Transcript • all fundamental with no underlying structure • Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 • No QM theory for.

• 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
P461 - particles I
1
When/where discovered
Nobel Prize?
g
Mostly Europe
1895-1920 Roentgen (sort of)1901
W/Z CERN
1983
Rubbia/vanderMeer1984
gluon DESY
1979
NO
electron Europe
1895-1905
Thomson 1906
muon Harvard
1937
No
tau
SLAC
1975
Perl 1995
ne
US
1953
Reines/Cowan 1995
nm
BNL
1962 Schwartz/Lederman/Steinberger
1988
nt
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
P461 - particles I
2
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”
P461 - particles I
3
Pi-mu coupling
K L  (m )atom  n
t
t t m
 t
t  t m
(no anom alies)
P461 - particles I
4
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 D states spin 3/2
• Charges = uuu(2) uud(1) udd(0) ddd(-1)
• N,D decay by strong interaction N  p/n +  with
lifetimes of 10-23 sec (pion is quark-antiquark
meson). Identify by looking at the invariant mass
and other kinematic distributions
   ud
1
 
(uu  dd )
2
   du
0
P461 - particles I
5
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
 1/ 2 
   

 n
  1 / 2
2  2  3 1
I1
pp
1
2
nn
( pn  np)
doublet
and 21  1 and 0
1
2
I  0 Iz
IZ
1
1
2
0
( pn  np)
0
1
P461 - particles I
6
Baryons and Mesons
• 3 quark combinations (like uud) are called
baryons. Historically first understood for u,d,s
quarks
• “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 antisymmetric
wavefunction (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
P461 - particles I
7
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
P461 - particles I
8
Baryons
D0
b  ssb ( 2008 )
 b  dsb ( 2007 )
also
0b  udb
0b  udb
 0b  usb
P461 - particles I
9
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  rgb  gbr  brg  rbg  grb  bgr
r
g b
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10
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
1
1
1
(     ) asym
2  2 
2
1
u d 
(ud  du) asym
2
• Add on third quark to get first term
(u1  1 d2  2  d1  1 u2  2  u1  1 d 2  2  d1  1 u2  2 )u3  3
• 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)
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11
Meson Wave Functions
• quark antiquark combinations. Governed by
SU(2) (spin) and strangenessSU(3) (SU(4))
for c-quark). But broken symmetries
   ud
1
(uu  dd )
2
   du
1
h8 
(uu  dd  2 ss )
6
1
h0 
(uu  dd  ss )
3
0 
C 0  0
Cu  u
as  0  gg
Cd  d
convention
h  h8 sin   h0 cos
h '  h8 cos  h0 sin 
• pions have no s quarks. The h’s (or the wf)
mix to find real particles  break SU(3)
meson

h
h’
r
w
f
mass
135,140
550
958
770
782
1019
Decay
no s
little s
mostly s
no s
little s
85% KK, 15% 
P461 - particles I
12
Hadron + Quark masses
• Mass of hadron = mass of constituent quarks
plus binding energy. As gluons have F=kx,
increase in energy with separationpositive
“binding” energy
• Bare quark masses:
u = 1-5 MeV
d = 3-9 MeV
s = 75-170 MeV c = 1.15 – 1.35 GeV
b = 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 Mev
proton = “3 u/d quarks” = 940 MeV
kaon = “1 s and 1 u/d” = 500 MeV
Omega = “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
P461 - particles I
13
Hadrons, Partons and Jets
• The quarks and gluons which make up a hadron
are 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 massdependent
• 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
P461 - particles I
14
Fragmentation functions
u,d,s
p
c
b
fraction of energy which
quark (or gluon) has for
either particle or jet
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15
Lepton and Baryon Conservation
• Strong and EM conserve particle type. Weak can
change but always leptonlepton or quarkquark
• 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
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16
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.
  p   K



NO
du  uud  uus  us
   p    K 0 YES
du  uud  uds  sd
   p    K   
YES
du  uud  uds  su  ud
P461 - particles I
17
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 blueantigreen) combos, 2 are colorless. Gluon
exchange usually color exchange. Can have
gluon-gluon interaction
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18
quark-gluon coupling
• why q-qbar and qqq combinations are stable
• 8 gluons each with color and anticolor. All
“orthogonal”. 2 are colorless gluons
rb
br
bg
rg
gr
gb
1
( rr  gg  2bb )
6
1
( rr  gg )
2
• coupling gluon-quark =
coupling gluon-antiquark =
r
+c
-c
b
vertex 1 +c
c
rb
r
b
r
b
2
vertex 2 +c
vertex 2 -c
P461 - particles I
c
2
19
P461 - particles I
20
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
Lx Ly  Ly Lx  Lx , Ly   iLz
L  Lx  iLy
L  W 
Lz  Z
• SU(2) used for 3D rotations
angular momentum (orbital and spin)
isospin (hadrons – broken)
weak interactions  weak “isospin”
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21
Group Theory – SU(3)
• 3x3 unitary matrices with det=1. 2n2-n2-1=8
parameters. Have group algebra
i ,  j   2ifijk fijk  0(any same) fijk  0(i  j  k )
• and representation of generators
 0 1 0
 0 0 1
0 0 0 






1   1 0 0  4   0 0 0  7   0 0  i 
 0 0 0
 1 0 0
0 i 0 






 0  i 0
0 0  i
1 0 0 





1 
2   i 0 0  5   0 0 0  8 
0
1
0


3
 0 0 0
i 0 0 
0 0  2






 1 0 0
 0 0 0




rb br bg
3   0  1 0  6   0 0 1 
 0 0 0
 0 1 0
rg gr gb




1
( rr  gg  2bb )
6
1
( rr  gg )
2
• and 3 color states
1
 0
 0
 
 
 
r   0 b   1 g   0
 0
 0
1
 
 
 
r  1 0 0)
 0  1
 0
   
 
1  1    0  1  0   0
 0  0
1
   
 
P461 - particles I
22
Pions
• Use as strong interaction example
• Produce in strong interactions
p  p  p p 0
p p  p n 
p n  p p 
• 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
A: p  p  d   
B: d     p  p
(2 s  1)(2 sd  1)
A
 function(m p , md , m )
B
(2 s p  1) 2
• Find S=0 for pions
P461 - particles I
23
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:
•
I
Iz
I
Iz
A:
p n  d  0
B: p  p  d   
p p -> d
pi+
Total
½ ½
0
1
1
½ ½
0
1
1
p n -> d
pi0
Total
½ ½
0
1
0 or 1
½ -½
0
0
0
• in the past we combined 2 spin ½ states to form
S=0 or 1
1
I  1, Iz  0 
( 1 / 2,1 / 2  1 / 2,1 / 2 )
2
1
I  0, Iz  0 
( 1 / 2,1 / 2  1 / 2,1 / 2 )
2
P461 - particles I
24
More Pions
• Reverse this and say eigentstate |p,n> is
combination of I=1 and I=0
0
I
(
d
)

I
(

)0
Z
Z
• reactions:
•
A:
p n  d  0
B:
p p  d  
1
p, n 
( I  1, Iz  0  I  0, Iz  0 )
2
| p, p   |11
, 
• 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
P461 - particles I
25
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
 0  gg
u
t  8  10 s
17
•
 0 (uds)  0 (uds)  g
t  7  10
 20
s
ubar
g
g
• 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
P461 - particles I
26
c-cbar and b-bbar Mesons
• Similar to u-ubar, d-dbar, and s-sbar
S  0 c (cc ) c b (bb )
S  1 J / (cc )  (bb )
• “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
f ( ss )  K  (us )  K  ( su )


 4S (bb )  B (ub )  B (bu )
• But if mass <2*meson decays EM. “easiest” way is
through virtual photons (suppressed for pions due
to spin)
c
cbar
g
m
m
P461 - particles I
27
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)
BF (  m  m  )  0.06
BF (  e  e  )  0.06
BF (  hadrons)  0.88
• Some of the decays into hadrons proceed through
virtual photon and some through a virtual
(colorless) gluon)

c
cbar
g
u
u
P461 - particles I
d
d



28
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 quarkantiquark 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   g  u  u  us  su
(etc)
Mass(ee)  ( Ee  Ee ) 2  ( pe  pe ) 2
e+
e-
g
q
qbar
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29
P461 - particles I
30
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
n  p  e   n e      0  e  n e
U
u
d
d
d
u
W
n
e
n   n  n 
     
 e   m  t 
 u  c  t 
     
 d   s b
• Charge current Weak interactions proceed
be exchange of W+ or W-. Couples to 2
members of weak doublets (provided
enough energy)
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31
Decays of Leptons
• Transition leptonneutrino emits virtual W
which then “decays” to all kinematically
available doublet pairs


m  e n e n m  100%
nm
m
ne
W
e
• For taus, mass=1800 MeV and W can decay
into en, mn, and u+d (s by mixing). 3
colors for quarks and so rate ~3 times
higher. t   e   n  n  17%
e
t
t  m n m nt


t     ( n )  n t
P461 - particles I
 18%
 65%
32
Weak Decays of Hadrons
• Can have “beta” decay with same number
of quarks in final state (semileptonic)
K    m n m


0
• or quark-antiquark combine (leptonic)
ne
u
W
d
e
  e n e or m n m



u
• or can have purely hadronic decays
s
u
u
uu
d
K   0  
K   0  0  
• Rates will be different: 2-body vs 3-body
phase space; different spin factors
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33
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
•
t
b
W
n
e, m , t
c
s
u
d
• the t quark decays before it becomes a
hadron. The outgoing b/c/s/u/d quarks are
seen as jets
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Top Quark Decay
• Very small rate of ts or td
• the quark states have a color factor of 3
• 

t  b  e  n e 11%
t  b  m  n m 11%
t  b  t nt

tt  (be )  (b e ) 1.2%
tt  b(e or m )  b (e or m ) 4.8%
tt  (bqq )  b (e or m )
11%
( 2 * .22* .66)

t  b  c  s 33%
t bu d
29%
tt  (bqq )  (b qq ) 44%
33%
t
b
W
•
e, m , t , c , u
n , s, d
P461 - particles I
35
How to Discover the
Quark
Top
• 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 bm)
• 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
channel em ee mm e  jets e  jets( m ) m  jets m  jets( m )
# events 2 0 1
5
3
3
3
bckgrnd .1 .3 .3
1.2
.9
.7
.4
• Total: 17 events in data collected from 1992-1995
with estimated background of 3.8 events
P461 - particles I
36
The First Top Quark Event
muon
electron
•
P461 - particles I
37
The First Top Quark Event
jet
•
P461 - particles I
38
Another Top Quark Event
jets
•
electron
P461 - particles I
39
Decay Rates: Pions
• Look at pion branching fractions (BF)
   m  n
BF  100%
  e n
BF  1.2 10
    0e n
BF  1.0 108


4
u
dbar
• t  2.6 108 s m  139.6MeV
• 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
en  total  BF (en )
 (2.6 108 sec)1 1.0 108  .4 sec1
P461 - particles I
40
Pi Decay to e-nu vs mu-nu
• Depends on phase space and spin factors
• in pion rest frame pion has S=0
   l    l  e, m
L+
nu
RHl  RHn
NO
LH l  LHn
• 2 spin=1/2 combine to give S=0. Nominally
can either be both right-handed or both lefthanded
• 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. Antparticles
which are LH.But easier for muon as
heavier mass
P461 - particles I
41
Polarization of Spin 1/2 Particles
• Obtain through Dirac equation and
polarization operators. Polarization defined
P
NR  NL
v

NR  N
c
v
P
c
RH  m  , e 
LH  m  , e 
• the degree of polarization then depends on
velocity. The fraction in the “right” and
“wrong” helicity states are:
1 1v
" right "  
2 2c
1 1v
" wrong "  
2 2c
• 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
P461 - particles I
42
Pion Decay Kinematics
• 2 Body decay. Conserve energy and
momentum m  En  El pl  pn  En
(m  En ) 2  El2  ml2  pl2
m2  ml2
 En 
2m
m2  ml2
El 
2m
• can then calculate the velocity of the
electron or muon
2
p En m2  ml2
vl  
 2
E El m  ml2
2m
v
1  2 l 2
c m  ml
m  140, mm  105, me  0.5  ve  0.99997c, vm  0.27c
• look at the fraction in the “wrong” helicity
to get relative spin suppression of decay to
electrons
2
2
m

m
m 
LHe
m
5


3
.
2

10
LHm  mm m2

2
e
2
P461 - particles I
43
Pion Decay Phase Space
• Lorentz invariant phase space plus energy
and momentum
conservation
3
3
d pl d pn
El Ev


 (m  El  En ) 3 ( pl  pn )
• gives the 2-body phase space factor
(partially a computational trick)
p2
dp
dE0
E0  m  En  El  p  p 2  ml2
dp
dp 1 m2  ml2


dE0 dm 2 m2
m2  ml2
as p 
2m
2
 m2  ml2  1 m2  ml2
2 dp

p
 
dE0  2m  2 m2
• as the electron is lighter, more phase space
(3.3 times the muon)
• Branching Fraction ratio is spin suppression
times phase space
BF (  e )
 3.2 105  3.3  104
BF (  m )
P461 - particles I
44
Muon Decay
• Almost 100% of the time muons decay by
m   e n e n m
t  2.2 106 sec mm  105.7 MeV
• Q(muon decay) > Q(pionmuon 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
P461 - particles I
45
Detecting Parity
Violation in muon decay
• Massless neutrinos are fully
polarized, P=-1 for neutrino and
Jm
Jn
P=+1 for antineutrino (defines

helicity)
m
n
• Consider + m+ e+ decay.
Since neutrinos are left-handed
  m  nm
PH1, muons should also be
polarised with polarisation P=
-v/c (muons are non-relativistic,
Je J Jn
so both helicity states are
m
n
allowed).
• If muons conserve polarization
e+ m n
when they come to rest, the
Jn
electrons from muon decay
  e  n + n
m
e
m
should also be polarized and
have an angular dependence:

I() 1 cos
3
P461 - particles I
46
Parity violation in +
m+ e+ decay
• Experiment by Garwin, Lederman,
Weinrich aimed to confirm parity
violation through the
measurements of I() for positrons.
• 85 MeV pion beam (+ ) 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.
P461 - particles I
47
Parity violation in + m+ 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 ms.
• Goal: to measure I() for
positrons.
• Conventional way: move
detecting system (telescope 3-4)
around carbon target measuring
intensities at various . 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.
P461 - particles I
48
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() 1
P461 - particles I

3
cos
49