[Paper Review] Further tests of special interactions of massive particles from the Z polarization rate in $e^+e^- o Zt\bar t$ and in $e^+e^- o ZW^+W^-$

Fernand M. Renard|arXiv (Cornell University)|Aug 16, 2018

High-Energy Particle Collisions Research3 citations

TL;DR

This paper proposes a comparative study of longitudinal Z boson polarization rates in $e^+e^- \to Zt\bar{t}$ and $e^+e^- \to ZW^+W^-$ processes to probe scale-dependent masses and final-state interactions of heavy particles. By analyzing kinematic distributions of invariant masses ($s_{t\bar{t}}$, $s_{Zt}$, etc.), it shows that opposite effects from $Z$ and top quark mass scale dependence can cancel in $Zt\bar{t}$, while $ZWW$ processes exhibit distinct sensitivity to $W/Z$ mass evolution and final-state interactions, enabling discrimination between new physics origins such as substructure or dark matter coupling.

ABSTRACT

We propose further tests of the occurence of scale dependent heavy particle masses (Z,W,t) and of strong final state interactions by comparing Z longitudinal polarization rates in different kinematical distributions of the $e^+e^- o Zt\bar t$ and in $e^+e^- o ZW^+W^-$ processes.

Motivation & Objective

• To test the presence of scale-dependent masses for $Z$, $W$, and top quarks in high-energy $e^+e^-$ collisions.
• To probe final-state interactions in $Zt\bar{t}$ and $ZW^+W^-$ processes through longitudinal Z polarization rates.
• To distinguish between contributions from top quark mass scale dependence, $Z/W$ mass scale dependence, and final-state interactions via comparative analysis of kinematic distributions.
• To identify signatures of new physics such as substructure or dark matter coupling through shape differences in $Z_L$ rate distributions.

Proposed method

• Computes longitudinal Z polarization rate $R_L = \sigma(Z_L)/[\sigma(Z_T) + \sigma(Z_L)]$ in $e^+e^- \to Zt\bar{t}$ and $e^+e^- \to ZW^+W^-$ processes.
• Introduces test forms for scale-dependent masses: $m_X(s) = m_X (m_{\text{th}}^2 + m_0^2)/(s + m_0^2)$ for $X = Z, W, t$.
• Models final-state interactions via multiplicative test factors: $(1 + C(s))$ with $C(x) = 1 + m^2/m_0^2 \ln(-x/(m_{\text{sum}})^2)$.
• Analyzes $Z_L$ rate distributions as functions of invariant masses: $s_{t\bar{t}}$, $s_{Zt}$, $s_{ZW^+}$, $s_{WW}$, etc.
• Compares shape variations in $Z_L$ rates under different assumptions: mass scale dependence vs. final-state interactions.
• Uses kinematic configurations at $\sqrt{s} = 5$ TeV and $\theta = \pi/2$ to illustrate sensitivity and distinguishability.

Experimental results

Research questions

• RQ1 How do scale-dependent $Z$ and $W$ masses affect the longitudinal Z polarization rate in $ZW^+W^-$ production?
• RQ2 How does scale-dependent top quark mass influence the $Z_L$ rate in $Zt\bar{t}$ production, and how does it interact with $Z$ mass effects?
• RQ3 Can final-state interactions in $t\bar{t}$, $Zt$, or $ZW^\pm$ systems be distinguished via $Z_L$ rate distributions?
• RQ4 What kinematic signatures allow discrimination between new physics effects from top quark substructure versus dark matter environments?

Key findings

• In $ZW^+W^-$ production, scale-dependent $W/Z$ masses increase the $Z_L$ rate, with distinct shape changes in $s_{WW}$ and $s_{ZW^\pm}$ distributions.
• In $Zt\bar{t}$ production, the $Z$ mass decrease increases $Z_L$ rate, while top quark mass decrease suppresses it due to Goldstone equivalence, leading to potential cancellation.
• The $s_{t\bar{t}}$ and $s_{Zt}$ distributions show opposite responses to $Z$ and top quark mass scale dependence, enabling cancellation effects that suppress observable signals.
• Final-state interactions produce unique, shape-distinctive effects in $s_{t\bar{t}}$, $s_{Zt}$, and $s_{ZW^\pm}$ distributions, differing from mass scale dependence effects.
• The combined analysis of $Zt\bar{t}$ and $ZW^+W^-$ processes allows disentangling the origin of new physics: whether from top quark mass scale dependence, $W/Z$ mass evolution, or final-state interactions.
• Kinematic distributions of $Z_L$ rates provide a sensitive probe for identifying BSM physics such as substructure or dark matter coupling, even with simple test forms.