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October 8, 2003

Skyrme Fun

A while back, I wrote about the possible discovery of an exotic baryon state, Φ +\Phi^+, with mass m=1540MeVm=1540 \mathrm{MeV}, width Γ<22MeV\Gamma\lt 22 MeV and flavour quantum numbers uudds¯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 10¯\overline{10} of SU(3)SU(3). By fitting the masses of two of these excitations to the observed N(1710) and Σ\Sigma(1880) resonances, they predicted that the lightest member of the 10¯\overline{10} would be the Φ +\Phi^+, with a mass and width (m=1530MeVm=1530 \mathrm{MeV}, Γ<15MeV\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 cN_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>1GeVm_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=3N_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 cN_c.

Posted by distler at October 8, 2003 12:40 AM

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