费米子散射中解析性的符号
Signs of analyticity in fermion scattering
摘要：
我们发现，狄拉克费米子的主导无关相互作用的符号是由S-矩阵的解析结构的约束。如果获得Regge行为，负号表示存在更高自旋的束缚态，其破坏色散积分的收敛并驱动相应的相关算子。对于核子-核子散射，一些低能相互作用的负性表明存在自旋为1的束缚态：氘核。我们将色散积分的发散与低能散射截面的“索末菲增强”联系起来。我们还讨论了如何使用微扰方法来理解依赖于轻夸克的质量上的低能核相互作用，这照亮了潜在的陷阱。最后，我们提出了将类似的推理应用于电弱有效拉格朗日中的电流-电流算子的可能性，其中没有束缚态破坏色散关系的收敛。
英文摘要：
We show that the signs of the leading irrelevant interactions for Dirac fermions are constrained by the analytic structure of the S-matrix. If Regge behavior obtains, negative signs indicate the presence of higher-spin bound states that spoil the convergence of the dispersion integrals and drive the corresponding operators relevant. For nucleon-nucleon scattering, the negativity of some of the low-energy interactions signals the presence of a spin-1 bound state: the deuteron. We connect the divergence of the dispersion integral to the "Sommerfeld enhancement" of the cross-section for low-energy scattering. We also discuss how this illuminates potential pitfalls in using perturbative methods to understand the dependence of the low-energy nuclear interaction on the masses of the light quarks. Finally, we suggest the possibility of applying similar reasoning to the current-current operators in the electroweak effective lagrangian, where no bound states spoil convergence of the dispersion relations.
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