Overview

Current knowledge of the muon lifetime is summarized in table  1 and is plotted in figure 1. All the experiments included in the PDG average were finished more than a decade ago. The essential features of the experiments are very similar and the approach was kept quite simple. Positive muons are brought to rest in a target (either one at a time or in a small bunch), and decay within a few microseconds. The two neutrinos escape unobserved but the decay positron is seen by a detector system which surrounds the stopping target; the time of the positron detection is registered by a TDC.

Naturally, beam stopping and detection techniques varied among the experiments listed in the table but several systematic issues were common to all. A residual polarization in the stopped muons presents a very serious potential problem. Muon precession can change with time the angular distribution of decay positrons. Any non-uniformities in the detector system will then lead to a direct timing error. Various techniques have been employed to account for the this potentially serious problem.

Another systematic issue, particularly for higher-rate experiments, is pileup, when two decay positrons enter the same detector element within a short period of time and are registered as one. Because the probability for this to occur is larger at the beginning of the measuring interval compared to at the end, it is a potentially serious source of systematic error. The effect of pileup can be mitigated by increasing detector segmentation, limiting the instantaneous rate, keeping phototube signals short and improving the time resolution of the readout electronics.

A critical feature of any lifetime determination is the demonstration that the timing measurement is stable from early-to-late times. Changes in the timing system because of gain shifts in detectors, time-dependent backgrounds, threshold shifts and so on must be evaluated carefully.

These and other experimental issues will be discussed in the sections which follow. However, it should be pointed out that all of the measurements listed in the table were limited by their statistical errors. The total number of events in the measurements listed below was about 4  x  10⁹. We plan to obtain several hundred times more data in order to reduce the uncertainty on $\tau_{\mu}$ to the 1 ppm level. Moreover, the systematic error of the most precise previous measurement was several times larger than that we hope to achieve. The challenges of our experiment will be to detect decay positrons at a rate which exceeds that of previous experiments by more than an order of magnitude and to address systematic errors which they could safely estimate or ignore.

Table 1: Previous Measurements of the Muon Lifetime

Measured Lifetime	$\mu^{\pm}$     Reference	Year
$\mu$s
$2.197\ 078 \pm 0.000\ 073$	+     Bardin[14]	1984
$2.197\ 025 \pm 0.000\ 155$	-     Bardin[14]	1984
$2.196\ 95 \pm 0.000\ 06$	+     Giovanetti[13]	1984
$2.197\ 11 \pm 0.000\ 08$	+     Balandin[12]	1974
$2.197\ 3 \pm 0.000\ 3$	+     Duclos[15]	1973
$2.197\ 03 \pm 0.000\ 04$	PDG Average[16]

Figure 1: Previous measurements of $\tau _{\mu ^+}$ compared to the present Particle Data Group average (gray band). See table 1 for references.

We propose to measure the positive muon lifetime to a precision of 1 part in 10⁶, i.e., to an absolute level of 2 picoseconds. In order to achieve a statistical precision of 1 ppm, approximately 10¹² muon decays have to be observed. If each decay is measured individually in sequence, then an average beam intensity of no more than 50 kHz can be used safely in order to ensure an uncontaminated measuring interval for each decay. While this method suffers no pile-up effects, its extension to 10¹² events requires several thousand hours of beam-on time. Alternatively, pulsed muon beams (the ``radioactive source'' mode) permits faster accumulation of events at the price of considerable additional experimental complexity. Here a burst of muons arrives during an interval short compared to the muon lifetime and is followed by a measuring period of multiple muon lifetime duration. A highly segmented detector is used to record the decay positron arrival times. An ideal cycle repeats at nearly 50 kHz with a minimum number of muon decays in each cycle. Unfortunately, no machine operates with such high frequencies.

For example, the Rutherford Appleton Laboratory Muon Facility has a time structure of 50 Hz. Still a new muon lifetime experiment with a goal of 3 ppm on $\tau_{\mu}$ is proposed [10] there in which 2  x  10⁴ muons per cycle are deposited in a target which is surrounded by a wire-chamber detector with more than 20,000 channels. The pileup issues are very serious and the demonstration that each timing channel is stable from early-to-late times following muon injection is staggering.

The FAST Collaboration has suggested [11] a novel approach to a high-precision muon lifetime measurement in a DC beam. Multiple asynchronous events are handled simultaneously in a device which serves as both the stopping target and as a highly segmented positron tracker. Currently existing DC beams can be used because the arrival and measuring times for each of the following normal sequences can overlap. Individual events consist of 1) a $\pi^+$ stoping inside the detector; 2) the $\pi^+$ decays to $\mu^{+}$ and the $\mu$ is observed because of its particularly large signal in the active detector/target; 3) the $\mu^{+}$ decays to $e^{+}\nu\bar{\nu}$ and the e⁺ track is observed. There are numerous challenges in this approach including the intrinsically asymmetric detector, the complexity of understanding pileup issues with overlapping track patterns, and the difficulty in establishing timing and gain calibration for each detector element without recording the energy deposition.

Our group has developed a very simple experiment which approaches the ideal situation for a ``pulsed" source. A chopped beam cycle consists of an ``accumulation period'' of $T_{acc} = 1~\mu$s followed by a decay ``measuring period'' of approximately $T_{mp} = 11~\mu$s as shown in figure 2. During the accumulation period, a small number of surface muons ($\approx 15$) would be delivered into a thin depolarizing target. During the measuring period, decay positrons will be observed using a segmented, fast detector. The segmentation greatly exceeds the number of stopped muons which means that the average number of positrons striking an individual timing element per cycle is $\ll 1$. Coupled with its fast speed, and double-hit rejection capability, the normal and potentially severe problem of pileup is miminized. The readout system uses custom waveform digitizers which not only provide stable timing samples, but also give energy information. The detector gains are constantly monitored and built-in threshold stability is guaranteed. This detector and its associated electronics are described in the sections which follow.

Figure 2: Illustration of the accumulation and measuring periods. A sequence of 15 muon arrivals results in an average of 12 muons remaining at the beginning of the measuring period.

In order to realize this method, a pulsed beam must be found. Our original LOI [2] was submitted to Brookhaven because we had determined that an operational mode of the main AGS ring could be used to deliver short bunches of beam to a beamline every $8.1 \mu$s (3 times around the ring for protons), and, in tests which followed the LOI this novel mode of extraction was demonstrated. A surface muon beam line had been built at the AGS but has been dormant for many years. The channel never performed at the expected level and it has become clear that an entirely new beam line would have to be built. This hurdle, coupled with the current very difficult funding climate for particle physics at the AGS has discouraged us with respect to submitting a full proposal to Brookhaven. The cost of the new beamline and the implied costs associated with a ``dedicated mode" of pulsed operation for our experiment greatly exceed the cost of the detector and all electronics. A recent discussion at PSI for artificially introducing time structure into one of the existing, high-quality surface muon channels is a much more attractive option and represents the main reason we are approaching PSI now with this proposal. Given the DC surface muon flux exceeding 10⁷ Hz, a chopped beam with a 10% on, 90% off type structure provides an average rate of 10⁶ muons per second. At this rate, the experiment can be accomplished in a few hundred hours. Accordingly, we are very interested in the development of a kicker for one of the muon channels. It would enable several highly optimized stopped muon experiments as suggested [3] in the LOI to PSI. We believe the experiment described next is optimized for this situation.