[Paper Review] Z polarization in $e^+e^- o ZWW $ for testing special interactions of massive particles

Fernand M. Renard|arXiv (Cornell University)|Jul 24, 2018

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates the $e^+e^- \to ZWW$ process to probe scale-dependent masses and final-state interactions of massive gauge bosons, showing that the longitudinal $Z$-boson polarization rate ($R_L$) is sensitive to such effects. Unlike top-quark production, $Z_{L}$ production in $ZWW$ is uniquely sensitive to $W$ and $Z$ mass scale dependence and $W_LW_L$ final-state interactions, offering complementary constraints on new physics beyond the Standard Model.

ABSTRACT

We show that the $ZWW$ production process may give complementary informations about scale dependent heavy particle masses and possible final state interactions as compared to previously studied top quark production processes. We illustrate the $p_Z$ distribution of the rate of longitudinal $Z_L$ component showing its sensitivity to these effects which may arise from heavy particle substructure or a dark matter (DM) environment.

Motivation & Objective

• To investigate whether the $e^+e^- \to ZWW$ process provides complementary sensitivity to scale-dependent masses and final-state interactions of massive particles compared to top-quark production processes.
• To analyze the $p_Z$-dependent longitudinal $Z$-boson rate ($R_L$) as a probe of $W$ and $Z$ mass scale dependence.
• To assess the impact of final-state $Z_LW_LW_L$ interactions, potentially arising from substructure or dark matter environments.
• To compare the sensitivity of $Z_{L}$ production in $ZWW$ to that of $Z_{L}$ in $Zt\bar{t}$ and $W_{L}t\bar{b}$ processes, highlighting differences due to mass combinations.
• To evaluate the potential of $ZWW$ production as a precision tool for probing new physics beyond the Standard Model.

Proposed method

• The study computes the longitudinal $Z$-boson production rate $R_L = \sigma(Z_LWW)/\sigma(Z_TWW + Z_LWW)$ as a function of $p_Z$ at $\sqrt{s} = 5$ TeV.
• It uses the equivalence between $Z_L$ and Goldstone boson ($G^0$) amplitudes in the high-energy limit, with $G^0WW$ amplitudes proportional to $m_W$ and $1/m_W$ in leading terms.
• A scale-dependent $W$ and $Z$ mass model is introduced: $m_{W,Z}(s) = m_{W,Z} (m_{\text{th}}^2 + m_0^2)/(s + m_0^2)$, with $m_0 = 2,4$ TeV.
• Final-state interactions are modeled via a test factor $(1 + C(s))$ with $C(x) = 1 + \frac{m_Z^2}{m_0^2} \ln\left(-x/(m_Z + m_W)^2\right)$, $m_0 = 0.5$ TeV, applied to $Z_LW_L^+W_L^-$ amplitudes.
• The $p_Z$-distributions of $R_L$ and $R_L^G$ (Goldstone equivalence) are computed and compared to identify deviations from the Standard Model.
• Kinematical structures such as subenergy and angular dependencies are suggested as tools to disentangle scale-dependent mass effects from final-state interaction effects.

Experimental results

Research questions

• RQ1 How does the $p_Z$-dependent longitudinal $Z$-boson rate in $e^+e^- \to ZWW$ respond to scale-dependent $W$ and $Z$ masses?
• RQ2 In what way does the $Z_{L}$ rate in $ZWW$ production differ from the $Z_{L}$ rate in $Zt\bar{t}$ and $W_{L}t\bar{b}$ processes in response to mass scale dependence?
• RQ3 To what extent can final-state $Z_LW_L^+W_L^-$ interactions mimic or be distinguished from scale-dependent mass effects in the $Z_{L}$ rate?
• RQ4 Can the $Z_{L}$ polarization in $ZWW$ production serve as a clean probe of new physics involving $W$ and $Z$ mass scale dependence?
• RQ5 What kinematical features (e.g., subenergy or angular dependence) can help disentangle scale-dependent mass effects from final-state interaction effects?

Key findings

• The $Z_L$ rate in $e^+e^- \to ZWW$ shows a distinct sensitivity to scale-dependent $W$ and $Z$ masses, with effects opposite in sign to those observed in $Zt\bar{t}$ and $Wt\bar{b}$ processes.
• The $p_Z$-distribution of $R_L$ reveals significant deviations from the Standard Model when $m_W(s)$ is scale-dependent, especially at low $p_Z$, due to interplay between $1/m_W$-enhanced amplitudes and $m_W^2/s$ corrections.
• Goldstone equivalence ($R_L^G$) is preserved in the $ZWW$ process at high $p_Z$, but deviations appear at low $p_Z$ due to $m_Z^2/s$ corrections, highlighting the importance of precision measurements.
• Final-state $Z_LW_L^+W_L^-$ interactions, modeled via the $C(x)$ factor, produce measurable distortions in the $p_Z$-distribution of $R_L$, which can be distinguished from mass scale effects through kinematical analysis.
• The $Z_{L}$ rate in $ZWW$ is uniquely sensitive to $W$ and $Z$ masses only, making it a complementary probe to top-quark processes for testing new physics involving gauge boson mass scale dependence.
• The study suggests that $ZWW$ production at $\sqrt{s} = 5$ TeV offers a promising channel for probing new physics, especially when combined with $HWW$ or $HZZ$ processes, though $H$ identification may be more challenging than $Z$.