[Paper Review] Probing the Majorana Nature and CP Properties of Neutralinos

Seong Youl Choi|ArXiv.org|Sep 6, 2004

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes two direct experimental methods to probe the Majorana nature and CP violation in neutralinos at future $e^+e^-$ linear colliders. The first method uses combined analysis of threshold pair production and end-point fermion invariant mass distributions in three-body decays; the second measures $Z$-boson polarization in two-body decays $\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z$. Key results show that even with only the two lightest neutralinos accessible, CP violation can be detected via $S$-wave enhancements in production and decay, and $Z$-boson helicity asymmetries confirm Majorana nature and signal CP violation.

ABSTRACT

Two powerful and straightforward methods are presented for probing the Majorana nature and CP violation of neutralinos at future $e^+e^-$ linear colliders.

Motivation & Objective

• To establish experimental methods for determining whether neutralinos are Majorana fermions and whether CP violation is present in the neutralino sector.
• To address the challenge of probing CP properties and Majorana nature when only the lightest neutralinos are kinematically accessible.
• To provide a direct, model-independent way to test fundamental SUSY parameters such as complex $M_1$, $M_2$, and $\mu$ phases.
• To enable early-stage detection of CP violation and Majorana nature in the neutralino system at $e^+e^-$ colliders.

Proposed method

• Analyzes threshold behavior of $e^+e^- \to \tilde{\chi}^0_i\tilde{\chi}^0_j$ pair production to detect $S$-wave enhancements indicative of CP violation.
• Examines the fermion invariant mass distribution near the end point of three-body decays $\tilde{\chi}^0_i \to \tilde{\chi}^0_j f\bar{f}$ to identify $S$-wave signals of CP violation.
• Uses the $Z$-boson polarization in two-body decays $\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z$ to probe CP violation and confirm Majorana nature.
• Applies selection rules based on intrinsic CP parity and orbital angular momentum to distinguish CP-invariant from CP-noninvariant scenarios.
• Relies on the fact that in CP-invariant cases, vector and axial-vector currents lead to distinct $S$- and $P$-wave production patterns, which break under CP violation.
• Uses the relation $\Gamma[\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z(+)] = \Gamma[\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z(-)]$ as a signature of Majorana nature, valid even in CP-noninvariant cases.

Experimental results

Research questions

• RQ1 Can $S$-wave enhancements in neutralino pair production and three-body decay end-point distributions signal CP violation in the neutralino system?
• RQ2 How can the $Z$-boson polarization in $\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z$ decays be used to probe CP violation and confirm the Majorana nature of neutralinos?
• RQ3 Can CP violation be detected even when only the two lightest neutralinos are accessible at $e^+e^-$ colliders?
• RQ4 What role do the complex phases of $M_1$ and $\mu$ play in breaking CP selection rules and enabling observable $S$-wave signals?
• RQ5 How do the helicity-dependent decay widths of the $Z$ boson in $\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z$ decays reflect CP violation in the neutralino sector?

Key findings

• The combined analysis of $e^+e^- \to \tilde{\chi}^0_1\tilde{\chi}^0_2$ near threshold and $\tilde{\chi}^0_2 \to \tilde{\chi}^0_1 l^+l^-$ near the end point reveals $S$-wave enhancements that signal CP violation, even with only the lightest neutralinos accessible.
• In the CP-invariant case, $S$-wave production and decay are mutually exclusive due to CP selection rules, but CP violation lifts this restriction, allowing simultaneous $S$-wave signals.
• For the parameter set $\tan\beta=10$, $|M_1|=100$ GeV, $M_2=150$ GeV, $|\mu|=400$ GeV, $\Phi_\mu=0$, the numerical simulation shows clear $S$-wave enhancement in both production and decay processes.
• The $Z$-boson helicity asymmetry $\Gamma(Z(+)) = \Gamma(Z(-))$ confirms the Majorana nature of neutralinos, as required by their purely imaginary vector and real axial-vector couplings.
• The ratio of longitudinal to transverse decay widths in $\tilde{\chi}^0_i \to \tilde{\chi}^0_j Z$ provides a direct probe of CP violation, independent of decay mode, when masses are measured precisely.
• Even when two-body decays are kinematically open, $Z$-boson polarization measurements remain a viable method to probe CP violation and Majorana nature in the neutralino system.