I may not be................................;}
As far as the research goes the material used for the mouthpiece is not likely to influence the sound particularly, but old assumptions die hard. Commonly alto players used Meyer HR mouthpieces for jazz, and tenor players often used Otto Link metal mouthpieces for jazz. However different materials can influence the overall size of the mouthpiece, so that a metal mouthpiece may well be smaller than the equivalent HR mouthpiece even though they are identical on the inside, and this may affect the comfort/playability of any particular mouthpiece. I play HR on alto and use metal or synthetic on tenor, both of which are no bigger than the HR alto. I personally find HR a little uncomfortable on Tenor due to the size, and the metal tenor is probably the easiest to "blast" air through, which is where metal may have an edge.
The smaller the chamber generally the more edgy/focussed or louder the mouthpiece is likely to be. You don't say whether you are a tenor or alto (or other) player so recommendations are hard. Also what sort of Jazz do you play - more mellow or brighter sounding. My guess is Tenor. Do say a bit more more about the sound you are looking for and maybe some helpful recommendations will be forthcoming.
Kind regards
Tom😎