Mum Stems And Buds Dying
Stems with flower buds drying up and dying
Certified GKH Gardening Expert
This appears to be bacterial blotch. Most likely, the soil remained wet for too long or did not dry out thoroughly between waterings.
You can attempt to correct with a fungicide, but since they are annuals they will probably not recover. Most likely, you will need to replant in fresh soil. You will want to wash your container out very thoroughly, also.
Here are a couple of articles that will help: