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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.[1] Hwa R C, Wang X N 2004 Quark-Gluon Plasma 3 (Singapore: World Scientific
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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]
Figure 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].
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
Figure 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 $.
图 3 采用幂律函数公式(2)拟合不同碰撞能量下, 中心快度区鉴别粒子平均横动量$ \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]
Figure 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].
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]
Figure 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].
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
Figure 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 $
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]
Figure 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].
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
Figure 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 $
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 
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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
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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
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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
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