Intrinsic Parity Assignments p proton+ n neutron+ d deuteron + charged pion Photon some so...
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Transcript of Intrinsic Parity Assignments p proton+ n neutron+ d deuteron + charged pion Photon some so...
Neutral Pions
98.798% 0 1.198% 0 e+e3.14105 % 0 e+ee+e
u
u
0
0
A
B
C
D
msTOTAL
0
2
2
0
0 has 0 spinso can’t produce net angular momentum!
0
A
B
C
D
Recall, under PARITY (inversion/reflections),R-handed spin→L-handed spin
The sign of HELICITY reverses under PARITY.
P: A→D
P: D→A
Note: So the parity invariant states must be
either A D with parity
We can for convenience, decompose circularly-polarized photons into
))()((21 tEitE
yx
+ right circularly polarized ms=+1
left circularly polarized ms=+1
yx EiE
2
1
A ± D = R1R2 ± L1L2each individual photon is PLANE polarized
yxyxyxyx EiEEiEEiEEiE 221122112
1
xyyxyyxx
xyyxyyxx
EEEEiEEEE
EEEEiEEEE
21212121
21212121
21
A + D
A D
yyxx EEEE 2121
xyyx EEEEi 2121
polarized planes PARALLEL
polarized planes PERPENDICULAR
In a direct product representation I can write:
The plane defined by the trajectories of e+e in pair productionare in the plane of the E-vector of the initial gamma ray.
Look at events where both s from the π0 decay both pair produce
and compare the orientation of the two planes:
0 90oThe π0 has ODD PARITY (1)
Dirac Equation
0),(
0),(
0
0
trmii
trmi
j
j
under parity exchange where r r
0),(00 trmii j
j +
Looks like this satisfies a new equation
No longerlooks likeDirac’s eq
That assumed P (r,t)→ (r,t)and simply neglects the 4-momentum-dependent spinor components!
tr ,Whereas satisfies the Dirac equation
(in the original coordinate system)
It is which satisfies Dirac in the inverted system. tr ,0
0),(
0),(
0),(
0),(
0),(
0
00
0
00
0
00
trmi
trmii
trmii
trmii
trmi
jj
jj
jj
0 0
applying r r
so
P (r,t)= 0 (r,t)
P (r,t)= 0 (r,t)
0 =
1 0 0 00 1 0 00 0 1 00 0 0 1
The parity of a fermion is the opposite of its antifermion.
You just showed in homework:
LbLaweak
J bLaL
PP 0†
ba
5
2105
21 11
††
.
.
.
baba 5
21
21
ba )1( 5
21
55
5005
55
†
VECTOR AXIAL VECTOR
This V-A coupling clearly identifies a parity-VIOLATING interaction
The relative sign between these two terms changes under PARITY!The full HAMILTONIAN cannot conserve parity!
As we have seenELECTROMAGNETIC and STRONG INTERACTION terms
in addition to free particle terms in the lagrangian
CONSERVE PARITY
Up until 1956 all the laws of physics were assumedto be “ambidextrous” (invariant under parity).
The biological handedness on earth was assumed to be an evolutionary accident.
• heart on left side• intestines winding in same sense• many chemicals synthesized by plants and animals definite handedness• DNA
(no underlying physical constraint)
1956
Chen Ning Yang Tsung Dao Lee
T.D. Lee andC.N. Yangchallenged theassumption thatthe laws of physicsare ambidextrous…
…pressing for more experimentalevidence for theconservation orviolation of parity
Recall: not ALL conservation principles survive decay!
Between Christmas of 1956 and New Year's Day, physicists at the National Bureau of Standards
operated the low temperature equipmentbeing assembled in this photograph.
The vertical tube (upper right)contained 60Co, a beta-ray counter,
and basic thermometry.
A vacuum flask (lower left) is being placed around the tubeto provide insulation to maintain low temperatures.
Chien-Shiung WuColumbia University
clock-wise: Ernest Ambler, Raymond W. Hayward, Dale D. Hoppes, Ralph P. Hudson
National Bureau of Standards
A crystal specimen ofcerium magnesium nitratecontaining a thin surfacelayer of of radioactive 60Co was supported in acerium magnesium nitratehousing within anevacuated glass vessel.
2 cm above an anthracenecrystal scintillator transmitted its light flashes through a lucite rod out to a photomultiplier.
The magnets on eitherside were used to coolby adiabatic demagnetization.
Inductance coils arepart of the thermometry.
Page 90, Ernest Ambler's Notebookfor December 27, 1956.
The first of two successful runs began at 12:04 (middle of page). Hudson's
notation “Field on” refers to the magnetic field produced by the solenoid.
The crystal was cooled and the 60Co nuclei were polarized in one direction.
Hudson later added “PARITY NOT CONSERVED!”
(see top of the page).
After again cooling the crystal andpolarizing the 60Co nuclei in the
opposite direction, the physicists observed the opposite behavior of
the -particle counts with time.
An initially high counting rate of -particles was observed to decrease as the crystal warmed and the 60Co nuclei became randomly polarized.
“ counts decrease”
For 60Co, at 1 K radiation pattern is uniform in all directions.
At lower temperatures the radiation pattern becomes distorted most easily detected by a -detector aligned with the sample axis though frequently an azimuthal detector is also used.
→ →
→
→
The distribution of emitted directions PEAK in the direction of nuclear spin
Jnucleus · pemittedelectron
→ →
identifying anobservable
quantity that isNOT invariant
to parity!
Here’s a physical processes whose mirror image does NOT occur in nature!