Artian's HVP Source-Access Reference Framework

BaBar full covariance as an HVP scalar/shape separator Version: 40.0 Concept DOI: 10.5281/zenodo.20732034 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 The two-pion channel is the dominant experimental pressure point in the Standard Model prediction of the muon anomalous magnetic moment. In the \(e^+e^-\to\pi^+\pi^-\) window, one can ask two different questions at once: how far the integrated \(a_\mu^{\rm HVP,LO}\) scalar sits from a frozen source prediction, and how far the resolved line shape sits from that same source after the scalar direction is removed. The HVP scalar readout is \[ a_{\mu,2\pi}^{\rm row} = \mathbf w_\mu^{T}\mathbf y, \qquad a_{\mu,2\pi}^{\rm QTT/BaBar} = \mathbf w_\mu^{T}\mathbf m_{\rm BaBar}^{\rm QTT}. \] Here \(\mathbf y\) is the BaBar binned row, \(\mathbf m_{\rm BaBar}^{\rm QTT}\) is the same-bin QTT source prediction read through the BaBar access map, and \(\Sigma_{\rm BaBar}\) is the recovered full covariance object. The row residual is \[ \mathbf r = \mathbf y_{\rm BaBar} - \mathbf m_{\rm BaBar}^{\rm QTT}. \] The scalar \(a_\mu\) direction is \[ \Delta a_\mu = \mathbf w_\mu^{T}\mathbf r, \qquad \sigma_{a_\mu}^{2} = \mathbf w_\mu^{T}\Sigma_{\rm BaBar}\mathbf w_\mu, \qquad z_{a_\mu} = \frac{\Delta a_\mu}{\sigma_{a_\mu}}. \] The covariance projection then separates the scalar direction from the shape-orthogonal residual: \[ \mathbf r_a = \Sigma_{\rm BaBar}\mathbf w_\mu \frac{\mathbf w_\mu^{T}\mathbf r} {\mathbf w_\mu^{T}\Sigma_{\rm BaBar}\mathbf w_\mu}, \qquad \mathbf r_{\rm sh} = \mathbf r-\mathbf r_a. \] The master split is \[ \chi_{\rm full}^{2} = z_{a_\mu}^{2} + \chi_{\rm sh}^{2}. \] For the primary BaBar window \[ 0.600<\sqrt{s}<0.880\ {\rm GeV}, \] the execution gives \[ a_{\mu,2\pi}^{\rm BaBar} = 370.0500101738473\times10^{-10}, \qquad a_{\mu,2\pi}^{\rm QTT} = 375.3514558287998\times10^{-10}. \] \[ \Delta a_\mu^{\rm BaBar-QTT} = -5.3014456549525\times10^{-10}, \qquad \sigma_{a_\mu} = 2.6838591160311\times10^{-10}. \] Thus the scalar pull is \[ z_{a_\mu} = -1.9753069836, \qquad p_{a_\mu} = 0.0482333212. \] The same covariance records the resolved shape-orthogonal sector as \[ \chi_{\rm sh}^{2} = 58495.38442559397, \qquad \nu_{\rm sh} = 139. \] The integrated HVP scalar and the resolved line shape are therefore different observables. In this release, the scalar \(a_\mu\) direction is a moderate full-covariance pull, while the shape-orthogonal sector identifies the remaining sub-percent timelike camera-map problem. The source is not retuned by the BaBar row: \[ \mathcal B_{\rm BaBar} = \{\mathbf y_{\rm BaBar},\Sigma_{\rm BaBar},z_{a_\mu},\chi_{\rm sh}^{2}\}, \qquad \frac{\partial R_{2\pi}^{\rm src,QTT}} {\partial\mathcal B_{\rm BaBar}} = 0. \] Status labels: Σ-HVP-BABAR-AMU-DIRECTION-DECOMPOSITION-CLOSED Σ-HVP-BABAR-COVARIANCE-ORTHOGONAL-SHAPE-SPLIT-CLOSED Σ-HVP-BABAR-AMU-DIRECTION-NUMERICAL-EXECUTION-CLOSED Σ-HVP-BABAR-SHAPE-ORTHOGONAL-CHI2-EXECUTION-CLOSED Σ-HVP-BABAR-BINNED-LINESHAPE-CONSISTENCY-STRESSED Σ-HVP-BABAR-ACCESS-CAMERA-MAP-PENDING Included files: Main PDF paper, Version 40.0, uploaded as the first/default preview file. Complete release ZIP containing the LaTeX source, execution scripts, receipts, CSV outputs, figures, render audit, checksum manifest, and reconstruction materials. Related anchors: Main QTT book: 10.5281/zenodo.17527179 Source-completion and winding framework: 10.5281/zenodo.20840233 A6 Hadamard center-sheet theorem: 10.5281/zenodo.20744161 Strong-coupling source theorem: 10.5281/zenodo.20625550 QuantumTraction DOI Map: quantumtraction.org/doi-map QTT Observatory: quantumtraction.org/observatory QTT Lexicon: quantumtraction.org/lexicon