Authors: Syed Afsar Abbas
The topological Skyrme has been actively studied in recent times (e.g. see Manton and Sutcliffe, Topological Solitons, Cam U Press, 2004) to understand the structure of the nucleons and the nucleus. Here through a consistent study of the electric charge, it is shown that just the Skyrme lagrangian by itself, gives charges as, Qp = 1/2 and Qn = − 1/2 ; shockingly missing their empirical values. This devastating problem is rectified, only by includig an extra term (not available at Skyrme’s time), arising from the Wess-Zumino anomaly. One then obtains Qu = 2/3 and Qd = − 1/3 , and thus giving the correct charges of the nucleon. It is also shown here (for the first time), that the combined Skyrme-Wess- Zumino lagrangian predicts, colour-number dependence of the electric charges as: Q(u) = 1/2(1 + 1/Nc ); Q(d) = 1/2(−1 + 1/Nc) for arbitrary colour-number of the QCD group SU(Nc). This gives 2/3 and -1/3 charges for Nc=3. Thus it is not good enough to just have the value of charges as 2/3 and -1/3. We show that it is important to have a proper colour dependence existing within the guts of the quark charges. Though the quarks have colour built into its guts, composite protons and neutrons built up of odd-number-of-colours of quarks, turn out to be colour-free with fixed values of 1 and 0 charges, respectively (and which is good for self-consistency of QCD+QED); while the proton and neutron built up of static (colour-independent) charges 2/3 and -1/3, develop explicit colour dependence (and which is disatrous for these models).
Comments: 10 Pages.
[v1] 2019-01-12 13:08:35
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