[Paper Review] Rare K decay: results and prospects

Littenberg, Laurence|arXiv (Cornell University)|Jan 17, 2002

Quantum Chromodynamics and Particle Interactions2 citations

TL;DR

This paper reviews experimental results and future prospects for rare kaon decays, focusing on their role in probing physics beyond the Standard Model (BSM), particularly lepton flavor violation (LFV) and one-loop processes sensitive to CKM matrix elements. It highlights that LFV searches in kaons have reached sensitivities corresponding to energy scales above 100 TeV, effectively ruling out many BSM models, and shifts focus to one-loop decays like K+ →π+νν̄ and KL →π⁰νν̄ as key probes for testing the unitarity triangle and constraining new physics.

ABSTRACT

Recent results on rare kaon decays are reviewed and prospects for future experiments are discussed.

Motivation & Objective

• To summarize recent experimental results on rare kaon decays and assess their sensitivity to physics beyond the Standard Model (BSM).
• To evaluate the role of one-loop processes, particularly KL →μ⁺μ⁻, K+ →π+νν̄, and KL →π⁰νν̄, in probing the CKM matrix and testing the unitarity triangle.
• To examine the theoretical and experimental challenges in isolating short-distance contributions from long-distance effects in rare decays.
• To assess future experimental prospects, including E949, CKM, E391a, and KPIO, for improving measurements of rare decay branching ratios.
• To explore alternative parameterizations of decay amplitudes in terms of λt = V∗tsVtd to improve comparison between kaon and B-meson physics.

Proposed method

• Reviews experimental results from kaon decay experiments at Brookhaven AGS and KTeV, focusing on rare decay modes with high sensitivity to LFV and new physics.
• Analyzes branching ratios of one-loop processes (e.g., K+ →π+νν̄, KL →μ⁺μ⁻, KL →π⁰νν̄) using the Wolfenstein parameterization and Inami-Lim functions to extract constraints on CKM parameters.
• Applies theoretical frameworks such as chiral Lagrangians and effective field theory to model long-distance contributions, particularly absorptive and dispersive amplitudes.
• Uses measured ratios like B(KL →μ⁺μ⁻)/B(KL →π⁺π⁻) and Babsγγ(KL →μ⁺μ⁻)/B(KL →π⁺π⁻) to isolate the dispersive component of KL →μ⁺μ⁻.
• Proposes an alternative parameterization in terms of λt = V∗tsVtd to avoid external uncertainties from Wolfenstein parameters (ρ, η) and improve comparison with B-meson results.
• Evaluates future experimental programs (E949, CKM, E391a, KPIO) and their potential to achieve 10⁻¹¹ to 10⁻¹² event-level sensitivity for K+ →π+νν̄ and 10% measurements of Im(λt).

Experimental results

Research questions

• RQ1 What are the current experimental limits on lepton flavor violating kaon decays, and what do they imply for new physics models?
• RQ2 How can the dispersive contribution to KL →μ⁺μ⁻ be isolated from long-distance effects, and what are the theoretical and experimental challenges in doing so?
• RQ3 To what extent do the branching ratios of one-loop rare kaon decays (e.g., K+ →π+νν̄, KL →π⁰νν̄) constrain the CKM matrix element λt and test the unitarity triangle?
• RQ4 How do future experiments like E949, CKM, and KPIO aim to improve sensitivity to rare kaon decays and test the Standard Model?
• RQ5 Can an alternative parameterization in terms of λt improve the comparison between kaon and B-meson physics in the context of unitarity triangle constraints?

Key findings

• The 90% CL upper limit on KL →μe is 4.7 × 10⁻¹², and on K+ →π+μ+e⁻ is 2.8 × 10⁻¹¹, indicating that lepton flavor violation in kaons is highly suppressed.
• The measured branching ratio for KL →μ⁺μ⁻ is (7.18 ± 0.17) × 10⁻⁹, with the absorptive contribution from KL →γγ accounting for (7.07 ± 0.18) × 10⁻⁹, leaving a 90% CL upper limit of 0.31 × 10⁻⁹ on the dispersive part.
• The branching ratio for K+ →π+νν̄ has been observed with a value consistent with the Standard Model, and future experiments aim for 10⁻¹¹/event sensitivity to improve precision.
• Theoretical calculations of the dispersive amplitude in KL →μ⁺μ⁻ show poor agreement with experimental limits unless the contribution from virtual photons (KL →γ*γ*) is included, which remains poorly constrained.
• The 90% CL constraint from KL →μ⁺μ⁻ and K+ →π+νν̄ on the λt plane is consistent with the 95% CL CKM fit, but future 10% measurements of |λt| and Im(λt) could reveal discrepancies indicating new physics.
• Future experiments such as E949 (10⁻¹¹/event), CKM (10⁻¹²/event), and KPIO (10% measurement of Im(λt)) are expected to provide critical tests of the SM through comparison of unitarity triangles from kaon and B-meson decays.