Deviations From Unitary Symmetry for Resonant States

R. H. Dalitz
1965 Proceedings of the Royal Society A  
The symmetry breaking interactions The fact that the meson or baryon states observed to have a particular spin-parity value appear grouped into unitary patterns of charge multiplets has made it appar ent that the strong nuclear interactions satisfy SU3 symmetry. At the same time, the large mass differences which exist between the charge multiplets constituting a given unitary multiplet show clearly that there also exist moderately strong inter actions which do not have this symmetry, although
more » ... ey satisfy the SU2 symmetry of charge independence and the gauge symmetry of hypercharge conservation. The simplest hypothesis possible for these symmetry breaking interactions is that they have the following unitary tensor form: This hypothesis, with L m s treated as a first order perturbation, leads t formula due to Gell-Mann (1961; 1962) and Okubo (1962). To second order in L m a , the formula M = a0+b1Y + b 2(I(I + 1) -£ F 2) + cx 7 2 + c2 Y ( I ( I + 1) -i 72) + c3(/(J + 1) -£ F 2)2 (2) has been obtained by Okubo (1963). Here the coefficient a0 includes the SU3symmetric mass value for the multiplet, as well as terms of second order in A; the coefficients bv b2 include terms of order A and A2, while cv c2 and c3 are of order A2. For meson multiplets, this expression is to be used for M 2, rather than for the mass M . It appears that the effective expansion parameter in the mass formula (2) is A ~ y $, at most. For the baryon octet, the first order mass formula is quite well satisfied. For any octet, there hold the relations pointed out by Rashid & Yamanaka (1963), namely Y{I(I+1)~£ 7 *) -J 7 , (3o) ( i ( / + i ) -i r 2)a = 2 ( / ( / + i ) -j r 2) -f r a , (36) in consequence of which the general formula (2) reduces to the form M = a0 + b'1Y + b ' (/( / +1) -c£ with b[ = 61 + | c2, & 2 = 62 + 2c3, and c[ = c fc3. Here leading order A2. If we neglect the electromagnetic mass contributions, and use the mean mass for each submultiplet, the second order contributions to (2') are restricted by the relation c[ = £[2 (N + S) -3A -2 ] = -6-5 ± 0*3 MeV, [ 183 ]
doi:10.1098/rspa.1965.0212 fatcat:muy6kv2cn5goxabw46nt7bn4ha