[Paper Review] Rare Kaon and Pion Decays

L. Littenberg|arXiv (Cornell University)|Dec 4, 2002

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper reviews recent experimental results and future prospects for rare kaon and pion decays, emphasizing their role as probes of physics beyond the Standard Model (BSM), particularly lepton flavor violation (LFV) and new physics in flavor-changing neutral currents. Key results include improved branching ratio limits for LFV decays such as $K_{L}\to\mu e$ and $K^{+}\to\pi^{+}\mu^{+}e^{-}$, and precise measurements of form factors in $K^{+}\to\ell^{+}\nu_{\ell}e^{+}e^{-}$ decays, with implications for CKM unitarity and chiral perturbation theory.

ABSTRACT

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

Motivation & Objective

• To review recent experimental results on rare kaon and pion decays, particularly those sensitive to physics beyond the Standard Model (BSM).
• To assess the sensitivity of rare decays to lepton flavor violation (LFV) and new physics in flavor-changing neutral currents.
• To evaluate the role of rare decays in testing chiral perturbation theory (χPT) and measuring fundamental CKM matrix elements such as $V_{ud}$ and $V_{td}$.
• To outline future experimental programs, including $K^{+}\to\pi^{+}\nu\bar{\nu}$ and $K_{L}\to\pi^{0}\nu\bar{\nu}$, aimed at precision tests of the unitarity triangle.

Proposed method

• Analysis of experimental data from high-statistics experiments such as AGS-865, AGS-871, and E865 at Brookhaven National Laboratory.
• Use of likelihood fits to extract form factors in $K^{+}\to\ell^{+}\nu_{\ell}e^{+}e^{-}$ decays, assuming resonance-dominated form factor behavior (e.g., $\rho(770)$, $K^{*}(892)$).
• Comparison of measured branching ratios and form factors with theoretical predictions from $\mathcal{O}(p^4)$ chiral perturbation theory and pion decay data.
• Application of kinematic reconstruction techniques to identify rare decay modes, including missing mass analysis for $K^{+}\to\ell^{+}\nu_{\ell}e^{+}e^{-}$.
• Use of $K^{+}\to\pi^{+}\nu\bar{\nu}$ and $K_{L}\to\pi^{0}\nu\bar{\nu}$ decays as clean probes of $V_{td}$ and the unitarity triangle.
• Evaluation of long-distance contributions via $K_{L}\to\mu^{+}\mu^{-}$ and $K_{L}\to\gamma\ell^{+}\ell^{-}$ to constrain dispersive amplitudes.

Experimental results

Research questions

• RQ1 What are the current experimental limits on lepton flavor violating kaon decays such as $K_{L}\to\mu e$ and $K^{+}\to\pi^{+}\mu^{+}e^{-}$, and what new physics scales do they probe?
• RQ2 How do form factors in $K^{+}\to\ell^{+}\nu_{\ell}e^{+}e^{-}$ decays constrain new physics models and chiral perturbation theory?
• RQ3 To what extent do rare kaon decays like $K^{+}\to\pi^{+}\nu\bar{\nu}$ and $K_{L}\to\pi^{0}\nu\bar{\nu}$ provide independent tests of the unitarity triangle and CKM matrix consistency?
• RQ4 Can $K_{L}\to\mu^{+}\mu^{-}$ and related decays help disentangle long-distance contributions and improve theoretical predictions for $K\to\pi\nu\bar{\nu}$?
• RQ5 What is the role of pion decays such as $\pi^{+}\to\pi^{0}e^{+}\nu_{e}$ in measuring $V_{ud}$ and testing CKM unitarity?

Key findings

• The branching ratio for $K^{+}\to e^{+}\nu_{e}e^{+}e^{-}$ was measured as $(2.48 \pm 0.14_{\text{stat}} \pm 0.14_{\text{syst}}) \times 10^{-8}$ with $m_{ee} > 150\,\text{MeV}$, based on 410 signal candidates and 40 background events.
• The branching ratio for $K^{+}\to\mu^{+}\nu_{\mu}e^{+}e^{-}$ was measured as $(7.06 \pm 0.16_{\text{stat}} \pm 0.26_{\text{syst}}) \times 10^{-8}$ with $m_{ee} > 145\,\text{MeV}$, based on 2679 signal candidates and 514 background events.
• The vector form factor $F_V$ was extracted as $112 \pm 15 \pm 10 \pm 3 \times 10^{-3}$, consistent with theoretical expectations and pion data.
• The axial-vector form factor $F_A$ was measured as $35 \pm 14 \pm 13 \pm 3 \times 10^{-3}$, in good agreement with $\mathcal{O}(p^4)$ χPT predictions.
• The tensor form factor $F_T$ was found to be $-4 \pm 7 \pm 7 \pm 0.4 \times 10^{-3}$, consistent with zero, though not sufficient to rule out a non-zero contribution.
• The ratio $R = F_A / F_V$ was measured as $227 \pm 13 \pm 10 \pm 9 \times 10^{-3}$, consistent with theoretical expectations and pion data.