论文标题
在$ λϕ^{4} $理论的多片生产的抑制指数
Suppression exponent for multiparticle production in $λϕ^{4}$ theory
论文作者
论文摘要
我们计算出在不间断的$（3+1）$ - 尺寸$ λϕ^4 $理论中产生$ n $粒子的概率。为此，我们在弱耦合方案$ {λ\ ll 1} $中以$ {n \ gg 1} $起作用的奇异解决方案的半经典方法。我们第一次在异常较大的最终状态乘法的区域中获得可靠的结果$ {n \ggλ^{ - 1}} $，其中概率以$ n $，$ n $，$ n $，$ n $，{\ cal p}（\ cal p}（\ mbox {\ mbox {forn）{forn）\ sim \ sim \ sim \ sim \ sim \ exp \ f_ \ f _ f _ f _ f _ f _ f _ f _ \ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ f _ n \}} $，其斜率$ f _ {\ infty} <0 $取决于产生的粒子的平均动能$ \ varepsilon $。在相反的情况下，$ {n \llλ^{ - 1}} $我们的数据匹配了众所周知的树级结果，它们在两个限制之间插值，以$ n \simλλ^{ - 1} $。总体而言，这证明了在$ {n \ gg 1} $和任意$ \ varepsilon $中对多颗粒生产概率的指数抑制。使用数值溶液，我们批判性地分析了文献中建议的多种Higgs玻色子产生的机制。用自发折断的对称性将我们的技术应用于标量理论可以在不久的将来消除（或确认）。
We compute the probability of producing $n$ particles from few colliding particles in the unbroken $(3+1)$-dimensional $λϕ^4$ theory. To this end we numerically implement semiclassical method of singular solutions which works at ${n \gg 1}$ in the weakly coupled regime ${λ\ll 1}$. For the first time, we obtain reliable results in the region of exceptionally large final state multiplicities ${n\gg λ^{-1}}$ where the probability decreases exponentially with $n$, ${{\cal P}(\mbox{few} \to n) \sim \exp\{f_\infty(\varepsilon) \, n\}}$, and its slope $f_{\infty}< 0$ depends on the mean kinetic energy $\varepsilon$ of produced particles. In the opposite case ${n\ll λ^{-1}}$ our data match well-known tree-level result, and they interpolate between the two limits at $n \sim λ^{-1}$. Overall, this proves exponential suppression of the multiparticle production probability at ${n\gg 1}$ and arbitrary $\varepsilon$ in the unbroken theory. Using numerical solutions, we critically analyze the mechanism for multiple Higgs boson production suggested in the literature. Application of our technique to the scalar theory with spontaneously broken symmetry can eradicate (or confirm) it in the nearest future.
