Lattice calculation of the strangeness magnetic moment of the nucleon

Abstract

We report on a lattice QCD calculation of the strangeness magnetic moment of the nucleon. Our result is G s M (0) = −0.36 ± 0.20. The sea contributions from the u and d quarks are about 80% larger. However, they cancel to a large extent due to their electric charges, resulting in a smaller net sea contribution of −0.097 ± 0.037µ N to the nucleon magnetic moment. As far as the neutron to proton magnetic moment ratio is concerned, this sea contribution tends to cancel out the cloud-quark effect from the Z-graphs and result in a ratio of −0.68 ± 0.04 which is close to the SU(6) relation and the experiment. The strangeness Sachs electric mean-square radius r 2 s E is found to be small and negative and the total sea contributes substantially to the neutron electric form factor.

Study of stochastic estimates of quark loops with unbiased subtraction

“…In Fig. 2 we plot the summed ratio of three to two point functions as a function of the time slice, from which one can obtain the magnetic form factor (see ref [2] for notations). Valence and sea quark mass is kept fixed at κ = 0.154.…”

“…For disconnected loop calculation A will be replaced by the inverse fermion matrix M −1 . Previously it was shown that the above variance for M −1 can be reduced substantially [8,2,3,5] by using a set of traceless matrices obtained from the hoping parameter expansion of the fermion matrix M as…”

“…Lattice QCD results also differ in conclusion. Our previous studies [2] suggest G s M (0) = −0.28 ± 0.10, while ref. [3] reported very tiny signal for G s M .…”

“…Whether we do lattice calculation for quenched or dynamical QCD, these quark loops contribute significantly to various hadronic matrix elements. For example, for nucleonic scalar (πN N -σ term) [1], vector (strange magnetic moment) [2,3], flavor-singlet axial (quark spin) [4], and tensor (quark orbital angular momentum) [5] channels, it is absolutely essential to consider disconnected quark loops. In particular, the strangeness content of the nucleon comes exclusively from these disconnected loops.…”

“…Summed ratio of three to two point functions for different number of noises from 30 to 300. m is the fitted slope which is related to the magnetic form factor [2].…”