I think you really need to name a couple particles like that if you're going to bring it up.

The most biased super-precise physics I can think of offhand is when someone measures a physical constant slightly wrong and then subsequent results all lean in the same direction. This happens more than once, most notably with fundamental electric charge, but it's absolutely nothing compared to a nonexistent value!

https://en.m.wikipedia.org/wiki/List_of_experimental_errors_... has https://en.m.wikipedia.org/wiki/Oops-Leon? But that is a single experiment which very specifically did not have a high sigma result.