Resolving the Two-Fold Ambiguity in Tau Momentum Reconstruction via a Self-Consistent Weighting Method
Abstract
The reconstruction of τ lepton momenta in e+e− → τ+τ− processes suffers from a two-fold kinematic ambiguity due to undetected neutrinos. We show that the common practice of retaining both solutions with equal weight systematically biases the extracted angular coefficients: the bias grows with the size of the cos2θ modulation of the production distribution f(cosθ), but remains resolvable even in the nearly uniform QED limit at the ψ(2S) threshold. We propose a self-consistent weighting method based on a fixed-point theorem: assigning normalized weights wi = f(cosθi)/[f(cosθ1)+f(cosθ2)] yields a weighted distribution h(x) = f(x)[1+ε(x)] with ε(x) ≪ 1 under a detailed balance condition. Monte Carlo simulations at √s=3.686~GeV and $4.8$~GeV show that the fixed-point iteration converges to the true angular coefficient α within statistical uncertainty, providing a robust framework for angular analysis without event-by-event ambiguity resolution.
Related
- Wideband Ambiguity Function Analysis And Quantification Protocols Of Hyperbolic Frequency-Modulated (Bio)Sonars
- Temperature--Hamiltonian Ambiguity in Strong-Coupling Quantum Equilibrium
- Ambiguity in matter sector for modified gravity involving δ 2 ℒm/δ gμ ν δ gα β and its implications to astrophysics and cosmology
- Green's functions and weighting fields for dielectric multilayer geometries
- Global equilibrium at order 𝒪(ℏ2): pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency
BibTeX
@misc{ping2026resolving,
title = {{Resolving the Two-Fold Ambiguity in Tau Momentum Reconstruction via a Self-Consistent Weighting Method}},
author = {Rong-Gang Ping},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01533},
eprint = {2611.01533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01533},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Resolving the Two-Fold Ambiguity in Tau Momentum Reconstruction via a Self-Consistent Weighting Method
AU - Rong-Gang Ping
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01533
UR - https://arxiv.org/abs/2611.01533
AB - The reconstruction of τ lepton momenta in e^+e^− → τ^+τ^− processes suffers from a two-fold kinematic ambiguity due to undetected neutrinos. We show that the common practice of retaining both solutions with equal weight systematically biases the extracted angular coefficients: the bias grows with the size of the cos^2θ modulation of the production distribution f(cosθ), but remains resolvable even in the nearly uniform QED limit at the ψ(2S) threshold. We propose a self-consistent weighting method based on a fixed-point theorem: assigning normalized weights w_i = f(cosθ_i)/[f(cosθ_1)+f(cosθ_2)] yields a weighted distribution h(x) = f(x)[1+ε(x)] with ε(x) ≪ 1 under a detailed balance condition. Monte Carlo simulations at √s=3.686~GeV and $4.8$~GeV show that the fixed-point iteration converges to the true angular coefficient α within statistical uncertainty, providing a robust framework for angular analysis without event-by-event ambiguity resolution.
ER -