Since its only 1/2 the plant it may be a disease/virus affecting the plant possibly in the root zone.

The link below scroll down to the wilt portion may assist in figuring out what may be going on.

Mark

Here is a link that might be useful: Check out this link

I see you are trying to support it some way...wire?...string? Did the branch fall over, get bumped into or blown over by wind? Is the branch being constricted by the string/wire? It may have been damaged and it is dying. If that's the case, just prune it off and chalk it up to experience. Take the pods inside and they may still ripen. Tomato cages are good supports for most pepper plants.

noinwi,

I think you solved the mystery.

Any disease should affect the whole plant.

Do you have any male dogs? ;-) sure looks like something after my boys have hiked their legs on it.
Pam