Weak isospin

It is easy to see from [59] that for nuclei with more than one nucleon the expression in (10.38) would contain an extra factor equal to the eigenvalue of the doubled third component 2T3 of the weak isospin operator. 

Leptons and quarks, the three families of basic fermions. T3 is the third component of the weak isospin, the rest of the notation is explained in the text step by step. The meaning of the subscript L and the apostrophe after some of the symbois is expiained in O Sect. 8... 

The other two interactions do conserve the parity of a system, i.e., remember which way a particle was polarized before the interaction, whereas the weak interaction maximally violates it. This maximal violation manifests itself in the fact that the particles emitted in weak interaction tend to be polarized left (their spin pointing preferentially against the direction of the momentum) and the antiparticles polarized right (spin and momentum having the same direction) independently of any former polarization this is indicated by the symbol L for left at the weak isospin doublets of the particles. The case of the neutrino is extreme in the limit of zero mass the neutrino can only exist left-polarized and the antineutrino only right-polarized. 

One took three different gauge theories, supplied them with some free parameters, added an ad hoc Higgs mechanism to make it work, and the result seems to function properly. It is not known exactly why those three symmetries create the three interactions although the U(l) symmetry is clearly related to the electromagnetic charge, the SU(2) to the weak isospin, and SU(3) to the three colors. It is not clear why there are exactly three fermion families and how the fermions of a family are related to each other (apart from the sum of their charges). It is not known why there is no antimatter in the Universe, and there is the deep mystery of dark matter astronomical observations indicate that about 90% of the mass of the Universe is invisible, probably non-baryonic matter that cannot be explained within the framework of the Standard Model (Amsler et al. 2008). 

It is then assumed that the weak interactions couple to the left-handed weak isospin doublets... 

A similar mechanism can be invoked to give mass to the quarks [though there may be other sources of mass for the quarks (see Section 20.3)], but this would leave the up-type quarks, the analogues of the neutrinos, massless. In order to construct an interaction invariant under weak SU(2) and weak U 1) which will give mass to the quarks with = 1/2, it turns out, on the basis of Table 9.2, that we need a Higgs doublet with Yw = —1-Recall that = has Y y = 1, and is a weak isospin doublet. Recall also, that for ordinary isospin, the nucleon doublet N = ( ) and the antinucleon doublet N = (jp) (note the minus sign ) transform identically under isospin rotations. By analogy... 

In the standard model the coupling of the Z to each flavour depends only on the weak isospin of the qq pair. The widths in the Born approximation are from (8.6.9)... 

Let us substitute wave functions, Eqs. (A.9) and (A. 10), taking count of Eqs. (A.ll) and (A. 12), into the matrix element in the initial expression, Eq. (8) (Section II). The weak-interaction Hamiltonian Hfj acts on the charge (isospin) wave functions of the leptons and of the radioactive nucleus n, as... 

The reason we include in our discussion, is the fact that this nucleus with T =, the JT = 10 two-body matrix elements, discussed above in connection with the increased binding provided by a potential with a weak tensor force, come into play. For which has isospin T = 2, these matrix elements do not occur. It is therefore instructive to compare the spectra obtained with all three Bonn potentials for these two nuclei. 

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