After the meeting, a few of us were discussing whether it's safe to make the excited state priors very tight in order to get better results for the h_c. The idea is that we don't care about the excited state, so it shouldn't matter much if they are too tight. But on the other hand, tightening them too much constrains the ground state fit in unnatural ways. The prior Jim used essentially constrains the splitting to be 600+-75 MeV, which is a tighter constraint than we can readily justify based on experiment. But how much does this affect the ground state?

Here's a plot to answer that question:

Here the black starred points are Jim's results for n_states=1,2,3. The points to the left/right (for multi-state fits only) are the result of decreasing/increasing the excited state prior widths by factors of sqrt(2). For the 2-state fit, it's clear that increasing the prior width increases the errorbar (and its asymmetry!), though not by a lot. The 3-state fit is much better behaved.

I'm not sure what conclusions to draw from this, but am throwing it out to everyone else for comments.