Title: Energy Dependence of Intermittency for Charged Hadrons in Au + Au collisions at RHIC

PA: Xiaofeng Luo, Yufu Lin, Zhiming Li, Jin Wu, Yuanfang Wu

Target Journal: Phys. Lett. B

Paper Draft:
https://drupal.star.bnl.gov/STAR/system/files/Paper_Draft_Intermittency.pdf

Analysis Note:
https://drupal.star.bnl.gov/STAR/system/files/Analysis_note_Intermittency_1.pdf

Abstract:
Density fluctuations near the QCD critical point can be probed via an intermittency analysis in relativistic heavy-ion collisions. We report the first measurement of intermittency in Au$+$Au collisions at $\sqrt{s_\mathrm{_{NN}}}$ = 7.7-200 GeV  measured by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The scaled factorial moments of identified charged hadrons are analyzed at mid-rapidity and within the transverse momentum phase space. We observe a power-law behavior of scaled factorial moments in Au$+$Au collisions and a decrease in the extracted scaling exponent ($\nu$) from peripheral to central collisions. The $\nu$ is consistent with a constant for different collisions energies in the mid-central (10-40\%) collisions. Moreover, the $\nu$ in the 0-5\% most central Au$+$Au collisions exhibits a non-monotonic energy dependence that reaches a possible minimum around $\sqrt{s_\mathrm{_{NN}}}$ = 27 GeV. The physics implications on the QCD phase structure are discussed.

Figure 1:
 


Fig. 1.  (a)-(d) The scaled factorial moments, $F_{q}(M)$($q=$ 2-6), of identified charged hadron ($h^{\pm}$) multiplicity in the most central (0-5\%) Au$+$Au collisions at four example energies in the $\sqrt{s_\mathrm{_{NN}}}$ = 7.7-200 GeV range. Solid (open) markers represent $F_{q}(M)$ of data (mixed events) as a function of $M^{2}$. (e)-(h) $\Delta F_{q}(M)$ ($q=$ 2-6) as a function of $M^{2}$ in the most central (0-5\%) Au$+$Au collisions at four example energies in double-logarithmic scale. Statistical uncertainties are obtained from the Bootstrap method.

Figure 2:

Fig. 2 (a)-(i) $\Delta F_{q}(M)$ ($q=$  3-6) as a function of $\Delta F_{2}(M)$ in the most central Au$+$Au collisions at $\sqrt{s_\mathrm{_{NN}}}$ = 7.7-200 GeV. The solid black lines represent the best power-law fit of $\Delta F_{q}(M)\propto \Delta F_{2}(M)^{\beta_{q}}$ with a fitting range of $\Delta F_{2}(M)$ from $M\in[30,100]$. The value of $\beta_{q}$ is the slope of the fitting line

Figure 3:


Fig. 3, (a) The scaling index, $\beta_{q}$ ($q=$ 3-6), as a function of $q-1$ in the most central (0-5\%) Au$+$Au collisions at $\sqrt{s_\mathrm{_{NN}}}$ = 7.7-200 GeV. The solid lines represent the best power-law fit of $\beta_{q}\propto (q-1)^{\nu}$. The statistical uncertainties of $\beta_{q}$ are smaller than the marker size. (b) The scaling exponent ($\nu$), as a function of average number of participant nucleons ($\langle N_{part}\rangle$), in Au$+$Au collisions at $\sqrt{s_\mathrm{_{NN}}}$ = 19.6-200 GeV. The data with the largest number of $\langle N_{part}\rangle$ correspond to the most central collisions (0-5\%), and the rest of the points are for 5-10\%, 10-20\%, 20-30\% and 30-40\% centrality, respectively. The systematic uncertainties of $\nu$ are shown in bars and the statistical uncertainties are smaller than the marker size. Both $\beta_{q}$ and $\nu$ at all energies are scaled by different factors.

Figure 4:

Fig. 4, Energy dependence of scaling exponent, $\nu$, of charged particles in Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7- 200 GeV. Red stars and blue circles represent $\nu$ in most central collisions (0-5%) and central collisions (10-40%), respectively. The statistical and systematical error are shown in bars and brackets, respectively. 

Summary:

(1) We have presented the first measurement of intermittency of charged particles in Au + Au collisions at $\sqrt{s_\mathrm{NN}}$ = 7.7-200 GeV measured by the STAR experiment at RHIC. Scaled factorial moments (up to sixth order) of identified charged particles including $p$, $\bar{p}$, $K^{\pm}$ and $\pi^{\pm}$ within $|\eta|<0.5$, have been measured at mid-rapidity and within the transverse momentum space.

(2) Distinct scaling behavior between the higher-order and second-order scaled factorial moments is observed in Au + Au collisions at various energies. Based on the scaling behavior, the extracted scaling exponent $\nu$, decreases monotonically from the peripheral to the central Au + Au collisions.

(3) A non-monotonic energy dependence is observed in the 0-5\% most central collisions with $\nu$ reaches a possible minimum around $\sqrt{s_\mathrm{_{NN}}}$ = 27 GeV. Whether the observed non-monotonic behavior is related to the CEP or not, detailed calculations from dynamical modelling of heavy-ion collisions with a realistic equation of state are needed.

Supporting Documents:

Presentation PWG:
https://drupal.star.bnl.gov/STAR/system/files/wujin-Intermittency-Analysis-of-Charge-April.pdf
https://drupal.star.bnl.gov/STAR/system/files/JinWu-Intermittency-Efficiency.pdf
https://drupal.star.bnl.gov/STAR/system/files/JinWu-Intermittency_CFPWG_20210114.pdf

STAR Collaboration Meeting:
2019-08-20
https://drupal.star.bnl.gov/STAR/system/files/JinWu-Intermittency-Collaboration%20meeting-Aug20_0.pdf
2021-03-02
https://drupal.star.bnl.gov/STAR/system/files/Jin-Intermittency-CF-CollaborationMeeting2021_0.pdf

QM19 poster:
https://drupal.star.bnl.gov/STAR/files/QM2019poster-JinWu-v5.pdf
QM22 poster:
https://indico.cern.ch/event/895086/contributions/4724876/

Workshop on QCD @ High Density:
https://drupal.star.bnl.gov/STAR/system/files/JinWu-Intermittency-High%20density%20QCD-workshop.pdf

ISMD 2021:
https://indico.cern.ch/event/848680/contributions/4430326/attachments/2282954/3879355/Intermittency-ISMD2021-STAR.pdf