### Colored Baryons Bound by Three-Body Forces

S. Y. Tsai
1977 Progress of theoretical physics
If one accepts the interpretation!) ~3 l that color-nonsinglet meson states have already revealed their existence in recent experiments, one would naturally like to raise the question : Where is the threshold of color-nonsinglet baryons? In the framework of the colored quark model of Han and Nambu'l we want in the present note to propose a new mass formula for baryons on the basis of the conjecture that it is primarily three-body forces operating in the colored SU (3) (denoted hereafter as SU
more » ... ) ") space which are responsible for the binding of three quarks inside a baryon. This formula predicts SU (3) 11 -decuplet baryons to be lower-lying than SU (3) "octet baryons, the former being of mass <;5 Ge V and the latter being unstable against decay into individual quarks. In developing their double SU (3) (SU (3) 1 ;< SU (3) ") scheme of the three-triplet quark model, Han and Nambu 4 l introduced twobody forces operating in the SU (3) 11 space to make ordinary hadrons possible as bound states of the triplets and expressed the total mass of a system of quarks and antiquarks as N M = N,1.t+ v2 :::s :::s FnA Ci) FAn(}). (1) i=j=j A,B Here JJ. is the rest mass of a free ordinary quark or anti-quark (denoted hereafter by q and q; q = u, d, s), N is the total number of the constituents of the system, v2 is a constant having dimension of mass, and FnA's (A, B=1, 2 or 3) are SU(3) matrices in the SU (3) 11 space for individual constituents. In the three-quartet quark model with a badly broken SU (4) 1 symmetry, Eq. (1) may be generalized as 5 l lvf= (N-N 1 ),a+N 1 ;;.' (1) I where ;J.' is the rest mass of a free charmed quark or anti-quark (denoted hereafter by c and c) and N' is the total number of c's and c's. The simple mass formula (1) reproduces in a natural way the empirical observations that SU (3) "-singlet states, among which are ordinary mesons and baryons, are lowest-lying and that their masses are simply equal to the sum of the effective masses of the constituents. One may interpret the interaction energy of the form in Eq. (1) as resulting from exchange of an SU (3) 11 -octet of vector gauge fields (gluons) between every pair of the constituents inside a hadron. 4 ), 6 l