11

Atmospheric Atmospheric Neutrinos, Neutrinos,

Muons, etc.Muons, etc.

Proton hits in atm Proton hits in atm Produces, Produces, , n, etc…, n, etc…

pp ee

22

Production of ParticlesProduction of Particlesby cosmics raysby cosmics rays

Primary cosmic rays:

+

+

e+

e

_

n

K

90% protons, 9% He nuclei

Air nuclei (Nitrogen & Oxygen)

33

Quantum Field Theories Quantum Field Theories included in Standard Modelincluded in Standard Model

QED=QuantumElectro Dynamics

QCD=QuantumChromo Dynamics

Electro-Weak

44

55

Models used to described general Models used to described general principlesprinciples

ClassicalClassical

MechanicsMechanics

Quantum Quantum

MechanicsMechanics

RelativisticRelativistic

MechanicsMechanics

Quantum Quantum

Field TheoryField Theory

What is missing? …What is missing? … Quantum Quantum GravityGravity

Small

Fa

st

66

Remember that in Special Remember that in Special RelativityRelativity

We have time dilation:We have time dilation:– t = t = T’ T’

We have space contraction:We have space contraction:– L = L’ / L = L’ /

Where Where = v/c and = v/c and = 1/sqrt(1 – = 1/sqrt(1 – 22) … what is ) … what is this in terms of energy, momentum & massthis in terms of energy, momentum & mass

77

Time Dilation Time Dilation t’ = tThe “clock” runs slower for an observer not in the “rest” frame

in atmosphere: Proper Lifetime= 2.2 x 10-6 s

c0.66 km decay path = c average in labaverage in lab

“ “lifetime” decay pathlifetime” decay path

.1 1.005 2.2 s 0.07 km

.5 1.15 2.5 s 0.4 km

.9 2.29 5.0 s 1.4 km

.99 7.09 16 s 4.6 km

.999 22.4 49 s 15 km

=pc/E=pc/E=E/mc=E/mc22

88

DecaysDecaysWe usually refer the decay time in the We usually refer the decay time in the particle’s rest frame as its particle’s rest frame as its proper timeproper time which which we denote we denote . .

99

Time Dilation IITime Dilation IIShort-lived particles like tau and B. Lifetime 10-12 sec c0.03 mm

time dilation gives longer path lengths

measure “second” vertex, determine “proper time” in rest frame

If measure L=1.25 mm

and v = .995c

t(proper)=L/v = .4 psL

Twin Paradox. If travel to distant planet at v~c then age less on spaceship then in “lab” frame

1010

Study of Decays (Study of Decays (AAB+C+…B+C+…) )

Decay rate Decay rate : “: “The probability per unit time that a The probability per unit time that a particle decaysparticle decays””

Lifetime Lifetime : “: “The average time it takes to decayThe average time it takes to decay” (at ” (at particle’s rest frame!)particle’s rest frame!)

Usually several decay modesUsually several decay modes

Branching ratio BRBranching ratio BR

We measure We measure tottot (or (or ) and BRs; we calculate ) and BRs; we calculate ii

1

toti

itot 1 and

toti i) modedecay (BR

t)0N(N(t)tNN -e dd

1111

as decay widthas decay widthUnstable particles have no fixed Unstable particles have no fixed mass due to the uncertainty mass due to the uncertainty principle:principle:

The Breit-Wigner shape:The Breit-Wigner shape:

We are able to measure only We are able to measure only one of one of , , of a particle of a particle( 1GeV( 1GeV-1-1 =6.582 =6.582××1010-25 -25 sec ) sec )

tm

220

2

max )2()Mm(

)2(N)m(N

MM00

NNmaxmax

0.5N0.5Nmaxmax

1212

Muon Muon decaydecay

± e± + + Cosmic ray muon stopping

in a cloud chamber anddecaying to an electron

decay electron track

Muon lifetime at rest: = . x - s . sMuon decay mean free path in flight:

c

cm

p

m

p

c-decay

2/v1

v

muons can reach the Earth surface after a path 10 km because the decay mean free path is stretched by the relativistic time expansion

p : muon momentum

c . km

Muon spin = ½

Decay electron momentum distribution

1313

Lepton Number ConservationLepton Number Conservation Electron, Muon and Tau Lepton Number

LeptonLepton Conserved Conserved QuantityQuantity

Lepton Lepton NumberNumber

ee--

LLee

+1+1

ee +1+1

LL

+1+1

+1+1

LL

+1+1

+1+1

Anti-Anti-LeptonLepton

Conserved Conserved QuantityQuantity

Lepton Lepton NumberNumber

ee++

LLee

-1-1

ee -1-1

LL

-1-1

-1-1

LL

-1-1

-1-1

We find that Le , L and L are each conserved quantities

1414

Basic principles of particle detectionBasic principles of particle detectionPassage of charged particles through matterInteraction with atomic electrons ionization

(neutral atom ion+ + free electron)excitation of atomic energy levels(de-excitation photon emission)

Ionization + excitation of atomic energy levels energy loss

proportional to (electric charge) of incident particle

Mean energy loss rate – dE dx

for a given material, function only of incident particle velocity

typical value at minimum:

dE dx = – MeV (g cm)

What causes this shape?

Momentum

pK

e

1515

Many detectors based on Many detectors based on IonizationIonization

Charged particlesCharged particles– interaction with interaction with

materialmaterial

++

+

++

++

+++

++

+----

----

--

---

-

“track of ionisation”

1616

Ionization & Energy lossIonization & Energy loss

Important for all Important for all charged particlescharged particles

2

)(2ln 2

222

2

I

mcDn

dx

dE e

• Bethe-Bloch Equation

velocity

Mean ionization potential(10ZeV)

Density of electrons

1717

IonizationIonization

In low fields the ions eventually recombine In low fields the ions eventually recombine with the electronswith the electrons

However under higher fields it is possible However under higher fields it is possible to separate the chargesto separate the charges

E++++++++

------- -

------- -

------- -

------- -

------- -

------- -

------- -

------- -

------- -

------- -

------- -

------- -

------- -

Note: e-’s and ions generally move at a different rate

1818

UnitsUnitsParticle Physicists use Natural Units:Particle Physicists use Natural Units:

Hence, we write the masses of some Hence, we write the masses of some standard particles in terms of energy standard particles in terms of energy (MeV, GeV):(MeV, GeV):

fmMeV3.197

MeVs10582.6Js100546.12

12234

c

h

c

kg10672.1MeV/.938

kg10109.9MeV/511.0272

312

cm

cm

p

e