Depends on your definition of producer and how you agree/contract to provide your services
If you are the kind of producer that means you create all the music then you are at the same level as the songwriter/composer
If you are the kind of producer who provides a service of getting the best out of performers managing the budgets (time and money) and contracting musicians then you are probably on a one time payment plan rather than an ongoing sharing of royalties
You can share in royalties if the songwriters (composers and lyricists) cut you in on the split sheet - some do, some don't; some will consider it, some won't!
Don't forget that in this game the people who must be paid up front or just after are the contracted musicians, the recording engineers, the mix engineers, the mastering engineers. Any money that flows from royalties will go towards paying of the advance (loan) from the label/venture capitalist/bank first and only after that has been finalised, does any one else see any of that royalty money
Singers, songwriters, band members, etc get paid on the smell of an oily split sheet in the never never of 4 or 5 quarters in the future - if that is what you want to pursue by all means sign a split sheet and expect to never see any money or to wait a very long time for any money