Intrinsic Parity Assignments

p proton +n neutron +d deuteron + charged pion Photon

some

so far…

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

→ →

→

→

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!

Of course we have already described experiments that determined

π → ν

alwaysleft-handed

alwaysleft-handed

Which strengthens the PARITY-VIOLATING observations:

(π → ν )P L L(π → ν )R R

doesn’t exist!

Weak interactions do NOT conserve parity!