2. a g b B-field points into page
Studying the deflection of these rays in magnetic fields,
Becquerel and the Curies establish  rays to be
charged particles

3. pi = 0 = pf = prifle + pbullet

4. -decay
-decay

5. Some Alpha Decay Energies and Half-lives
Isotope KEa(MeV) t1/2 l(sec-1)
232Th 1010 y 10-18
238U 109 y 10-18
230Th 104 y 10-13
238Pu years 10-10
230U days 10-7
220Rn seconds 10-2
222Ac seconds
216Rn msec 104
212Po msec 106
216Rn msec 106

6. A B Potassium nucleus Before decay: After decay:
1930 Series of studies of nuclear beta decay, e.g.,
Potassium goes to calcium 19K  20Ca40
Copper goes to zinc Cu64 30Zn64
Boron goes to carbon 5B12  6C12
Tritium goes to helium 1H3  2He3
Potassium nucleus
Before decay:
After decay: A B A) B)
C) both the same
Which fragment has a greater
momentum?
energy?

7. 1932 Once the neutron was discovered, included the more fundamental
n  p + e
For simple 2-body decay, conservation of energy and momentum
demand both the recoil of the nucleus and energy of the emitted
electron be fixed (by the energy released through the loss of mass)
to a single precise value.
Ee = (mA2 - mB2 + me2)c2/2mA
but this only seems to match
the maximum value
observed on a spectrum of beta ray energies!

8. The beta decay spectrum of tritium ( H  He).
No. of counts per unit energy range 5 10 15 20
Electron kinetic energy in KeV
The beta decay spectrum of tritium ( H  He).
Source: G.M.Lewis, Neutrinos
(London: Wykeham, 1970), p.30)

9. -decay spectrum for neutrons
Electron kinetic energy in MeV

10. n  p e- +
charge ?
mass
MeV MeV MeV
neutrino
??? ?
the Fermi-Kurie plot.
The Fermi-Kurie plot
looks for any gap between
the observed spectrum
and the calculated Tmax
neutrino mass < 5.1 eV < me /100000
 0

11. on the principle of energy conservation, but Pauli couldn’t buy that:
Niels Bohr hypothesized the existence of quantum mechanical restrictions
on the principle of energy conservation, but Pauli couldn’t buy that:
Wolfgang Pauli

12. Dear Radioactive Ladies and Gentlemen,
as the bearer of these lines, to whom I graciously ask you to listen,
will explain to you in more detail, how because of the "wrong" statistics
of the N and Li6 nuclei and the continuous beta spectrum, I have hit
upon a desperate remedy to save the "exchange theorem" of statistics
and the law of conservation of energy. Namely, the possibility that there
could exist in the nuclei electrically neutral particles, that I wish to call
neutrons, which have spin 1/2 and obey the exclusion principle and which further differ
from light quanta in that they do not travel with the velocity of light. The mass of the
neutrons should be of the same order of magnitude as the electron mass and in any
event not larger than 0.01 proton masses. The continuous beta spectrum would then
become understandable by the assumption that in beta decay a neutron is emitted in
addition to the electron such that the sum of the energies of the neutron and the
electron is constant...
I agree that my remedy could seem incredible because one should have seen those
neutrons much earlier if they really exist. But only the one who dare can win and the
difficult situation, due to the continuous structure of the beta spectrum, is lighted by a
remark of my honoured predecessor, Mr Debye, who told me recently in Bruxelles:
"Oh, It's well better not to think to this at all, like new taxes". From now on, every
solution to the issue must be discussed. Thus, dear radioactive people, look and judge.
Unfortunately, I cannot appear in Tubingen personally since I am indispensable here
in Zurich because of a ball on the night of 6/7 December. With my best regards to you,
and also to Mr Back Your humble servant . W. Pauli, December 1930

13. "I have done a terrible thing. I have postulated a particle
that cannot be detected."

14. 1936 Millikan’s group shows at earth’s surface
Primary proton
1936 Millikan’s group shows at earth’s surface
cosmic ray showers are dominated by
electrons, gammas, and
X-particles
capable of penetrating deep underground
(to lake bottom and deep tunnel experiments)
and yielding isolated single cloud chamber tracks

15. 0.000002 sec 1937 Street and Stevenson 1938 Anderson and Neddermeyer
determine X-particles
are charged
have 206× the electron’s mass
decay to electrons with
a mean lifetime of 2msec
sec

16.  1947 Lattes, Muirhead, Occhialini and Powell observe pion decay
Cecil Powell (1947)
Bristol University 

17. C.F.Powell, P.H. Fowler,
D.H.Perkins
Nature 159, 694 (1947)
Nature 163, 82 (1949)

18. Consistently
~600 microns
(0.6 mm) 

20. m+ p+ m+ energy always predictably fixed by Ep p+ m+ + neutrino?
Under the influence of a magnetic field m+ p+
m+ energy
always
predictably fixed
by Ep
simple 2-body decay!
p+ m+ + neutrino?
charge ?
spin ½ ?

21. n p + e- + neutrino? p+ m+ + neutrino? Then m- e- + neutrino?
??? m e
As in the case of decaying radioactive isotopes,
the electrons’s energy varied, with a maximum
cutoff (whose value was the 2-body prediction)
3 body decay! e m
2 neutrinos

22. p + neutrino  n + e+ ? observed
1953, 1956, 1959
Savannah River (1000-MWatt)
Nuclear Reactor in South Carolina
looked for the inverse of the process
n  p + e- + neutrino
p + neutrino  n + e+ ?
with estimate flux of
51013 neutrinos/cm2-sec
Cowan & Reines
observed
2-3 p + neutrino events/hour
also looked for
n + neutrino  p + e-
but never observed!

23. Homestake Mine Experiment 1967 built at Brookhaven labs
615 tons of tetrachloroethylene
Neutrino interaction 37Cl37Ar
(radioactive isotope, ½ = 35 days)
Chemically extracting the 37Ar,
its radioactivity gives the number
of neutrino interactions in the vat
(thus the solar neutrino flux).
Results: Collected data
(24 years!!)
gives a mean of 2.5±0.2 SNU
while theory predicts 8 SNU
(1 SNU = 1 neutrino interaction
per second for 10E+36 target atoms).
This is a neutrino deficit of 69%.

24. Underground Neutrino Observatory
Now an interlude…to tie this in with one of those logos on the cover page.
The proposed next-generation
underground water Čerenkov detector
to probe physics beyond the sensitivity of the highly successful
Super-Kamiokande detector in Japan

25. water Čerenkov detector 40 m tall 40 m diameter
The SuperK detector
is a
water Čerenkov detector
40 m tall
40 m diameter
stainless steel cylinder
containing
50,000 metric tons
of ultra pure water
The detector is located 1 kilometer below Mt. Ikenoyama inside the Kamioka zinc mine.

26. The main sensitive region is 36 m high, 34 m in dia viewed by 11,146 inward facing Hamamatsu photomultiplier tubes surrounding 32.5 ktons of water

27. Underground Neutrino Observatory
650 kilotons
active volume:
440 kilotons
20 times larger
than
Super-Kamiokande
$500M
The optimal detector depth to perform
the full proposed scientific program of
UNO  4000 meters-water-equivalent
or deeper
major components: photomultiplier tubes, excavation, water purification system.

28. e+, + ( +)  assigned L = -1 n p + e- + neutrino _
Konopinski & Mahmoud
introduce LEPTON NUMBER to account for
which decays/reactions are possible,which not
e,  ( )  assigned L = +1
e+, + ( +)  assigned L = -1
n p + e- + neutrino _ _  _
p + neutrino  n + e+
  n + e+
n +   p + e- ?? ??

29. Brookhaven National Laboratory
1962 Lederman,Schwartz,Steinberger
Brookhaven National Laboratory
using a  as a source of  antineutrinos
and a 44-foot thick stack of steel
(from a dismantled warship hull)
to shield everything but the ’s
found 29 instances of
 + p  + + n
but none of
 + p  e+ + n
1988 Nobel Prize in Physics
"for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino"

30. So not just ONE KIND of neutrino, the leptons are associated
into “families” e e     p  e- e- e e n 

31. Helicity “handedness”
For a moving particle state, its lab
frame velocity defines an obvious
direction for quantization ms s
fraction of spin “aligned” in this direction
For spin-½
S = 
·p=H   1 2
though
 ^
|Sz|
|S|
mSħ
s(s+1)ħ mS
s(s+1) = =
Notice individual spin-½ particles have
HELICITY +1 (ms = +½) RIGHT-HANDED
HELICITY +1 (ms = -½) LEFT-HANDED
spin
spin v v s s

32. v s spin However: HELICITY +1 (ms = +½) RIGHT-HANDED not “aligned”
HELICITY +1 (ms = -½) LEFT-HANDED
not “aligned”
just mostly so
But helicity (say of an electron) is not some LORENTZ-INVARIANT
quantity! Its value depends upon the frame of reference: Imagine a
right-handed electron traveling to the right when observed in a frame
itself moving right with a speed > v.
spin v
It will be left-handed! s

33. m < 5.1 eV << me = 0.511003 MeV
So HELICITY must NOT appear in the Lagrangian for
any QED or QCD process (well, it hasn’t yet, anyway!).
HELICITY is NOT like some QUANTUM NUMBER.
It is NOT unambiguously defined.
But what about a massless particle (like the  or…the neutrino?)
m < 5.1 eV << me = MeV e
m < 160 keV 
m < 24 MeV 
Recall for a massless particle: v = c
Which means it is impossible (by any change of reference frame)
to reverse the handedness of a massless particle.
HELICITY is an INVARIANT
a fundamental, FIXED property of a neutrino or photon.

34. Experimentally what is generally measured is a ratio
comparing the number of a particles in a beam, or from a source,
that are parallel or anti-parallel to the beams direction.
Helicity =
Longitudinal polarization turns out to be hard to measure;
Transverse polarization is much easier to detect.
There are several schemes for rotating
the polarization of massive particles.

35. magnetic bending precesses spin
Electro-static bending
magnetic bending precesses spin - - - - - - - - + + + + + - +
to analyzer + - + + - + - + +
aluminum
light element
(metallic)
reflector e-
Coulomb scattering
doesn’t alter
spin direction!
decay source
analyzer

36. Crossed magnetic/electric fields: E B selects the velocity v= c
but the spin precesses about the B-filed direction E E E B B B
Can be built/designed to rotate the spin by a pre-calculated amount
(say 90O)
Following any scheme for rotating spins, beams of particles can be
Spin analyzed by punching through a thin foil of some heavy element!

37. Head-on view of approaching nuclei+ + m
m ,s oppositely aligned! s

38. Sees B of approaching nuclei UP
electron passing nuclei on the right 
Sees B of approaching nuclei UP + + m
“orbital” angular momentum of nuclei
m ,s oppositely aligned!
(  up!) s
positive!
The  interaction makes the potential energy increase with r

39. gives a positive (repulsive) force
negative 
The interaction makes the potential energy increase with r So
gives a positive (repulsive) force
which knocks electrons to the RIGHT!

40. + + electron passing nuclei on the left
Sees B of approaching nuclei DOWN + + m s
“orbital” angular momentum of nuclei
(  down!)
negative! So
gives an attractive force
knocks electrons to the LEFT!

41. H = + for e+, + H = - for e-, - When positive more electrons
scatter LEFT
than RIGHT
When negative
more RIGHT than LEFT
EXPERIMENTALLY
The weak decay products , e v c
predominantly
right-handed
H = for e+, + v c
H = for e-, -
predominantly
left-handed

42. Until 1960s
assumed, like s neutrinos come in both helicities: +1 and -1
…created in ~equal numbers (half polarized +1, half -1)
1961
1st observed PION DECAYS at REST _
(where ,  come out back-to-back)
spins  ,
(each spin-½)
oppositely
aligned! _  
 
spin-0
Were these half +1, half -1?
No! Always polarized RIGHT-HANDED!
So these must be also! + 
 +
Each ALWAYS left-handed!

43. ALL NEUTRINOS ARE LEFT-HANDED ALL NEUTRINOS ARE RIGHT-HANDED
Helicity = ms/s = -1
ALL NEUTRINOS ARE RIGHT-HANDED
Helicity = ms/s = +1

44.  j  -sj 0 Dirac Equation (spin-½ particles) (  p my  0 0 sj
( 0 p0  • p y  my
 j 
p • ( ) = ( )
0 s
-s 0
p • s
- p • s
where p • s = px( ) + py( ) + pz( )
0 1
1 0
0 -i
i 0
1 0
0 -1
= ( )
pz px-ipy
px+ipy pz

45. y (r,t) = a exp[i/h(Et-p • r)]u(E,p) a e(i/h)xm pmu(E,p)
Our “Plane wave” solutions (for FREE Dirac particles)
y (r,t) = a exp[i/h(Et-p • r)]u(E,p) a e(i/h)xm pmu(E,p)
(  p mu = ( )( )
which gave
E/c-mc p•s uA
p•s E/c-mc uB
from which we note:
uA = ( p • s ) uB uB = ( p • s ) uA c
E-mc2 c
E+mc2

46. ( g 5 -(p • s )I )y = -img 1g 2g 3y c g 0 -pxg1-pyg 2-pzg 3 = my
Dirac Equation (spin-½ particles) E c
g 0 -pxg1-pyg 2-pzg 3 = my
recall
g 5=ig 0g 1g 2g 3
multiply from left by (-ig 1 g 2 g 3 )
-ig 1g 2g 3g 0 = +ig 0g 1g 2g 3
= g 5
since g mg n= -g ng m
-ig 1g 2g 3g 1 = -i(g 1)2g 2g 3 = +ig2g 3
= +i(s2s3)( )( )
= +i(is1)( ) = s1I
since
(g i)2 = -I
0 1
-1 0
0 1
-1 0
-1 0
0 -1
so -px g 1  - px s 1I
-ig 1g 2g 3g 2 = s2I
-ig 1g 2g 3g 3 = s3I
( g 5 -(p • s )I )y = -img 1g 2g 3y E c

47. ( g 5 -(p • s )I )y = -img 1g 2g 3y ( |p|g 5 -(p • s )I )y = 0
This gives an equation
that looks MORE complicated!
How can this form be useful?
( g 5 -(p • s )I )y = -img 1g 2g 3y E c
For a ~massless particle (like the or any a relativistic Dirac particle E >> moc2)
E=|p|c as mo (or at least mo<<E)
Which then gives:
( |p|g 5 -(p • s )I )y = 0
or:
( g 5 -p • s I )y = 0 ^
s 0
0 s
s I =
What do you think this looks like?
p • s I ^
is a HELICITY OPERATOR!

48. ( p • s I )u(p) = u(p) ( g 5 -p • s I )y = 0 So 5 “measures”
In Problem Set #5 we saw that if the z-axis was
chosen to be the direction of a particle’s momentum
were all
well-defined
eigenspinors
of Sz
i.e.
( p • s I )u(p) = u(p) ^
“helicity states”
( g 5 -p • s I )y = 0 So ^
5 “measures”
the helicity of y
g 5y = (p • s I )y ^

49. (p • s I)u(p) g 5u(p) = = uA uB uB uA g 5u(p)= Looking specifically at
For massless Dirac particles (or in the relativistic limit)
(p • s I)u(p)
g 5u(p)= ^

50. uL(p)= u(p) We’ll find a useful definition in the “left-handed spinor”
Think:
“Helicity=-1”
(1- 5) 2
uL(p)= u(p)
In general NOT an exact helicity state (if not massless!)
Since 5u(p) = ±u(p)
for massless or relativistic Dirac particles
if u(p) carries helicity +1
u(p) if u(p) carries helicity -1
if neither it still measures how close
this state is to being pure left-handed
separates out the “helicity -1 component”
Think of it as a “projection operator” that
picks out the helicity -1 component of u(p)

51. 5 v(p) = -(p· I)v(p) vL(p)= v(p) uR(p) = u(p) vR(p)= v(p)
 
5 v(p) = -(p· I)v(p)
Similarly, since for ANTI-particles:
again for m 0
(1+ 5) 2
we also define:
vL(p)= v(p)
with corresponding “RIGHT-HANDED” spinors:
(1+ 5) 2
(1- 5) 2
uR(p) = u(p)
vR(p)= v(p)
and adjoint spinors like
since
 5†= 5
since  5   = -   5

52. Chiral Spinors Particles uL = ½(1- 5)u uR = ½(1+ 5)u uL = u ½(1+ 5)
Anti-particles
vL = ½(1+ 5)v
vR = ½(1- 5)v
vL = v ½(1- 5)
vR = v ½(1+ 5)
Note: uL+ uR = ( )u + ( )u = u
as well as ( ) ( ) u = ( ) u
=( ) u =( ) u = uL
as well as ( ) ( ) u = uR = uR
1- 5 2
1+ 5 2
Truly PROJECTION
OPERATORS!
1- 5 2
1- 5 2
1-2 5+( 5)2 4
2-2 5 4
1- 5 2
1+ 5 2
1+ 5 2
1+ 5 2