Revealing the Two-Fold Ambiguity: Tau Momentum Reconstruction and Its Impact on Entanglement Observables
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918523905769472 |
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| author | Zhou, Xiang Zhang, Jianyong Wan, Xia Wang, Youkai Mo, Xiaohu |
| author_facet | Zhou, Xiang Zhang, Jianyong Wan, Xia Wang, Youkai Mo, Xiaohu |
| contents | The neutrinos produced in $τ$ decays cannot be directly detected, making the reconstruction of $τ$ kinematics challenging and affecting measurements of quantum correlations such as spin entanglement. For the process $e^+e^- \to τ^+τ^- \to π^+ \barν_τπ^-ν_τ$, the kinematic constraints allow the $τ$ momenta to be reconstructed up to a well-known two-fold ambiguity, regardless of the presence of an intermediate resonance state. In this paper, we present a geometric interpretation of this ambiguity and propose a numerical reconstruction method based on singular value decomposition (SVD). Using only the information from visible final-state particles and decay kinematics, the method reconstructs the two possible solutions for the $τ^+τ^-$ pair. The reconstruction performance is validated with Monte Carlo simulations in typical collider environments. We further investigate the impact of the spurious solution on spin-entanglement measurements and show that reliable entanglement signals can still be extracted even when the true and spurious solutions cannot be experimentally distinguished. This work provides a practical approach for $τ$-lepton kinematic reconstruction and spin-entanglement measurements in $e^+e^-$ collider experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26724 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revealing the Two-Fold Ambiguity: Tau Momentum Reconstruction and Its Impact on Entanglement Observables Zhou, Xiang Zhang, Jianyong Wan, Xia Wang, Youkai Mo, Xiaohu High Energy Physics - Phenomenology The neutrinos produced in $τ$ decays cannot be directly detected, making the reconstruction of $τ$ kinematics challenging and affecting measurements of quantum correlations such as spin entanglement. For the process $e^+e^- \to τ^+τ^- \to π^+ \barν_τπ^-ν_τ$, the kinematic constraints allow the $τ$ momenta to be reconstructed up to a well-known two-fold ambiguity, regardless of the presence of an intermediate resonance state. In this paper, we present a geometric interpretation of this ambiguity and propose a numerical reconstruction method based on singular value decomposition (SVD). Using only the information from visible final-state particles and decay kinematics, the method reconstructs the two possible solutions for the $τ^+τ^-$ pair. The reconstruction performance is validated with Monte Carlo simulations in typical collider environments. We further investigate the impact of the spurious solution on spin-entanglement measurements and show that reliable entanglement signals can still be extracted even when the true and spurious solutions cannot be experimentally distinguished. This work provides a practical approach for $τ$-lepton kinematic reconstruction and spin-entanglement measurements in $e^+e^-$ collider experiments. |
| title | Revealing the Two-Fold Ambiguity: Tau Momentum Reconstruction and Its Impact on Entanglement Observables |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2605.26724 |