My new particle has zero mass, like the photon, but it oscillates between states. Three states, these being high, low, and level. In level state, the Petrino is stable, and sits inert on its world line, going with the flow, completely disinterested in doing anything remotely energetic. In this state it can be influenced by other particles and forces, but won't do anything in response. In low state, it acquires a capacity to interact and will respond, if somewhat vaguely, to what is going on in its field of cause and effect. In high state, it does exactly as it likes and won't take no for an answer, becoming very influential and much more likely to affect than to be affected by. Like the photon, it can be transformed into many material conditions due to its incredible flexibility.
I'd give it an equation, but I don't do equations. If someone else wants to, be my guest. Send it to me - I'd love to see what the formula looks like. The Petrino's relationship with gravity is flexible too, so you shouldn't have any infinities to worry about. Its relationship with gravity accords to its energy, not to mass, because it doesn't have any. Petrinos don't need mass - matter would just get in the way of its freedom to do as it wishes.
Possibly in Bflat.
When it does, I want your word on just one thing. The Petrino belongs to me.