The authors obtain the exact solution of the Schrodinger equation for a particle confined to (i) an equilateral triangle, (ii) a tetrahedral box with corners (- pi / square root 2,- pi / square root 2,- pi / square root 2), ( pi / square root 2,- pi / square root 2, pi /2); (- pi / square root 2, pi / square root 2, pi /2) and ( pi square root 2, pi / square root 2,- pi /2). The energies are: for (i) E nl =(8h(cross) 2 pi 2 /9mL 2 )(n 2 +l 2 -ln) where L is the side of the triangle and l, n are distinct non-zero integers and for (ii), E lmn =(h(cross) 2 /8m)*(3(l 2 +m 2 +n 2 )-2lm-2mn-2nl) where l, m and n are distinct non-zero integers. The wavefunctions have been classified according to the irreducible representation of the corresponding symmetry groups.
We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process e+e−→τ+τ− at a center-of-mass energy of s=10.579 GeV . The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ in the τ+τ− center-of-mass frame. We analyze events in which both τ leptons decay to hadrons, using a combination of decay channels τ−→π−ντ , τ−→π−π0ντ , and τ−→π−π+π−ντ . The spin orientation of the τ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024
This document contains the Python simulation code for the M²FA model asdescribed in NCT V.IV (The Alert Constant λ = 0.3 — Part II: A Hybrid Constantof Order, Wave, and Practical Utility). The code implements:• Validation of the fundamental relation λ=4H/πφ• Exploration of ontological porosity ε = 0.2%• Demonstration of the two safety margins (21.3% and 21.5%)• Statistical analysis over 1,000,000 runs• Visualization of the hybrid nature of λThe simulation is fully reproducible. The code demonstrates that λ = 0.3 is ahybrid constant, emerging from the relation between Order (H, φ, 4) and Wave (π).Keywords: M²FA, NCT V.IV, Alert Constant λ, hybrid constant, golden ratio,decoherence, order and wave, ontological porosity.Related publications:• NCT II: 10.5281/zenodo.19950456• NCT II.3: 10.5281/zenodo.20037122• NCT V: 10.5281/zenodo.21188867• NCT V.II: 10.5281/zenodo.21351682• NCT V.III: 10.5281/zenodo.21398367• NCT V.IV: 10.5281/zenodo.21429945