Energy Scaling of Minimum-Bias Tunes

TL;DR

This work presents a framework to probe the universality of minimum-bias event modeling by performing independent, energy-specific tunings of MPI+pT-ordered shower parameters using Professor with Pythia 6.4. Focusing on three key parameters— the infrared regularization scale $p_{ _ot0}$, the proton transverse-mass shape parameter PARP83, and the color reconnection strength PARP78—the authors map how these parameters scale with energy from 630 GeV to 7 TeV via MB observables. They find that $p_{ _ot0}$ follows the expected power-law scaling, PARP83 shows only mild potential deviations, and PARP78 exhibits a clear energy dependence, marking color reconnection as the main source of non-universality. The study demonstrates a practical methodology to diagnose universality in MC tunes and provides energy-specific tunes, underscoring the need for refined CR modeling in collider simulations.

Abstract

We propose that the flexibility offered by modern event-generator tuning tools allows for more than just obtaining "best fits" to a collection of data. In particular, we argue that the universality of the underlying physics model can be tested by performing several, mutually independent, optimizations of the generator parameters in different physical regions. For regions in which these optimizations return similar and self-consistent parameter values, the model can be considered universal. Deviations from this behavior can be associated with a breakdown of the modeling, with the nature of the deviations giving clues as to the nature of the breakdown. We apply this procedure to study the energy scaling of a class of minimum-bias models based on multiple parton interactions (MPI) and pT-ordered showers, implemented in the Pythia 6.4 generator. We find that a parameter controlling the strength of color reconnections in the final state is the most important source of non-universality in this model.

Figures (3)

• Figure 1: Energy scaling of charged-particle multiplicities in pp in three different phase space regions (top: inclusive, middle: central, bottom: central hard). Left: Dependence on the scaling of the $p_{\perp 0}$ parameter for two different Pythia models, represented by Tune A and Perugia 0, respectively. The solid vertical line represents the reference energy, 1800 GeV, at which PARP(82) is defined for both models. Right: Dependence on the PDF set, for the Perugia 0 model. For reference, Tune A without MPI is also shown (dotted lines).
• Figure 2: Energy scaling of charged-particle multiplicities in pp in three different phase space regions (top: inclusive, middle: central, bottom: central hard). Left: two different impact parameter profiles. Right: three different color-reconnection strengths. For reference, Tune A without MPI is also shown (dotted lines). For all other curves, the parameters of Perugia 0 were used, except for the modifications indicated on the plots.
• Figure 3: Energy dependence of the the three tune parameters, from top to bottom: $\mathtt{PARP(82)}$, $\mathtt{PARP(83)}$, and $\mathtt{PARP(78)}$. Independent optimizations (blue/shaded lines) compared to global fit curve (red solid curves). Left:$N_{\mathrm{ch}}\ge 1$ sample. Right:$N_{\mathrm{ch}}\ge 6$ sample.