L\'evy $\alpha$-stable model for the non-exponential low-$|t|$ proton-proton differential cross section

TL;DR

This paper generalizes the ReBB model for proton-proton scattering by incorporating Le9vy e1-stable distributions, enabling better fits to low-ta0 data and extending the model's applicability to a broader kinematic range.

Contribution

The paper introduces a Le9vy e1-stable extension of the ReBB model, allowing for improved description of elastic pp scattering at low t and broader energy ranges.

Findings

Successful fit of the generalized model to 8 TeV data

Extension of the model's validity to lower t values

Demonstration that e1<2 provides a better data description

Abstract

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 non-excludible way,\linebreak i.e., with a confidence level greater than or equal to 0.1\% in the center of mass energy range \linebreak 546 GeV $\leq\sqrt{s}\leq$ 8 TeV and in the squared four-momentum transfer range 0.37 GeV$^2$ $\leq -t\leq$ 1.2 GeV$^2$. Considering, instead of Gaussian, a more general L\'evy $\alpha$-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 L\'evy $\alpha$-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 $\sqrt{s} =$ 8 TeV.