Ultrahigh energy predictions of proton-air cross sections from accelerator data: An update
At {radical}(s)=57{+-}7 TeV, the Pierre Auger Observatory (PAO) measured the p-air inelastic production cross section, {sigma}{sub p-air}{sup prod}=475{+-}22(stat){+-}{sub 15}{sup 20}(syst) mb, assuming a proton cosmic ray beam with a 25% helium contamination. From a Glauber calculation, they found the inelastic pp cross section, {sigma}{sub inel}=90{+-}7(stat){+-}{sub 11}{sup 9}(syst){+-}1.5(Glaub) mb. Our parameterization of pp and pp total cross sections, {sigma}{sub tot}, using analyticity constraints and unitarity gives accurate extrapolations to ultrahigh energies, and after using a Glauber calculation, accurate predictions for {sigma}{sub p-air}{sup prod}. We find (i) a pp total cross section, {sigma}{sub tot}=133.4{+-}1.6 mb and (ii) {sigma}{sub p-air}{sup prod}=483{+-}3 mb, independently determining a 19% helium contamination. Using our 57 TeV value for pp {sigma}{sub tot}[M. M. Block and F. Halzen, arXiv:1109-2041], we find a pp inelastic cross section, {sigma}{sub inel}=92.9{+-}1.6 mb, agreeing with POA.