Weak isospin conservation

Sep 2019
21
3
low nuclear orbit
I've heard that weak isospin "is always conserved" and yet "isn't directly observed to be conserved" due to interaction with the Higgs. What does that mean?

It seems to be that in some interactions (these examples also include the Higgs itself):
Higgs decay -> W+ and W-
Higgs decay -> Tau and Antitau
... weak isospin is not actually conserved. In those examples the Higgs had a weak isospin of -1/2, but its resultant particles have a combined weak isospin of zero.

Since electric charge = weak isospin + (weak hypercharge)/2, algebraically it can be shown that just because electric charge is conserved, weak isospin isn't necessarily. For example, if a hypothetical particle had weak isospin 1 and weak hypercharge 1, its electric charge would be 3/2 (= 1 + (1)/2). If it decayed into some other hypothetical particle with weak isospin 1/2 and weak hypercharge 2, that particle's electric charge would be 3/2 as well (= 1/2 + (2)/2) so electric charge would be conserved, but weak isospin would not be. This is just a hypothetical example to show that algebraically electric charge conservation doesn't imply weak isospin conservation.

So when it's stated that weak isospin is conserved, what does that mean?