Vacuum muon decay and interaction with laser pulses

TL;DR

The paper shows that a finite-duration laser pulse can modify vacuum muon decay through which-way interference between decay paths that do and do not interact with the pulse. It combines a perturbative weak-field analysis for finite pulses with a strong-field Volkov treatment, deriving a suppression factor $\mathcal{R}[\Omega]$ with $\Omega = \dfrac{\xi_{\mu}^{2}\;\Phi\;\langle g^{2}\rangle}{2\;\eta_{\mu}}$ and a phase factor $F(a)=\frac{1}{2}\left[1+e^{iS_{a}(\Phi)}\right]$, predicting up to a factor of about 2 reduction in the decay rate and fringe structure in the emitted electron spectrum. The effect does not require $\chi_{\mu} \sim O(1)$ and can be realized with current laser capabilities, offering a new handle on electroweak decays in strong fields. The results generalize to other electroweak decays with charged particles and motivate all-optical experimental tests.

Abstract

Muons decay in vacuum mainly via the leptonic channel to an electron, a muon neutrino and an electron antineutrino. Previous investigations have concluded that muon decay can only be significantly altered in a strong electromagnetic field when the muonic strong-field parameter is of order unity, which is far beyond the reach of lab-based experiments at current and planned facilities. In this letter, an alternative mechanism is presented in which a laser pulse affects the vacuum decay rate of a muon outside the pulse. Quantum interference between the muon decaying with or without interacting with the pulse generates fringes in the electron momentum spectra and can increase the muon lifetime by up to a factor 2. The required parameters to observe this effect are available in experiments today.

Figures (8)

• Figure 1: First two orders of perturbative expansion in charge-field coupling $\xi$, $\textsf{T}=\textsf{T}_{00}+\textsf{T}_{10}+\textsf{T}_{01}+\textsf{T}_{20}+\textsf{T}_{11}+\textsf{T}_{02}$ respectively.
• Figure 2: Spacetime diagram showing various positions of muon decay, a) before, b) during or c) after laser pulse (grey shaded region), where dashed lines indicate interaction with the pulse.
• Figure 3: Electron polar distribution in the rest frame of the muon $d\textsf{W}_{\tiny\textsf{vac}}/d[\cos(\theta_{q})]$ for different values of the input parameter $\Omega$.
• Figure 4: Electron energy distribution in the rest frame of the muon $d\textsf{W}_{\tiny\textsf{vac}}/dq^{0}$ for different values of the input parameter $\Omega$.
• Figure 5: A plot of the function $\mathcal{R}[\Omega]$ (solid line). The leading-order perturbative and asymptotic limits are indicated with dashed lines and the gridline is at $\mathcal{R}[\Omega] = 1/2$.