Transcript Multiplet Structure - Isospin and Hypercharges

Multiplet Structure - Isospin and
Hypercharges
• As far as strong interactions are concerned, the
neutron and the proton are the two states of
equal mass of a nucleon doublet. A glance at
Tables 27.2B, C shows that particles can be
grouped in multiplets of equal mass but
different charges. Examples are shown below:
• An important outcome of the multiplicity
number M of an equal mass group is the
concept of Isospin I. This is not a true
mechanical spin but its quantum-mechanical
derivation follows similar lines to that of
electron spin in spectroscopy and obeys
similar rules so that we put M = 2I + 1 for the
charge multiplicity,
• In the case of the nucleon doublet it is reasonable
to assume that they are two states of the same
nuclear particle. They are distinguished only by
their charge and thus by the interaction of the
proton with the electromagnetic field. The
Isospin I = 1/2 is assigned to all nucleons but with
the component I3 = 1/2 for the proton and I3 = 1/2 for the neutron. Here I3 = ±1/2 is the z
component of I . Thus the proton and neutron
form a doublet with the same Isospin. Similarly
for the pion triplet we have M = 3 and 1 = 1 giving
• The kaons are grouped into two pairs with I3 =
± 1/2 for each pair. These are
• Finally, the delta particle , has four states, viz. ,
• for which I =3/2 and the I3 values are 3/2, 1/2,
-1/2and -3/2 respectively. In general there are
2I+1 isospin states for a particle of given I
Using these data we now obtain isospins as
follows:
• Since Y and B are each conserved in strong
and electromagnetic interactions S must also
be so conserved. As S is a function of the
quantum numbers Y and B it becomes
redundant if Y and B are used, although it is
still frequently used.
Classification of Elementary Particles
• By inspection of the list of particles now available
and the multiplet structures to which they
conform it is possible to regroup the mesons and
baryons (all the strongly interacting particles),
using only three of the conserved quantities just
discussed. These are B, Y and I and we can now
refer to these as conserved quantum numbers.
This gives only four basic meson groups eta, pi,
and the two kaon groups according to their B, Y
and I values. These are shown in Table 27.4,
where M is the charge multiplicity.
• These are the well-established resonances.
There are many more which are not fully
confirmed but which would still fit the above
patterns. They are being actively researched. It
is evident then that the large number of
particles can be reduced to simpler descriptions
of families or regularities by the application of
the conservation laws. These regularities or
symmetries are not fortuitous. Is it possible
therefore to devise a physical or mathematical
model which would enable us to explain the
above properties of all the known particles, and
so help us in our search for new particles by
predicting their properties in much the same
way as searching for unknown elements in the
periodic table?