_{1}

^{*}

The magnetic moments of the baryon octet are derived from a first principle’s theory, the scalar strong interaction hadron theory, and are in approximate agreement with data. It is conjectured that this agreement may be improved by including the “spin-orbit coupling” term not evaluated here.

The existing treatments of baryon magnetic moment are all phenomenological and based upon models [

The baryon magnetic moment has been treated [

These two approximations are removed here and the factor 1/3 drops out; the results are now in approximate agreement with data. This paper is thus nearly the same as the 1994 paper [

Here, I, II and III refer to the three quarks, x stands for the 4 vector x^{m}, c and y the baryon wave functions in space time where the undotted and dotted spinor indices run from 1 to 2, F_{b} the interquark scalar strong interacton ([

The d function is not a Lorentz invariant. Further, z, u, and v stand for the internal coordinates z_{I}, z_{II} and z_{III}, respectively, x the internal baryon function, p, s, q the flavors of the three quarks, m_{3op} the quark mass operator ([_{op}_{ }the quarks charge operator ([

The normalized internal functions for the octet baryons reads ([

In passing, it is pointed out that these internal functions [_{psq} = (x^{psq})^{*} via [

These q’s are given on lines 2 and 3 of

Gauge invariance of (1) is shown in the same way as that for mesons in ([

. Octet baryon magnetic moments from (17) using the q’s from (5). There are no data for S^{0}, only the transition magnetic moment S^{0} ® L

proton | neutron | L | S^{+}^{} | S^{0} | S^{-}^{} | X^{0}^{} | X^{-}^{} | |
---|---|---|---|---|---|---|---|---|

q_{I}/e = q_{III}/e | 1/2 | -1/6 | -1/12 | 1/2 | 1/12 | -1/3 | -1/6 | -1/3^{} |

q_{II}/e from (5) | 0 | 1/3 | 1/6 | 0 | -1/6 | -1/3 | 1/3 | -1/3 |

m_{b} (17) | 3 | -1.997 | -0.841 | 2.367 | 0.787 | -0.783 | -1.427 | -0.71 |

m_{b} data [2] | 2.793 | -1.913 | -0.613 | 2.458 | 1.61(S^{0}®L) | -1.16 | -1.25 | -0.6507 |

Taking the left operator of (1b) and operating it on (1a) and making use of (1b, 3-6) leads to [

where _{3op} ([_{B}(c,q) by reversing the roles of (1a) and (1b). Note that the three braced operators refer to different coordinates and therefore commute with each other.

Following [

so that by relations of the type of (2),

The relative energies in [

In the the absence of electromagnetic perturbation or putting the A´s to zero, (1) reduces to the zeroth order equations ([

(a) illustrates the general (9a), (b) the zeroth order quark-diquark configuration with x_{I} = x_{III} = x_{I}_{,III}, d = 1/2 in (9a), ([4] (10.1.1)), X_{0} denotes the zeroth order laboratory coordinates, (c) special case of (a) with c = 1/2 and d = 1/3, giving a maximally allowed E_{1b} in (16)

where the subscript 1 denotes first order pertubation, E_{0} denotes the baryon mass and

Let the external magnetic field be

where j_{g}(X) is a gauge functon. With (9), we find

The apparoximation made beneath (4.1) in [

After inserting (10) into (7), we wish to obtain the perturbed baryon energy E_{1b} as a function of the first order q´s there. With (2), (9), (11), and

The zeroth order part of the remaining two braces in (7) is found from (9) and

The first order parts of the second and third braces in (7) are analogously found; the associated zeroth order parts are of the same form as the last of (14). The first order part of (7) now reads

Here, it has been noted that _{0 }differ by a quantity independent of each of them so that_{b} for a free baryon and m_{3op} are not affected by the perturbative A fields and operate only on zeroth order wave functions. The argument of c and F_{b} has thus been changed to reflect that _{B}_{1} denotes the first order part of (8).

The dominating contributions to the energy shift E_{1b} in the first term of (15) comes from the three qs_{3} terms on the left of (15) which contribute equally, but of opposite signs, to E_{1b} for spin up and spin down wave function components shown in (16b) below. The second and third terms on the right of (15) are just the zeroth order part of (7, 8) and can be absorbed into it. The first and last terms on the right of (15) do not contain s_{3} splitting term and their contributions to E_{1b }are of the same sign for the spin up and down components. These contributions, to the degree that they are of equal magnitude, cancel out in the evaluation of the magnetic moment. These two terms will be ignored here to arrive at an approximate expression of the magnetic moment.

The zeroth order c on the remaining left of (15) for the spinor index c = 1, 2 are eigenfunctions of the qs_{3} operators; we obatin the equivalent of [

The doublet wave functions ([_{0}(r) and f_{0}(r) have been plotted in ([

The space dependent part associated with O_{b} in (16a) drops out, just like that in [_{1b} is found for c = 1/2 and d = 1/3, same as [_{p} be the proton massn magnetic moment reads

which is 3 times the 1994 result ([

The baryon magnetic moment has been treated for the first time starting from a first principle’s theory, the scalar strong interaction hadron theory, that the predicted results are in approximate agreement with data which lends further support to the fact that this theory is basically viable and can replace QCD at low energies.

It is conjectured that the difference between the last two lines in _{B1} on the right of (15). This “rest” term arises from the strong quark-diquark interaction F(r); its effect resembles spin-orbit coupling in atomic physics. Its inclusion calls for numerical integration. The last term of (15) can be balanced off by including the equally probable spin down m = -1/2 wave functions of [_{g}(X) in (11); the simplest form is a constant which does not contribute to (11).