Effect of Pions in Cosmic Rays
  The effects of pions for vacuum polarization in background magnetic fields are considered. The effects of quark condensates is also briefly addresses. Although these effects are out of the measurement accuracy of laboratory experiments they may be relevant for gamma-ray burst propagation. In particular, for emissions from the center of the galaxy, we show that the mixing between the neutral pion and photons results in a deviation of the gamma-ray spectrum from the standard power-law in the TeV range. 
P. Castelo Ferreira and J. Dias de Deus