Experimental aspects of the Quantum Tomography of tau lepton pairs at a Higgs factory collider

TL;DR

This paper proposes a method for fully reconstructing tau pair events at a Higgs factory collider, enabling precise quantum tomography of tau spins and their entanglement, with emphasis on detector performance requirements.

Contribution

It introduces a comprehensive kinematic reconstruction technique for tau pairs, facilitating optimal spin correlation measurements at electron-positron colliders.

Findings

Full kinematic reconstruction yields multiple solutions per event.

Photon angular resolution of ~0.1 mrad is critical for precise spin measurements.

Photon energy resolution and vertex detector performance are less impactful.

Abstract

Quantum Tomography of tau lepton pairs produced at a Higgs Factory collider will enable measurements of their spin correlations arising from quantum entanglement. Such measurements rely on the ability to measure the components of and correlations between the taus' spins. We present a method to fully reconstruct the kinematics of tau pair events at an electron-positron Higgs factory collider, making use of measured particles' momenta and impact parameters. This procedure results in several consistent solutions per event, which can be assigned weights according to various event properties. Full kinematic reconstruction allows the optimal extraction of the taus' spin orientation via polarimeters. We estimate the precision with which polarimeters can be reconstructed in an ideal detector, and quantify the effects of more realistic detector performance. We conclude that for this analysis, achieving a photon angular resolution of around 0.1~mrad is the most crucial aspect of detector performance, while photon energy resolution and vertex detector performance are significantly less important.