, regardless of the task. Critically, we find evidence consistent with a mechanistic model in which connector hubs tune the connectivity of their neighbors to be more modular while allowing for task appropriate information integration across communities, which increases global modularity and cognitive performance