AI 中文总结
本文通过$\text{O}(p^4)$阶完成II型跷跷板模型到HEFT的树级匹配，构造完整LNV HEFT算符基，对比相关理论明确额外标量效应，探讨其对多类物理过程的意义。
AI 中文摘要
我们通过手征展开中的$\boldsymbol{\text{O}}(p^4)$阶，完成了II型跷跷板模型到希格斯有效场论（HEFT）的完整树级匹配。采用非线性场表象和初级HEFT幂次计数方案，我们保留了对独立重标量质量、中性标量混合角及三重态真空期望值的依赖，未在这些参数中引入额外展开。为系统描述轻子数破坏，我们利用编码轻子数破坏插入的$\boldsymbol{B-L}$电荷和 custodial 取向的复装扮 spurion，构造了$\boldsymbol{\text{O}}(p^4)$阶下完整且无冗余的轻子数破坏（LNV）HEFT算符基，包含其全部味多重度。该基通过希尔伯特级数计数得到独立验证。随后，我们将匹配结果与对应的实三重态扩展及先前提出的破缺相有效场论进行比较，这些比较明确了额外CP-odd和双荷标量态的效应，表明在进行适当参数展开后可得到重叠的破缺相结果，而HEFT保留了未展开的非线性电弱结构。我们进一步讨论了其对希格斯和电弱精密可观测量、矢量玻色子散射、多希格斯产生、反常规范耦合、顶夸克过程、无中微子双β衰变、带电轻子味破坏及同号双轻子产生的代表性意义。
英文摘要
We perform the complete tree-level matching of the type-II seesaw model onto the Higgs effective field theory (HEFT) through $\mathcal{O}(p^4)$ in the chiral expansion. Employing a nonlinear field representation and the primary-HEFT power-counting scheme, we retain the dependence on the independent heavy-scalar masses, the neutral-scalar mixing angle, and the triplet vacuum expectation value without introducing additional expansions in these parameters. To systematically describe lepton-number violation, we construct a complete and nonredundant basis of LNV HEFT operators through $\mathcal{O}(p^4)$, including their full flavor multiplicities, using a complex dressed spurion that encodes the $B-L$ charge and custodial orientation of the LNV insertion. The basis is independently validated by Hilbert-series counting. We then compare our matching results with those for the corresponding real-triplet extension and with a previously proposed broken-phase effective field theory. These comparisons identify the effects of the additional CP-odd and doubly charged scalar states and show that the overlapping broken-phase results are recovered after the appropriate parameter expansion, while HEFT retains the unexpanded nonlinear electroweak structure. We further discuss representative implications for Higgs and electroweak precision observables, vector-boson scattering, multi-Higgs production, anomalous gauge couplings, top-quark processes, neutrinoless double-beta decay, charged-lepton flavor violation, and same-sign dilepton production.
Comments49 pages
