• all fundamental with no underlying structure • Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 • No QM theory for.
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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
I1
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
P461 - particles I
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)
P461 - particles I
11
Meson Wave Functions
• quark antiquark combinations. Governed by
SU(2) (spin) and strangenessSU(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 wf)
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 separationpositive
“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
P461 - particles I
15
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
P461 - particles I
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
P461 - particles I
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 iLz
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”
P461 - particles I
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
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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
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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
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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
P461 - particles I
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)
P461 - particles I
31
Decays of Leptons
• Transition leptonneutrino 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 en, mn, 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
P461 - particles I
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
P461 - particles I
34
Top Quark Decay
• Very small rate of ts or td
• 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 bu d
29%
tt (bqq ) (b qq ) 44%
33%
t
b
W
•
e, m , t , c , u
n , s, d
P461 - particles I
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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 bm)
• 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 1.0 108
4
u
dbar
• t 2.6 108 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 )
(2.6 108 sec)1 1.0 108 .4 sec1
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
m2 ml2
En
2m
m2 ml2
El
2m
• can then calculate the velocity of the
electron or muon
2
p En m2 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 m2
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 m2 ml2
dE0 dm 2 m2
m2 ml2
as p
2m
2
m2 ml2 1 m2 ml2
2 dp
p
dE0 2m 2 m2
• as the electron is lighter, more phase space
(3.3 times the muon)
• Branching Fraction ratio is spin suppression
times phase space
BF ( e )
3.2 105 3.3 104
BF ( m )
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44
Muon Decay
• Almost 100% of the time muons decay by
m e n e n m
t 2.2 106 sec mm 105.7 MeV
• 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
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
PH1, 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