Measuring the Muon Lifetime

Transcription

1 WJP, PHY38 (200) Wabash Journal of Physics v4.0, p. Measuring the Muon Lifetime L.W. Lupinski, R. Paudel, and M.J. Madsen Department of Physics, Wabash College, Crawfordsville, IN (Dated: March, 200) In this experiment we are using the light gathered from the entry of the muon in a scintillator bar and its decay to measure the lifetime of the muon. We found the muon lifetime to be 2.4 ±. µs (95%CI), which does not agree with the accepted value of ± µ (95%CI) [7]. The disagreement between these values is likely due to the relatively small amount of data we collected. In order to aid future investigation of the muon velocity we include a circuit diagram for generating nanosecond light pulses. Muons are the elementary particles belonging to the lepton family in the Standard Model of particle physics. Leptons appear to be pointlike, that is, with no apparant internal structure, and seem to be truly elementary [] There are six leptons: electron, muon, tau and three flavored neutrinos for each of them. The properties of each of the particles in the lepton family are listed in Table [2]. Particle Symbol Anti- Mass Mean Main Decay Name Particle (MeV/c 2 Lifetime (s) Modes Electron e e Stable e Neutrino ν e ν e <3 0 6 Muon µ µ e ν e ν µ µ-neutrino ν µ ν µ <0.9 Tau τ τ µ ν µ ν τ, e ν e ν-neutrino ν τ ν τ TABLE I: The properties of the lepton family in the Standard Model of particle physics. Muons are created when cosmic rays enter the earth s atmosphere. Most muons are produced at about 5 km above sea level, therefore, traveling at about the speed of light, they take roughly 50 microseconds to reach sea level. The lifetime of a muon is about

2 WJP, PHY38 (200) Wabash Journal of Physics v4.0, p.2 2 microseconds, however since the muons are moving close to the the speed of light the muon, the trip to sea level takes about 52 ns in the muons reference frame as a result of relativistic time dilation[3]. However when the muon enters a scintillator it has a small chance of colliding with the molecules of the scintillator, causing the muon to come to a stop. Once the muon stops it then decays. When a muon decays it splits into a muonneutrino, an electron and an anti-electron-neutrino. Both the muon entering the scintillator and the expelled electron interact with the scintillator s molecules to emit light, this process is illistrated in Figure. Our mathematical model for muon decay is N(t) = N 0 e t/τ, () where N is the number of muons at timet, N 0 is the initial number of muons, and τ is the muon lifetime. Solving for lnn we find, lnn = t τ + C, (2) where N is the number to muons, t is time, τ is lifetime, and C is a constant whose value depends on the number of initial muons. a) γ b) c) d) γ ν μ μ - μ - W e - ν e FIG. : a) The muons enter the scintillator causing photons to be emitted. b) In a small number of cases the muon collides with a molecule in the scintillator causing the muon to stop. c) The muon then decays in the scintillator, splitting into an anti-muon neutrino, an anti-electron neutrino and an electron. d) The emitted electron also causes photons to be emitted in the scintillator. In previous years groups at Wabash College have obtained muon lifetimes of 2.26 ±.2 µs [4], µs [5], and ±.024 µs [6]. Our setup for measuring the time between light pulses consists of a PMT connected to a scintillator, which is wrapped in black electrical tape in order to reduce the likelihood of background photons entering the scintillator. When a muon enters the scintillator it emits

3 WJP, PHY38 (200) Wabash Journal of Physics v4.0, p.3 photons which are detected and amplified by the PMT; the muon then decays creating another light pulse several microseconds after the first. The signal proceeds to a Discriminator set to level trigger mode. The Discriminator cleans up the pulses, reduces the background noise and generates a NIMS pulsed based on a trigger level of 0.9V. The discriminator also splits the signal which is sent through a short cable, and a long delay cable, creating two signals. The signals progress from the Discriminator to the Time to Amplitude Converter which converts the delay between decay signals into a voltage difference, this process is illustrated by Figure 2. The output from the TAC is binned by a Multi-Channel Analyzer (MCA). We used a gate generator to make a signals of known length, which were also calibrated using an oscilloscope, which we used to calibrate the MCA s bin number to a given pulse length. Stop Enter Discriminator Decay Start (Delay Line) TAC MCA Δt ΔV Bin # FIG. 2: The fast and delayed signals from the discriminator enter the TAC. The TAC then converts the time between pulses into a voltage signal which the MCA puts into a bin number and is sent to the computer to be analyzed. We took four sets of muon decay data for 2 hours each giving a total of about 700 valid muon decay events. After converting from bin number to µs, we fit the lnn vs. t to a weighted linear fit giving a slope of 2.4 ±. µs (95%CI), which does not agree with the accepted value of ± µ (95%CI) [7]. A histogram of these decay events is shown in figure 3. The error on the data is given by the statistical N, where N is number of counts at a given time. In order to obtain a better value of the muon lifetime we would need to collect data for a longer period of time. In the future this research line could measure muon velocity, using two PMTs. In order to calibrate the PMTs for a nano second time scale we constructed an electronic board to generate a pulse of about 0 ns of LED light. We use a combination of NOT and AND gate to generate the pulse. The pulse is then sent to an LED driver which consists of a 440 transistor as shown in Figure 5.

4 WJP, PHY38 (200) Wabash Journal of Physics v4.0, p.4 00 Counts Time μs FIG. 3: A histogram of valid muon decay events measured. A weighted linear fit to the logarithmic data yields a muon lifetime of 2.4 ±. µs (95%CI). A 2 V B A 0 B LED ohms pulse width (0 ns) FIG. 4: The circuit diagram shows a nano-second pulse generator connected to an LED driver. On the bottom-left is the signal at position A and position B. We use the response time of the NOT gate which is about 0 ns as the pulse width. [] Thornton, Stephen T. ; Rex, Andrew, Modern Physics for Scientists and Engineers Third Edition, Thomson Books, 2006.

5 WJP, PHY38 (200) Wabash Journal of Physics v4.0, p.5 [2] C. Amsler et al. (Particle Data Group), Physics Letters B667, (2008) and 2009 partial update for the 200 edition [3] The Speed and Decay of Cosmic-Ray Muons: Experiments in Relativistic Kinematics- The Universal Speed Limit and Time Dilalation, MIT Department of Physics (2007). [4] Haris Amin, Measuring Cosmic-Ray Muon Lifetime, Wabash Journal of Physics 2007 [5] A. L. Fritsch, T. F. Pizarek, Wabash Journal of Physics 2008 [6] D. R. Brown, S.R. Krutz, M.J. Milliman, Wabash Journal of Physics 2009 [7] D.B. Chitwood, Phys. Rev. Lett. 99, (2007)