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Title: Bayesian analysis of light-front models and the nucleon’s charmed sigma term

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 7; Related Information: CHORUS Timestamp: 2017-10-23 12:32:17; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Hobbs, T. J., Alberg, Mary, and Miller, Gerald A. Bayesian analysis of light-front models and the nucleon’s charmed sigma term. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.074023.
Hobbs, T. J., Alberg, Mary, & Miller, Gerald A. Bayesian analysis of light-front models and the nucleon’s charmed sigma term. United States. doi:10.1103/PhysRevD.96.074023.
Hobbs, T. J., Alberg, Mary, and Miller, Gerald A. 2017. "Bayesian analysis of light-front models and the nucleon’s charmed sigma term". United States. doi:10.1103/PhysRevD.96.074023.
title = {Bayesian analysis of light-front models and the nucleon’s charmed sigma term},
author = {Hobbs, T. J. and Alberg, Mary and Miller, Gerald A.},
abstractNote = {},
doi = {10.1103/PhysRevD.96.074023},
journal = {Physical Review D},
number = 7,
volume = 96,
place = {United States},
year = 2017,
month =

Journal Article:
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This content will become publicly available on October 23, 2018
Publisher's Accepted Manuscript

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  • The principles behind the detailed results of a light-front mean field theory of finite nuclei are elucidated by deriving the nucleon mode equation using a simple general argument, based on the idea that a static source in equal time coordinates corresponds to a moving source in light front coordinates. This idea also allows us to solve several simple toy model examples: scalar field in a box, (1+1)-dimensional bag model, three-dimensional harmonic oscillator and the Hulthen potential. The latter provide simplified versions of momentum distributions and form factors of relevance to experiments. In particular, the relativistic correction to the mean squaremore » radius of a nucleus is shown to be very small. Solving these simple examples suggests another more general approach--the use of tilted light front coordinates. The simple examples are made even simpler. (c) 2000 The American Physical Society.« less
  • We present an analysis of selection biases in the M{sub bh}-{sigma} relation using Monte Carlo simulations including the sphere of influence resolution selection bias and a selection bias in the velocity dispersion distribution. We find that the sphere of influence selection bias has a significant effect on the measured slope of the M{sub bh}-{sigma} relation, modeled as {beta}{sub intrinsic} = -4.69 + 2.22{beta}{sub measured}, where the measured slope is shallower than the model slope in the parameter range of {beta} > 4, with larger corrections for steeper model slopes. Therefore, when the sphere of influence is used as a criterionmore » to exclude unreliable measurements, it also introduces a selection bias that needs to be modeled to restore the intrinsic slope of the relation. We find that the selection effect due to the velocity dispersion distribution of the sample, which might not follow the overall distribution of the population, is not important for slopes of {beta} {approx} 4-6 of a logarithmically linear M{sub bh}-{sigma} relation, which could impact some studies that measure low (e.g., {beta} < 4) slopes. Combining the selection biases in velocity dispersions and the sphere of influence cut, we find that the uncertainty of the slope is larger than the value without modeling these effects and estimate an intrinsic slope of {beta} = 5.28{sup +0.84}{sub -0.55}.« less
  • Exploiting the unique connection between the division algebras of the complex numbers (C), quaternions (H), octonions ({Omega}) and the essential Hopf maps {ital S}{sup 2{ital n}{minus}1} {r arrow} {ital S}{sup {ital n}} with {ital n}=2, 4, 8, we study {ital S}{sup {ital n}{minus}2}-membrane solitons in three {ital D}-dimensional KP(1) {sigma}-models with a Hopf term, ({ital D}, K)=(3, C), (7, H), and (15, {Omega}). We present a comprehensive analysis of their topological phase entanglements. Extending Polyakov's approach to Fermi--Bose transmutations to higher dimensions, we detail a geometric regularization of Gauss' linking coefficient, its connections to the self-linking, twisting, writhing numbers ofmore » the Feynman paths of the solitons in their thin membrane limit. Alternative forms of the Hopf invariant show the latter as an Aharono--Bohm--Berry phase of topologically massive, rank ({ital n}{minus}1) antisymmetric tensor {ital U}(1) gauge fields coupled to the {ital S}{sup {ital n}{minus}2}-membranes. Via a {ital K}-bundle formulation of the dynamics of electrically and magnetically charged extended objects these phases are shown to induce a dyon-like structure on these membranes. We briefly discuss the connections to harmonic mappings, higher dimensional monopoles and instantons. We point out the relevance of the Gauss--Bonnet--Chern theorem on the connection between spin and statistics. By way of the topology of the infinite groups of sphere mappings {ital S}{sup {ital n}} {r arrow} {ital S{ital n}}, {ital n}=2, 4, 8, we also analyze the implications of the Hopf phase on the fractional spin and statistics of the membranes. {copyright} 1989 Academic Press, Inc.« less
  • Exact separated atom nuclei and center of nuclear charge centered partial wave solutions for the Schroedinger equation are obtained for the 1s sigma, 2s sigma, 3s sigma, 2p sigma, 3d sigma, and 3p sigma states of HeH/sup 2 +/ as a function of the internuclear separation R and the number of partial waves used to represent the wave functions for the molecules. If the expansion center is chosen appropriately one-center techniques are in general very efficient for these Coulomb dominated interactions relative to molecules like H/sub 2//sup +/(1s sigma/sub g/) which have a large electron exchange contribution to their interactionmore » energy. In general the center of nuclear charge is not the most suitable expansion center for heteronuclear molecules for most values of R. 50 references.« less