Elementary Particle Populations

基本粒子数量

When the temperature is well above a threshold temperature defined by

当温度远高于由定义的阈值温度时

kT_threshold = mc²

then particles may be treated statistically. Here k is the Boltzmann constant, and this definition of threshold temperature involves setting the average thermal energy equal to the rest mass energy. When the temperature is much higher than the threshold temperature, then one can presume that particle-antiparticle pairs can be freely created from the thermal energy, and will therefore exist in thermal equilibrium with their surroundings. The contribution of a given type of particle will then be proportional to the "effective number of species" of that particle.

然后，粒子可以被统计地处理。这里k是玻尔兹曼常数，这个阈值温度的定义涉及将平均热能设定为静止质量能。当温度远高于阈值温度时，可以假设粒子-反粒子对可以从热能中自由产生，并因此与周围环境处于热平衡状态。某一类粒子的贡献则将与该粒子的“有效物种数”成正比。

Particle 质点	Symbol 符号	Rest energy (MeV) 静止能量（MeV）	Threshold temperature (10⁹ K) 阈值温度 (10⁹ K)	Effective number of species 有效物种数	Mean lifetime (s) 平均寿命 (s)
Photon 光子	γ	0	0	1 x 2 x 1 = 2	Stable 稳定
Neutrinos 中微子	υ_e,υ_e	0	0	2 x 1 x 7/8 = 7/4	Stable 稳定
Neutrinos 中微子	υ_μ,υ_μ	0	0	2 x 1 x 7/8 = 7/4	Stable 稳定
Electron 电子	e^-,e⁺	0.5110	5.930	2 x 2 x 7/8 = 7/2	Stable 稳定
Muon 缪子	μ^-,μ⁺	105.66	1226.2	2 x 2 x 7/8 = 7/2	2.197 x 10^-6
Pion 介子	π⁰	134.96	1566.2	1 x 1 x 1 = 1	0.8 x 10^-16
Pion 介子	π⁺,π^-	139.57	1619.7	2 x 1 x 1 = 2	2.60 x 10^-8
Proton 质子	p,p	938.26	10,888	2 x 2 x 7/8 = 7/2	Stable 稳定
Neutron 中子	n,n	939.55	10,903	2 x 2 x 7/8 = 7/2	920

After Weinberg, First Three Minutes. The underline indicates the anti-particle.

The effective number of species is the product of three factors:

2 if the particle has a distinct antiparticle, 1 if not.

2 如果粒子有对应的反粒子，否则为1。

The number of possible orientations of the particles spin.

粒子自旋的可能取向数目。

7/8 if the particle must obey the Pauli exclusion principle, 1 if not.

若粒子必须遵守泡利不相容原理，则为7/8；若不遵守，则为1。

有效物种数是三个因素的乘积：

The effective number of species is important for the calculation of the energy when a collection of particle is at a high enough temperature so that it can be considered to act like radiation. Under those condition, such as in modeling the early processes in the big bang, the Stefan Boltzmann law can be used to calculate the energy associated with the particles.

当一组粒子在足够高的温度下可以被视为辐射时，有效物种数对于计算能量是重要的。在模拟大爆炸早期过程的条件下，可以使用斯特藩-玻尔兹曼定律来计算与粒子相关的能量。

kT 阈值 = mc²（见 Weinberg，《前三个分钟》）。下划线表示反粒子。