Subatomic Physics

212 Additive Conservation Laws
are produced strongly but decay weakly. Pais made the first step to the solution of
the paradox by suggesting that V particles are always produced in pairs. (24) The
complete solution came from Gell-Mann and from Nishijima, who both introduced
anewquantumnumber. (25) Gell-Mann called it strangeness and the name stuck.
We shall describe the assignment of this new additive quantum number by using
well-established hadronic reactions. (26)
We begin by assigning strangeness S = 0 to nucleons and pions, and note that
strangeness is not defined for leptons. Strangeness is assumed to be a conserved
quantity in all interactions that are not weak:
�
Si = const. in hadronic and electromagnetic interactions. (7.42)
i
We have introduced here the first example of a “broken” symmetry: S is assumed
to be conserved in hadronic and electromagnetic interactions but violated in weak
ones. With such a quantum number, the mystery of copious production and slow
decay can be explained easily. Consider the production reaction pπ − → Λ 0 K 0 and
assign a strangeness S = 1 to K 0 . The total strangeness on both sides of the
reaction must be zero, since only nonstrange particles are present initially. The Λ 0
consequently must have strangeness −1 and Pais’ rule is explained: In reactions
involving only nonstrange particles in the initial state, strange particles must be
produced in pairs. Moreover, a single strange particle cannot decay hadronically or
electromagnetically to a state involving only nonstrange particles; such decays must
proceed by the weak interaction, and they are therefore slow. Thus the observed
long lifetime of the strange particles is also explained.
The assignment of strangeness flavor to the various hadrons is based on reactions
that are observed to proceed hadronically. By definition, the strangeness of the
positive kaon is set equal to 1:
The reaction
S(K + )=1. (7.43)
pπ − −→ nK + K −
(7.44)
is observed to proceed with a cross section characteristic of hadronic interactions,
and it therefore yields
S(K − )=−1. (7.45)
24A. Pais, Phys. Rev. 86, 663 (1952).
25M. Gell-Mann, Phys. Rev. 92, 833 (1953); T. Nakano and K. Nishijima, Prog. Theor. Phys.
10, 581 (1953).
26The assignment is much easier now than in 1952 or 1953. An enormous number of reactions
are known now, whereas Pais, Gell-Mann, and Nishijima had to work with very few clues and had
to make imaginative guesses.