# The Role of Baryon Number Conservation in Measurements of Fluctuations

## TL;DR

This paper explains how net-baryon number conservation influences net proton fluctuation measurements in heavy-ion collisions, emphasizing the role of two-particle correlations and the balance function shape over QCD susceptibilities.

## Contribution

It demonstrates that net proton fluctuation magnitudes are governed by two-particle correlations and balance functions, highlighting the importance of differential measurements over integral cumulants.

## Key findings

- Fluctuations are proportional to the integral of the proton-antiproton balance function.
- The shape and width of the balance function significantly affect fluctuation measurements.
- Radial flow impacts the width of the balance function, influencing fluctuation results.

## Abstract

I discuss the role and impact of net-baryon number conservation in measurements of net proton fluctuations in heavy-ion collisions. I show that the magnitude of the fluctuations is entirely determined by the strength of two particle correlations. At LHC and top RHIC energy, this implies the fluctuations are proportional to the integral of the balance function (BF), $B^{p\bar p}$ of protons and anti-protons, while in the context of the RHIC beam energy scan (BES), one must also account for correlations of "stopped" protons. The integral of $B^{p\bar p}$ measured in a $4\pi$ detector depends on the relative cross-sections of processes yielding $p\bar p$ and those balancing the proton baryon number via the production of other anti-baryons. The accepted integral of $B^{p\bar p}$ further depends on the shape and width of the BF relative to the width of the acceptance. The magnitude of the measured second order cumulant of net proton fluctuations thus has much less to do with QCD susceptibilities than with the creation/transport of baryons and anti-baryons in heavy-ion collisions, and most particularly the impact of radial flow on the width of the BF. I thus advocate that net-proton fluctuations should be studied by means of differential BF measurements rather integral correlators.