[Paper Review] Z Polarization in $e^+e^- o t\bar t Z$ for testing the top quark mass structure and the presence of final interactions

Fernand M. Renard|arXiv (Cornell University)|Mar 28, 2018

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes measuring Z boson polarization in $e^+e^- \to t\bar{t}Z$ as a probe of top quark mass structure and new physics. By analyzing the longitudinal $Z_L$ fraction ($R_L$), it shows that deviations from the Standard Model (SM) prediction—especially $R_L \propto m_t^2$—can reveal top quark compositeness or final-state interactions linked to mass generation, including potential dark matter couplings.

ABSTRACT

We show that the measurement of the $Z$ polarization in the $e^+e^- o t\bar t Z$ process would allow an interesting determination of the role of the top quark mass. This can be used for testing the possibility of top compositeness or of the occurence of final state interactions related to the mass generation in particular the interaction with dark matter.

Motivation & Objective

• To investigate how the longitudinal Z boson fraction ($R_L$) in $e^+e^- \to t\bar{t}Z$ encodes information about the top quark mass structure.
• To test whether non-standard effects—such as top quark compositeness or final-state interactions with dark matter—modify the $R_L$ rate.
• To explore whether kinematic-dependent top quark mass effects or $Z_L$-mediated final-state interactions can be detected through $Z$ polarization measurements.
• To provide a phenomenological framework for future high-energy $e^+e^-$ colliders to probe top quark mass generation mechanisms.

Proposed method

• Compute the $Z_L$ production rate ($\sigma(t\bar{t}Z_L)$) relative to total $Z$ polarization in $e^+e^- \to t\bar{t}Z$ using SM Feynman diagrams (a–e), including gauge cancellations at high $p_Z$.
• Use the ratio $R_L = \sigma(t\bar{t}Z_L) / \sigma(t\bar{t}Z_T + Z_L)$ as the key observable, comparing it to the equivalent $R_L(G^0)$ for Goldstone boson production.
• Introduce an effective, kinematically dependent top quark mass $m_t(s) = m_t (m_0^2 + m_{\text{th}}^2)/(s + m_0^2)$ to model compositeness effects.
• Model final-state interactions via a phenomenological test factor $C(x) = 1 + \frac{m_t^2}{m_0^2} \ln\left(-x/(m_Z + m_t)^2\right)$ for $Z_L t$ and $Z_L \bar{t}$ scattering, with $m_0 = 0.5$ TeV.
• Compare results with SM predictions and $b\bar{b}Z$ processes to isolate top quark mass effects.
• Perform kinematic integrations with cuts to avoid collinear singularities and analyze $R_L$ dependence on $p_Z$, $\theta_Z$, and subenergy scales $s_{Zt}, s_{Z\bar{t}}, s_{t\bar{t}}$.

Experimental results

Research questions

• RQ1 How does the $Z_L$ fraction ($R_L$) in $e^+e^- \to t\bar{t}Z$ depend on the top quark mass in the Standard Model?
• RQ2 Can a kinematically dependent effective top quark mass—arising from compositeness—produce measurable deviations in $R_L$?
• RQ3 Can final-state interactions involving longitudinal $Z$ bosons and top quarks (e.g., $Z_L t \to Z_L t$) modify $R_L$ in ways detectable beyond SM predictions?
• RQ4 What kinematic signatures would indicate a connection between top quark mass generation and dark matter interactions via $Z_L$-mediated final-state processes?

Key findings

• In the SM, $R_L$ at high $p_Z$ is proportional to $m_t^2$, matching the $G^0$ production ratio due to the equivalence principle, confirming the $m_t^2$ dependence of $Z_L$ production.
• For $\theta_Z = \pi/2$, $R_L$ in $t\bar{t}Z$ closely matches $R_L(G^0)$ at high $p_Z$, validating the SM prediction and the role of $m_t^2$ scaling.
• With an effective $m_t(s)$ model, $R_L$ decreases significantly at high $p_Z$ when $m_0 = 2$ or $4$ TeV, indicating detectable deviations from SM due to compositeness.
• Final-state $Z_L t$ and $Z_L \bar{t}$ interactions modeled via $C(x)$ lead to enhanced $R_L$ at low $p_Z$, with effects amplified when including $G^0 \to Z_L$ transitions.
• The $b\bar{b}Z$ process shows a much smaller $R_L$ than $t\bar{t}Z$, confirming the $m_t^2/m_b^2$ scaling and the sensitivity of $R_L$ to top quark mass.
• Arbitrary choices of $C(x)$ and $m_0 = 0.5$ TeV produce kinematically dependent $R_L$ modifications, demonstrating that $Z$ polarization can probe non-standard mass generation mechanisms.