源自泛函匹配的有效拉格朗日量
Effective Lagrangians from functional matching
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中文总结 AI 辅助
本研究回顾一种泛函匹配变体方法，通过背景场方法、按区域展开分离圈图效应与软硬模式，以希格斯单态扩充为例推导重粒子单圈阶EFT，且计算与EFT类型无关，转化为SMEFT需引入费米子算符。
中文摘要 AI 辅助
我们简要回顾一种泛函匹配的变体方法，该方法以自上而下的方式推导重粒子单圈阶的有效场论（Effective Field Theory，EFT）。该方法积出对应于质量本征态的重场，即通过对角化质量矩阵消除混合效应之后的重场。我们采用背景场方法分离树图和圈图效应，利用按区域展开（expansion by regions）分离硬模式与软模式。我们以标准模型的希格斯单态扩充（Higgs Singlet Extension）为例对该方法进行说明，其中额外希格斯玻色子的质量$M_\mathrm{H}$被视为大质量，且希格斯混合角$\alpha$被假定按$1/M_\mathrm{H}$标度，以保证在大$M_\mathrm{H}$极限下的退耦。我们的计算与所得EFT的类型（SMEFT与HEFT）无关。最终所得的EFT拉格朗日量可以转化为SMEFT形式，但代价是需要引入费米子EFT算符，尽管在求解重希格斯场的泛函积分时不会直接生成这类算符。
英文摘要
We briefly review a variant of functional matching to derive an Effective Field Theory (EFT) for heavy particles at the one-loop level in the top-down approach. The method integrates out heavy fields that correspond to mass eigenstates, i.e. after removing mixing effects by diagonalizing mass matrices. Tree- and loop-level effects are separated by employing the background-field method, hard and soft modes are separated with the use of the expansion by regions. The method is exemplified for the Higgs Singlet Extension of the Standard Model where the mass $M_\mathrm{H}$ of the additional Higgs boson is considered large, and the Higgs mixing angle $α$ is assumed to scale like $1/M_\mathrm{H}$, in order to guarantee decoupling in the large-$M_\mathrm{H}$ limit. Our calculation is agnostic w.r.t. the type (SMEFT vs. HEFT) of the emerging EFT. Eventually the emerging EFT Lagrangian can be transformed into SMEFT form, but only at the cost of introducing fermionic EFT operators, although no such operators are directly generated upon solving the functional integral over the heavy Higgs field.
