Signals for fluctuating constituent numbers in small systems

TL;DR

This paper addresses the need to model fluctuations in the number of partons participating in heavy-ion collisions by embedding a PDF-driven sampling mechanism into the TRENTo initial-condition framework. By drawing parton momentum fractions from parton distribution functions and enforcing a momentum-transfer dependent cutoff $x_{min}=Q^2/s$, the authors generate event-by-event fluctuations in the nucleon parton count $m$ and study the resulting impact on initial-state geometry. The analysis shows that fluctuations imprint the strongest signals in small systems and particularly in odd eccentricities $\\epsilon_3$ and $\\epsilon_5$, with the ratio $\\epsilon_3/\\epsilon_5$ emerging as a robust observable to constrain $m$. The work outlines extensions to include transverse momentum distributions (TMDs) and virtuality effects, and suggests incorporating the odd-harmonic ratio into future analyses of small-system collisions to better constrain sub-nucleonic structure in initial-state models; data and code are available on GitHub.

Abstract

We propose an extension of the initial condition model TRENTo for sampling the number of partons inside the nucleons that participate in a heavy-ion collision. This sampling method is based on parton distribution functions (PDFs) and therefore has a natural dependence on the momentum transferred in the collision and the scale being probed during the collision. We examine the resulting distributions and their dependence on the momentum transfer. Additionally, we explore the sensitivity of different observables on the number of partons using the TRENTo framework and the estimators available therein for final-state observables.

Figures (10)

• Figure 1: Parton distribution functions as function of Bjorken $x$, taken from UCL HEP group Harland-Lang:2014zoa. The distribution functions sharply rise for $x\to 0$, resulting in smaller values of $x$ being favored. The cutoff $x_{min}$ ensures that the PDFs are finite and have a maximum value, ensuring a finite number of partons in the sampling process.
• Figure 2: Probability distribution for the number of partons for different values of $Q^2$. All distributions are bounded from below by three through the presence of the valence quarks.
• Figure 3: Average number of partons in each nucleon as function of momentum transfer $Q^2$. The average number of partons increases with $Q^2$, since the parton distribution functions become more peaked towards $x=0$, due to the higher scattering resolution. The increase stagnates due to the increasing cutoff $x_{min}$.
• Figure 4: Standard deviation of the parton number distribution as function of $Q^2$. The standard deviation decreases for increasing $Q^2$ due to the underlying distributions being more peaked at higher momentum transfer and a higher momentum cutoff $x_{min}$.
• Figure 5: Down quark PDF for different values of $Q^2$. The distribution function is more narrow for larger values of $Q^2$, driving the sampled $x$ towards $x_\text{min}$. Through the increase of this cut-off, the sampling range is restricted, leading to fewer fluctuations in the total number of partons.