Inferred cosmic-ray spectrum from ${\it Fermi}$-LAT $\gamma$-ray   observations of the Earth's limb
  Recent accurate measurements of cosmic-ray (CR) species by ATIC-2, CREAM, and PAMELA reveal an unexpected hardening in the proton and He spectra above a few hundred GeV, a gradual softening of the spectra just below a few hundred GeV, and a harder spectrum of He compared to that of protons. These newly-discovered features may offer a clue to the origin of high-energy CRs. We use the ${\it Fermi}$ Large Area Telescope observations of the $\gamma$-ray emission from the Earth's limb for an indirect measurement of the local spectrum of CR protons in the energy range $\sim 90~$GeV-$6~$TeV (derived from a photon energy range $15~$GeV-$1~$TeV). Our analysis shows that single power law and broken power law spectra fit the data equally well and yield a proton spectrum with index $2.68 \pm 0.04$ and $2.61 \pm 0.08$ above $\sim 200~$GeV, respectively. 
Fermi-LAT Collaboration: M. Ackermann, M. Ajello, A. Albert, A.   Allafort, L. Baldini, G. Barbiellini, D. Bastieri, K. Bech...
astro-ph.HE