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Paper text:
magnetic moments are an important fundamental property of particles .
they determine dynamical response of a bound system to external perturbations , and provide valuable insight into internal strong interaction structure .
there are at least two ways to extract the magnetic moment .
one is from form factors ( three - point functions ) where an extrapolation to @xmath1 is required .
the other is the external field method using only two - point functions  @xcite .
here we report a calculation in the latter .
it is an extension of our work on electric and magnetic polarizabilities  @xcite .    in order to place a magnetic field on the lattice
, we construct an analogy to the continuum case .
the fermion action is modified by the minimal coupling prescription @xmath2 where @xmath3 is the charge of the fermion field and @xmath4 is the vector potential describing the external field . on the lattice ,
the prescription amounts to a modified link variable @xmath5 . choosing @xmath6 , a constant magnetic field b can be introduced in the @xmath7-direction
. then the phase factor is @xmath8 on a finite lattice with periodic boundary conditions , to get a constant magnetic field , b has to be quantized by the condition @xmath9 to ensure that the magnetic flux through plaquettes in the xy - plane is contant .
however , for @xmath10 and @xmath11 , the lowest field would give the proton a mass shift of about 390 mev , which is too large ( the proton is severely distorted ) .
we abandon the quantization condition and choose to work with smaller fields . to minimize the boundary effects , we work with fixed ( or dirichlet ) b.c . in the x - direction and large @xmath12 , so that quarks originating in the middle of the lattice have little chance of propagating to the edge .
we use @xmath0 lattice at @xmath13 , and six kappa values @xmath14=0.1515 , 0.1535 , 0.1545 , 0.1555 , corresponding to pion mass of 1015 , 908 , 794 , 732 , 667 , 522 mev .
the strange quark mass is set at @xmath14=0.1535 .
the souce location is ( x , y , z , t)=(12,1,1,2 ) .
we analyzed 87 configurations .
the following five dimensionless numbers @xmath15=+0.00036 , -0.00072 , + 0.00144 , -0.00288 , + 0.00576 give four small b fields at @xmath16=-0.00108 , + 0.00216 , -0.00432 , + 0.00864 for both u and d ( or s ) quarks .
note that `` small '' here is in the sense that the mass shift is only a fraction of the proton mass : @xmath17 0.6 to 4.8% at the smallest pion mass . in absolute terms , @xmath18 tesla .
the mass shift in the presence of small fields can be expanded as a polynomial in b , @xmath19 to eliminate the contamination from the even - power terms , we calculate mass shifts both in the field @xmath20 and its reverse @xmath21 , then take the difference and divide by 2 .
so our calcaulation is equivalent to 11 separate spectrum calculations : 5 orignal @xmath22 values , 5 reversed , plus the one at zero field to set the baseline . for a dirac particle of spin @xmath23 in uniform fields , @xmath24 where the upper sign means spin up and the lower sign means spin - down , and @xmath25 .
we tried the following three methods to extract the g factors , and found they are equivalent within statistical errors .
@xmath26 @xmath27 @xmath28 the results quoted are from eq .
fig .  [ octp_linear_shift ] displays a typical mass shift as a function of the field for the proton .
there is good linear behavior going through the origin , an indication that contamination from the higher terms has been effectively eliminated .
we only use the two smallest field values to do the linear fit .
[ mag_pn ] shows the results for the proton and the neutron .
the line is a simple chiral fit using the ansatz @xmath29 a more advanced chiral extrapolation could be carried out , using , for example , the prescription in ref .
@xcite . fig .
[ mag_osig ] to fig .
[ mag_dxi ] show the results for other particles .
the agreement with experiment for the @xmath30 is encouraging since no extrapolation is needed for this point .
the experimental value for @xmath31 ( slightly shifted for better view ) is taken from ref .
@xcite . finally , fig .
[ mag_pdecdp ] shows the proton and @xmath31 together .
the opposite curvatures are a signature of quenched chiral physics .
a similar behavior has been observed by  @xcite using the form factor method .
we present a calculation of the magnetic moments of the baryon octet and decuplet using the external field method and standard wilson gauge and fermion actions in the quenched approximation . 
 progressively smaller static magnetic fields are introduced on a @xmath0 lattice at beta=6.0 and the pion mass is probed down to about 500 mev . 
 magnetic moments are extracted from the linear response of the masses to the external field .