Anomalous tensor magnetic moments and form factors of the proton in the self-consistent chiral quark-soliton model

We investigate the form factors of the chiral-odd nucleon matrix element of the tensor current. In particular, we aim at the anomalous tensor magnetic form factors of the nucleon within the framework of the SU(3) and SU(2) chiral quark-soliton model. We consider $1/N_c$ rotational corrections and linear effects of SU(3) symmetry breaking with the symmetry-conserving quantization employed. We first obtain the results of the anomalous tensor magnetic moments for the up and down quarks: $\kappa_{T}^{u}=3.56$ and $\kappa_{T}^{d}=1.83$, respectively. The strange anomalous tensor magnetic moment is yielded to be $\kappa_{T}^{s}=0.2\sim -0.2$, that is compatible with zero. We also calculate the corresponding form factors $\kappa_{T}^{q}(Q^{2})$ up to a momentum transfer $Q^{2}\leq 1\,\mathrm{GeV}^{2}$ at a renormalization scale of $0.36\,\mathrm{GeV}^{2}$.