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Atmospheric Muon Lifetime, Standard
Model of Particles and the Lead
Stopping Power for Muons
CIOLI BARAZANDEH, ANGEL GUTARRA-LEON AND WALERIAN MAJEWSKI
MENTOR: WALERIAN MAJEWSKI, DEPARTMENT OF PHYSICS
NORTHERN VIRGINIA COMMUNITY COLLEGE, ANNANDALE, VA
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!
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.
Some of the goals addressed by
Experiment 1-Muon Monitoring

Mean Lifetime (in material and in vacuum)

Average Flux Intensity

Day vs. Night Flux
Time Dilation (based on literature data about flux increase with
altitude)

 Average Muon Speed


Average kinetic energy
Standard model applications
The Primary Apparatus

Three components:
Plastic Scintillator
 “Mr. Muon:” power supply, control box
 Analog to digital converter card in computer

Additions: Lead
shielding
New measurements with
added lead shielding
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 lowenergy (<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.
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
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.
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.
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
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
Expected Flux
φ(l):
From the estimated Emax and
estimated (from this
extrapolated graph) range L
of the most energetic
stoppable in detector muons,
we can find dφ/dl = Emax/L
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.
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).
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.
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
Archeology

Used to unearth buried ruins by painting a picture of the interior with
different energy muons.
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
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.
Fuel

This would be done similarly to above, except possibly with a more
portable solution, such as a form of cart.
Calibration

Muons as a known value can be used to calibrate equipment in highenergy accelerators.
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.
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 Letters 5.1 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 B 598 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)
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!
Dictionary of
terms
BELOW!
Basic Interactions
Dictionary Slide 2
The four fundamental forces of nature
Weak
Property/Interaction
Electromagnetic
Gravitation
(Electroweak)
Acts on:
Particles
experiencing:
Particles mediating:
Strong
Fundamental
Residual
Mass - Energy
Flavor
Electric charge
Color charge
Atomic nuclei
All
Quarks, leptons
Electrically charged
Quarks, Gluons
Hadrons
W+ W− Z0
γ
Gluons
Mesons
Graviton (theoretical)
Strength in the scale
of quarks:
10−41
10−4
1
60
Not applicable
to quarks
Strength in the scale
of
protons/neutrons:
10−36
10−7
1
Not applicable
to hadrons
20
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.
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
Leptons

The cow goes Mu!

Include muons as 2nd gen.

All include neutrinos as secondary, “massless” particles which help to fulfill
the standard model.
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.
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.
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.