What are realistic and unrealistic values for the high energy gamma ray spectral indices of pulsar wind nebulae?
You might find these websites for your answers:


https://www.cv.nrao.edu/course/astr534/SynchrotronSpectrum.html
http://astronomy.swin.edu.au/cosmos/S/Synchrotron+Emission
https://ui.adsabs.harvard.edu/abs/2006MNRAS.371.1441S/abstract


We have a large amount of high energy emission these days, and the third reference shows the distribution from 394 GRBs.