Speaker
Description
It is known that the Real Extended Bialas-Bzdak (ReBB) model describes the proton-proton ($pp$) and proton-antiproton ($p\bar p$) differential cross section data in a statistically not excludible way, i.e., with a confidence level greater than 0.1% in the center of mass energy range 546 GeV $\leq\sqrt{s}\leq 8$ TeV and in the squared four-momentum transfer range 0.37 GeV$^2$ $\leq -t\leq1.2$ GeV$^2$. Considering, instead of Gaussian, a more general Lévy $\alpha$-stable shape for the parton distributions of the constituent quarks and diquarks 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 Lévy $\alpha$-stable generalization of the Bialas-Bzdak model and show that a simplified version of this model can be successfully fitted, indeed with $\alpha<2$, to the non-exponential, low $-t$ differential cross-section data of elastic proton-proton scattering at $\sqrt{s} = 8$ TeV.
