Rescaling of quantized skyrmions: From nucleon to heavy flavored baryons

Abstract

The role of rescaling (expansion or squeezing) of quantized skyrmions is studied for the spectrum of baryons beginning with nucleon and $\Delta(1232)$, and with flavors strangeness, charm or beauty. The expansion of skyrmions due to the centrifugal forces has influence on the masses of baryons without flavor ($N$ and especially $\Delta$). The rescaling of skyrmions has smaller influence on the spectrum of strange baryons, it is more important for the case of charm, and is crucial for baryons with beauty quantum number, where strong squeezing takes place. Two competing tendencies are clearly observed: expansion of skyrmions when isospin (or spin) increases, and squeezing with increasing mass of the flavor. For the case of beauty baryon $\Lambda_b$ satisfactory agreement with data can be reached for the value $r_b= F_B/F_\pi \simeq 2.6 $, for the case of $\Sigma_b$ there should be $r_b\sim 2$, so for the beauty flavor the method seems to be not quite satisfactory because of certain intrinsic discrepances. Some pentaquark states with hidden strangeness, charm or beauty are considered as well.