费米耦合常数 费米耦合常数记为 G F {\displaystyle G_{F}} ,是描写弱相互作用强度的一个物理常数:[1] G F ( ℏ c ) 3 = 2 8 g 2 m W 2 = 1.16637 ( 1 ) × 10 − 5 GeV − 2 . {\displaystyle {\frac {G_{\text{F}}}{(\hbar c)^{3}}}={\frac {\sqrt {2}}{8}}{\frac {g^{2}}{m_{\text{W}}^{2}}}=1.16637(1)\times 10^{-5}\;{\textrm {GeV}}^{-2}\ .} 这里g 是弱相互作用的耦合常数, 和 mW 是W玻色子的质量. 在标准模型中, 费米常数和 希格斯场真空期望值 关系是: v = ( 2 G F ) -1/2 ≃ 246.22 GeV {\displaystyle v=({\sqrt {2}}G_{\text{F}})^{\text{-1/2}}\simeq 246.22\;{\textrm {GeV}}} [2] 费米常数的测量[编辑] 费米常数的测量是通过测量 μ {\displaystyle \mu } 的寿命得到的, μ {\displaystyle \mu } 寿命公式: ℏ τ μ = G F 2 m μ 5 192 π 2 F ( ρ ) [ 1 + H 1 ( ρ ) α ^ ( m μ ) π + H 2 ( ρ ) α ^ 2 ( m μ ) π 2 ] , {\displaystyle {\frac {\hbar }{\tau _{\mu }}}={\frac {G_{F}^{2}m_{\mu }^{5}}{192\pi ^{2}}}F(\rho ){\biggl [}1+H_{1}(\rho ){\frac {{\widehat {\alpha }}(m_{\mu })}{\pi }}+H_{2}(\rho ){\frac {{\widehat {\alpha }}^{2}(m_{\mu })}{\pi ^{2}}}{\biggl ]},} 这里 ρ = m e 2 m μ 2 {\displaystyle \rho ={\frac {m_{e}^{2}}{m_{\mu }^{2}}}} 和 F ( ρ ) = 1 − 8 ρ + 8 ρ 3 − ρ 4 − 12 ρ 2 ln ρ = 0.99981295 , {\displaystyle F(\rho )=1-8\rho +8\rho ^{3}-\rho ^{4}-12\rho ^{2}\ln \rho =0.99981295,} H 1 ( ρ ) = 25 8 − π 2 2 − ( 9 + 4 π 2 + 12 ln ρ ) ρ + 16 π 2 ρ 3 / 2 + O ( ρ 2 ) = − 1.80793 , {\displaystyle H_{1}(\rho )={\frac {25}{8}}-{\frac {\pi ^{2}}{2}}-{\Big (}9+4\pi ^{2}+12\ln \rho {\Big )}\rho +16\pi ^{2}\rho ^{3/2}+{\mathcal {O}}(\rho ^{2})=-1.80793,} H 2 ( ρ ) = 156815 5184 − 518 81 π 2 − 895 36 ζ ( 3 ) + 67 720 π 4 + 53 3 π ln 2 − ( 0.42 ± 0.002 ) had − 5 4 π 2 ρ + O ( ρ ) = 6.64 , {\displaystyle H_{2}(\rho )={\frac {156815}{5184}}-{\frac {518}{81}}\pi ^{2}-{\frac {895}{36}}\zeta (3)+{\frac {67}{720}}\pi ^{4}+{\frac {53}{3}}\pi \ln 2-(0.42\pm 0.002)_{\text{had}}-{\frac {5}{4}}\pi ^{2}{\sqrt {\rho }}+{\mathcal {O}}(\rho )=6.64,} α ^ ( m μ ) − 1 = α − 1 + 1 3 π ln ρ + O ( α ) = 135.901 {\displaystyle {\widehat {\alpha }}(m_{\mu })^{-1}=\alpha ^{-1}+{\frac {1}{3\pi }}\ln \rho +{\mathcal {O}}(\alpha )=135.901} 参考资料[编辑] ^ D. Chitwood et al., Phys.Rev.Lett. 99 (2007) 032001 ^ Plehn, Tilman; Rauch, Michael. Phys. Rev. D. 2005, 72: 053008. Bibcode:2005PhRvD..72e3008P. arXiv:hep-ph/0507321 . doi:10.1103/PhysRevD.72.053008. 引文使用过时参数coauthors (帮助); 缺少或|title=为空 (帮助)