Negative parity 70-plet baryon masses in the 1 / N c expansion
/ Authors
/ Abstract
The masses of the negative parity $\mathrm{SU}(6)$ 70-plet baryons are analyzed in the ${1/N}_{c}$ expansion to order ${1/N}_{c}$ and to first order in $\mathrm{SU}(3)$ breaking. At this level of precision there are 20 predictions. Among them there are the well known Gell-Mann\char21{}Okubo and equal spacing relations, and four new relations involving $\mathrm{SU}(3)$ breaking splittings in different $\mathrm{SU}(3)$ multiplets. Although the breaking of $\mathrm{SU}(6)$ symmetry occurs at zeroth order in ${1/N}_{c},$ it turns out to be small. The dominant source of the breaking is the hyperfine interaction which is of the order of ${1/N}_{c}.$ The spin-orbit interaction, of zeroth order in ${1/N}_{c},$ is entirely fixed by the splitting between the singlet states $\ensuremath{\Lambda}(1405)$ and $\ensuremath{\Lambda}(1520),$ and the spin-orbit puzzle is solved by the presence of other zeroth order operators involving flavor exchange.
Journal: Physical Review D