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Perturbative Pions and the Effective Range Expansion

1999/04/19 by Thomas D. Cohen, Cohen, Thomas D.
Physics and Astronomy · #FOS: Physical sciences #High-Energy Particle Collisions Research #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #nucl-th

paper · pdf · doi:10.48550/arxiv.nucl-th/9904052

13 pages; Talk given at INT Workshop on Nuclear Physics with Effective FIeld Theory, Feb. 1999

arxiv created 1999/04/19 · openalex publication_date 1999/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this talk the Q counting scheme to implement effective field theory is discussed. It is pointed out that there are two small mass scales in the problem mπ and 1/a with 1/a ≪ mπ. It is argued that while the expansion based on 1/a being small compared to the underlying short distance scales works well, the chiral expansion may not. The coefficients of the effective range expansion are sensitive to the chiral physics and are very poorly described in Q counting at lowest nontrivial order. A ``shape function'' is introduced which again is sensitive to pionic physics and insensitive to fitting procedures. It is also poorly described in Q counting.

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