Lattice calculation of the magnetic moments of $\Delta$ and ${\Omega }^{-}$ baryons with dynamical clover fermions

We calculate the magnetic dipole moment of the $\Delta (1232)$ and ${\Omega }^{-}$ baryons with $2+1$ flavors of clover fermions on anisotropic lattices using a background magnetic field. This is the first dynamical calculation of these magnetic moments using a background field technique. The calculation for ${\Omega }^{-}$ is done at the physical strange quark mass, with the result in units of the physical nuclear magneton ${\mu }_{{\Omega }^{-}}=-1.93\pm 0.08\pm 0.12$ (where the first error is statistical and the second is systematic) compared to the experimental number: $-2.02\pm 0.05$. The $\Delta$ has been studied at three unphysical quark masses, corresponding to pion mass $m_{\pi }=366$, 438, and 548 MeV. The pion mass dependence is compared with the behavior obtained from chiral effective field theory.

Figure 1

In this figure we show the magnetic moment in units of the physical nuclear magneton for the three input magnetic fields used, as well as quadratic fits to each data set, to remove residual $B^2$ dependence in the magnetic moments.

Figure 2

Chiral effective field theory calculations of Ref. 13 for the $m_{\pi }$ dependence of ${\mu }_{{\Delta }^{+}}$, in units of the physical nuclear magneton. Both real and imaginary parts of ${\mu }_{\Delta }$ are displayed. For the former, the bands show a theoretical error estimate, as described in the text. The value at the physical pion mass corresponds with the experiment of Ref. 14, where both statistical and systematic errors are displayed.