Schur 消去法处理膜局域化 Higgs 质量谱，以及 $\epsilon\to0$/$N\to\infty$ 非交换性的判据
Schur elimination of brane-localised Higgs mass spectra, and the criteria for the $ε\to0$/$N\to\infty$ non-commutativity
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中文总结 AI 辅助
该研究通过 Schur 补精确消除膜局域化 Higgs 的 KK 塔，证明两种极限顺序的不一致源于单个求和的不连续性，并给出两个必要判据，适用于散射、跷跷板等构造。
中文摘要 AI 辅助
在许多标准模型的 5D 扩展中，Higgs 玻色子被局域化在额外维度的单个点上，并与体费米子耦合。计算费米子质量谱需要边界正则化，而在求和 Kaluza-Klein 塔之前或之后移除该正则化可能给出不同结果，如文献 Barcelo:2014kha 所示。由于耦合通过仅两个重叠数到达任何 KK 模式，整个塔可以通过 Schur 补精确消除；两种极限顺序之间的不一致因此归结为单个求和，我们直接证明了其不连续性。这种不连续性的出现需要两个条件：耦合足够尖锐以使求和条件收敛，以及在接触点具有互补行为的第二通道。这两个条件都不依赖于存在额外维度，甚至不依赖于需要求和的离散塔。同样的检验适用于普通散射中的接触相互作用、光学定理背后的虚部，以及跷跷板、门户和钟表机构构造。这两个条件是否满足决定了类似的歧义是否起作用。
英文摘要
In many 5D extensions of the Standard Model, the Higgs boson is localised to a single point along the extra dimension, where it couples to bulk fermions. Computing the fermion mass spectrum then requires a boundary regulator, and removing it before or after summing the Kaluza-Klein tower can give different answers, as shown in Ref.~\cite{Barcelo:2014kha}. Because the coupling reaches any KK mode through only two overlap numbers, the whole tower can be eliminated exactly by a Schur complement; the disagreement between the two orders of limit then reduces to a single sum, whose discontinuity we prove directly. This discontinuity needs two conditions to appear: a coupling sharp enough to leave the sum conditionally convergent, and a second channel with complementary behaviour at the point of contact. Neither condition depends on having an extra dimension, or even a discrete tower to sum. The same test applies to contact interactions in ordinary scattering, the imaginary part behind the optical theorem, and seesaw, portal, and clockwork constructions. Whether the two conditions are met determines whether a similar ambiguity plays any role.
发表机构
- International Institute of Information Technology, Hyderabad（印度信息技术海德拉巴国际研究所）
机构由 AI 辅助整理，请以论文原文为准。
