AI 中文总结
本研究构建描述μ子-质子电弱相互作用的非相对论拉格朗日量，通过振幅匹配确定领头阶系数及α阶修正，结合EFT费米耦合结果算出μ氢单态、三重态俘获率的精确数值。
AI 中文摘要
我们构建了一个描述μ子-质子电弱相互作用的非相对论拉格朗日量。通过匹配含非相对论核子与相对论轻子的理论，我们确定了领头阶系数。针对这些系数最具影响的$\u003cmath\u003e\u003cmi mathvariant=\"script\"\u003eO\u003c/mi\u003e\u003c/math\u003e(α)$修正，我们通过将自由μ子在质子上俘获的非相对论振幅与相应相对论振幅匹配来确定。我们利用该非相对论有效场论框架计算μ氢中的俘获率，纳入了α阶及最高达$1/m_μ$阶的辐射修正。结合此前在EFT（有效场论）中推导的费米耦合结果，我们得到单态与三重态俘获率分别为$Γ({}^1 S_0) = 724.07 \pm 5.45~\rm{s}^{-1}$和$Γ({}^3 S_1) = 11.55 \pm 0.18~\rm{s}^{-1}$。
英文摘要
We construct a non-relativistic Lagrangian that describes muon-proton electroweak interactions. We determine the leading order coefficients by matching onto the theory with non-relativistic nucleons and relativistic leptons. The most impactful $\mathcal{O}(α)$ corrections to those coefficients are determined by matching the non-relativistic amplitudes for capture of a free muon on a proton to the corresponding relativistic one. We use our non-relativistic effective field theory framework to calculate the capture rate in muonic hydrogen, thereby including radiative corrections of order $α$ and up to order $1/m_μ$. Using results for the Fermi coupling previously derived in EFT, we obtain singlet and triplet capture rates of $Γ({}^1 S_0) = 724.07 \pm 5.45~\rm{s}^{-1}$ and $Γ({}^3 S_1) = 11.55 \pm 0.18~\rm{s}^{-1}$, respectively.
Comments11 pages, 3 figures
