2015/01/31 by M. Alhakami, Mohammad H. Alhakami, Michael C. Birse
Mathematics · Physics and Astronomy · #Amplitude #Effective field theory #Energy (signal processing) #Excitation #Field theory (psychology) #High-Energy Particle Collisions Research #Mathematical physics #Mathematics #Meson #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #State (computer science) #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevd.91.054019
published as Phys. Rev. D 91, 054019 (2015) · 5 pages, 1 figure; more discussion of pion exchange added
arxiv created 2015/02/23 · openalex publication_date 2015/03/13 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a new power counting for the effective field theory describing a near-threshold state with unstable constituents, such as the X(3872) meson. In this counting, the momenta of the heavy particles, the pion mass and the excitation energy of the unstable constituent---the D* in the case of the X---are treated as small scales, of order Q. The difference \ensuremathδ between the excitation energy of the D* and the pion mass is smaller than either by a factor \ensuremath∼20. We therefore assign \ensuremathδ an order Q2 in our counting. This provides a consistent framework for a double expansion in both \ensuremathδ/m_\ensuremathπ and the ratio of m_\ensuremathπ to the high-energy scales in this system. It ensures that amplitudes have the correct behavior at the three-body threshold. It allows us to derive, within an effective theory, various results which have previously been obtained using physically motivated approximations.