Speaker
Description
The Muon $g-2$ experiment at Fermilab has measured the anomalous magnetic moment of the muon ($a_{\mu} \equiv (g_{\mu} -2)/2$) to a precision of 127 parts-per-billion. During the experiment, `fills' of $\mathcal{O}\left( 10^5 \right)$ $3.1\,\text{GeV}/\text{c}$ muons were injected into the $g-2$ storage ring, of which $\approx 5{\small,}000$ muons were stored and decay over the course of $700\,\mu\text{s}$. These stored muons decay into positrons which spiral inward and impact a series of PbF$_2$ crystal calorimeters read out by silicon photomultipliers (SiPMs) positioned around the inner radius of the storage ring. Over the course of each fill, calorimeter gain stability at the $5 \times 10^{-4}$ level was required to meet our systematics goals even as the instantaneous rate of positrons changed by 5 orders of magnitude. The gain of the calorimeter was monitored by a dedicated laser system, which corrected for the effect of the large flash of particles at injection and pulse-pair SiPM pixel effects with recovery on the $\mathcal{O}(15\,\text{ns})$ timescale. After the conclusion of the final running period, a series of tests were conducted at the University of Washington to resolve an observed residual gain-like effect after these corrections were applied. Here we describe these measurements, the discovery of the cause of the gain change --- the cumulative perturbations the positrons themselves have on the detector gains long after injection, each on the $\mathcal{O}(4-8\,\mu\text{s})$ timescale and with a relative amplitude of $\leq 10^{-4}$ --- and the application of the correction in the final publication.
