Multiparton Interactions with an x-dependent Proton Size

TL;DR

This work introduces an x-dependent transverse proton size within the MPI framework of Pythia 8 by modeling the parton density as a Gaussian with width a(x)=a0(1+a1 ln(1/x)). The approach links the x-dependent parton distribution to the impact-parameter overlap, altering MPI probabilities, cross sections, and the structure of MB and UE observables. Through comparisons with single Gaussian, double Gaussian, and overlap profiles across Z0, Drell–Yan, and MB/UE observables, the study shows that a modest x-dependence (a1 ≈ 0.15) can yield a stable overall size while affecting MPI activity in a way that trends toward improved LHC data description, albeit requiring retuning of pT0. The framework is positioned as a practical extension to Pythia 8.150, enabling more flexible and data-driven MPI modelling with future LHC tests.

Abstract

Theoretical arguments, supported by other indirect evidence, suggest that the wave function of high-x partons should be narrower than that of low-x ones. In this article, we present a modification to the variable impact parameter framework of Pythia 8 to model this effect. In particular, a Gaussian hadronic matter profile is introduced, with a width dependent on the x value of the constituent being probed. Results are compared against the default single- and double-Gaussian profiles, as well as an intermediate overlap function.

Figures (12)

• Figure 1: (a) The rise of the total and non-diffractive $\mathrm{p}\mathrm{p}$ cross section with energy, and (b) the ratio $a_0(E_{\mathrm{CM}}) / a_0(200\,\mathrm{GeV})$, over the same energy range, for a set of different $a_1$ values
• Figure 2: Root-mean-squared value of (a) $\bar{n}$ and (b) $P_\mathrm{int}$ as a function of the centre-of-mass energy
• Figure 3: $\mathrm{Z^0}$ production in $\mathrm{p}\mathrm{p}$ collisions at $7\,\mathrm{TeV}$. (a) The impact parameter distribution, (b) enhancement factor of the hard interaction, (c) number of MPI and (d) inclusive $p_{\perp}$ spectrum of MPI per event. The ratio plot in (d) is normalised to the single Gaussian result
• Figure 4: The $\tau$ distribution of low mass Drell-Yan (DY), $\mathrm{Z^0}$ and $\mathrm{Z}'$ events in $\mathrm{p}\mathrm{p}$ collisions at $\sqrt{s} = 7\,\mathrm{TeV}$
• Figure 5: Low-mass Drell-Yan, $\mathrm{Z^0}$ and $\mathrm{Z}'$ production in $\mathrm{p}\mathrm{p}$ collisions at $\sqrt{s} = 7\,\mathrm{TeV}$. (a) The impact parameter distribution and (b) enhancement factor of the hard interaction per event. The single Gaussian distributions are identical between the three processes