Limits on Neutron Lorentz Violation from the Stability of Primary Cosmic   Ray Protons
  Recent evidence appears to confirm that the ultra-high-energy primary cosmic ray spectrum consists mostly of protons. The fact that these protons can traverse large distances to reach Earth allows us to place bounds on Lorentz violations. The protons neither emit vacuum Cerenkov radiation nor $\beta$-decay into neutrons, and this constrains six previously unmeasured coefficients in the neutron sector at the 5 x 10^(-14) level. Among the coefficients bounded here for the first time are those that control spin-independent boost anisotropy for neutrons. This is a phenomenon which could have existed (in light of the preexisting bounds) without additional fine tuning. There are also similar bounds for others species of hadrons. The bounds on Lorentz violation for neutral pions are particularly strong, at the 4 x 10^(-21) level, eleven orders of magnitude better than previous constraints. 
Brett Altschul