Nucleon and $\Delta$ isobar in a strong magnetic field

Abstract

We investigate the static properties of the nucleon in the presence of strong magnetic fields and discuss the consequent changes of the nucleon structure, based on the Skyrme model. The results show that at large values of the magnetic field ($\sim10^{17}$ to $10^{18} \mathrm{G}$), which is supposed to appear in heavy-ion collision experiments at RHIC energies, the soliton starts to deviate from the spherically symmetric form and its size starts to change. At extremely large values of the magnetic field ($\sim 10^{19}$ G), which may be found at the LHC experiments, the soliton becomes more compact than in free space. The results also show that in the presence of the external magnetic field, the mass of the nucleon tends to increase in general and the mass degeneracy of the $\Delta$ isobars from isospin symmetry will be lifted. We also discuss the changes in the mass difference between the $\Delta$ and the nucleon, $\Delta m_{\Delta\mathrm{N}}$, due to the influence of the external magnetic field. We find that $\Delta m_{\Delta\mathrm{N}}$ increases as the strength of the magnetic field grows.