I gave some iron chelate last week and the situation look the same, I am thinking that this branch as a root problem.
For what I know Mugo pine have a direct connection between the branch and the root, the black pine not, so if some root have problems the relative branch have problem, that way some branch have this problem and the other are super green
So I am thinking that can be too much water with a bad soil.
The plant have had a slip repot with the original soi, I just removed a little bit of the old soil because the plant was really very week so I put in a bigger pot with pure pumice.
Probably the difference in substrate and also the old soil give some problem to the roots, I gave root anti fungine ( FOSETIL ALLUMINIUM) and I move the plant under cover so she takes sun but no rain.
We will see next days
Good branch
Sick ones