Paper Title:  Kaon Femtoscopy in the High Baryon Density Region
 PAs: Wensong Cao, Bijun Fan, Youquan Qi, Li'Ang Zhang, Xin Dong, Chuan Fu, Xiaofeng Luo, Shusu Shi, Yaping Wang, Nu Xu, Yingjie Zhou
 Target Journal: PRL / PLB

 Abstract: 
Kaons, unlike pions, are less affected by resonance decays and have smaller hadronic cross-sections, offering a clearer view of the particle-emitting source. We report the first ENERGY DEPENDENT measurements of the K^{+}-K^{+} and K^{0}_{S}-K^{0}_{S} femtoscopic correlations from Au + Au collisions at \sqrt{s_{NN}} = 3.0, 3.2, 3.5, 3.9, and 4.5 GeV, measured by the STAR experiment at RHIC. A systematic analysis of one-dimensional kaon correlation functions is presented with the limited event statistics. For comparison, positive pion (\pi^{+}-\pi^{+}) correlation functions are also studied with the same fashion. Extracted radius parameter R_{inv} and correlation strength \lambda are found to be consistent between charged kaon and neutral-kaon within uncertainties and show no clear energy dependence. While both kaon’s R_{inv} are lower than that of pion’s, and \lambda are larger than that of pion’s. Unlike observed at higher collision energies, the measured kaon source size parameters do not follow the m_T-scaling extracted from pion correlation functions implying that the strange hadrons are not fully thermalized with light hadrons in collisions at the high baryon density region. In addition, it is observed that the neutral kaon abundance asymmetry is decreased as a function of collision energy. The underlying physics will be discussed within the framework of the hadronic transport model UrQMD calculations. 

Figure 1:

Fig. 1: Particle identifications of K^{+} (a) and K^{0}_{S}, from combination of \pi^{+} and \pi^{-} pairs, (b), from the \sqrt{s_{NN}} = 3.0 Gev Au+Au minimum biased collisions. In order to achieve desirable purity (90\% for K^{0}_{S}, 95\% for K^{+} and 99\% for \pi^{+}) for the correlation function analysis, STAR detectors TPC, TOF and (plus eTOF at \sqrt{s_{NN}} = 3.5 GeV and 3.9 GeV) are used for particle identification. Red-lines are the results of these mass discussions and the vertical dotted blue lines indicate the mass region used for the correlation function analysis presented.

Figure 2:

Fig. 2: Energy dependence of the particle acceptances for \pi^{+}(upper panels), K^+ (middle panel) and K_{S}^{0} (bottom panel) shown as p_{T} vs. rapidity from \sqrt{s_{NN}} = 3.0, 3.2, 3.5, 3.9 and 4.5 GeV Au+Au collisions. Dashed red boxes indicate the acceptance region used in the correlation function analysis. In the mid-panel, the long dashed black lines show the momentum cuts based on the requirement of purity, which set the up limits in \pt for the charged Kaon acceptance at mid-rapidity.

Figure 3:

Fig. 3: Energy dependence of the one-dimension correlation functions of \pi^{+}-\pi^{+} (upper panel), K^{+}-K^{+} (middle panel) and K^{0}_{S}-K^{0}_{S} (bottom panel) from \sqrt{s_{NN}} = 3.0, 3.2, 3.5, 3.9 and 4.5 GeV Au + Au collisions at 0-60 \% centrality. Vertical lines and open boxes represent the statistical and systematic uncertainties, respectively. Open circles show the correlation function with the effect of only quantum statistics, and the results of a Gaussian source to the correlation function are shown by the dashed lines.  The blue bands are correlation functions calculated from transport model UrQMD plus a correlation package CRAB.

Figure 4:

Fig. 4: Energy dependence of the Gaussian source parameters R_{inv} (a), correlation strength \lambda (b) and abundance asymmetry for K^{+}-K^{-} (triangle) and K^{0}-\overline{K}^{0} (solid circle) (c). For comparison, one-dimension Gaussian source parameters from pi^{+}-pi^{+} correlation functions are also shown in panels (a) and (b) as open blue squares. Results from transport model UrQMD are shown as dashed lines. Panel (d) shows m_{T} dependence of the R_{inv} with scaling factor f(\gamma) = 1 / \sqrt{(\sqrt{\gamma_{T}} + 2) / 3}. While dashed-lines represent the m_{T}-scaling fit to pion data at each collision energy. The results of UrQMD calculations are shown as blue and yellow bands for pions and kaons, respectively.

Summary:

1. First measurements of Kaon femtoscopy in nuleus-nuleus collisions at high baryon density region, and source parameters are extracted.

2. Kaon results seem not follow the <m_{T}> scaling from pion correlation functions which may indicate no equilibrium amongst pions and Kaons at these collisions.

3. The abundance asymmetry parameter of K^{0} is determined and they are decreasing as a function of the collision energy which is consistent with the pair production becomes more important at higher collision energies.

4. Within uncertainty hadronic transport model (UrQMD) plus afterburner (CRAB) calculations for Kaon reproduced all of the above observations.

Analysis Note: 
https://drupal.star.bnl.gov/STAR/blog/lazhang/FXT-KKCF-Analysis-note

presentation links:
K_{s}^{0}:
https://drupal.star.bnl.gov/STAR/system/files/20220721CFPWG_LiAngZhang.pdf
https://drupal.star.bnl.gov/STAR/system/files/20220913_LiAngZhang_FXTK0sK0sCF.pdf
https://drupal.star.bnl.gov/STAR/system/files/20230301LiAngUpdateAndPaperProposal_v3.pdf
https://drupal.star.bnl.gov/STAR/system/files/20230425LiAngK0s-K0sCFUpdate.pdf
https://drupal.star.bnl.gov/STAR/system/files/20230629STARBESIIWorkshop_LiAngZhang_BijunFan.pdf
https://drupal.star.bnl.gov/STAR/system/files/20230803LiAngK0s-K0sCFUpdate.pdf
https://drupal.star.bnl.gov/STAR/system/files/K0sK0sCFUpdates_LiAngZhang_PreliminaryRequest.pdf
https://drupal.star.bnl.gov/STAR/system/files/K0sK0sA0F0Par_LiAngZhang.pdf

K^{+}:
https://drupal.star.bnl.gov/STAR/system/files/K_CF_0.pdf
https://drupal.star.bnl.gov/STAR/system/files/sys_K_CF_6.pdf
https://drupal.star.bnl.gov/STAR/system/files/KK_CF_3GeV_0.pdf
https://drupal.star.bnl.gov/STAR/system/files/collaboration%20meeting_0.pdf
https://drupal.star.bnl.gov/STAR/system/files/KK_CF_FXT_3p85_Collabration_meeting_bijunFan.pdf
https://drupal.star.bnl.gov/STAR/system/files/KK_3p2GeV_CF_0525_pwg.pdf
https://drupal.star.bnl.gov/STAR/system/files/deltaphistar_3p2_KK.pdf
https://drupal.star.bnl.gov/STAR/system/files/preliminary_request_3p2_KK_230601_0.pdf
https://drupal.star.bnl.gov/STAR/system/files/Preliminary_request_KK_HBT_3p2to3p9_Bijun_230810_v2.pdf
https://drupal.star.bnl.gov/STAR/system/files/Collabration_meeting_KK_HBT_FXT_Bijun_231017sss.pdf
https://drupal.star.bnl.gov/STAR/system/files/Charged_Kaon_HBT_STAR_FXT_with_eTOF_0111.pdf

Pion:
https://drupal.star.bnl.gov/STAR/system/files/PION3.0-5.2_3D%2B1D%28Gauss%2BLevy%29.pdf

Both:
https://drupal.star.bnl.gov/STAR/system/files/KKCF20240815PWG.pdf
https://drupal.star.bnl.gov/STAR/system/files/KKCFPaperProposal_v5_0.pdf
https://drupal.star.bnl.gov/STAR/system/files/KKCFPaperProposalDraft_v6_20240411.pdf