L & eacute;vy a-Stable Model for the Non-Exponential Low-|t| Proton-Proton Differential Cross-Section

It is known that the Real Extended Bialas-Bzdak (ReBB) model describes the protonproton ( pp) and proton-antiproton ( p (-)p) 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 <= root 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 Levy alpha-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 alpha = 2 special case. Extending the model to alpha < 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 Levy alpha-stable generalization of the Bialas-Bzdak model and show that a simplified version of this model can be successfully fitted, with alpha < 2, to the non-exponential, low t differential cross-section data of elastic proton-proton scattering at p s = 8 TeV.