The Wigner bound, setting an upper limit on the scattering effective range, is examined at different orders of contact effective field theory. Using cutoff regulator we show that the bound loosens when higher orders of the theory are considered. For a sharp and a Gaussian regulators, we conjecture an analytic formula for the dependence of the Wigner bound on the theory's order. It follows that the bound vanishes in the limit of infinite order. Using a concrete numerical example we demonstrate that the above surmise still holds after renormalization at finite cutoff. Studying the 3-body system with this example, we have found that limiting the permissible range of cutoffs by the Wigner bound, we avoid the Thomas collapse, and don't need to promote the 3-body force to leading order.

中文翻译：

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去除非微扰有效场论中的 Wigner 界

设置散射有效范围上限的 Wigner 界在接触有效场理论的不同阶数下进行了检查。使用截止调节器，我们表明当考虑理论的更高阶时，界限会放松。对于锐性和高斯调节器，我们推测维格纳界对理论阶数的依赖性的解析公式。因此，边界在无限阶的极限中消失。使用一个具体的数值例子，我们证明了上述假设在有限截止点重整化后仍然成立。用这个例子研究三体系统，我们发现通过 Wigner 界限制截断的允许范围，我们避免了 Thomas 崩溃，并且不需要将三体力提升到领先阶。