极高能量下多Higgs过程的图解计算：用MadGraph标度F圣杯
Diagrammatic computation of multi-Higgs processes at very high energies: scaling F holy grail with MadGraph
摘要：
在非常高的能量下，自发破缺的规范理论中的多粒子末态的散射振幅随产生的粒子数的增加而成因子地增长。使用简单的标量场理论模型，有和没有VEV，我们计算的总截面与多达7个粒子在末级微扰理论与MadGraph的领导秩序。通过探索已知的多粒子率与粒子数的标度性质，我们确定从这些一般的$n$点截面在大$n$限制。在我们所考虑的高多重性区域中，n>>1且λ n=固定，微扰理论与高阶回路效应强耦合，从而增加λ n的幂。在近似中，只有领先的回路的影响，我们表明，相应的微扰截面指数增长，并最终违反微扰么正性。这发生在令人惊讶的低能量标度~50 TeV与多重性以上~130。预计在达到这些尺度之前，修复机制或理论的扩展必须设置，可能涉及先验弱耦合理论中的新的非微扰动力学。
英文摘要：
At very high energies scattering amplitudes in a spontaneously broken gauge theory into multi-particle final states are known to grow factorially with the number of particles produced. Using simple scalar field theory models with and without the VEV, we compute total cross-sections with up to 7 particles in the final state at the leading order in perturbation theory with MadGraph. By exploring the known scaling properties of the multi-particle rates with the number of particles, we determine from these the general $n$-point cross-sections in the large-$n$ limit. In the high-multiplicity regime we are considering, n>>1 and lambda n=fixed, the perturbation theory becomes strongly coupled with the higher-order loop effects contributing increasing powers of lambda n. In the approximation where only the leading loop effects are included, we show that the corresponding perturbative cross-sections grow exponentially and ultimately violate perturbative unitarity. This occurs at surprisingly low energy scales ~50 TeV with multiplicities above ~130. It is expected that a repair mechanism or an extension of the theory has to set-in before these scales are reached, possibly involving a novel non-perturbative dynamics in the a priori weakly coupled theory.
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