all fundamental with no underlying structure • Leptons...

P461 - particles I 1

• all fundamental with no underlying structure

• Leptons+quarks spin ½ while photon, W, Z, gluons spin 1

• No QM theory for gravity

• Higher generations have larger mass


When/where discovered

γ Mostly Europe 1895-1920 Roentgen (sort of)1901W/Z CERN 1983 Rubbia/vanderMeer1984

gluon DESY 1979 NO

electron Europe 1895-1905 Thomson 1906

muon Harvard 1937 No

tau SLAC 1975 Perl 1995

νe US 1953 Reines/Cowan 1995

νµ BNL 1962 Schwartz/Lederman/Steinberger 1988ντ FNAL 2000 NO

u,d SLAC 1960s Friedman/Kendall/Taylor 1990

s mostly US 1950s NO

c SLAC/BNL 1974 Richter/Ting 1976

b FNAL 1978 NO (Lederman)

t FNAL 1995 NO

muon – Street+Stevenson had “evidence” but Piccione often gets credit in the 1940s as measured lifetime

Nobel Prize?


Couplings and Charges

• All charged particles interact electromagnetically

• All particles except gamma and gluon interact weakly (have nonzero “weak” charge) (partially semantics on photon as mixing defined in this way) A WWZ vertex exists

• Only quarks and gluons interact strongly; have non-zero “strong” charge (called color). This has been tested by:

magnetic moment electron and muon

H energy levels (Lamb shift)

“muonic” atoms. Substitute muon for electron

pi-mu atoms

• EM charge just electric charge q

• Weak charge – “weak” isospin in i=1/2 doublets used for charged (W) and have I3-Aq for neutral current (Z)

• Strong charge – color charge triplet “red” “green”“blue”


Pi-mu coupling

)(

)(

anomaliesno

K atomL

πµπ

µπ τττττ

τ

νπµ

≅+

=

+→


Strong Force and Hadrons

• p + p -> p + N*

• N* are excited states of proton or neutron (all of which are baryons)

• P = uud n = udd (bound by gluons) where u = up quark (charge 2/3) and d = down quark (charge -1/3)

• About 20 N states spin ½ mass 938 – 2700 MeV

• About 20 ∆ states spin 3/2• Charges = uuu(2) uud(1) udd(0) ddd(-1)

• N,∆ decay by strong interaction N p/n + π with lifetimes of 10-23 sec (pion is quark-antiquarkmeson). Identify by looking at the invariant mass and other kinematic distributions

ud

dduu

du

−⇒

−⇒

⇒

−

+

π

π

π

)(2

10


ISOSPIN

• Assume the strong force is ~identical between

baryons (p,n,N*) and between three pions

• Introduce concept of Isospin with (p,n) forming

an isopsin doublet I=1/2 and pions in an isopsin

triplet I=1, and quarks (u,d) in a I=1/2 doublet

• Isospin isn’t spin but has the same group algebra

SU(2) as spin and so same quantum numbers and

addition rules

p

ndoublet

and and

I I I I

pp

pn np pn np

nn

Z z

⇒

−

⊗ = ⊕ ⇒ →

= =

+ −

−

1 2

1 2

2 2 3 1 1 0

1 0

1

0 0

1

12

12

1

2

1

2

/

/

( ) ( )


Baryons and Mesons

• 3 quark combinations (like uud) are called baryons. Historically first understood for u,d,squarks

• “plotted” in isospin vs strangeness. Have a group of 8 for spin ½ (octet) and 10 (decuplet) for spin 3/2. Fermions and so need antisymmetricwavefunction (and have some duplication of quark flavor like p = uud)

• Gell-Mann tried to explain using SU(3) but badly broken (seen in different masses) but did point out underlying quarks

• Mesons are quark-antiquark combinations and so spin 0 or 1. Bosons and need symmetric wavefunction (“simpler” as not duplicating quark flavor)

• Spin 0 (or spin 1) come in a group of 8 (octet) and a group of 1 (singlet). Again SU(3) sort of explains if there are 3 quarks but badly broken as seen in both the mass variations and the mixing between the singlet and octet


Baryons and Mesons

• Use group theory to understand: -what states are allowed - “mixing” (how decay) - state changes (step-up/down) - magnetic moments of

• as masses are so different this only partially works – broken

• SU(2) Isospin –very good (u/d quark same mass) SU(3) for s-quark – good with caveats SU(4) with c-quark – not so good


Baryons

D0

)2007(

)2008(

dsb

ssb

b

b

=Ξ

=Ω−

−

also

usb

udb

udb

b

b

b

=Ξ

=Σ

=Λ

0

0

0


Baryon Wave Functions

• Totally Antisymmetric as 3 s=1/2 quarks -

Fermions

• S=3/2. spin part must be symmetric (all

“aligned”). There are some states which

are quark symmetric (uuu,ddd,sss). As all

members of the same multiplet have the

same symmetries quark and spin are

both symmetric

• to be antisymmetric, obey Pauli

exclusion, need a new quantum number

“color” which comes in 3 (at least)

indices. Color wavefunctions:

r g b

r g b

r g b

rgb gbr brg rbg grb bgr= + + − − −


Baryon Wave Functions

• S=1/2. color part is like S=3/2. So spin*quark flavor = symmetric. Adding 3 spin = ½ to give S=1/2 produces “mixed” spin symmetry.

• First combine two quarks giving symmetric 1<->2

• Add on third quark to get first term

• Cycle 1 2 3 1 8 more terms. And then multiply by 6 color terms from S=3/2 page (4*9*6=216 terms)

• Why no charge 2 or charge -1particles like the proton or neutron exist the need for an antisymmetric wavefunction makes the proton the lightest baryon (which is a good thing for us)

12

12

1

2

1

2

⊗ ⇒ ↑ ↓ − ↓ ↑

⊗ ⇒ −

( )

( )

asym

u d ud du asym

( )u d d u u d d u u1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 3 3↑ ↓ − ↑ ↓ − ↓ ↑ + ↓ ↑ ↑


Meson Wave Functions

• quark antiquark combinations. Governed by SU(2) (spin) and strangenessSU(3) (SU(4)) for c-quark). But broken symmetries

• pions have no s quarks. The η’s (or the ω+φ)mix to find real particles break SU(3)

meson mass Decay

π 135,140 no s

η 550 little sη’ 958 mostly s

ρ 770 no s

ω 782 little s

φ 1019 85% KK, 15% πππ

)(3

1

)2(6

1

)(2

1

0

8

0

ssdduu

ssdduu

ud

dduu

du

++⇒

−+⇒

−⇒

−⇒

⇒

−

+

η

η

π

π

π

conventiondCduCu

asC

=−=

→+= γγπππ 000

θηθηη

θηθηη

sincos'

cossin

08

08

+=

+−=


Hadron + Quark masses

• Mass of hadron = mass of constituent quarks plus binding energy. As gluons have F=kx, increase in energy with separationpositive“binding” energy

• Bare quark masses: u = 1-5 MeV d = 3-9 MeVs = 75-170 MeV c = 1.15 – 1.35 GeVb = 4.0–4.4 GeV t = 169-179 GeV

• Top quark decay so quickly it never binds into a hadron. No binding energy correction and so best determined mass value (though < 300 t quark decays observed)

• Other quark masses determined from measured hadron masses and binding energy model pion = “2 u/d quarks” = 135 Mevproton = “3 u/d quarks” = 940 MeVkaon = “1 s and 1 u/d” = 500 MeVOmega = “3 s quarks” = 1672 MeV

• High energy p-p interactions really q-q (or quark-gluon or gluon-gluon). “partons” emerge but then hadronize. Called “jets” whose energy and momentum are mostly original quark or gluon


Hadrons, Partons and Jets

• The quarks and gluons which make up a hadronare called partons (Feynman, Field, Bjorken)

• Proton consists of: -3 valence quarks (about 40% of momentum) -gluons (about 50% opf the momentum) -“sea” quark-antiquark pairs

• The sea quarks are constantly being made/annihilated from gluons and can include heavier quarks (s,c,b) with probability mass-dependent

• X = p/p(total) is the momentum fraction and each type of particle has a probability to have a given X (parton distribution function or pdf)

• PDFs mostly measured in experiments using nu,e,mu,p etc. Some theoretical modeling

• Even at highest energy collisions, quarks still pointlike particles (no structure) as distances of 0.002 F (G. Blazey et al)

• single quark produces other gluons and quarks jet. Have similar fragmentation function


Fragmentation functions

p

u,d,s

c

b

fraction of energy which

quark (or gluon) has for

either particle or jet


Lepton and Baryon Conservation

• Strong and EM conserve particle type. Weak can change but always leptonlepton or quarkquark

• So number of quarks (#quarks-#antiquarks) conserved. Sometimes called baryon conservation B.

• Number of each type (e,mu,tau) conserved L conservation

• Can always create particle-antiparticle pair

• But universe breaks B,L conservation as there is more matter than antimatter

• At small time after big bang #baryons = #antibaryons = #leptons = #antileptons (modulo spin/color/etc) = ~#photons (as can convert to particle-antiparticle pairs)

• Now baryon/photon ratio 10-10


Hadron production + Decay

• Allowed production channels are simply quark counting

• Can make/destroy quark-antiquark pairs with the total “flavor” (upness = #up-#antiup, downness, etc) staying the same

• All decays allowed by mass conservation occur quickly (<10-21 sec) with a few decaying by EM with lifetimes of ~10-16 sec) Those forbidden are long-lived and decay weakly and do not conserve flavor.

π

π

π π

− + −

−

− + −

+ → +

+ → +

+ → +

+ → +

+ → + +

+ → + +

p K NO

du uud uus us

p K YES

du uud uds sd

p K YES

du uud uds su ud

Σ

Λ

Λ

0


Hadrons and QCD

• Hadrons are made from quarks bound

together by gluons

• EM force QuantumElectroDynamics QED

strong is QuantumChromoDynamics QCD

• Strong force “color” is equivalent to electric

charge except three different (identical)

charges red-green-blue. Each type of quark

has electric charge (2/3 up -1/3 down, etc)

and either r g b (or antired, antiblue,

antigreen) color charge

• Unlike charge=0 photon, gluons can have

color charge. 8 such charges (like blue-

antigreen) combos, 2 are colorless. Gluon

exchange usually color exchange. Can have

gluon-gluon interaction


quark-gluon coupling

• why q-qbar and qqq combinations are stable

• 8 gluons each with color and anticolor. All

“orthogonal”. 2 are colorless gluons

• coupling gluon-quark = +χ coupling gluon-antiquark = -χ

)(2

1

)2(6

1

ggrrbgrggr

bbggrrgbrbbr

−

−+

r

r

b

b

br

rb

vertex 1 +χ

vertex 2 +χ

vertex 2 -χ

2χ+

2χ−


Group Theory• W/Z bosons and gluons carry weak charge and

color charge (respectively)Bosons couple to

Bosons

• SU(2) and SU(3) which have 3 and 8 “base”

vectors can be used to represent weak and strong

forces. The base vectors are the W+,W-,Z and the 8

gluons. Exact (non-broken) symmetry

• The group algebra tells us about boson interaction.

So for W/Z use

• SU(2) used for 3D rotations

angular momentum (orbital and spin)

isospin (hadrons – broken)

weak interactions weak “isospin”

[ ]ZLWLiLLL

LiLLLLLL

zyx

zyxxyyx

⇔⇔±=

==−±

±±

h,


Group Theory – SU(3)• 3x3 unitary matrices with det=1. 2n2-n2-1=8

parameters. Have group algebra

• and representation of generators

• and 3 color states

[ ] )(0)(02, kjifsameanyfif ijkijkijkji ≠≠≠==λλ

=

−=

−

=

−

=

−

=

−=

=

=

010

100

000

000

010

001

200

010

001

3

1

00

000

00

000

00

00

00

00

000

001

000

100

000

001

010

63

852

741

λλ

λλλ

λλλ

i

i

i

i

i

i

)(2

1

)2(6

1

ggrrbgrggr

bbggrrgbrbbr

−

−+

( )001

1

0

0

0

1

0

0

0

1

=

=

=

=

r

gbr 0

1

0

0

0

0

1

0

1

0

11 =

=

λλ


Pions• Use as strong interaction example

• Produce in strong interactions

• Measure pion spin. Mirror reactions have

same matrix element but different phase

space/kinematics term. “easy” part of phase

space is just the 2s+1 spin degeneracy term

• Find S=0 for pions

p p p p

p p p n

p n p p

+ → + +

+ → + +

+ → + +

+

−

π

π

π

0

A p p d

B d p p

function m m ms s

s

A

B

p d

d

p

:

:

( , , )( )( )

( )

+ → +

+ → +

=+ +

+

+

+

π

πσσ π

π2 1 2 1

2 1 2


More Pions• Useful to think of pions as I=1 isospin triplet and

p,n is I=1/2 doublet (from quark plots)

• Look at reactions:

• p p -> d pi+ Total

I ½ ½ 0 1 1

Iz ½ ½ 0 1 1

p n -> d pi0 Total

I ½ ½ 0 1 0 or 1

Iz ½ - ½ 0 0 0

• in the past we combined 2 spin ½ states to form

S=0 or 1

A p n d

B p p d

:

:

+ → +

+ → + +

π

π

0

I Iz

I Iz

= = = +

= = = −

1 01

21 2 1 2 1 2 1 2

0 01

21 2 1 2 1 2 1 2

, ( / , / / , / )

, ( / , / / , / )


More Pions• Reverse this and say eigentstate |p,n> is

combination of I=1 and I=0

• reactions:

•

• then take the “dot product” between |p,n>

and |d,pi0> brings in a 1/sqrt(2) (the

Clebsch-Gordon coefficient)

• Square to get A/B cross section ratio of 1/2

A p n d

B p p d

:

:

+ → +

+ → + +

π

π

0

p n I Iz I Iz

p p

, ( , , )

| , | ,

= = = + = =

>= >

1

21 0 0 0

11

0)()( 0 == πZZ IdI


EM Decay of Hadrons

• If a photon is involved in a decay (either final state or virtual) then the decay is at least partially electromagnetic

•

• Can’t have u-ubar quark go to a single photon as have to conserve energy and momentum (and angular momentum)

• Rate is less than a strong decay as have coupling of 1/137 compared to strong of about 0.2. Also have 2 vertices in pi decay and so (1/137)2

• EM decays always proceed if allowed but usually only small contribution if strong also allowed

s

udsuds

s

20

00

17

0

107

)()(

108

−

−

×=

+Λ→Σ

×=

→

τ

γ

τ

γγπ u

ubar

γ

γ


c-cbar and b-bbar Mesons

• Similar to u-ubar, d-dbar, and s-sbar

• “excited” states similar to atoms 1S, 2S, 3S…1P, 2P…photon emitted in transitions. Mass spectrum can be modeled by QCD

• If mass > 2*meson mass can decay strongly

• But if mass <2*meson decays EM. “easiest” way is through virtual photons (suppressed for pions due to spin)

)()(/1

)()(0

bbccJS

bbccS b

Υ=

=

ψ

χχ

)()()(4

)()()(

ubBbuBbbS

usKsuKss

−+

−+

+→Υ

+→φ

c

cbar

γ µ+

µ−


c-cbar and b-bbar Meson

EM-Decays• Can be any particle-antiparticle pair whose pass is less than psi or upsilon: electron-positron, u-ubar, d-dbar, s-sbar

• rate into each channel depends on charge2(EM coupling) and mass (phase space)

• Some of the decays into hadrons proceed through virtual photon and some through a virtual (colorless) gluon)

c

cbar

γ

88.0)(

06.0)(

06.0)(

=→

=→

=→−+

−+

hadronsBF

eeBF

BF

ψψ

µµψ

u

u

d

d

+π

−π


Electromagnetic production

of Hadrons

• Same matrix element as decay. Electron-positron pair make a virtual photon which then “decays” to quark-antiquark pairs. (or mu+-mu-, etc)

• electron-positron pair has a given invariant mass which the virtual photon acquires. Any quark-antiquark pair lighter than this can be produced

• The q-qbar pair can acquire other quark pairs from the available energy to make hadrons. Any combination which conserves quark counting, energy and angular momentum OK

e+

e-

γ q

qbar

22 )()()(

)(

−+−+ +−+=

+→+→→+ −+

eeeeppEEeeMass

etcussuuuee γ


Weak Decays

• If no strong or EM decays are allowed,

hadrons decay weakly (except for stable

proton)

• Exactly the same as lepton decays. Exactly

the same as beta decays

• Charge current Weak interactions proceed

be exchange of W+ or W-. Couples to 2

members of weak doublets (provided

enough energy)

ee eepn νππν ++→⇔++→ −−− 0

U

d

d

u

d

u

We

ν

b

t

s

c

d

u

e τν

µνν


Decays of Leptons• Transition leptonneutrino emits virtual W

which then “decays” to all kinematically

available doublet pairs

• For taus, mass=1800 MeV and W can decay

into e+ν, µ+ν, and u+d (s by mixing). 3 colors for quarks and so rate ~3 times

higher.

%100≈++→ −−µννµ ee

%65)(

%18

%17

≈++→

≈++→

≈++→

−−

−−

−−

τ

τµ

τ

νππτ

ννµτ

νντ

n

e e

Weµ

µν eν


Weak Decays of Hadrons• Can have “beta” decay with same number

of quarks in final state (semileptonic)

• or quark-antiquark combine (leptonic)

• or can have purely hadronic decays

• Rates will be different: 2-body vs 3-body

phase space; different spin factors

µνµνπ ++→ −−− ore e

We

d

u eν

µνµπ ++→ ++ 0K

++

++

++→

+→

πππ

ππ00

0

K

Ks

u

u d

uuu


Top Quark Decay• Simplest weak decay (and hadronic).

• M(top)>>Mw (175 GeV vs 81 GeV) and so

W is real (not virtual) and there is no

suppression of different final states due to

phase space

•

• the t quark decays before it becomes a

hadron. The outgoing b/c/s/u/d quarks are

seen as jets

t b

W

τµ ,,eν

cud

s


Top Quark Decay• Very small rate of ts or td

• the quark states have a color factor of 3

•

•

t b

W

uce ,,,, τµds ,,ν

%33

%33

%11

%11

%11

dubt

scbt

bt

bt

ebt e

++→

++→

++→

++→

++→

−+

+−

τ

µ

ντ

νµ

ν

%44)()(

)66.*22.*2(

%29)()(

%8.4)()(

%2.1)()(

qqbqbqtt

orebqbqtt

oreborebtt

ebbett

+→

=

+→

+→

+→

υµ

υµυµ

υυ


How to Discover the

Top Quark

• make sure it wasn’t discovered before you start

collecting data (CDF run 88-89 top mass too

heavy)

• build detector with good detection of electrons,

muons, jets, “missing energy”, and some B-ID (D0

Run I bµ)• have detector work from Day 1. D0 Run I: 3 inner

detectors severe problems, muon detector some

problems but good enough. U-LA cal perfect

• collect enough data with right kinematics so

statistically can’t be background. mostly W+>2 jets

• Total: 17 events in data collected from 1992-1995

with estimated background of 3.8 events

4.7.9.2.13.3.1.

3335102#

)()(

bckgrnd

events

jetsjetsjetsejetseeeechannel µµµµµµµ ++++


The First Top Quark Event

•

muon

electron


The First Top Quark Event

•

jet


Another Top Quark Event

•electron

jets


Decay Rates: Pions

• Look at pion branching fractions (BF)

•

• The Beta decay is the easiest. ~Same as neutron beta decay

• Q= 4.1 MeV. Assume FT=1600 s. LogF=3.2 (from plot) F= 1600

• for just this decay gives “partial”T=1600/F=1 sec or partial width = 1 sec-1

MeVms

BFe

BFe

BF

6.139106.2

100.1

102.1

%100

8

80

4

=×=

×≅→

×≅+→

≅+→

−

−++

−++

++

τ

νππ

νπ

νµπu

dbar

1818 sec4.100.1sec)106.2(

)(

−−−− =×××=

×Γ=Γ νπνπ eBFtotale


Pi Decay to e-nu vs mu-nu

• Depends on phase space and spin factors

• in pion rest frame pion has S=0

• 2 spin=1/2 combine to give S=0. Nominally can either be both right-handed or both left-handed

• But parity violated in weak interactions. If m=0 all S=1/2 particles are LH and all S=1/2 antiparticles are RH

• neutrino mass = 0 LH

• electron and muon mass not = 0 and so can have some “wrong” helicity. Antparticleswhich are LH.But easier for muon as heavier mass

L+ nuν

ν

µυπ

LHLH

NORHRH

ell

l

l

+

+

=+→ ++ ,


Polarization of Spin 1/2 Particles

• Obtain through Dirac equation and polarization operators. Polarization defined

• the degree of polarization then depends on velocity. The fraction in the “right” and “wrong” helicity states are:

• fraction “wrong” = 0 if m=0 and v=c

• for a given energy, electron has higher velocity than muon and so less likely to have “wrong” helicity

−−

++

−−=

−+=+−

≡

eLHc

vP

eRHc

v

NN

NNP

R

LR

,

,

µ

µ

c

vwrong

c

vright

2

1

2

1""

2

1

2

1"" −=+=


Pion Decay Kinematics

• 2 Body decay. Conserve energy and momentum

• can then calculate the velocity of the electron or muon

• look at the fraction in the “wrong” helicityto get relative spin suppression of decay to electrons

π

π

π

πν

νπ

νννπ

m

mmE

m

mmE

pmEEm

EppEEm

ll

l

lll

ll

22

)(

2222

2222

+=

−=⇒

+==−

==+=

cvcvmmm

mm

mm

E

E

E

pv

ee

l

l

l

l

27.0,99997.05.0,105,140

22

22

==⇒===

+−

===

µµπ

π

πν 22

221

l

l

mm

m

c

v

+=−

π

5

2

22

2

2

102.3 −+

+

×=+

≅π

µπ

µµ m

mm

m

m

LH

LHe e


Pion Decay Phase Space

• Lorentz invariant phase space plus energy and momentum conservation

• gives the 2-body phase space factor (partially a computational trick)

• as the electron is lighter, more phase space (3.3 times the muon)

• Branching Fraction ratio is spin suppression times phase space

)()( 333

ννπν δδ ppEEm

E

pd

E

pdll

vl

l rr−−−

2

222

22

0

2

22

2

22

0

22

0

0

2

2

1

2

22

1

π

π

π

π

π

π

π

π

π

νπ

m

mm

m

mm

dE

dpp

m

mmpas

m

mm

dm

dp

dE

dp

mppEEmEdE

dpp

ll

ll

ll

+

−=⇒

−=

+==

++=+==

45 103.3102.3)(

)( −− =∗×=→→

µυπυπ

BF

eBF


Muon Decay

• Almost 100% of the time muons decay by

• Q(muon decay) > Q(pionmuon decay) but there is significant spin suppression and so muon’s lifetime ~100 longer than pions

• spin 1/2 muon 1/2 mostly LH (e) plus 1/2 all LH( nu) plus 1/2 all RH (antinu)

• 3 body phase space and some areas of Dalitz plot suppressed as S=3/2

• electron tends to follow muon direction and “remember” the muon polarization. Dirac equation plus a spin rotation matrix can give the angular distribution of the electron relative to the muon direction/polarization

MeVm

e e

7.105sec102.2 6 =×=

++→−

−−

µ

µ

τ

ννµ


Detecting Parity

Violation in muon decay• Massless neutrinos are fully polarized, P=-1 for neutrino and P=+1 for antineutrino (defines

helicity)• Consider π+→ µ+→ e+ decay. Since neutrinos are left-handed P≡≡≡≡Η=−1, muons should also be polarised with polarisation P=-v/c (muons are non-relativistic, so both helicity states are allowed).

• If muons conserve polarization when they come to rest, the electrons from muon decay should also be polarized and

have an angular dependence:

ν µ+

π+

Jν Jµ

π+ → µ+ + νµ

e+ νµ+

Je Jνν

Jν

Jµ

µ+ → e+ + νe + νµ

I(θ) =1−α3cosθ


Parity violation in π+→µ+→ e+ decay

• Experiment by Garwin, Lederman,

Weinrich aimed to confirm parity

violation through the

measurements of I(θ) for positrons.• 85 MeV pion beam (π+ ) from

cyclotron.

• 10% of muons in the beam: need

to be separated from pions.

• Pions were stopped in the carbon

absorber (20 cm thick)

• Counters 1-2 were used to separate

muons

• Muons were stopped in the carbon

target below counter 2.


Parity violation in π+→ µ+→ e+ decay

• Positrons from muon decay were detected by a telescope 3-4, which required particles of range >8 g/cm2 (25 MeV positrons).

• Events: concidence between counters 1-2 (muon) plus coincidence between counters 3-4 (positron) delayed by 0.75-2.0 µs.

• Goal: to measure I(θ) for positrons.

• Conventional way: move detecting system (telescope 3-4) around carbon target measuring intensities at various θ. But very complicated.

• More sophisticated method: precession of muon spin in magnetic field. Vertical magnetic field in a shielded box around the target.

• The intensity distribution in angle was carried around with the muon spin.


Results of the experiment by

Garwin et al.

• Changing the field (the magnetising current), they could change the rate (frequency) of the spin precession, which will be reflected in the angular distribution of the emitted positrons.

• Garwin et al. plotted the positron rate as a function of magnetising current (magnetic field) and compared it to the expected distribution:

I(θ) =1−α3cosθ

all fundamental with no underlying structure • Leptons...

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