Energetics of the quantum graphity universe

Abstract

Quantum graphity is a background independent model for emergent geometry, in which space is represented as a dynamical graph. The high-energy pre-geometric starting point of the model is usually considered to be the complete graph, however we also consider the empty graph as a candidate pre-geometric state. The energetics as the graph evolves from either of these high-energy states to a low-energy geometric state is investigated as a function of the number of edges in the graph. Analytic results for the slope of this energy curve in the high-energy domain are derived, and the energy curve is determined exactly for small number of vertices N . To study the whole energy curve for larger (but still finite) N , an epitaxial approximation is introduced. This work may open the way to compare predictions from quantum graphity with observations of the early universe, making the model falsifiable.

Weak charged and neutral current induced one pion production off the nucleon

“…The middle panel shows the results with a cut on center of mass energy of 1.4 GeV(W < 1.4GeV ), while in the bottom panel a cut of W < 1.6GeV is introduced while calculating total scattering cross section. Data points quoted as ANL extracted and BNL extracted are the reanalyzed data by Wilkinson et al [32]. Other data points in figures are the results from ANL [28] and BNL [29] experiments.…”

“…We chose M A∆ = 1.026GeV corresponding to the world average value obtained from the experimental analysis of quasielastic scattering events [68], and then vary C A 5 (0) to obtain a good description of reanalyzed data [32] of ANL and BNL experiments for ν µ p → µ − pπ + reaction. While fitting the reanalyzed data for the reaction ν µ p → µ − pπ + , the contributions to the cross section is predominantly obtained from ∆(1232) resonant terms and the background terms have a little contribution.…”

“…The role of interference between non-resonant and ∆(1232) dominant terms is studied. The results are compared with the reconstructed data of ANL and BNL experiments reanalyzed by Wilkinson et al [32] on ν µ p → µ − pπ + channel to fix the N-∆ transition form factors and have been applied to study all the pion production channels from proton and neutron targets which are induced by charged and neutral weak currents with neutrino and antineutrino beams. We have also performed calculations using different cuts on center of mass energy i.e.…”

“…understanding of presently reported data [32] from reanalysis/reconstruction of ANL [28] and BNL [29] data set in a chiral invariant effective Lagrangian field theoretical model using ∆(1232) dominance and non-resonant background terms will be highly useful for the purpose of determining various parameters like N −∆ transition form factors, needed to describe the basic reaction mechanism of single pion production and its application to study nuclear medium and FSI effects. In this paper, we have presented the results for the total scattering cross sections for pion production from nucleons.…”

“…These data, when used to fix various parameters of theoretical models of reaction mechanisms for single pion production, give rise to considerable uncertainties in the determination of these parameters, which in turn lead to higher uncertainties in predicting the single pion production cross section from nuclear targets. Recently reanalysis of the old bubble chamber data by the two independent groups have tried to arrive at a consistent set of data from ANL [28] and BNL [29] experiments either by minimizing the neutrino flux uncertainties [30,31] or by reconstructing the data using the cross section ratio for single pion production to the quasielastic processes, and observed quasielastic cross sections [32]. It is hoped that the use of reanalyzed/reconstructed data on free nucleon targets will help towards a better understanding of pion production reaction mechanism.…”