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PaperFlowindAuandOORun21

Updated on Wed, 2025-06-18 21:21. Originally created by slhuang on 2024-10-01 12:05.

Title: Measurements of Multiplicity Dependent v2 and v3 in O+O and d+Au Collisions

PA:

Shengli Huang(1), Jinhui Chen(2), Roy Lacey(1), Jiangyong Jia(1), Prithwish Tribedy(3), Zaining Wang(2), Zhengxi Yan(1), ChunjianZhang(2)
1.SBU 2.Fudan 3. BNL

Analysis note:
https://drupal.star.bnl.gov/STAR/starnotes/private/PSN0863

paper draft:
1)PWGC: drupal.star.bnl.gov/STAR/system/files/OOPaper-7.pdf

2)GPC Request: https://drupal.star.bnl.gov/STAR/system/files/OOPaper-3.pdf

Target Journal: PRL

PWGC review:
drupal.star.bnl.gov/STAR/blog/slhuang/PWGC-Slide-OO-and-dAu-flow-paper

PWG presentation:

•For O+O:

•https://drupal.star.bnl.gov/STAR/blog/slhuang/OO-Glauber-Update

•https://drupal.star.bnl.gov/STAR/blog/slhuang/di-hadron-correlation-OO

•https://drupal.star.bnl.gov/STAR/system/files/OOnewpreliminary.pdf

•https://drupal.star.bnl.gov/STAR/blog/slhuang/Qm2023-preliminary

•https://drupal.star.bnl.gov/STAR/system/files/OOPWGMay-17-2023-Shengli.pdf

•https://drupal.star.bnl.gov/STAR/system/files/OOPWGMay10-2023-Shengli.pdf

 

•For d+Au: 

•https://drupal.star.bnl.gov/STAR/blog/slhuang/PWGJune112024

•https://drupal.star.bnl.gov/STAR/blog/slhuang/PWGJun182024




Abstract:

In this paper, the elliptic and triangular flow harmonics ($v_2$ and $v_3$) are measured as a function of multiplicity in first-ever $^{16}$O+$^{16}$O and $d$+Au collisions at $\sqrtsNN$ = 200 GeV. The elliptic flow harmonic ($v_2\{2\}$ and $v_{2}\{4\}$), obtained via two- and four-particle correlations, respectively, exhibit a strong system dependence, whereas the triangular flow harmonic ($v_{3}\{2\}$) is nearly system-independent. The ratio $v_{n}\{2\}/\varepsilon_{n}\{2\}$ is found system-independent for eccentricity $\varepsilon_{n}\{2\}$ with sub-nucleon fluctuations. Moreover, $v_{2}\{4\}/v_{2}\{2\}$ is consistent with $\varepsilon_{2}\{4\}/\varepsilon_{2}\{2\}$ in central $d$+Au collisions, while is lower than $\varepsilon_{2}\{4\}/\varepsilon_{2}\{2\}$ in central $^{16}$O+$^{16}$O collisions. These findings provide critical insights into the origin of collectivity in small systems and enhance our understanding of nucleon-nucleon correlations and alpha cluster structure in high-energy nuclear collisions.

Figure 1:


The $c_n\{2\}$ values (for $n=2,3$) as a function of charged-particle multiplicity ($N_\text{ch}$) in \oo and \dau collisions at $\sqrt{s_{NN}}$ = 200 GeV. Left panels (a,c) show results before nonflow subtraction, while right panels (b,d) present values after nonflow subtraction using the $c_1$ method. Substantial nonflow contributions are evident at low multiplicities. After subtraction, $c_2\{2\}$ in \dau increases with $N_\text{ch}$, while in \oo it shows a weaker dependence, consistent with the spherical geometry of the $^{16}$O nucleus. In contrast, $c_3\{2\}$ values remain similar between the two systems after subtraction, indicating that triangularity is primarily driven by initial-state fluctuations.




Figure 2:

Panels (a) and (d) show the $v_n\{2\}$ values (for $n=2,3$) after nonflow subtraction as a function of $N_{\text{ch}}$ for \dau and \oo collisions. Panels (b), (c), (e), and (f) present the ratios $v_n\{2\}/\varepsilon_n\{2\}$, where $\varepsilon_n\{2\}$ is calculated from Glauber model simulations with and without sub-nucleon fluctuations, for $n=2$ and $n=3$, respectively. The results indicate that the linear scaling relation between flow coefficients and initial eccentricities holds for both $v_2$ and $v_3$, with notably better agreement when sub-nucleon fluctuations are included, especially for $v_3$.

Figure3:



Panels (a) and (b) show the $v_2\{2\}(\rm{subtr.})$ and $v_2\{4\}$ values as a function of $N_{\rm{ch}}$ in \dau and \oo collisions. (c) and (d) show the ratio $v_2\{4\}/v_2\{2\}(\rm{subtr.})$ compared with the corresponding initial-state eccentricity ratio $\varepsilon_2\{4\}/\varepsilon_2\{2\}$ from PHOBOS Glauber model including sub-nucleon fluctuations. The $^{16}$O configurations is based on NLEFT models that include nucleon-nucleon correlations and possible $\alpha$-clustering. In \dau collisions, the ratio remains near 0.9 with weak multiplicity dependence, consistent with the deuteron-driven initial geometry. In contrast, \oo collisions exhibit a significant decrease in $v_2\{4\}/v_2\{2\}(\rm{subtr.})$ at high $N_{\rm{ch}}$, suggesting enhanced flow fluctuations not fully captured by current initial-state models.

 

Summary:

In summary, we report measurements of the integrated $v_2$ and $v_3$ in 0.2 $< p_{\rm T}<$ 2.0 GeV/c ranges as a function of multiplicity in \oo and \dau collisions, using two- and four-particle correlations. Those measurements provide new insights into the role of initial geometry and fluctuations in small-system collectivity. The $v_2\{2\}$ and $v_3\{2\}$ values, after nonflow subtraction, exhibit distinct patterns consistent with differences in initial-state eccentricities predicted by Glauber model calculations with sub-nucleonic fluctuations. The scaling behavior of $v_n\{2\}/\varepsilon_n\{2\}$ for elliptic and triangular harmonics supports the applicability of hydrodynamic-like response even in small systems. Measurements of $v_2\{4\}$ and its ratio to $v_2\{2\}$ further indicate that flow fluctuations are sensitive to the intrinsic geometry and light nuclei nuclear structure, particularly highlighting deviations in \oo collisions that may need high-order corrections in describing nucleon-nucleon correlations or alpha cluster structure of low-lying even-parity states of $^{16}$O in NLEFT model. Further, cluster configurations from other first-principles calculations and microscopic models incorporating in initial-state and hydrodynamic models are significantly more necessary, and, therefore, provide more advances in the understanding of the degree of alpha cluster formation across energy scales. These results provide crucial constraints for theoretical descriptions of collectivity in small collision systems.



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