Propagation of B mesons in the atmosphere

Collisions of cosmic rays in the atmosphere may produce heavy hadrons of very high energy. The decay length of a $B$ meson of energy above $10^7$ GeV is larger than 1 km, implying that such a particle tends to interact in the air before it decays. We show that the fraction of energy deposited in these interactions is much smaller than in proton and pion collisions. We parameterize their elasticity and determine the average number of interactions and the atmospheric depth at the decay point for different initial energies. We find that the profile of a $3\times 10^9$ GeV bottom shower may be very different from the profile of a proton shower of the same energy, defining either a very deep maximum, or two maxima, or other features that cannot be parameterized with a single Gaisser-Hillas function. Finally, we discuss under what conditions a bottom hadron inside the parent air shower may provide observable effects.