Are The Righteous Brothers jazz?

are their songs jazz?

The Righteous Bros. were Rythm and Blues / Soul. They had an album called "Blue Eyed Soul".

I'd call them pop. Jazz can mean many things to many people, but I've never heard of a definition that would include them.

Listen to Diana Krall. She sings jazz well. She's a good contemporary starting point, I think.

Definitely not, more like pop.

They are definitely pop. Some of their songs might have jazzy characteristics or moments (I don't know all of their music well enough to say) but their music itself is not jazz.