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Hi people: I keep reading one day that weak isospin is exactly conserved by all interactions; other days that sometimes weak isospin is *not* conserved. Can anyone clear this one up?!
Ask there for processes that violate the conservation?other days that sometimes weak isospin is *not* conserved.
The weak isospin is not conserved by any interaction... The left-handed components of all elementary fermions are assigned weak isospin 1/2. The right-handed components have T_{w} = 0. The non-conservation of weak isospin is already apparent in the fact that, with the possible exception of the massless neutrino, there is no particle with a definite handedness and therefore with a defined weak isospin.
The Higgs field is chosen to be an isospin doublet specifically to guarantee that the interaction term e_{R} v E_{L} = (singet) (doublet) (doublet) comes out to be invariant under isospin, and consequently conserves isospin. The vacuum state spontaneously breaks the symmetry, but that's unrelated to the effect of the interaction term with fermions.Isospin is exactly conserved before symmetry breaking but it is not conserved after symmetry breaking because the Higgs field is not an isospin singlet and it forms a condensate. Particles are moving through this condensate at all times and interacting with it.
Spontaneous symmetry breaking is not what's involved. As the book points out, any interaction that fails to preserve handedness, fails to conserve weak isospin.
Also, the electromagnetic interaction disconserves weak isospin, the photon being a mixture of T_{w} = 1 and T_{w} = 0.
I am talking about the weak isospin. I am not sure how post #6, which says that symmetry breaking is not involved, is consistent with #8, which looks like the Higgs breaks this symmetry. If someone can write some math and explain this.I am getting confused with the isospins...
What kind of isospin are we talking about? The SU(2) of the SM is broken by the Higgs mechanism...
The SU(2) isospin which appears in the strong sector is conserved by strong interactions (in the limit of massless quarks) and is broken (except for the 3rd component) by electromagnetic...
But...what I find in wikipedia(Weak isospin, the second paragraph) is that The weak isospin conservation law relates the conservation of T3; all weak interactions must preserve T3. It is also conserved by the other interactions and is therefore a conserved quantity in general. (Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3.[1]).Quoting from this Google book:
But...what I find in wikipedia(Weak isospin, the second paragraph) is that The weak isospin conservation law relates the conservation of T3; all weak interactions must preserve T3. It is also conserved by the other interactions and is therefore a conserved quantity in general. (Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3.[1]).
So I am confused again...
Sorry, I didn't see that difference. Thanks to point it out.I think one needs to distinguish between the "weak isospin" (##T##, ##\vec{T}##, ##I##) and "third component of the weak isospin" (##T_3##, ##I_3##). The first one is apparently what this book is referring too, while the conservation law from wikipedia is about the latter one (note the next sentence after your quote: "For this reason T3 is more important than T and often the term "weak isospin" refers to the "3rd component of weak isospin".").
But...what I find in wikipedia(Weak isospin, the second paragraph) is that The weak isospin conservation law relates the conservation of T3; all weak interactions must preserve T3. It is also conserved by the other interactions and is therefore a conserved quantity in general. (Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3.[1]).
So I am confused again...