An effective field theory for coupled-channel scattering

Thomas D. Cohen; Boris A. Gelman; U. Van Kolck

doi:10.1016/j.physletb.2004.03.020

An effective field theory for coupled-channel scattering

Thomas D. Cohen
, Boris A. Gelman
, U. Van Kolck

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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 Λ^-2 rather than Λ^-1 (the scaling of the same-channel coupling and the scaling in a single-channel case) where Λ 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.

Original language	English (US)
Pages (from-to)	57-66
Number of pages	10
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	588
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physletb.2004.03.020
State	Published - May 20 2004
Externally published	Yes

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.physletb.2004.03.020

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title = "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 Λ-2 rather than Λ-1 (the scaling of the same-channel coupling and the scaling in a single-channel case) where Λ 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.",

author = "Cohen, \{Thomas D.\} and Gelman, \{Boris A.\} and \{Van Kolck\}, U.",

note = "Funding Information: The authors would like to thank M. Alberg, B. El-Bennich and R.G.E. Timmermans for useful discussions about optical potentials and the system. The authors acknowledge the hospitality of the Institute for Nuclear Theory at the University of Washington, Seattle, where most of this research was conducted during the Fall 2003 INT Program on “Theories of Nuclear Forces and Nuclear Systems”. B.A.G. gratefully acknowledges the hospitality of the staff and members of the Theory Group for Quarks, Hadrons and Nuclei at the University of Maryland, College Park, where part of the work was done. U.v.K. thanks RIKEN, Brookhaven National Laboratory and the US Department of Energy [DE-AC02-98CH10886] for providing the facilities essential for the completion of this work. This work was supported in part by the US Department of Energy under grants DE-FG02-93ER-40762 (T.D.C.) and DE-FG03-01ER-41196 (B.A.G., U.v.K.), and by the Alfred P. Sloan Foundation (U.v.K.).",

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N2 - 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 Λ-2 rather than Λ-1 (the scaling of the same-channel coupling and the scaling in a single-channel case) where Λ 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.

AB - 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 Λ-2 rather than Λ-1 (the scaling of the same-channel coupling and the scaling in a single-channel case) where Λ 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.

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An effective field theory for coupled-channel scattering

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