We report on the charged-particle multiplicity dependence of net-proton cumulant ratios up to sixth order from $\sqrt{s}=200$ GeV $p$+$p$ collisions at the Relativistic Heavy Ion Collider (RHIC). The measured ratios $C_{4}/C_{2}$, $C_{5}/C_{1}$, and $C_{6}/C_{2}$ decrease with increased charged-particle multiplicity and rapidity acceptance. Neither the Skellam baselines nor PYTHIA8 calculations account for the observed multiplicity dependence. In addition, the ratios $C_{5}/C_{1}$ and $C_{6}/C_{2}$ approach negative values in the highest-multiplicity events, which implies that thermalized QCD matter may be formed in $p$+$p$ collisions.
(c) Charged-particle multiplicity distribution.
(d) Event-by-event net-proton multiplicity distributions for $|y|<0.5$ and $0.4<p_{\rm{T}}<2.0$ GeV/$c$ at two ranges of charged particle multiplicity as indicated in the legend.
Net-proton cumulant ratios, (a) $C_{2}/C_{1}$, (b) $C_{3}/C_{2}$, (c) $C_{4}/C_{2}$, (d) $C_{5}/C_{1}$, and (e) $C_{6}/C_{2}$ as a function of charged-particle multiplicity from $\sqrt{s}=200$ GeV $p$+$p$ collisions. Black solid lines and red bands represent the statistical and systematic uncertainties, respectively. Cyan points represent event averages for $3 < m_{\rm ch}^{\rm TPC} < 30$, and they are plotted at the corresponding value of $m_{\rm ch}^{\rm TPC}$. The uncertainties on the cyan points are smaller than the marker size. The Skellam baselines are shown as dotted lines. The results of the PYTHIA8 calculations are shown by hatched-golden bands. The golden bands at $m_{\rm ch}^{\rm TPC}\approx 6$ are the results from the PYTHIA8 calculations averaged over multiplicities.
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