There aren't any specific to shotgun. The FBI penetration standards are an attempt to quantify what it takes for a projectile to reliably hit the vital organs of a threat.
https://pistol-forum.com/showthread....formance-Facts
The typical FBI tests in ordnance gelatin are the standard used for measurement for all firearms. Note that there isn't a 1:1 comparison of penetration in ordnance gelatin and flesh as flesh is a heterogeneous medium (Some tissue is very elastic, some is very hard, and some is very inelastic) DocGKR did a good writeup on defensive munitions for the 12 gauge in the following thread:
https://pistol-forum.com/showthread....or-LE-duty-use
Some of the pictures disappeared, but the data is still solid.
The temporary stretch cavity you see in the first 3/4 of that gel block on impact shows you the synergistic effect of multiple projectiles hitting about the same place at about the same time and how it tends to pulverize tissue. Then the pellets radiate out from the entrance as they are each acted on by the physics of passing through tissue and spread out to hit more structures inside the body.
To put it bluntly, properly performing buckshot is the most destructive thing you can lay on another living creature short of ordnance.
Poorly performing loads like birdshot don't carry enough energy and are stopped very shallowly inside flesh. Think of the difference between being hit by a golf ball and a ping-pong ball. The ping pong ball simply cannot carry enough energy to do any serious damage because it's too light. Same happens with birdshot and smaller buckshot pellets:
That shallow penetration has real-world consequences.
Birdshot used against an oblivious coed at probably 10 feet or so is insufficient to stop her from walking away and calling the cops.
Shotguns aren't magic. We're trying to hit the same things with a shotgun as we are with a rifle or a pistol because that's how you reliably incapacitate a threat. A properly loaded shotgun just does more damage to those critical structures per press of the trigger than handguns or rifles because of the projectiles that they fire. Multiple projectiles hitting roughly the same spot at the same time overwhelms the ability of tissue to stretch. A slug punches a big damn hole in tissue and causes no small amount of temporary stretch itself.
But it needs to penetrate deep enough (past the FBI minimums) to reliably hit the stuff that turns bad guys off.