Soft interactions in Herwig++

TL;DR

The paper addresses the challenge of modeling soft, non-perturbative interactions in hadron collisions within Herwig++. It develops an eikonal-based MPI framework that includes a soft component and introduces simple and hot-spot variants to connect to total and elastic cross sections. The authors implement the soft extension in Herwig++ and demonstrate a reasonable description of Tevatron minimum-bias and underlying-event data, while showing that extrapolations to the LHC remain uncertain due to cross-section and PDF uncertainties. The work highlights the interplay between non-perturbative parameters and PDFs and points to future directions including diffractive contributions and color correlations to further refine the model.

Abstract

We describe the recent developments to extend the multi-parton interaction model of underlying events in Herwig++ into the soft, non-perturbative, regime. This allows the program to describe also minimum bias collisions in which there is no hard interaction, for the first time. It is publicly available from versions 2.3 onwards and describes the Tevatron underlying event and minimum bias data. The extrapolations to the LHC nevertheless suffer considerable ambiguity, as we discuss.

Figures (7)

• Figure 1: Total cross sections (black) in the two parameterizations of Donnachie and LandshoffDonnachie:1992nyDonnachie:2004pi. In blue the QCD jet production cross section above 2 GeV is shown.
• Figure 2: Multiplicity and _t^ sum$p_t^{\rm sum}$ in the transverse region. CDF data are shown as black circles, Herwig++ without MPI as magenta dots, with MPI using MRST Martin:2001es PDFs as solid red and with CTEQ6L Pumplin:2002vw as cyan dashed. The lower plot shows the statistical significance of the disagreement between the Monte Carlo predictions and the data. The legend on the upper plot shows the total $\chi^2$ for all observables, whereas the lower plot for each observable has its $\chi^2$ values.
• Figure 3: Left: The parameter space of the simple eikonal model at the Tevatron. The solid curves come from $\sigma{\rm inc}_{\rm soft}{$σ^ inc_ soft$}>0$ for three different PDF sets. The horizontal lines come from $b{\rm el}{$b_ el$} = 16.98 \pm 0.25 \text{ GeV}^{-2}$sigma_tot_CDFAbe:1993xx. The excluded regions are shaded. The dashed lines indicate the preferred parameter ranges from the fit to Tevatron final-state dataBahr:2008dy. Right: The equivalent plot for the LHC. The additional (dashed) constraints come from requiring the total number of scatters to be less than 10.
• Figure 4: Parameter space of the improved eikonal model for the Tevatron (left) and LHC (right). The solid curves impose a minimum allowed value of ^2$\mu^2$, for a given value of _t^ min$p_t^{\rm min}$ by requiring a valid description of _ tot$\sigma_{\rm tot}$ and _ el$b_{\rm el}$ with positive ^ inc_ soft$\sigma^{\rm inc}_{\rm soft}$. The excluded regions are shaded. We used the MRST 2001 LOMartin:2001es PDFs for these plots.
• Figure 5: ^ inc_ soft$\sigma^{\rm inc}_{\rm soft}$ as a function of energy. Each of the three different curves shows the soft cross section that would appear when the respective parameterization for the total cross section is used. Curves that do not reach out to 30 TeV correspond to parameter choices that are unable to reproduce _ tot$\sigma_{\rm tot}$ and _ el$b_{\rm el}$ correctly at these energies.