论文标题
具有共振领域的非宗派主义有效领域理论
Nonrelativistic Effective Field Theory with a Resonance Field
论文作者
论文摘要
我们使用有效的场理论（EFT）讨论了两个粒子的非层次散射中的浅共振，该理论（EFT）包括具有共振的量子数的辅助场。我们在系统扩展中构建了明显的重新归一化散射幅度，直至近代领先的顺序。对于狭窄的共振，幅度是扰动的，除了在谐振电线杆附近。它自然在低能区域的零，类似于Ramsauer-TownSend效应。对于广泛的共鸣，在EFT有效性方面，几乎所有地方的领先幅度几乎无扰动。我们在没有辅助场的情况下恢复了EFT的结果，这等同于有效范围扩展，散射长度较大和有效范围。我们还考虑了另外的微调调整，即使对于广泛的共鸣，也会导致低能幅度零。我们表明，在所有情况下，当辅助场不是幽灵的情况下，重质量的要求确保共振极在复杂动量平面的下半部分，如其他参数所预期的那样。 EFT扩展的系统特征是用具有潜在理论的玩具模型来体现的。
We discuss shallow resonances in the nonrelativistic scattering of two particles using an effective field theory (EFT) that includes an auxiliary field with the quantum numbers of the resonance. We construct the manifestly renormalized scattering amplitude up to next-to-leading order in a systematic expansion. For a narrow resonance, the amplitude is perturbative except in the immediate vicinity of the resonance poles. It naturally has a zero in the low-energy region, analogous to the Ramsauer-Townsend effect. For a broad resonance, the leading-order amplitude is nonperturbative almost everywhere in the regime of validity of the EFT. We regain the results of an EFT without the auxiliary field, which is equivalent to the effective-range expansion with large scattering length and effective range. We also consider an additional fine tuning leading to a low-energy amplitude zero even for a broad resonance. We show that in all cases the requirement of renormalizability when the auxiliary field is not a ghost ensures the resonance poles are in the lower half of the complex momentum plane, as expected by other arguments. The systematic character of the EFT expansion is exemplified with a toy model serving as underlying theory.
