Atmospheric Muon Lifetime, Standard Model of Particles and the Lead Stopping Power for Muons

1. Atmospheric Muon Lifetime, Standard Model of Particles and the Lead Stopping Power for Muons Cioli Barazandeh, Angel Gutarra-leon and Walerian Majewski Mentor: WalerianMajewski, Department of Physics Northern Virginia Community College, Annandale, VA

2. Experiments • Hello, and welcome to my Presentation! • Today, I will be speaking about experiments in the lab of the NVCC chapter of the Society of Physics Students! • Specifically, about the Muon one! • There are two iterations: The present iteration and the altered future iteration!

3. Experiment 1-Muon Monitoring • The purpose of this project was to demonstrate that it is possible to perform experiments with subatomic particles in an undergraduate laboratory of a community college, using a simple muon detector. • Our group performed some introductory experiments to test the performance and experimental options presented by our muon detector.

4. Some of the goals addressed by Experiment 1-Muon Monitoring • MeanLifetime(inmaterial and in vacuum) • Average Flux Intensity • Dayvs. NightFlux • TimeDilation (based on literature data about flux increase with altitude) • AverageMuon Speed • Average kinetic energy • Standard model applications

5. The Primary Apparatus • Threecomponents: • Plastic Scintillator • “Mr.Muon:”power supply,controlbox • Analog to digital converter card in computer

6. Additions: Lead shielding New measurements with added lead shielding

7. Rationale • We want to count in our detector the total flux of all passing cosmic charged particles, including muons of both charge signs with average energies of around 4 GeV. • Separately, we will count the flux of low-energy (<160 MeV) muons which are stopped in our detector and are identified by their decay to electron (and two escaping neutrinos) • By adding then an increasing number of layers of lead above the detector, we will find the attenuation of both low-energy muon flux, and of the flux of any-energy unidentified cosmic particles.

8. Objectives of New Series of Experiments • Free muon’s mean lifetime τ0 • Flux of muons in air at sea level: ф = dN/dAdt integrated over directions • Average muon stopping power (energy loss per unit distance) in lead: dE/dl • Standard Model (SM) applications: using τ and some experimental masses, we should be able to calculate the weak force coupling constant gw, the elementary electric charge e and the vacuum expectation value of the Higgs field v

9. Plan • We will collect the statistics of our muon decay events, providing us with its lifetime τ and the energy spectra of incoming muons and their decay electrons. • The measurements of muon flux ф = dN/dAdt will be done without and with an increasing number of the lead plates covering the detector. • We plan to use up to four lead stacked plates 12”x12”x1/2”. • We will build the supporting structure for lead plates to be positioned above our detector, reaching the final lead thickness of about 5 cm.

10. Electron and Muon Energy Spectra and Example Graph for Electrons Each time a cosmic ray particle hits the detector, it releases energy. The detector then reports the energy of the particle, as well as the energy – in case of the stopped muons - of the emitted electron (in arbitrary units), tallying these events afterwards. We will graph the cosmic ray energy of unspecified particles passing through our detector, as well as the energy of stopped muons, with which they enter the detector, and of decay electrons, accounting for the errors in our readings.

11. Muon Stopping Power dE/dx = ρdE/dl in Plastic Scintillator With β = v/c, γ = (1-β2)-1/2, p-momentum, E- kinetic energy, for our muons: • p=γmv=βγmc⇒βγ=p/mc~E/106MeV~1, β~1/√2=0.70 →μ is relativistic, and so it is a minimally ionizing particle, MIP • For MIP in plastic: dE/dx~2MeVcm2/g⇒ dE/dl =ρdE/dx • With ρ~1g/cm3 for plastic scintillator • ⇒ dE/dl= 1g/cm3 ×2MeVcm2/g = 2MeV/cm  After we multiply this by the height of our detector, of 80 cm, we obtain 160 MeV as the maximal kinetic energy of our muons stopped in the detector

12. Muon Absorption– In Lead! • The lead should stop ~ 20% of the low-energy muons from reaching the scintillator. The scintillator will be able to identify only muons with kinetic energies below 160 MeV, which make about 1% of all muons at sea level, of average energy of 2-4 GeV

13. Expected Fluxφ(l): From the estimated Emaxand estimated (from this extrapolated graph) range L of the most energetic stoppable in detector muons, we can find dφ/dl = Emax/L

14. Stopping of Muons in Lead • From our graph of muon flux ф(l), l being the thickness of the layer of lead covering the detector, we can find L= ф0/(dф/dl) as the range until stopped of our most energetic muons at Emax . Then we will receive • dE/dl = Emax/L = Emax (dф/dl)/ф0 . • We will compare this with the accepted value of muon’s rate of energy loss in lead at minimal ionization: for lead with its dE/dx = 1.22 MeVcm2/g and density ρ = 11.350 g/cm3 we expect to have dE/dl = ρdE/dx = 11.350 x 1.122 MeV/cm = 12.73 MeV/cm.

15. Project Significance • Our muon experiment is very distinct from most other experiments which rely on two scintillation counters working in coincidence, to identify passing muons. We with our single detector will identify stopped muons by their unique decay signature. • We want to demonstrate that the first- and second-year students at community colleges can be doing experiments at the most fundamental level. Using high-energy cosmic ray particles available freely at the college physics lab, we can experiment with four of the 12 elementary particles of nature: muon, electron, muonic neutrino and electronic neutrino (the last ones both escaping undetected).

16. Expected results and analysis • Muon Stopping Power in Lead = - dE/dx = – dE/ρdl, ρ is Pb density, l is the length traversed in lead plate, x=ρl. We will be looking for dE/dl = energy lost by muon on one cm depth in lead. • From our graph of muon flux ф(l), we can find L= ф0/(dф/dl) as the range until stopped of our most energetic muons at Emax . Then we will receive mean dE/dl = Emax/L = Emax (dф/dl)/ф0 . • We will compare this with the accepted value of muon’s rate of energy loss in lead of 12.73 MeV/cm at minimal ionization, which result should apply to our relativistic muons. • Our experimental muon lifetime τ will be compared with the accepted value of 2.197 μs, our calculated (from our τ) gW = 8(3π3ĥ/2τmµc2)1/4(MW/mμ) with accepted gw= 0.653, our calculated e=gwsinϑ√ħcε0 with the textbook value of 1.6x10-19 C, and our calculated v = 2MWc2/gw√ℏc= (2τmμc2/3π3ℏ)1/4 (mµc2/4√ℏc) with accepted v=236 GeV/√ĥc. A tolerable agreement to within several percent will confirm the accessibility of high-energy physics experiments to early undergraduate students.

17. Practical applications of such research • Archeology • Corrections to Neutrino Flux Estimates • Detecting Smuggled Nuclear Weapons in Cargo • Nuclear Fuel Detection at Nuclear Disaster Sites • Calibrating Equipment at Particle Accelerators

18. Archeology • Used to unearth buried ruins by painting a picture of the interior with different energy muons.

19. Corrections • Muons are already relatively well known • The actual values could be used via the connections to neutrinos to make corrections to ensure degrees of certainty of unknown values

20. Nuclear Weapons • Muon detectors can be laid out underneath a road in order to detect extra scattering, which comes from extra shielding often used to hide nuclear weapons. This can allow police to catch these people before the bombs are set off.

21. Fuel • This would be done similarly to above, except possibly with a more portable solution, such as a form of cart.

22. Calibration • Muons as a known value can be used to calibrate equipment in high-energy accelerators.

23. Acknowledgements • We would like to thank the Society of Physics Students and the NVCC Educational Foundation for their generous support, and the Thomas Jefferson National Accelerator Facility in Newport News, VA for the donation of our scintillator. • Finally, we would like to thank Dr. Walerian Majewski for his encouragement, guidance, and tireless dedication to teaching.

24. Citations • NIST Physical Measurement Laboratory. n.d. http://www.physics.nist.gov (accessed 2015) • Reitner R A, Romanowski T A, Sutton R B and Chidley B G 1960 Precise measurements of the mean lives of µ + and µ - mesons in carbon. Physical Review Letters5.1 22-3 • Ye J and Coan T E n.d.Muon Physics (Report of Rutgers University) • Pierce M and Tekniska K April 2003 Measuring the Lifetime of Cosmic Ray Muons (Report, Section of Experimental Particle Physics) • L3 Collaboration et al 2004 Measurement of the atmospheric muon spectrum from 20 to 3000 GeV Physics Letters B598 1-2; 15-32 • Schwartz M D 2014 Quantum Field Theory and the Standard Model. (Cambridge: Cambridge University Press) • Giffith D 2008 Introduction to Elementary Particles. (Verlag: Wiley-VCH) • Quigg C 2013 Gauge Theories of the Strong, Weak and Electromagnetic Interactions. (Princeton: Princeton University Press)

25. Obligatory Recruitment Message • We are a very small lab-focused SPS community who will present posters and research at conferences around the general Metropolitan Washington area. • So please, help us in our goal to advance early physics research of freshman-sophomore students!

26. Below! Dictionary of terms

27. Basic Interactions

28. Dictionary Slide 2

29. Bosons • Bosons are effectively the guards and police of the universe. • Includes photon, W-, W+ and Z0 (electroweak), and gluons (strong). • Are not normally affected by the forces that they mediate (but can be in the case of gluons) • Can include the Higgs Boson.

30. Fermions • Basic stuff: Includes quarks from before and Leptons • Reiterate: Quarks are up, down, charm, strange, top, bottom • Leptons are electron neutrino, electron, muon neutrino, muon, tau neutrino, tau. • All half spins of ½+ integer n

31. Leptons • The cow goes Mu! • Include muons as 2nd gen. • All include neutrinos as secondary, “massless” particles which help to fulfill the standard model.

32. Gluons • Primordial Elmer’s glue of quarks and strong interactions, they carry energy and charge between these particles and are noted for holding the atom together.

33. Antimatter • It exists. • This does not come up often, but a certain amount of antimatter is necessary in certain particles (especially in the regulator mesons) which allows it to be used and / or synthesized practically and (sort of) predictably by the standard model.

34. Mesons • Sort of the “anti-basic” particle of the group, mesons are often composed of one matter quark and one antimatter quark of varying types. There are about 140 of them, and are somewhat related to bosons, as protons and neutrons are related to fermions.