1. presented by Steve Kliewer Muon Lifetime Experiment: A Model

2. Experimental design Parameters affecting expected count rate Source of muons Detection of muons and electrons (detector efficiency) Capture of low energy muons Decay of muons into electron Loss of electrons in cavity Expected frequency of timed muon decay. Overview

3. To better understand the processes involved in muon capture, decay, and detection so that we can better predict the effects of changes in geometry and cavity medium. Purpose

4. The Muon Lifetime Experiment Design 80 cm 20 cm A muon enters thru A and is trapped in the cavity. After a time it decays and an electron exits thru A, B, C or D. A frequency graph of counts vs decay time is analyzed Muons, no matter how old they may already be, decay exponentially. N = N 0 e -t/  dN/dt = -N /   = -N / dN/dt This is the Muon Lifetime

5. The Muon Lifetime Experiment Continued 80 cm 20 cm The cavity is filled with phone books:  = Density = 0.64 g/ cm 3 V = Volume = 32000 cm 3 A = Top Surface area = 1600 cm 2 Timing starts when count: A and not( B or C or D) Timing stops when count: A xor B xor C xor D or timeout

6. N D = N  * f 1 * f 2 * f 3 N D = frequency of timed muon decay (counts/s) N  = Frequency of incoming, trappable muons f 1 = Fraction of incoming muons that are detected (detector efficiency) f 2 = Probability that a decay electron will escape f 3 = Fraction of escaping electrons that are detected Expected Count Rate

7. Primary Cosmic Rays are particles accelerated by astrophysical sources: e.g. AGN, supernovae, solar flares Mostly made up of protons (some electrons and helium, C, O, & Fe nuclei) Energies from a few GeV to more than 100 TeV They are charged particles and therefore are affected by magnetic fields both interstellar as well as Earth’s. Cosmic Rays in Space

8. Cosmic Ray interactions

9. Cosmic Rays Particles ParticleMass  = mean lifePrimary decay SymMeV/c 2 s pProton938> 10 25 n/a  ± Pion, charged1402.6 x 10 -8  ±   0 Pion, neutral1358 x 10 -17 2  K ± Kaon, charged4941.2 x 10 -8  ±  K 0 Kaon, neutral49810 -10  +  -, 2  0 EElectron0.51>10 24 n/a  Muon105.72.2 x 10 -6 e ±  e  e Neutrino, Elec 10 25 n/a  Neutrino, muon 10 6 s?

10. Primary Cosmic particles interact with our atmosphere via strong force, bremstrahlung, Cerenkov radiation, as well as ionization Strong Interactions produce kaons & pions These particles decay almost immediately into , , e, , &  rays interact by electron-positron pair production  particles decay very quickly to  & e. electrons are quickly stopped by the dense atmosphere Most  are produced at 15km altitude, They lose about 2 GeV to ionization and arrive at the surface with a mean energy of about 4 GeV. Cosmic Rays in Our Atmosphere

11. From the Review of Particle Physics: Mean energy is ≈ 4 GeV Energy spectrum (dN/dE) is flat below ≈ 1 GeV Low energy muons (E < ≈ 1 GeV) are mostly vertical. (Solid angle ≈ 1 sr) Cosmic Rays at Sea-Level

12. Muon Energy Spectrum Derived from Fig. 20.4 of Particle Data Review dN/dE = 0.004 µ/(GeV cm 2 s sr) For energies up to 1 GeV

13. Muon Trapping Muons will be trapped in the paper-filled, 30 cm deep cavity if they have energies: 0 < E µ < 50 MeV  E µ = 50 MeV  E ≈ 1.21 * R + 11 dE/dx ≈ 1.2 MeV/cm Based on: pdg.lbl.gov  = 0.64 g/cm 3

14. Incoming Muon Rate The expected rate of trapped muons is: N  = dN/dE *  E * A * S dN/dE = count rate per GeV per cm 2 per steradian  E = Range of muon energies trapped A = Area of top of detector S = Solid angle of incoming muon directions that are included N  = 0.004 (1/GeV cm 2 s sr) * 0.05 GeV * 1600 cm 2 * 1 sr N  = 0.32 muons/s = 19 muons / min

15. The passage of muons is detected using a plastic scintillator (polyvinyl toluene) 1.dE/dx ≈ 2 MeV/cm 2.Refractive index = 1.58 3.Max emission = 425 nm 4.Pulse width = 2.5 ns The PM tube and electronics detect the pulse with an efficiency, f 1, which is determined experimentally: f 1 ≈ 0.9 ≈ f 3 Detection: scintillator & PM

16. µ→ e +  e +  Rest masses: m µ = 106 MeV/c 2 M e = 0.5 MeV/c 2 M e = 3 eV/c 2 M  = 0.19 MeV/c 2 105 MeV of kinetic energy will be randomly partitioned between the resultant three particles. Decay

17. E 2 = m 2 + p 2 (c = 1) As long as m << E then E ≈ p Momentum and energy must be conserved. The momentum (energy) of the electron can be, at most, ½ (i.e. 52 MeV) of the available momentum. Electron energies

18. Electron Range  E ≈ 1.9 * R - 5.9 dE/dx = 1.9 Mev/cm Based on: pdg.lbl.gov  = 0.64 g/cm 3 The average distance to escape the cavity is 12 cm. Therefore, We will assume that Electrons will be trapped in the paper filled cavity if they have energies: 0 < E e < 14 MeV  E e = 14 MeV

19. Electron Energy Spectrum Electrons with energies up to 14 out of 52 MeV ( =.26) will be lost. The fraction of electrons that will escape the cavity, f 2 ≈.8

20. N D = N  * f 1 * f 2 * f 3 N D = frequency of timed muon decay (counts/s) N  = Frequency of incoming, trappable muons = dN/dE *  E  * A * S A = W * L  E  ≈ 1.21 * H + 11 f 1 = Fraction of incoming muons that are detected (detector efficiency) f 2 = Probability that a decay electron will escape ≈  E e / 52 MeV ≈ 1 - (1.9 * R - 5.9) / 52 f 3 = Fraction of escaping electrons that are detected N D = 0.32 muons/s * 0.9 * 0.8 * 0.9 N D = 0.2 decays/s = 12 decays/min Expected Count Rate

21. We should expect a count rate of decay electrons from trapped muons of about 10 per minute Conclusion