New physics, the cosmic ray spectrum knee, and $pp$ cross section
  measurements
  We explore the possibility that a new physics interaction can provide an
explanation for the knee just above $10^6$ GeV in the cosmic ray spectrum. We
model the new physics modifications to the total proton-proton cross section
with an incoherent term that allows for missing energy above the scale of new
physics. We add the constraint that the new physics must also be consistent
with published $pp$ cross section measurements, using cosmic ray observations,
an order of magnitude and more above the knee. We find that the rise in cross
section required at energies above the knee is radical. The increase in cross
section suggests that it may be more appropriate to treat the scattering
process in the black disc limit at such high energies. In this case there may
be no clean separation between the standard model and new physics contributions
to the total cross section. We model the missing energy in this limit and find
a good fit to the Tibet III cosmic ray flux data. We comment on testing the new
physics proposal for the cosmic ray knee at the Large Hadron Collider.
