Rice University Physics 332 LIFETIME OF THE MUON I. INTRODUCTION...2! II. MEASUREMENT PROCEDURES...3! III. ANALYSIS PROCEDURES...7!

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1 Rice University Physics 332 LIFETIME OF THE MUON I. INTRODUCTION...2! II. MEAUREMENT PROCEDURE...3! III. ANALYI PROCEDURE...7! Revised July 2011

2 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 10 2 m -2 s -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 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. 2

3 II. Measurement procedures Figure 1 shows the counter geometry for the experiment. A cylinder of scintillator,, serves as a stopping target for µ ±. Paddles of scintillator, and, surround. Appropriate photomultipliers, not shown in the figure, detect events in the various counters. The signature of a stopped cosmic ray in is, assuming is above and that most cosmic rays come from above. When the stopped µ ± decays, the e ± will almost certainly stop within, so the signal of a decay is. 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, into coincidence with, using a calibrated TAC; 3. Wire and verify the start/stop logic; 4. et up the TAC/PHA system for run conditions; 5. Accumulate events for 2-3 days; 6. Recalibrate TAC/PHA to check for drifts. Fig. 1 End view of counter geometry for lifetime measurement. Delay Discriminator A B V A B C 2/2 3/3 NEG IN DLY'D MARK Gate/Delay TART CONV. TOP TAC To PHA Fig. 2 Overall logic diagram for the experiment. 3

4 TART 30 ns CONV. TOP To PHA Delay TAC Discriminator Fig. 3 Electronics configuration for measuring arrival time relative to. Each of these procedures is detailed below. More information on NIM module operation is given in the PHY 331 Topical notes, while PHA operation is explained in the UC30 manual. 1. et one HV supply to negative polarity and connect cables from the front and rear to and. et the other HV supply to positive polarity and connect to. Turn on the HV and set to V for, and V for. 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 or occurs simultaneously with an event in the electrical pulse from will arrive after the pulse from or, as sketched in Fig. 4. To obtain a proper veto, we must delay the, pulses so that the pulse completely overlaps the pulse at the coincidence circuit. To do this, connect the discriminator outputs for and to the TART/TOP inputs of the TAC, using cables of the same length. et the TAC for 7V full range output, 50ns time scale, and P 30 ns 30 ns lag no added delay correct delay on P Fig. 4. Timing diagram for PMT pulses 4

5 Table I. Typical Parameters High voltage:, = V = Thresholds:,, = 30 mv Count Rates:, = 1900/100 s = 2200/100 s = 90/100 s (straight-through particles) = 200/100 s (stopping µ ±, TART) = 1800/100 s (decay µ ±, TOP) Good event rate to PHA! 1/minute. connect the low-impedance output to the UC 30 input. tart the UC 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 pulse within the pulse. It should be about 30 ns of delay. The same setting should work for, since the counters and cables are identical, but you could repeat the test with 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 listed in Table I, setting the logic modules as required. Fig. 5 shows how to use the positive-input counter with fast negative NIM pulses. If there are significant discrepancies, say more than a factor of two, you should check with the instructor. When the rates are satisfactory set the logic modules to the data-taking configuration shown in Fig. 2. Be sure to record the count rates for later reference. fast NIM NEG. IN GATE PO. DEL OUT INPUT INT. Gate/Delay Counter Timer Fig. 5 Operating the visual counter from a NIM pulse. 5

6 4. We next set up and calibrate the TAC/PHA system for accumulating decay data. et the TAC for 7 V output and 10 µs full scale range. The gate/delay generator adds about 0.5 µs delay to the stop signal, so that small intervals do not fall into the non-linear portion of the TAC response. The actual setting is not critical so just set the pot to half-scale on the 1.1 µs range. To calibrate the time scale, connect the TART and TOP outputs of the time calibrator to the TAC in place of the outputs of the logic gates. (The calibrator stop signal should go through the gate/delay module just like the real signal.) Obtain a time calibration spectrum and perform a linear fit to the peak channel numbers vs time. 5. If the time calibration is satisfactory, replace the calibrator signals with the outputs of the logic gates. tart the acquisition and check that events with significant delay appear at about 1/minute. There will be a much higher rate of events near t = 0 due to inefficient vetoing, but these are not real decays. At least 48 hours of running will be needed to accumulate 2-3 thousand events to define the decay curve. It is prudent to save the accumulated data to a file once or twice a day, so that you do not lose everything to a power or equipment failure. To do this, halt the acquisition and save the data as a tab separated variable (TV) file. Continue the acquisition without erasing the memory. hould there be some sort of failure, you may be able to use the last saved file. 6. At the completion of the run save the final data set as a tab separated variable (TV) file for later analysis. Calibrate the TAC and measure the various rates again to check for any slow drifts in the apparatus. If all seems in order, proceed to the analysis. 6

7 III. Analysis procedures The data analysis consists of converting the channel number to time, and then fitting an exponential plus background to the counts vs time graph. A calculation of! 2 will serve to validate the fit. The decay time, with uncertainty, is the only fit parameter of physical significance. The following general comments may assist the use of the software you choose. A text editor will allow you to examine the TV file to separate extraneous headers and labels from actual data. Many analysis packages can read numerical data directly from a TV file, or you can use cut/paste to transfer the needed columns. As mentioned, early channels will be contaminated by instrumental artifacts. Fit only the clearly exponential portion of the decay. The raw histogram is spread over far too many bins, most of which will have very few counts. Adjacent bins should be combined to get data points across the valid decay spectrum. 7