Modeling pion and proton total cross-sections at LHC

Abstract

To settle the question whether the growth with energy is universal for different hadronic total cross-sections, we present results from theoretical models for πp, and (pp,pp) total cross-sections. We show that present and planned experiments at LHC can differentiate between different models, all of which are consistent with presently available (lower energy) data . This study is also relevant for the analysis of those very high energy cosmic ray data which require reliable πp total cross-sections as seeds. A preliminary study of the total ππ cross-sections is also made.

Introduction to the physics of the total cross section at LHC

“…Notice that for pion cross sections, the onset of the high energy region may be considered to start earlier, as one can see from a compilation of ππ and π p total cross sections, shown in Fig. 34 from [149]. In this figure, the overlaid curves correspond to the same model as in Fig.…”

“…In this regime, partons of momentum p = x P h are extracted from a hadron of momentum P h with a 1/x spectrum and scatter into final state partons of transverse moment p t , with a strength calculable through Fig. 34 Proton and pion total cross sections, as indicated, from [149].…”

“…Reprinted from [149], ©(2010) with permission from Elsevier the asymptotic freedom expression for the strong coupling constant, given to lowest order as…”

“…It also appears that when performing a parametrisation of the low energy contribution, the hard part plays a role to ameliorate the overall description, from low to hard energies. Examples of these two different procedures can be found in our application of the BN model to pion scattering [149] and to studies of inelastic cross section at LHC7 [41]. In addition, from a microscopic point of view, mini-jets are the only pQCD phenomenon to which one can ascribe the drive of the rise of the total cross section.…”

“…[94], the first of these two low energy parametrisations has the same expression for A(b, s) as in the hard pQCD calculation, except that the value of q max is chosen ad hoc to reproduce the low-energy data. The second parametrisation is self explaining, and we have started using it when describing π -p and ππ scattering [149]. Then the elastic and the inelastic total cross sections follow from the usual formulae.…”