Revised production cross-section of γ-rays in p–p collisions with LHC data for the study of TeV γ-ray astronomy

We present the production cross-section of γ-rays based on data of p–p collisions at the Large Hadron Collider (LHC), revising the previous semi-empirical formula mainly for (1) the inelastic cross-section in p–p collisions, σ pp ( E 0 ) , and 2) the inclusive γ-ray spectrum in the forward region, σ pp → γ ( E 0 , E γ ) . We find that the previous cross-section gives a significantly softer spectrum than found in the data of LHC. In this paper, we focus our interest mainly upon the LHC forward (LHCf) experiment, giving γ-ray spectra in the very forward region with the pseudo-rapidity η ∗ ≳ 8.8 in the center of mass system (CMS), which have not been reported so far. We also give the pseudo-rapidity distribution of charged hadrons with - 3 ⩽ η ∗ ⩽ 3 obtained by ALICE and TOTEM experiments, both with LHC. We find that the revised cross-section reproduces quite well the accelerator data over the wide energy range from GeV to 30 PeV for projectile protons, corresponding approximately to 100 MeV to 3 PeV for secondary γ-rays. The production cross-section of γ-rays produced in the forward region is essential for the study of γ-ray astronomy, while not important are those produced in the central region in CMS, and of much less importance in the backward. We discuss also the average transverse momentum of γ-rays, p ¯ t , and the average inelasticity transferred to γ-rays, k ¯ γ ∗ , obtaining that the former increases very slowly with p ¯ t = 100 ∼ 220 MeV/c for E 0 = 1 GeV ∼ 26 PeV , and the latter is almost independent of E 0 , with k ¯ γ ∗ ≈ 1 / 6 , while we cannot exclude the possibility of a small increase of k ¯ γ ∗ .