Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Octet Baryon Magnetic Moments from an SU (3) Flavor-Symmetric
Lattice QCD Calculation†∗1 on behalf of the NPLQCD Collaboration
Tiburzi∗1on behalf of the NPLQCD Collaboration
B. Tiburzi,

where: Q = diag( 23 , − 13 , − 13 ) is the quark electriccharge matrix; the octet baryon ﬁelds are described bya matrix B, which can be expanded in terms of SU (3)F
8agenerators, B = a=1 B a λ2 ; and, angled brackets areused to denote ﬂavor traces.
The Coleman-Glashow moments are directly calculated by NPLQCD using an SU (3)F -symmetric ensemble of gauge conﬁgurations with the octet meson massmπ ∼ 800 MeV, and with the addition of backgroundmagnetic ﬁelds coupled to the valence quarks. Asidefrom tiny electrodynamic eﬀects  1%, there are noquark-disconnected contributions to the baryon magnetic moments at an SU (3)F -symmetric point due tothe condition Q = 0. The determination of μD andμF at this quark mass is very precise, see Fig. 1.
Away from the limit of SU (3)F symmetry, theColeman-Glashow moments can be obtained with additional assumptions. From calculations performed using an Nf = 2 + 1 ensemble of gauge conﬁgurations,with a corresponding pion mass of mπ ∼ 450 MeV, theoctet baryon magnetic moments are also determined.
The nucleon moments are utilized to determine μDand μF , because SU (3)F breaking only arises from thestrange quark in the sea. This eﬀect is proportional to†∗1Condensed from the article arXiv:1609.03985
Department of Physics, The City College of New York(CUNY); and RIKEN Nishina Center- 131 -

The external-ﬁeld technique and its more recent generalizations are powerful tools with which to compute
structural properties of hadrons using lattice QCD(LQCD). Such external magnetic ﬁeld computations
have been performed recently by NPLQCD, in particular: the ﬁrst computation of the magnetic moments oflight nuclei1) , the computation of the magnetic transition moment that dominates the np → dγ radiativecapture process2) , the determination of magnetic polarizabilities of light nuclei3) , and the evidence suggesting the unitary limit of two-nucleon interactions might
be achieved in strong magnetic ﬁelds4) . In this summary, however, we do not focus on few-nucleon physics;
instead, we concern ourselves with the single-baryon
sector in order to review the computation of magnetic
moments within the lowest-lying octet of baryons.
In the limit of SU (3) ﬂavor symmetry, in which
mu = md = ms , the octet baryon magnetic moments
are determined by just two parameters. These are theColeman-Glashow moments, μD and μF , which appear
in the Hamiltonian densitye μD B{Q, B} + μF B[Q, B] , (1)σ ·B
H=−2MB         


Fig. 1. Determined values of the Coleman-Glashow magnetic moments, μD and μF , as a function of the pionmass obtained from LQCD and experiment.

(ms − m)/Nc , where m = 12 (mu + md ), and Nc is thenumber of colors. The eﬀect is estimated to be 6%
on this ensemble. The same argument is applied toestimate the Coleman-Glashow moments from the experimental values of the nucleon moments, where thestrange sea-quark eﬀect is at the level of 11%.a) The
results obtained are depicted in Fig. 1.
The integer values μD = 3 and μF = 2 arise from theSU (6) symmetry of the nonrelativistic quark model. It
is quite surprising how little quark-mass dependence
exists in these moments, and how robust the nonrelativistic quark model appears to be as a function of thepion mass. Chiral-limit values of these moments arealso estimated, but the large uncertainties from chiralextrapolation currently preclude deﬁnite conclusions.
References
1) S. R. Beane et al. [NPLQCD Collaboration], Phys. Rev.
Lett. 113, 252001 (2014), arXiv:1409.3556 [hep-lat].
2) S. R. Beane et al. [NPLQCD Collaboration], Phys. Rev.
Lett. 115, 132001 (2015), arXiv:1505.02422 [hep-lat].
3) E. Chang et al. [NPLQCD Collaboration], Phys. Rev. D
92, 114502 (2015), arXiv:1506.05518 [hep-lat].
4) W. Detmold et al. [NPLQCD Collaboration], Phys. Rev.
Lett. 116, 112301 (2016), arXiv:1508.05884 [hep-lat].
a)

Notice that SU (3)F -breaking quark-disconnected contributions are proportional to (ms − m)/Nc2 , and are hence subleading compared to those estimated above.