Acta Physica Hungarica 54 (3--4), pp. 333--335 (1983)

QUARK INTERACTION ENERGIES AND BARYON MAGNETIC MOMENTS

TEJ K. ZADOO and G. Q. SOFI

Department of Physics, S. P. College, Srinagar 190001, India

(Received in revised form 8 November 1982)

Ir is pointed out that exact values of the magnetic moments of SU(3) baryons can be obtained by assuming the dependence of the magnetic moments on the quark interaction energy.

lntroduction

Baryon magnetic moments have attracted great attention during the last few years. Many authors [1-9] employing different techniques have calculated these. The Coleman-Glashow (CG) formulas [10] for the hyperon moments reveal a rather confusing situation; the 2~ + moment is consistent with the CG formula, the A moment which has been measured to good precision deviates significantly from the CG value #A = --0.957. Norte of the other theoretical approaches used so lar have been able to give an overall satisfactory fit.

In this note we presenta fit to the magnetic moments of SU(3) baryons in terms of the quark interaction energies.

Magnetic moments of SU(3) baryons

The mass ofa baryon which is made up of three quarks ql, ql and q2 is given by [I1]

3 B(ql, ql, q2)=2m(qx)+m(q2) + -~ V(ql, ql, 1)+

! 1 3 + -~ V(ql,q2, 1) + ~- V(q,,q~,O) + -~ V(ql,q2,0)+A, (1)

where ro(q) is the mass of the quark q, V(ql, q.. s) is the interaetion term representing the pairing energy between q~ and q2, the third index r~;-~senting the spin, and A is a eonstant. In analogy to SU(3) we assume that the magnetic moment of a baryon is

8* Acta Physica Hungarica 54. 1983

334 TEJ K. ZADOO and G. Q. SOFI

dependent on the charges of the quarks [12-1 and the interaction energies. In analogy to Eq. (1) we write that the magnetic moment of a baryon B is given by

3 1 pn=aQl +aQ2 +aQ3 + ~ V'(ql ,ql , 1) + ~- V'(ql,qz, 1)+

3 1 + ~ V'(qt,q2,0 ) + --~ V'(qt,q2,0 ), (2)

where Q is the charge of the quark 1 and V'(ql, ql, 1) means the interaction term, etc. We assume that in Eq. (2) the interaction energy does not depend on the spin, i.e.

V'(ql, ql, 1)= V'(q~, q~, 0) and V'(qt, q2, 1) = V'(ql, q2, 0).

Then, the Eq. (2) will be modified to

#~n) = a(Q1 + Q2 + Q3) + V'(ql , q l ) + 2 V'(ql , q2)- (3)

The magnetic moments of SU(3) baryons will l~e given by

P(uud) = a + V'(uu) + 2V'(ud)

N(ud,:l) = V'(d,t) + 2 V'(u,i)

Z+(uss)= a+ V'(uu)+ 2V'(us)

S - (dds) = - a + V'(dd) + 2 V'(ds)

~~ V'(ss) +2V'(us)

- (dss) = - a + V'(ss) + 2 V'(ds)

A(udanti, s) = V'(ud) + V'(ds) + V'(us)

Fitting the values of a and Vas follows

a = -0 .788

V(uu)= 3.738 V(dd)= - 1.75 V(ss)= -0 .580

V(ud) = - 0.080 V(ds) = - 0.224 V(us) = - 0.310

The values of the magnetic moments obtained from these values are glven in Table I.

Acta Physica Hungarica 54, 1983

QUARK INTERACTION ENERGIES

T a b l e !

Comparison between the experimental and predicted values of the magnetic moments

Baryon Predicted value Experimental value

P 2.79 2.79 N - 1.91 - 1.91 Z '+ 2.33 2.33 Z ' - - 1 . 4 1 - 1.41 S- ~ - 1.20 - 1.20 ~ - -0.240 - 1.85 .75 A -0.614 -0.614

335

Conclusion

From our results one can conclude that the q u a r k ~ u a r k interaction, which has been usually neglected, has certain deeper influence on the magnetic moments. The discrepancy between the theory and the experiment may be due to relativistic effects, the effects of the q0 sea (meson current) which have to be examined thoroughly and due to the fact that the interaction term V'(q~,q2, 1) may not be exactly equal to V'(ql, q2, 0). These have to be thoroughly examined.

References

1. A. de Rujula, H. Georgi and S. L. Glashow, Phys. Rey., DI2, 147, 1975. 2. M. Ahmad and Tej K. Zadoo, II Nuovo Cimento, 36A, 86, 1976. 3. M. Slaughter and S. Oneda, Phys. Rev., Dl4, 1319, 1976. 4. M. Ahmad and Tej K. Zadoo, Phys. Rey., Dl5, 2483, 1977. 5. A. Bohm, Phys. Rey., DlS, 2547, 1978. 6. H. J. Lipkin, Phys. Rey. Lett., 41, 1629, 1978. 7. Y. Tomozawa, Phys. Rev., Dl9, 1626, 1978. 8. H. J. Lipkin, Phys. Lett., 89B, 358, 1980. 9. G. Brown, M. Rho and V. Vento, Phys. Lett., 97B, 423, 1980.

10. S. Coleman and S. L. Glashow, Phys. Rey. Lett., 6, 423, 1961. li . Tej K. Zadoo and M. Ahmad, lnd. J. Pure and Appl. Phys., 17, 152, 1979. 12. J. J. Kokkedee, The Quark Model, Benjamin, New York, 1969.

Acta Phvsica Hungarica 54 1983