Lévy α-Stable Model for the Non-Exponential Low-|t| Proton–Proton Differential Cross-Section

Abstract

It is known that the Real Extended Bialas–Bzdak (ReBB) model describes the proton–proton (pp) and proton–antiproton (pp¯) differential cross-section data in a statistically non-excludible way, i.e., with a confidence level greater than or equal to 0.1% in the center of mass energy range 546 GeV ≤s≤8 TeV and in the squared four-momentum transfer range 0.37 GeV2 ≤ −t ≤ 1.2 GeV2. Considering, instead of Gaussian, a more general Lévy α-stable shape for the parton distributions of the constituent quark and diquark inside the proton and for the relative separation between them, a generalized description of data is obtained, where the ReBB model corresponds to the α=2 special case. Extending the model to α<2, we conjecture that the validity of the model can be extended to a wider kinematic range, in particular, to lower values of the four-momentum transfer −t. We present the formal Lévy α-stable generalization of the Bialas–Bzdak model and show that a simplified version of this model can be successfully fitted, with α<2, to the non-exponential, low −t differential cross-section data of elastic proton–proton scattering at s=8 TeV.