Subatomic Physics

7.3. The Baryon Number 207
antineutron. (See Section 5.10 for a discussion of antiparticles.) Leptons, photons,
and mesons are assigned A = 0. (Particle physicists use B for baryon number, but
we follow the convention of the nuclear physicists here.) The additive conservation
law for the baryon number then reads
� Ai = const. (7.31)
The extent to which Eq. (7.31) holds can be described by a limit on the lifetime of
the nucleons. A geochemical method examining decays of nucleons in 130 Te gives a
lower limit of 1.6 × 10 25 y. (9) A better limit is found by measuring possible decays
in a large quantity of water, which contains many protons, and with very large
counters that are shielded from cosmic rays by being deep underground. (10) The
limit then becomes about 10 30 y; for the specific decay p → e + π 0 , the lower limit is
1.6 × 10 33 y. (11) We do not have to live in fear of wasting away through the decay
of nucleons.
The discovery of strange particles led to a generalization of the law of nucleon
conservation. Consider, for instance, the decays
Λ ◦ −→ nπ 0
Σ +
�
0 −→ pπ
−→ Λe + v
Σ − −→ nπ − .
In each of these decays, the baryon number is conserved if it is generalized to read
A =1 forp, n, Λ, Σ, Ξ, Ω
and A = −1 for the corresponding antiparticles. Similarly, resonances and nuclei
can be characterized by their baryon number A. Since nuclei are built up from
protons and neutrons, the baryon number A is identical to the mass number, introduced
in Section 5.9. Hypernuclei are similar to nuclei, but one or two nucleons are
replaced by a hyperon.
As in the case of the electric charge, the question of the symmetry responsible
for baryon conservation arises. Again, a global gauge transformation
ψ ′ = ψe iɛA
(7.32)
leads formally to the conservation law, Eq. (7.31). If the gauge invariance were a
local one then there should be a long range field, similar to the electromagnetic
9J.C. Evans and R.J. Steinberg, Science 197, 989 (1977).
10S. Weinberg, Sci. Amer. 231, 50 (July 1974); J. M. Lo Secco, F. Reines, and D. Sinclair, Sci.
Amer. 252, 54 (June 1985).
11PDG. Also J. Bartelt et al., Phys. Rev. Lett. 50, 651 (1983); M. Goldhaber in Interactions
and Structures in Nuclei, (R. J. Blin-Stoyle and W. D. Hamilton, eds.) Adam Hilger, Philadelphia,
1988, p. 99.