2019/04/04 by N. G. Stefanis, Stefanis, N. G.
Computer Science · Physics and Astronomy · #Bayesian Methods and Mixture Models #Data Analysis #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1904.02631
openalex publication_date 2019/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the evaluation of the transition form factor (TFF) Fγ*γπ0(Q2) by means of QCD theory and by state-space reconstruction from topological data analysis. We first calculate this quantity in terms of quark-gluon interactions using light cone sum rules (LCSRs). The spectral density includes radiative corrections in leading, next-to-leading, and next-to-next-to-leading-order of perturbative QCD. Besides, it takes into account the twist-four and twist-six terms. The hard-scattering part in the LCSR is convoluted with various pion distribution amplitudes with different morphologies in order to obtain a wide range of predictions for the form factor, including two-loop evolution which accounts for heavy-quark thresholds. We then use nonlinear time series analysis to extract information on the long-term Q2 behavior of the measured scaled form factor in terms of state-space attractors embedded in ℝ3. These are reconstructed by applying the Packard-Takens method of delays to appropriate samplings of the data obtained in the CLEO, BABAR, and Belle single-tagged e+e- → e+e-π0 experiments. The corresponding lag plots show an aggregation of states around the value Q2Fγ*γπ0(Q2) ≈ 0.165± 0.005 GeV pertaining to the momentum interval Q2∈ [9-11]~GeV2. We argue that this attractor portrait is a transient precursor of a distribution of states peaking closer to the asymptotic limit Q2Fγ*γπ0(Q2→ ∞)=√(2)fπ~GeV. More data with a regular increment of 1~GeV2 in the range between 10 and 25~GeV2 would be sufficient to faithfully determine the terminal portrait of the attractor.