高能重离子碰撞中心快度区鉴别粒子的平均横动量

谢浈; 李景行; 郑华; 张文超; 朱励霖; 刘星泉; 谭志光; 周代梅; BonaseraAldo

doi:10.7498/aps.73.20240905

摘要

末态粒子的平均横动量$\langle p_{\mathrm{T}}\rangle$是高能重离子碰撞实验中的一个重要观测量. 它反映了软质强子的特性和热核物质的性质, 对其研究有助于获取碰撞系统的演化信息与规律. 基于相对论重离子对撞机(RHIC)上的STAR、PHENIX实验组和大型强子对撞机(LHC)的ALICE实验组提供的金核-金核(Au+Au)和铅核-铅核(Pb+Pb)碰撞中心快度区实验数据, 唯象公式能很好地描述不同碰撞能量下, 鉴别粒子平均横动量$\langle p_{\mathrm{T}}\rangle$随碰撞中心度、每核子对的平均碰撞次数、每核子对平均产生的带电粒子多重数赝快度密度及每次碰撞平均产生的带电粒子多重数赝快度密度的依赖关系. 结果表明, 鉴别粒子平均横动量$\langle p_{\mathrm{T}}\rangle$与碰撞中心度呈线性关系, 而与每核子对的平均碰撞次数$ {2N_{{\mathrm{coll}}}}/{N_{{\mathrm{part}}}}$、每核子对平均产生的带电粒子多重数赝快度密度$\dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$及每次碰撞平均产生的带电粒子多重数赝快度密度$\dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$呈幂律关系. 同时, 发现鉴别粒子平均横动量$\langle p_{\mathrm{T}}\rangle$与碰撞中心度以及每核子对的平均碰撞次数唯象公式中的拟合参数与碰撞能量呈现非常好的幂律函数关系. 因此, 碰撞中心度及每核子对的平均碰撞次数是研究鉴别粒子平均横动量的优选物理量. 本文结果可用于对实验上在其他碰撞能量下鉴别粒子平均横动量的预测.

关键词:

Abstract

The average transverse momentum $\left\langle p_{\mathrm{T}} \right\rangle$ of final particles is an important observable in high-energy heavy-ion collision experiments. It reflects the properties of soft hadrons and thermonuclear matter, and it can also be used to deduce the information about the evolution of collision systems. By using the phenomenological linear and power-law functions, we study the dependence of the average transverse momentum $\langle p_{\mathrm{T}}\rangle$ at midrapidity in Au + Au and Pb + Pb collisions from the STAR, PHENIX and ALICE Collaborations on four normalized physical quantities, i.e. the collision centrality, the average number of binary collisions per participant pair $\dfrac{2N_{{\mathrm{coll}}}}{N_{{\mathrm{part}}}}$, the average pseudorapidity density of charged particles per participant pair $\dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$ and the average pseudorapidity density of charged particles per binary collision $\dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $. The results show that the average transverse momentum $\langle p_{\mathrm{T}} \rangle$ of identified particles exhibits a good linear relationship with collision centrality, and it follows a nice power-law relationship with the average number of binary collisions per participant pair $\dfrac{2N_{{\mathrm{coll}}}}{N_{{\mathrm{part}}}}$, the average pseudorapidity density of charged particles per participant pair $\dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$, and the average pseudorapidity density of charged particles per binary collision $\dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta}$. It is also found that the fitting parameters in the proposed phenomenological functions for the average transverse momentum $\langle p_{\mathrm{T}} \rangle$ with collision centrality and the average number of binary collisions per participant pair follow a power-law function with collision energy, which endows the phenomenological approach with predictive ability. Therefore, the collision centrality and the average number of binary collisions per participant pair are good physical quantities for studying the average transverse momentum of identified particles in high-energy heavy-ion collisions. The results in this study can be used to predict the average transverse momentum of identified particles at other collision energy of which the experimental data are not available so far. The mass ordering of the average transverse momentum of identified particles, i.e. $\text{π}^{-},\;{\mathrm{K}}^{-} $ and $\bar{{\mathrm{p}}}$, is also discussed and explained by the particle production time related to energy conservation, at a given collision centrality and energy.

Keywords:

作者及机构信息

1.
陕西师范大学物理学与信息技术学院, 西安　710119

2.
华中师范大学夸克与轻子物理教育部重点实验室, 武汉　430079

3.
四川大学物理学院, 成都　610064

4.
四川大学原子核科学技术研究所, 成都　610064

5.
长沙学院电子信息与电气工程学院, 长沙　410003

6.
华中师范大学粒子物理研究所, 武汉　430079

7.
德州农工大学回旋加速器实验室, 美国得克萨斯州大学城　TX 77843

8.
意大利南方国家实验室, 意大利卡塔尼亚　95123

通信作者: 郑华, zhengh@snnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11905120)、华中师范大学夸克与轻子物理教育部重点实验室开放基金(批准号: QLPL2024P01)和四川省自然科学基金面上项目(批准号: 2024NSFSC0420)资助的课题.

Authors and contacts

1.
School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China

2.
Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan 430079, China

3.
College of Physics, Sichuan University, Chengdu 610064, China

4.
Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China

5.
School of Electronic Information and Electrical Engineering, Changsha University, Changsha 410003, China

6.
Institute of Particle Physics, Central China Normal University, Wuhan 430079, China

7.
Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA

8.
Laboratori Nazionali del Sud, INFN, Catania 95123, Italy

Corresponding author: Zheng Hua, zhengh@snnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11905120), the Open Fund of Key Laboratory of Quark and Lepton Physics in Central China Normal University, China (Grant No. QLPL2024P01), and the Natural Science Foundation of Sichuan Province, China (Grant No. 2024NSFSC0420).

文章全文 : translate this paragraph

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施引文献

图 1 采用线性函数公式(1)对不同碰撞能量下, 中心快度区鉴别粒子的平均横动量$ \langle p_{\mathrm{T}} \rangle $与碰撞中心度关系的拟合结果. 金核-金核碰撞能量为7.7 GeV (a); 11.5 GeV (b); 14.5 GeV (c); 19.6 GeV (d); 27 GeV (e); 39 GeV (f); 62.4 GeV (g); 130 GeV (h); 200 GeV (i). 铅核-铅核碰撞能量为2.76 TeV (j); 5.02 TeV (k). 实验数据来自文献[7—11]

Fig. 1. Linear fits with Eq. (1) to the experimental midrapidity $ \langle p_{\mathrm{T}} \rangle $ versus centrality for the identified particles in Au + Au collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{7.7\;GeV}}$ (a), 11.5 GeV (b), 14.5 GeV (c), 19.6 GeV (d), 27 GeV (e), 39 GeV (f), 62.4 GeV (g), 130 GeV (h), 200 GeV (i), and in Pb + Pb collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{2.76\;TeV}}$ (j), 5.02 TeV (k). The experimental data are taken from Refs. [7–11].

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图 2 (1)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}} \rangle $随碰撞中心度关系的拟合参数　(a) 斜率绝对值$ |a_1 | $; (b) 截距 $ b_1 $与每核子对质心碰撞能量$ \sqrt{s_{{{\rm NN}}}} $的关系

Fig. 2. The collision energy $ \sqrt{s_{{{\rm NN}}}} $ dependence of the fitting parameters from Eq. (1): (a) For the absolute values of slope $ |a_1 | $; (b) for the intercepts $ b_1 $.

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图 3 采用幂律函数公式(2)拟合不同碰撞能量下, 中心快度区鉴别粒子平均横动量$ \langle p_{\mathrm{T}} \rangle $与每核子对的平均碰撞次数关系的拟合结果. 金核-金核碰撞能量为14.5 GeV (a); 62.4 GeV (b); 130 GeV (c); 200 GeV (d). 铅核-铅核碰撞能量为2.76 TeV (e); 5.02 TeV (f). 实验数据来自文献[8—11, 56]

Fig. 3. Power-law fits with Eq. (2) to the experimental midrapidity $ \langle p_{\mathrm{T}} \rangle $ versus $ {2 N_{{\mathrm{coll}}}}/{N_{{\mathrm{part}}}} $ for the identified particles in Au + Au collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{14.5\;GeV}}$ (a), 62.4 GeV (b), 130 GeV (c), 200 GeV (d), and in Pb + Pb collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{2.76\;TeV}}$ (e), 5.02 TeV (f). The experimental data are taken from Refs. [8–11, 56].

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图 4 (2)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $随每核子对的平均碰撞次数关系的拟合参数(a)系数$ a_2 $和(b)指数$ b_2 $与每核子对质心碰撞能量$ \sqrt{s_{{{\rm NN}}}} $的关系

Fig. 4. Collision energy $ \sqrt{s_{{{\rm NN}}}} $ dependence of the fitting parameters from Eq. (2): (a) For the coefficient $ a_2 $; (b) for the power $ b_2 $

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图 5 采用幂律函数公式(3)拟合不同碰撞能量下, 中心快度区的平均横动量$ \langle p_{\mathrm{T}} \rangle $与每核子对平均产生的带电粒子多重数赝快度密度关系的拟合结果. 金核-金核碰撞能量$ \sqrt{s_{{{\rm NN}}}}={\rm{7.7\;GeV}}$ (a); 62.4 GeV (b); 200 GeV (c). 铅核-铅核碰撞能量$ \sqrt{s_{{{\rm NN}}}}= $$ {\rm{2.76\;TeV}}$(d). 实验数据来自文献[7—11, 56—59]

Fig. 5. Power-law fits with Eq. (3) to the experimental midrapidity $ \langle p_{\mathrm{T}} \rangle $ versus $ \dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $ for the identified particles in Au + Au collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{7.7\;GeV}}$ (a), 62.4 GeV (b), 200 GeV (c), and in Pb + Pb collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{2.76\;TeV}}$ (d). The experimental data are taken from Refs. [7–11, 56–59].

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图 6 (3)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $随每核子对平均产生的带电粒子多重数赝快度密度的拟合参数(a)系数$ a_3 $和(b)指数$ b_3 $与每核子对质心碰撞能量$ \sqrt{s_{{{\rm NN}}}} $的关系

Fig. 6. Collision energy $ \sqrt{s_{{{\rm NN}}}} $ dependence of the fitting parameters from Eq. (3): (a) For the coefficient $ a_3 $; (b) for the power $ b_3 $

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图 7 采用幂律函数公式(4)拟合不同碰撞能量下, 中心快度区的平均横动量$ \langle p_{\mathrm{T}}\rangle $与每次碰撞平均产生的带电粒子多重数赝快度密度关系的拟合结果. 金核-金核碰撞能量$ \sqrt{s_{{{\rm NN}}}}={\rm{14.5\;GeV}}$ (a); 62.4 GeV (b); 130 GeV (c); 200 GeV (d). 铅核-铅核碰撞能量$ \sqrt{s_{{{\rm NN}}}}={\rm{2.76\;TeV}}$ (e); 5.02 TeV (f). 实验数据来自文献[8—11, 56—59]

Fig. 7. Power-law fits with Eq. (4) to the experimental midrapidity $ \langle p_{\mathrm{T}}\rangle $ versus $ \frac{1}{N_{{\mathrm{coll}}}}\frac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $ for the identified particles in Au + Au collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{14.5\;GeV}}$ (a), 62.4 GeV (b), 130 GeV (c), 200 GeV (d), and in Pb + Pb collisions at $ \sqrt{s_{{{\rm NN}}}}={\rm{2.76\;TeV}}$ (e), 5.02 TeV (f). The experimental data are taken from Refs. [8–11, 56–59].

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图 8 (4)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $随每次碰撞平均产生的带电粒子多重数赝快度密度的拟合参数(a)系数$ a_4 $和(b)指数$ b_4 $与每核子对质心碰撞能量$ \sqrt{s_{{{\rm NN}}}} $的关系

Fig. 8. Collision energy $ \sqrt{s_{{{\rm NN}}}} $ dependence of the fitting parameters from Eq. (4): (a) For the coefficient $ a_4 $; (b) for the power $ b_4 $

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表 A1 (1)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $与碰撞中心度C关系的拟合参数及相应的$ \chi^2/{\rm NDF} $

Table A1. Fitting parameters of the $ \langle p_{\mathrm{T}}\rangle $ versus centrality for the identified particles from Eq. (1) and the corresponding $ \chi^2/{\rm NDF} $.

碰撞系统, 碰撞能量	粒子种类	截距$ b_1 /(\mathrm{GeV}\cdot c^{-1}) $	斜率$ a_1 /(\mathrm{GeV}\cdot c^{-1}) $	$ \chi^2/{\rm NDF} $
	$ \text{π}^{-} $	$ 0.382\pm 0.011 $	$ -7.01\times10^{-4} \pm 2.47\times10^{-4} $	0.311/7
Au+Au, 7.7 GeV	$ {\mathrm{K}}^{-} $	$ 0.545 \pm 0.013 $	$ -1.59\times10^{-3}\pm 2.72\times10^{-4} $	0.337/7
	$ \bar{{\mathrm{p}}} $	$ 0.794\pm 0.030 $	$ -4.05\times10^{-3} \pm 6.07\times10^{-4} $	0.211/7
	$ \text{π}^{-} $	$ 0.388\pm 0.011 $	$ -5.39\times10^{-4} \pm 2.50\times10^{-4} $	0.397/7
Au+Au, 11.5 GeV	$ {\mathrm{K}}^{-} $	$ 0.566 \pm 0.016 $	$ -1.46\times10^{-3}\pm 3.47\times10^{-4} $	0.531/7
	$ \bar{{\mathrm{p}}} $	$ 0.815\pm0.036 $	$ -3.87\times10^{-3} \pm 7.24\times10^{-4} $	0.097/7
	$ \text{π}^{-} $	$ 0.397\pm 0.012 $	$ -6.19\times10^{-4} \pm 2.69\times10^{-4} $	0.238/7
Au+Au, 14.5 GeV	$ {\mathrm{K}}^{-} $	$ 0.572 \pm 0.018 $	$ -1.44\times10^{-3}\pm 3.79\times10^{-4} $	0.323/7
	$ \bar{{\mathrm{p}}} $	$ 0.827\pm0.039 $	$ -3.37\times10^{-3} \pm 8.04\times10^{-4} $	0.122/7
	$ \text{π}^{-} $	$ 0.398\pm 0.014 $	$ -5.08\times10^{-4} \pm 3.12\times10^{-4} $	0.195/7
Au+Au, 19.6 GeV	$ {\mathrm{K}}^{-} $	$ 0.578 \pm 0.020 $	$ -1.42\times10^{-3}\pm 4.30\times10^{-4} $	0.149/7
	$ \bar{{\mathrm{p}}} $	$ 0.845\pm0.042 $	$ -3.55\times10^{-3} \pm 8.64\times10^{-4} $	0.066/7
	$ \text{π}^{-} $	$ 0.410\pm 0.014 $	$ -6.08\times10^{-4} \pm 3.19\times10^{-4} $	0.093/7
Au+Au, 27 GeV	$ {\mathrm{K}}^{-} $	$ 0.588 \pm 0.020 $	$ -1.24\times10^{-3}\pm 4.48\times10^{-4} $	0.179/7
	$ \bar{{\mathrm{p}}} $	$ 0.857\pm0.043 $	$ -3.52\times10^{-3} \pm 8.81\times10^{-4} $	0.134/7
	$ \text{π}^{-} $	$ 0.417\pm 0.015 $	$ -5.84\times10^{-4} \pm3.25\times10^{-4} $	0.151/7
Au+Au, 39 GeV	$ {\mathrm{K}}^{-} $	$ 0.615 \pm 0.021 $	$ -1.22\times10^{-3}\pm 4.71\times10^{-4} $	0.138/7
	$ \bar{{\mathrm{p}}} $	$ 0.882\pm 0.054 $	$ -3.46\times10^{-3} \pm 1.11\times10^{-3} $	0.091/7
	$ \text{π}^{-} $	$ 0.409\pm 0.007 $	$ -5.46\times10^{-4} \pm 2.11\times10^{-4} $	0.755/7
Au+Au, 62.4 GeV	$ {\mathrm{K}}^{-} $	$ 0.663\pm0.016 $	$ -1.80\times10^{-3}\pm 3.20\times10^{-4} $	0.712/7
	$ \bar{{\mathrm{p}}} $	$ 0.984\pm 0.025 $	$ -3.87\times10^{-3} \pm 5.46\times10^{-4} $	0.501/7
	$ \text{π}^{-} $	$ 0.400\pm0.009 $	$ -6.57\times10^{-4} \pm 3.24\times10^{-4} $	0.384/6
Au+Au, 130 GeV	$ {\mathrm{K}}^{-} $	$ 0.666 \pm 0.020 $	$ -1.54\times10^{-3} \pm 4.19\times10^{-4} $	0.478/6
	$ \bar{{\mathrm{p}}} $	$ 1.01\pm 0.042 $	$ -3.77\times10^{-3}\pm8.05\times10^{-4} $	0.275/6
	$ \text{π}^{-} $	$ 0.427\pm0.012 $	$ -7.75\times10^{-4} \pm 2.73\times10^{-4} $	0.234/7
Au+Au, 200 GeV	$ {\mathrm{K}}^{-} $	$ 0.720\pm0.033 $	$ -2.18 \times10^{-3} \pm 6.49\times10^{-4} $	0.145/7
	$ \bar{{\mathrm{p}}} $	$ 1.10\pm0.050 $	$ -4.58\times10^{-3}\pm 9.55\times10^{-4} $	0.222/7
	$ \text{π}^{-} $	$ 0.532\pm0.010 $	$ -9.28\times10^{-4} \pm 2.34\times10^{-4} $	1.099/7
Pb+Pb, 2.76 TeV	$ {\mathrm{K}}^{-} $	$ 0.886 \pm 0.017 $	$ -1.95\times10^{-3} \pm 3.80\times10^{-4} $	0.960/7
	$ \bar{{\mathrm{p}}} $	$ 1.40\pm 0.020 $	$ -5.26\times10^{-3}\pm 4.58\times10^{-4} $	3.124/7
	$ \text{π}^{-} $	$ 0.586\pm0.012 $	$ -1.16\times10^{-3} \pm 2.88\times10^{-4} $	0.707/7
Pb+Pb, 5.02 TeV	$ {\mathrm{K}}^{-} $	$ 0.943 \pm 0.008 $	$ -1.84\times10^{-3} \pm 1.93\times10^{-4} $	6.723/7
	$ \bar{{\mathrm{p}}} $	$ 1.50\pm 0.013 $	$ -5.97\times10^{-3}\pm 2.91\times10^{-4} $	12.752/7

下载: 导出CSV

表 A2 (2)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $与每核子对的平均碰撞次数$ {2 N_{{\mathrm{coll}}}}/{N_{{\mathrm{part}}}} $关系的拟合参数及相应的$ \chi^2/{\rm NDF} $

Table A2. Fitting parameters of the $ \langle p_{\mathrm{T}}\rangle $ versus $ {2 N_{{\mathrm{coll}}}}/{N_{{\mathrm{part}}}} $ for the identified particles from Eq. (2) and the corresponding $ \chi^2/{\rm NDF} $.

碰撞系统, 碰撞能量	粒子种类	系数$ a_2/(\mathrm{GeV}\cdot c^{-1})$	指数$ b_2 $	$ \chi^2/{\rm NDF} $
	$ \text{π}^{-} $	$ 0.330\pm0.019 $	$ 0.118\pm 0.049 $	0.180/7
Au+Au, 14.5 GeV	$ {\mathrm{K}}^{-} $	$ 0.418\pm0.025 $	$ 0.198\pm 0.052 $	0.235/7
	$ \bar{{\mathrm{p}}} $	$ 0.482\pm 0.045 $	$ 0.343\pm 0.082 $	0.110/7
	$ \text{π}^{-} $	$ 0.344\pm0.019 $	$ 0.104\pm 0.040 $	0.519/7
Au+Au, 62.4 GeV	$ {\mathrm{K}}^{-} $	$ 0.462\pm0.021 $	$ 0.214\pm 0.038 $	0.413/7
	$ \bar{{\mathrm{p}}} $	$ 0.566\pm 0.034 $	$ 0.330\pm 0.047 $	0.352/7
	$ \text{π}^{-} $	$ 0.318\pm0.032 $	$ 0.132\pm 0.066 $	0.375/6
Au+Au, 130 GeV	$ {\mathrm{K}}^{-} $	$ 0.481\pm 0.033 $	$ 0.186 \pm0.051 $	0.448/6
	$ \bar{{\mathrm{p}}} $	$ 0.583\pm 0.049 $	$ 0.318\pm 0.067 $	0.215/6
	$ \text{π}^{-} $	$ 0.338\pm0.020 $	$ 0.128 \pm 0.045 $	0.149/7
Au+Au, 200 GeV	$ {\mathrm{K}}^{-} $	$ 0.482\pm0.038 $	$ 0.221\pm 0.065 $	0.184/7
	$ \bar{{\mathrm{p}}} $	$ 0.617\pm 0.050 $	$ 0.322 \pm 0.066 $	0.304/7
	$ \text{π}^{-} $	$ 0.430\pm0.017 $	$ 0.096 \pm 0.024 $	0.623/7
Pb+Pb, 2.76 TeV	$ {\mathrm{K}}^{-} $	$ 0.674 \pm 0.027 $	$ 0.124 \pm 0.024 $	0.527/7
	$ \bar{{\mathrm{p}}} $	$ 0.848\pm 0.029 $	$ 0.227\pm 0.020 $	1.731/7
	$ \text{π}^{-} $	$ 0.460\pm 0.020 $	$ 0.105\pm 0.026 $	0.405/7
Pb+Pb, 5.02 TeV	$ {\mathrm{K}}^{-} $	$ 0.741 \pm 0.014 $	$ 0.105\pm 0.011 $	3.765/7
	$ \bar{{\mathrm{p}}} $	$ 0.889\pm 0.017 $	$ 0.230\pm 0.011 $	7.564/7

下载: 导出CSV

表 A3 (3)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $随每核子对平均产生的带电粒子多重数赝快度密度$ \dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $的拟合参数及相应的$ \chi^2/{\rm NDF} $

Table A3. Fitting parameters of the $ \langle p_{\mathrm{T}}\rangle $ versus $ \dfrac{2}{N_{{\mathrm{part}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $ for the identified particles from Eq. (3) and the corresponding $ \chi^2/{\rm NDF} $.

碰撞系统, 碰撞能量	粒子种类	系数$ a_3 /(\mathrm{GeV}\cdot c^{-1})$	指数$ b_3 $	$ \chi^2/{\rm NDF} $
	$ \text{π}^{-} $	$ 0.366\pm0.007 $	$ 0.220\pm 0.142 $	0.263/5
Au+Au, 7.7 GeV	$ {\mathrm{K}}^{-} $	$ 0.509\pm 0.008 $	$ 0.418\pm 0.117 $	0.551/5
	$ \bar{{\mathrm{p}}} $	$ 0.700\pm 0.019 $	$ 0.828 \pm 0.200 $	0.548/5
	$ \text{π}^{-} $	$ 0.366\pm0.01 $6	$ 0.195\pm 0.170 $	0.063/5
Au+Au, 14.5 GeV	$ {\mathrm{K}}^{-} $	$ 0.494\pm 0.022 $	$ 0.361\pm 0.174 $	0.237/5
	$ \bar{{\mathrm{p}}} $	$ 0.631\pm 0.044 $	$ 0.689 \pm 0.269 $	0.235/5
	$ \text{π}^{-} $	$ 0.351\pm0.047 $	$ 0.232\pm 0.299 $	0.105/5
Au+Au, 19.6 GeV	$ {\mathrm{K}}^{-} $	$ 0.427\pm 0.057 $	$ 0.590\pm 0.304 $	0.462/5
	$ \bar{{\mathrm{p}}} $	$ 0.473\pm 0.093 $	$ 1.15 \pm 0.465 $	0.621/5
	$ \text{π}^{-} $	$ 0.346\pm0.045 $	$ 0.261\pm 0.254 $	0.081/5
Au+Au, 27 GeV	$ {\mathrm{K}}^{-} $	$ 0.460\pm0.060 $	$ 0.378\pm 0.254 $	0.123/5
	$ \bar{{\mathrm{p}}} $	$ 0.489\pm 0.094 $	$ 0.893 \pm 0.371 $	0.245/5
	$ \text{π}^{-} $	$ 0.333\pm0.070 $	$ 0.290\pm 0.309 $	0.083/5
Au+Au, 39 GeV	$ {\mathrm{K}}^{-} $	$ 0.428\pm 0.090 $	$ 0.472\pm 0.315 $	0.146/5
	$ \bar{{\mathrm{p}}} $	$ 0.405\pm 0.153 $	$ 1.02 \pm 0.546 $	0.142/5
	$ \text{π}^{-} $	$ 0.317\pm0.038 $	$ 0.260\pm 0.136 $	0.331/6
Au+Au, 62.4 GeV	$ {\mathrm{K}}^{-} $	$ 0.357\pm 0.036 $	$ 0.644\pm 0.127 $	0.662/6
	$ \bar{{\mathrm{p}}} $	$ 0.379\pm 0.050 $	$ 0.997 \pm 0.158 $	0.507/6
	$ \text{π}^{-} $	$ 0.290\pm0.042 $	$ 0.257\pm 0.127 $	0.356/6
Au+Au, 130 GeV	$ {\mathrm{K}}^{-} $	$ 0.410\pm 0.045 $	$ 0.388\pm 0.105 $	0.452/6
	$ \bar{{\mathrm{p}}} $	$ 0.440\pm 0.062 $	$ 0.674 \pm 0.142 $	0.481/6
	$ \text{π}^{-} $	$ 0.266\pm0.056 $	$ 0.344 \pm 0.171 $	0.278/6
Au+Au, 200 GeV	$ {\mathrm{K}}^{-} $	$ 0.286\pm0.087 $	$ 0.683\pm 0.247 $	0.190/6
	$ \bar{{\mathrm{p}}} $	$ 0.291\pm 0.089 $	$ 0.989 \pm0.259 $	0.383/6
	$ \text{π}^{-} $	$ 0.325\pm 0.036 $	$ 0.230 \pm 0.058 $	0.862/7
Pb+Pb, 2.76 TeV	$ {\mathrm{K}}^{-} $	$ 0.471\pm0.052 $	$ 0.295\pm 0.058 $	1.182/7
	$ \bar{{\mathrm{p}}} $	$ 0.442\pm0.041 $	$ 0.538\pm 0.048 $	3.699/7
	$ \text{π}^{-} $	$ 0.305\pm0.045 $	$ 0.282\pm 0.071 $	0.924/7
Pb+Pb, 5.02 TeV	$ {\mathrm{K}}^{-} $	$ 0.502\pm 0.030 $	$ 0.272\pm 0.029 $	8.162/7
	$ \bar{{\mathrm{p}}} $	$ 0.373\pm0.023 $	$ 0.602\pm 0.030 $	20.985/7

下载: 导出CSV

表 A4 (4)式拟合鉴别粒子平均横动量$ \langle p_{\mathrm{T}}\rangle $随每次碰撞平均产生的带电粒子多重数赝快度密度$ \dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $的拟合参数及相应的$ \chi^2/{\rm NDF} $

Table A4. Fitting parameters of the $ \langle p_{\mathrm{T}}\rangle $ versus $ \dfrac{1}{N_{{\mathrm{coll}}}}\dfrac{{\mathrm{d}}N_{{\mathrm{ch}}}}{{\mathrm{d}}\eta} $ for the identified particles from Eq. (4) and the corresponding $ \chi^2/{\rm NDF} $.

碰撞系统, 碰撞能量	粒子种类	系数$ a_4 /(\mathrm{GeV}\cdot c^{-1}) $	指数$ b_4 $	$ \chi^2/{\rm NDF} $
	$ \text{π}^{-} $	$ 0.326\pm 0.044 $	$ -0.156\pm 0.128 $	0.001/5
Au+Au, 14.5 GeV	$ {\mathrm{K}}^{-} $	$ 0.400\pm0.056 $	$ -0.290\pm 0.137 $	0.026/5
	$ \bar{{\mathrm{p}}} $	$ 0.425\pm0.094 $	$ -0.547\pm 0.211 $	0.052/5
	$ \text{π}^{-} $	$ 0.357\pm0.021 $	$ -0.185\pm 0.098 $	0.411/6
Au+Au, 62.4 GeV	$ {\mathrm{K}}^{-} $	$ 0.484\pm0.021 $	$ -0.424\pm 0.086 $	1.108/6
	$ \bar{{\mathrm{p}}} $	$ 0.606\pm 0.036 $	$ -0.674 \pm 0.109 $	1.402/6
	$ \text{π}^{-} $	$ 0.331\pm0.026 $	$ -0.391 \pm 0.190 $	0.347/6
Au+Au, 130 GeV	$ {\mathrm{K}}^{-} $	$ 0.519\pm0.025 $	$ -0.503\pm 0.137 $	0.720/6
	$ \bar{{\mathrm{p}}} $	$ 0.665\pm 0.038 $	$ -0.850\pm 0.181 $	0.384/6
	$ \text{π}^{-} $	$ 0.381\pm0.013 $	$ -0.251 \pm 0.124 $	0.053/6
Au+Au, 200 GeV	$ {\mathrm{K}}^{-} $	$ 0.589\pm0.023 $	$ -0.430\pm 0.170 $	0.420/6
	$ \bar{{\mathrm{p}}} $	$ 0.826\pm 0.033 $	$ -0.627\pm 0.174 $	0.704/6
	$ \text{π}^{-} $	$ 0.526\pm 0.009 $	$ -0.171\pm 0.042 $	0.511/7
Pb+Pb, 2.76 TeV	$ {\mathrm{K}}^{-} $	$ 0.874 \pm0.015 $	$ -0.221 \pm 0.043 $	0.353/7
	$ \bar{{\mathrm{p}}} $	$ 1.36 \pm 0.018 $	$ -0.402\pm 0.036 $	1.187/7
	$ \text{π}^{-} $	$ 0.587\pm 0.013 $	$ -0.167\pm 0.041 $	0.204/7
Pb+Pb, 5.02 TeV	$ {\mathrm{K}}^{-} $	$ 0.946\pm 0.008 $	$ -0.169\pm 0.018 $	1.997/7
	$ \bar{{\mathrm{p}}} $	$ 1.52\pm 0.014 $	$ -0.369\pm 0.018 $	2.886/7

下载: 导出CSV

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