Power counting for three-body decays of a near-threshold state

Abstract

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, delta, between the excitation energy of the D* and the pion mass is smaller than either by a factor ~20. We therefore assign delta an order Q^2 in our counting. This provides a consistent framework for a double expansion in both delta/m_pi and the ratio of m_pi to the high-energy scales in this system. It ensures that amplitudes have the correct behaviour 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.

arXiv comment5 pages, 1 figure; more discussion of pion exchange added

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• Employing spin symmetry to disentangle different models for the XYZ states
• Galilean-Invariant XEFT
• Strong decays of $T_{cc}^{+}$ at NLO in an effective field theory
• Revisiting $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in XEFT
• Hadronic decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Short-range interactions and narrow resonances in effective field theory
• Chiral dynamics of S-wave baryon resonances