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13.4 ELEMENTARY PARTICLE QUANTUM NUMBERS

Finding order in apparent chaos

The interactions and decays of the hundreds of known elementary particles and reso-

nances form what seems to be a bewildering array. Order can be brought into this

situation by assigning certain quantum numbers to each entity and establishing which

of these numbers are conserved and which can change in a given process. We are

already familiar with two such quantum numbers, namely those that describe a particle’s

charge and spin. These quantum numbers are always conserved. In this section we

shall look at some of the other quantum numbers that have proved useful in under-

standing the behavior of elementary particles.

Baryon and Lepton Numbers

One set of quantum numbers is used to characterize baryons and the three families of

leptons. The baryon numberB 1 is assigned to all baryons, and B

1 to all

antibaryons; all other particles have B 0. The lepton numberLe 1 is assigned to

the electron and the e-neutrino, and Le

1 to their antiparticles; all other particles

have Le 

0. In a similar way the lepton numberL 1 is assigned to the muon and

the -neutrino, and the lepton numberL 1 to the tau lepton and its neutrino.

The significance of these numbers is that, in every process of whatever kind, the total

values of B, Le, L, and Lseparately remain constant: the number of baryons and of

each kind of lepton, reckoning a particle as and its antiparticles as , never changes.

An example of particle-number conservation is the decay of the neutron, in which

B 1 and Le 0 before and after:

n^0 →pee

Neutron decay Le:00 1  1

B:  1 10 0

This is the only way in which the neutron can decay and still conserve both energy and

baryon number B.The apparent stability of the proton is also a consequence of the need

to conserve these quantities: there are no baryons of smaller mass, hence it cannot decay.

Example 13.1

Show that pion decay, muon decay, and pair production conserve the lepton numbers LeandL.

Solution

Pion decay →  

L:0 1  1

Muon decay →e  e

Le:0 10  1

L:  10  10

Pair production  →ee

Le:0 1  1

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