论文标题
在$ d \ geq 2 $中散射大量标量粒子的非扰动界限
Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d \geq 2$
论文作者
论文摘要
我们研究了质量$ m $的标量粒子的两到两个散射幅度。为简单起见，我们假设存在$ \ mathbb {z} _2 $对称性，并且粒子为$ \ mathbb {z} _2 $奇数。我们考虑了两类幅度：完全非扰动的幅度和具有截止比例$ m $的有效野外理论（EFT）。使用原始数值方法，我们可以强加完全的非线性单位性，我们以$ 2 \ leq d \ leq 4 $时空维度为两种振幅的各种时空尺寸构建了新的界限。我们表明，我们的边界比仅使用线性化的单位性或阳性获得的界限要强得多。我们讨论了界限对约束EFT的应用。最后，我们将界限与$ ϕ^4 $理论以弱耦合计算的幅度进行比较，并发现它们使边界饱和。
We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale $M$. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in $2 \leq d \leq 4$ space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in $ϕ^4$ theory computed perturbatively at weak coupling, and find that they saturate the bounds.
