Study $γγ\to τ^+τ^-$ process including $τ^+ τ^-$ spin information in Pb-Pb ultraperipheral collision and at Lepton collider

TL;DR

This work develops a spin-density-matrix framework for the photon-photon-induced process $\gamma\gamma \to \tau^+ \tau^-$ in Pb-Pb ultraperipheral collisions and at lepton colliders, providing LO and NLO EW predictions for cross sections and spin observables. The analysis shows NLO EW effects are numerically small for the studied observables, establishing a precise SM baseline for spin correlations characterized by $C_{ab}$ and the rotation-invariant entanglement measure $D$. A key finding is that, while inclusive entanglement criteria do not indicate entanglement ($D>-1/3$), a differential study as a function of $m_{\tau\tau}$ reveals $D<-1/3$ near the threshold, corresponding to a dominant $^1S_0$ spin configuration and genuine entanglement. This work provides a methodological template for exploiting angular and spin information in photon-induced $\tau$-pair production at current and future high-energy colliders.

Abstract

We study the $γγ\to τ^+τ^-$ process including full $τ^+ τ^-$ spin information in Pb--Pb ultraperipheral collision and at lepton colliders. We present the predictions for the corresponding cross sections and spin correlations at NLO electroweak precision, and find that the NLO electroweak contributions are numerically small for the observables considered. Additionally, we use the spin correlations obtained in this paper to analyze the quantum entanglement in the $τ^+τ^-$ system of the $γγ\to τ^+τ^-$ process. Our results show that there is a genuine entangled configuration near the $τ^+τ^-$ invariant mass threshold. This work is helpful for studying the $τ$-pair production induced by photon-photon collision at high energy colliders.

Figures (2)

• Figure 1: $t$-channel $\tau^+\tau^-$ production via photon fusion at LC (left) and in Pb-Pb UPC (right). The corresponding $u$-channel contributions are these diagrams involving $\tau$-pair exchange.
• Figure 2: The differential entanglement observable $D$ is shown as a function of the $\tau$-pair invariant mass $m_{\tau\tau}$ for $\sqrt{s_{NN}} = 5.02$ TeV in UPC. The representative mass interval displayed is $m_{\tau\tau}\in[2 m, 15]$ GeV. The yellow dashed and green dash-dotted curves represent the LO and NLO EW results, respectively. The horizontal blue dashed line indicates the entanglement threshold at $D=-1/3$. Negative values near $\tau^+\tau^-$ invariant mass threshold reflect the dominance of spin singlet configurations, while the transition toward positive $D$ at higher masses signals the onset of spin-triplet states and reduced entanglement.