Also as above. I have run a lot, and have never found any jacket that works better than not not wearing a jacket.
I usually just wear a wicking T-Shirt. If cold then a Helly Hansen Lifa, with a T-shirt over the top. If very cold then a merino Helly Hansen Lifa with a t-shirt over the top.
I find that this also works very well in rain, keeping me warm and without chafing. In very heavy rain, I’ll just wait 30 minutes before setting off, heavy rain rarely lasts.
*Disclaimer – if you are heading out across remote areas of moors/mountains then you might want to carry a shell.