Search for a cosmologically relevant boson in muon decay

Experiments looking for a lepton-flavor-violating decay ${\mu }^{+}\to e^{+}{X}^0$ are reviewed in light of present-day germanium detector technology, with an eye on scenarios where a long-lived, slow-moving massive boson $X^0$ might have a cosmological impact. A broad swath of interesting, unexplored parameter space very close to the kinematic limit of the decay is found to be within the reach of a new proposed search. A number of possible roles for $X^0$ in past and present epochs can be investigated.

Figure 1

Top: conventional display of sensitivity to ${\mu }^{+}\to e^{+}{X}^0$ in BR vs $m_X$ space. A vertical line indicates the mass of the parent muon. Bottom: alternative view in BR vs speed of the emitted boson. Vertical lines denote the escape velocity from the Milky Way, and the lowest energy measurable by modern point-contact germanium detectors [23, 24].

Figure 2

Expected background in the LEGe detector, dominated by annihilation in flight and escape of high-energy Michel positrons. A secondary component arises from low-energy Michel positron trajectories contained within the crystal. Steady-state environmental backgrounds are small by comparison. Lines from Pb fluorescence and ${}^{68,71}\mathrm{Ge}$ electron capture (EC) can be identified. Inset: excellent LEGe energy resolution, measured by the author using alpha-induced x-ray emission from labeled materials.

Figure 3

Top: offline analysis of a digitized LEGe preamplifier waveform containing a 150 eV pulser-induced signal. A line shows the wavelet-denoised trace, displaying characteristic rise and decay times. Bottom: Dots correspond to the fast derivative of the denoised trace. A line joins them following median filtering. Conditions on minimum amplitude and width for the resulting peak reject low-frequency noise, pinpointing the onset of bona fide low-amplitude signals.

Figure 4

Continuous slow-down approximation (CSDA) positron track length in germanium, derived from [58, 59]. Inset: MCNPX-simulated depth of antimuon implantation for the LEGe detector run considered in the text. Notice scale.