Neutron in Strong Magnetic Fields

A relativistic world-line Hamiltonian for strongly interacting $3q$ systems in a magnetic field is derived from the path integral for the corresponding Green’s function. The neutral baryon Hamiltonian in the magnetic field obeys the pseudomomentum conservation and allows a factorization of the c.m. and internal motion. The resulting expression for the baryon mass in the magnetic field is written explicitly with the account of hyperfine, one pion exchange, and one gluon exchange (color Coulomb) interaction. The neutron mass is fast decreasing with the magnetic field, losing $1/2$ of its value at $eB\sim 0.25{\mathrm{GeV}}^2$ and is nearly zero at $eB\sim 0.5{\mathrm{GeV}}^2$. Possible physical consequences of the calculated mass trajectory of the neutron, $M_n(B)$, are presented and discussed.

Figure 1

The dynamical baryon mass (without gluon exchange and hf interaction) in GeV as a function of $eB$.

Figure 2

The color Coulomb potential contribution in GeV as a function of $eB$. One can see a saturation at $eB>4{\mathrm{GeV}}^2$ due to a quark loop contribution in the gluon exchange.

Figure 3

The hyperfine diagonal contribution $⟨V_{hf}⟩=\tilde{b}-2\tilde{d}$ from Eq. (64) to the neutron mass in GeV as a function of $eB$.

Figure 4

The neutron mass with hf correction included vs $eB$. The solid line refers to the region where the approximations made are reliable. The dotted line refers to the state $|--+⟩$ with hf as a perturbation. The dashed line shows a possible form of the behavior, satisfying the stabilization theorem.