Rice University Physics 332 LIFETIME OF THE MUON I. INTRODUCTION .....................................................................................................................................................2!II. MEASUREMENT PROCEDURES.......................................................................................................................3!III. ANALYSIS PROCEDURES .................................................................................................................................7! Revised July 20112 I. Introduction In this experiment you will measure the lifetime of an elementary particle, the muon, using instruments and techniques typical of high energy particle physics. Unlike the usual particle physics experiment, our source of muons is cosmic rays rather than an accelerator. The counting rate is therefore quite low and the experiment needs to run two to three days to obtain adequate statistics. Fortunately all that is required is patience, since the data acquisition system is designed for unattended operation. Cosmic rays have been extensively studied to learn about particle interactions and about astrophysical processes. Briefly, primary cosmic rays, consisting of energetic charged particles (one joule protons have been observed) and photons strike the upper atmosphere. Various secondary particles are produced, but only photons, !, muons, µ±, and neutrinos, ", are sufficiently long-lived and penetrating to reach sea level in significant numbers. Very approximately, the total muon flux through a horizontal surface at sea level is 1.7 x 102 m-2s-1, equally divided between positive and negative charges. The mean energy of the muons arriving at the surface is about 2 GeV, allowing the average muon to penetrate 2-3 m of concrete. Neutrinos do not interact at any reasonable rate, and photons do not decay, so the only particle decays we are likely to observe are due to muons. Essentially all free muons decay according to µ±! e±+" +" (1) with an exponential decay time of 2.197 µs in the rest frame. Negative muons can also vanish through capture by nuclei. For the low-Z nuclei in our target the effect of µ- capture is to shorten the apparent lifetime of the negative muons by about 10%. If we can stop a group of muons and note how long they take to decay, we should obtain a lifetime in reasonable agreement with the accepted value.3 II. Measurement procedures Figure 1 shows the counter geometry for the experiment. A cylinder of scintillator, S, serves as a stopping target for µ±. Paddles of scintillator, P1 and P2, surround S. Appropriate photomultipliers, not shown in the figure, detect events in the various counters. The signature of a stopped cosmic ray in S is P1• S • P2, assuming P1 is above S and that most cosmic rays come from above. When the stopped µ± decays, the e± will almost certainly stop within S, so the signal of a decay is P1• S • P2. The coincidence requirement will discriminate against non-cosmic sources of radiation, so random backgrounds from natural radioisotopes turn out not to be a problem. The required electronics is shown in Fig. 2. To acquire decay data we need to do the following: 1. Connect the scintillators to HV and verify operation; 2. Bring P1,P2 into coincidence with S, using a calibrated TAC; 3. Wire and verify the start/stop logic; 4. Set up the TAC/PHA system for run conditions; 5. Accumulate events for 2-3 days; 6. Recalibrate TAC/PHA to check for drifts. SP1P2 Fig. 1 End view of counter geometry for lifetime measurement. P1ABVABC2/23/3DiscriminatorNEGINDLY'DMARKSTARTSTOPTACCONV.Gate/DelayP1P2DelayP2SP1P1• S •P2P1• S •P2ToPHAP2 Fig. 2 Overall logic diagram for the experiment.4 Each of these procedures is detailed below. More information on NIM module operation is given in the PHYS 331 Topical notes, while PHA operation is explained in the UCS30 manual. 1. Set one HV supply to negative polarity and connect cables from the front and rear to P1 and P2. Set the other HV supply to positive polarity and connect to S. Turn on the HV and set to -1800 V for P1,P2 and +1300 V for S. Take the anode signals through the discriminators, as shown in Fig. 3, but do not connect the TAC yet. Check that the discriminator thresholds are about 30 mV (read as 300 mV at the test point). Verify that negative-going NIM pulses appear at the outputs of the discriminators, with the approximate widths shown in Fig. 3. The rates are low, so the scope display will be dim. 2. When an event in P1 or P2 occurs simultaneously with an event in S the electrical pulse from S will arrive after the pulse from P1 or P2, as sketched in Fig. 4. To obtain a proper veto, we must delay the P1, P2 pulses so that the P1 pulse completely overlaps the S pulse at the coincidence circuit. To do this, connect the discriminator outputs for P1 and S to the START/STOP inputs of the TAC, using cables of the same length. Set the TAC for 7V full range output, 50ns time scale, and P1DiscriminatorSTARTSTOPTACCONV.P1P2DelayP2SToPHA50 ns30 ns50 ns Fig. 3 Electronics configuration for measuring P1 arrival time relative to S. P50 ns30 nsSno added delay correct delay on P50 ns30 nslag Fig. 4. Timing diagram for PMT pulses5 connect the low-impedance output to the UCS 30 input. Start the UCS 30 acquisition program, and configure it for direct-in PHA mode. A conversion gain of 256 channels will give sufficient time resolution. If the time scales are set correctly, you will get a clear peak in the TAC histogram corresponding to the distribution of lag times. Note the position and width of the peak and then calibrate the TAC time scale so that you can compute the average lag time. Use this to estimate the amount of delay needed to center the S pulse within the P1 pulse. It should be about 30 ns of delay. The same setting should work for P2, since the counters and cables are identical, but you could repeat the test with P2 to be sure. 3. Connect the discriminator outputs to the inputs of the logic gates according to Fig. 2. To preserve the signal timing, all corresponding cables in the critical signal paths must be the same length. To check your work, use the counter to measure the rates at the logic outputs