[Paper Review] Invisible decays of neutral hadrons

Wanpeng Tan|arXiv (Cornell University)|Jun 17, 2020

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper proposes that invisible decays of long-lived neutral hadrons—such as $K^0_L$, $K^0_S$, $\Lambda^0$, and $\Xi^0$—arise from ordinary-mirror particle oscillations within a newly developed mirror matter model. By equating the $CP$-violation and mirror symmetry-breaking scales, the model predicts precise branching fractions of $9.9\times10^{-6}$ for $K^0_L$, $1.8\times10^{-6}$ for $K^0_S$, $4.4\times10^{-7}$ for $\Lambda^0$, and $3.6\times10^{-8}$ for $\Xi^0$, all detectable at existing accelerators.

ABSTRACT

Invisible decays of neutral hadrons are evaluated as ordinary-mirror particle oscillations using the newly developed mirror matter model. Assuming equivalence of the $CP$ violation and mirror symmetry breaking scales for neutral kaon oscillations, rather precise values of the mirror matter model parameters are predicted for such ordinary-mirror particle oscillations. Not only do these parameter values satisfy the cosmological constraints, but they can also be used to precisely determine the oscillation or invisible decay rates of neutral hadrons. In particular, invisible decay branching fractions for relatively long-lived hadrons such as $K^0_L$, $K^0_S$, $Λ^0$, and $Ξ^0$ due to such oscillations are calculated to be $9.9 imes 10^{-6}$, $1.8 imes 10^{-6}$, $4.4 imes 10^{-7}$, and $3.6 imes 10^{-8}$, respectively. These significant invisible decays are readily detectable at existing accelerator facilities.

Motivation & Objective

• To address the lack of experimental searches for invisible decays in long-lived neutral hadrons like $K^0_L$, $K^0_S$, $\Lambda^0$, and $\Xi^0$, despite their potential to reveal new physics.
• To explore whether the mirror matter model, with spontaneous mirror symmetry breaking, can explain large invisible decay rates in light hadrons.
• To derive precise predictions for invisible decay branching fractions by equating the scales of $CP$ violation and mirror symmetry breaking.
• To test the viability of these predictions against cosmological constraints and existing experimental limits.
• To motivate future experimental searches at existing and planned facilities by demonstrating detectable signal levels.

Proposed method

• Adopts a mirror matter model with no explicit cross-sector interactions, where ordinary and mirror particles only interact gravitationally until mirror symmetry is spontaneously broken.
• Uses the observed $CP$ violation in neutral kaon systems to constrain the mirror symmetry breaking scale, assuming equivalence between $CP$-violation and mirror symmetry-breaking scales.
• Applies the vacuum oscillation formula $P(t) = \sin^2(2\theta) \sin^2(\frac{1}{2}\Delta t)$ to model ordinary-mirror hadron oscillations, with $\theta$ as the mixing angle and $\Delta$ as the mass splitting.
• Derives the mixing strength $\sin^2(2\theta)$ from the $K^0$-$K^{0'}$ oscillation parameters, using the known $CP$-violating parameter $\epsilon_K$.
• Calculates invisible decay branching fractions using the oscillation probability and the hadron's lifetime, assuming oscillation dominates over standard decays.
• Validates predictions against cosmological constraints and compares with experimental limits on other decay modes (e.g., $\bar{\nu}\nu$, $\bar{\nu}\nu\bar{\nu}\nu$).

Experimental results

Research questions

• RQ1 Can the mirror matter model predict large, detectable invisible decay branching fractions for long-lived neutral hadrons like $K^0_L$ and $\Lambda^0$?
• RQ2 What is the quantitative link between $CP$ violation in $K^0$ systems and mirror symmetry breaking in the mirror matter model?
• RQ3 Do the predicted invisible decay rates for $K^0_L$, $K^0_S$, $\Lambda^0$, and $\Xi^0$ satisfy cosmological constraints and remain within detectable ranges at existing facilities?
• RQ4 How do cosmic anisotropy and revised dark energy estimates affect the mirror matter model's parameters and predictions?
• RQ5 To what extent does the assumption of a universal relative mass splitting scale hold across different hadron systems, particularly $D^0$ and $B^0$?

Key findings

• The mirror matter model predicts an invisible decay branching fraction of $9.9 \times 10^{-6}$ for $K^0_L$, arising from $K^0$-$K^{0'}$ oscillations.
• For $K^0_S$, the invisible decay branching fraction is predicted to be $1.8 \times 10^{-6}$, significantly larger than in standard model decays.
• The $\Lambda^0$ baryon is predicted to have an invisible decay branching fraction of $4.4 \times 10^{-7}$, making it a promising target for detection.
• The $\Xi^0$ hyperon is predicted to decay invisibly with a branching fraction of $3.6 \times 10^{-8}$, consistent with the model’s scaling behavior.
• Cosmic anisotropy data slightly modifies the $n$-$n'$ mixing strength to $\sin^2(2\theta_{nn'}) = 1.6 \times 10^{-5}$, which remains within experimental limits.
• The model predicts $B_{\text{inv}}(\Xi^0) \simeq 2.8 \times 10^{-8}$, $B_{\text{inv}}(D^0) \simeq 1.1 \times 10^{-10}$, and $B_{\text{inv}}(B^0) \simeq 2.7 \times 10^{-10}$ under revised cosmological parameters.