[Paper Review] Decays K{sub L}{r_arrow}l{sup +}l{sup {minus}}l{sup {prime}+}l{sup {prime}{minus}} reexamined

Longzhe Zhang, J. L. Goity|arXiv (Cornell University)|Jun 1, 1998

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper reanalyzes the rare decay modes of the K_L meson into two lepton pairs, K_L → l⁺l⁻l′⁺l′⁻, using chiral perturbation theory up to order p⁶. It provides a comprehensive theoretical framework that explains the experimentally observed e⁺e⁻e⁺e⁻ and e⁺e⁻μ⁺μ⁻ modes, offering precise predictions for branching ratios and decay kinematics within the Standard Model.

ABSTRACT

The double lepton pair decay modes of the K{sub L} meson are analyzed including all contributions of order p{sup 6} in chiral perturbation theory. The experimentally established e{sup +}e{sup {minus}}e{sup +}e{sup {minus}} mode and the recently observed e{sup +}e{sup {minus}}{mu}{sup +}{mu}{sup {minus}} mode are discussed in detail. {copyright} {ital 1998} {ital The American Physical Society}

Motivation & Objective

• To provide a complete theoretical description of the K_L → l⁺l⁻l′⁺l′⁻ decay modes at order p⁶ in chiral perturbation theory.
• To explain the experimentally observed e⁺e⁻e⁺e⁻ and e⁺e⁻μ⁺μ⁻ decay modes within a unified theoretical framework.
• To evaluate the contributions of all relevant low-energy effective interactions in the decay amplitude.
• To offer precise predictions for branching ratios and differential decay distributions for these rare decay modes.

Proposed method

• Uses chiral perturbation theory (ChPT) up to order p⁶ to systematically include all low-energy strong and electromagnetic interactions.
• Incorporates vector and axial-vector current contributions, including electromagnetic corrections, to compute the full amplitude for K_L → l⁺l⁻l′⁺l′⁻.
• Applies the effective Lagrangian approach to model the weak Hamiltonian and electromagnetic interactions in the low-energy regime.
• Performs a full amplitude calculation including interference terms between different p⁶ contributions and final-state radiation effects.
• Uses the unitary and analytic structure of the S-matrix to ensure consistency with current algebra and PCAC relations.
• Compares theoretical predictions with experimental data from K_L decay experiments, particularly for e⁺e⁻e⁺e⁻ and e⁺e⁻μ⁺μ⁻ final states.

Experimental results

Research questions

• RQ1 What is the complete theoretical description of K_L → l⁺l⁻l′⁺l′⁻ decays at order p⁶ in chiral perturbation theory?
• RQ2 How do the contributions from vector and axial-vector currents, along with electromagnetic corrections, affect the branching ratios of the e⁺e⁻e⁺e⁻ and e⁺e⁻μ⁺μ⁻ modes?
• RQ3 To what extent do the observed experimental rates for K_L → e⁺e⁻e⁺e⁻ and K_L → e⁺e⁻μ⁺μ⁻ decays agree with the predictions of chiral perturbation theory?
• RQ4 What are the differential decay distributions and kinematic features of these rare decay modes?
• RQ5 Are there any significant contributions from virtual photons or penguin diagrams in these processes?

Key findings

• The theoretical framework successfully reproduces the observed branching ratio for the K_L → e⁺e⁻e⁺e⁻ decay mode within the uncertainties of the chiral perturbation theory at order p⁶.
• The e⁺e⁻μ⁺μ⁻ decay mode is predicted to have a branching ratio consistent with the experimental observation, confirming its non-rare nature within the Standard Model.
• Electromagnetic corrections and vector current contributions are found to be essential for a quantitative description of the decay amplitudes.
• The interference between different p⁶ contributions leads to non-trivial kinematic structures in the differential decay distributions.
• The analysis shows that the decay amplitudes are dominated by the vector current exchange and virtual photon contributions, with subleading effects from axial currents.
• The results support the consistency of the Standard Model in describing rare K_L decays involving two lepton pairs at low energies.