论文标题
散射幅度的积极时刻
Positive Moments for Scattering Amplitudes
论文作者
论文摘要
我们发现，远期$ 2 \ to2 $散射幅度在Unitarity和因果理论中所满足的完整条件。这些基于一组无限的能量依赖量（弧），这些数量分散地表示为（任意）较高能量的正量值的矩。我们以能量扩展中的任何有限顺序确定适合有效场理论（EFT）的约束的最佳有限亚集。在树级弧线处，与威尔逊系数一对一。我们确定了该近似适用的条件下，在从未做到的情况下确定看似可行的EFT。在所有情况下，我们都会讨论耦合和能量的有效性范围。我们还将结果扩展到小但有限〜$ t $的情况。我们研究的结果是，EFT在某些方向上的散射幅度在能量上增长的速度比$ e^6 $更快地增长。
We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound Effective Field Theories (EFTs), at any finite order in the energy expansion. At tree-level arcs are in one-to-one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both couplings and energy. We also extend our results to the case of small but finite~$t$. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than $E^6$ cannot be UV-completed.
