An effective field theory for coupled-channel scattering

Abstract

The problem of describing low-energy two-body scattering for systems with two open channels with different thresholds is addressed in the context of an effective field theory. In particular, the problem where the threshold is unnaturally small and the cross section at low energy is unnaturally large is considered. It is shown that the lowest-order point coupling associated with the mixing of the channels scales as ${\Lambda }^{-2}$ rather than ${\Lambda }^{-1}$ (the scaling of the same-channel coupling and the scaling in a single-channel case) where $\Lambda$ is the ultraviolet cutoff. The renormalization of the theory at lowest order is given explicitly. The treatment of higher orders is straightforward. The potential implications for systems with deep open channels are discussed.

8 pages, 2 figures; references added

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• Renormalization Group Analysis of Boundary Conditions in Potential Scattering
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• Implications of the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ as two different states
• Predicting the ${\bar{D}}_s^{(\ast )}{D}_s^{(\ast )}$ bound states as the partners of $X(3872)$
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• A combined analysis of the $Z_c(3900)$ and the $Z_{cs}(3985)$ exotic states
• Naturalness in Nuclear Effective Field Theories
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• Zero-Range Effective Field Theory for Resonant Wino Dark Matter I. Framework
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• Extraction of $ND$ scattering lengths from the ${\Lambda }_b\to {\pi }^{-}p{D}^0$ decay and properties of the ${\Sigma }_c(2800{)}^{+}$
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• Classification of Coupled-Channel Near-Threshold Structures
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• Effective range expansion with a long-range force
• Closed-channel parameters of Feshbach resonances
• Development of a Cox-Thompson inverse scattering method to charged particles
• $K^{-}d\to \pi \Lambda N$ reaction with in-flight kaons for studying the $\Lambda N$ interaction