ALL original music is copyrightable.

Although I don't have any jingles out there myself, I have worked with a couple of jingle-writers in the past. My experience says the following (although IANAL):

Jingles are normally licensed to either the product manufacturer or the marketing/production company doing the advertising and hired by the product manufacturer.

Jingles can also be done as a work for hire - not recommended.

Normally, the copyright is still held by the writer. If it's a radio spot, then it's simply a "master use" license. If it's for a TV commercial, then a synchronization license would also be required.

I'm pretty sure that Barry Manilow was collecting royalties for "You deserve a break today" for years, and would be surprised if he sold off those rights. I don't know for sure about PRO involvement though. It may be more what's written into the licensing contract.

For instance, there can be special arrangements such as if the jingle gets used only regionally vs nationally, and what the royalties would be if it gets used for more than a year, or if additional video or TV commercials are made using the same jingle...all those areas are negotiable.