Musings

Skyrme Fun

A while back, I wrote about the possible discovery of an exotic baryon state, $\Phi^+$, with mass $m=1540 \mathrm{MeV}$, width $\Gamma\lt 22 MeV$ and flavour quantum numbers $u u d d \overline{s}$. Truth be told, this was but one of several observations of the same resonance.

What I didn’t say was that this flurry of experimental work was actually the result of a theoretical prediction of the existence of this state on the basis of Skyrme model calculations by Diakonov, Petrov & Polyakov. They found a set of states in the $\overline{10}$ of $SU(3)$. By fitting the masses of two of these excitations to the observed N(1710) and $\Sigma$(1880) resonances, they predicted that the lightest member of the $\overline{10}$ would be the $\Phi^+$, with a mass and width ($m=1530 \mathrm{MeV}$, $\Gamma\lt 15 \mathrm{MeV}$) extremely close to the (now) experimentally-observed values.

Recently, Itzhaki, Klebanov, Ouyang, and Rastelli have looked a little more closely at the large-$N_c$ Skyrme Model. They argue that, in the “bound state” approach of Callan & Klebanov (Nucl. Phys. B262 (1985) 365), this resonance does not appear — unless you do something rather artificial, like crank up the SU(3) symmetry-breaking ($m_s \gt 1\mathrm{GeV}$).

I don’t know what to make of this. Diakonov et al’s “rigid rotator” approximation results at $N_c=3$ are way too good to be dismissed out-of-hand. It would be sad if there weren’t a clean way to derive them from large-$N_c$.