Lévy $\alpha$-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 ($p\bar{p}$) 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 $\le \sqrt{s}\le$ 8 TeV and in the squared four-momentum transfer range 0.37 GeV${}^2$ $\le -t\le$ 1.2 GeV${}^2$. Considering, instead of Gaussian, a more general Lévy $\alpha$-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 Lévy $\alpha$-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.

13 pages, 2 figures

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