Rescaling of quantized skyrmions: From nucleon to heavy flavored baryons

The role of rescaling (expansion or squeezing) of quantized Skyrmions is studied for the spectrum of baryons beginning with nucleon and $\mathrm{\Delta }(1232)$ and with flavors strangeness, charm, or beauty. The expansion of Skyrmions due to the centrifugal forces has influence on the masses of baryons with $u$ and $d$ flavors ($N$ and especially $\mathrm{\Delta }$). In the chirally symmetrical case [Adkins, Nappi, and Witten, Nucl. Phys. B228, 552 (1983)], numerical results are confirmed analytically. The rescaling of Skyrmions has some influence on the spectrum of strange baryons, is more important for the case of charm, and is crucial for baryons with a beauty quantum number, where strong squeezing takes place. Two competing tendencies are clearly observed: expansion of Skyrmions when the isospin (or spin) of the baryon increases and squeezing with the increasing mass of the flavor. For beauty the method seems to be not satisfactory, because the ratio $r_b=F_B/F_{\pi }$ necessary to obtain the observed masses of baryons is different for ${\mathrm{\Lambda }}_b$ and ${\mathrm{\Sigma }}_b$ and should be considerably greater than this ratio (theoretical), given in the literature. The approach itself for the case of beauty can be considered as some kind of a "toy model"; however, the necessity of rescaling of quantized Skyrmions is firmly established. Some pentaquark states with hidden strangeness, charm, or beauty are considered as well.