Abstract
Chiral extrapolations of the binding energy of the X (3872) molecular state are investigated using an explicitly renormalizable framework free of finite cut-off artefacts. Insights into the binding mechanisms are discussed: if the X is less bound with the growing pion mass, its binding energy is governed by the explicit pion mass dependence from one-pion exchange; an opposite behaviour would indicate the importance of the pionmass dependent short-range interactions, in addition to pionic effects. The important role of the three-body DDπ dynamics is emphasised.
Highlights
EPJ Web of Conferences [5,6,7] that the X is a bound state of D D∗ because of its close proximity to the D D∗ threshold and because of its appropriate quantum numbers
Insights into the binding mechanisms are discussed: if the X is less bound with the growing pion mass, its binding energy is governed by the explicit pion mass dependence from one-pion exchange; an opposite behaviour would indicate the importance of the pionmass dependent short-range interactions, in addition to pionic effects
In ref. [15] the pion mass dependence of the X binding energy was investigated within the EFT framework based on the non-perturbative solution of the non-relativistic Lippmann-Schwinger-type integral equations for the D D∗ problem with the leading-order (LO) potential consisting of the onepion-exchange (OPE) and the pion-mass dependent contact interaction
Summary
EPJ Web of Conferences [5,6,7] that the X is a bound (or virtual) state of D D∗ because of its close proximity to the D D∗ threshold and because of its appropriate quantum numbers. In analogy to the deuteron, the X is amenable to the effective field theory treatment, see [8,9,10] for various studies within pionless framework and [11,12,13,14,15,16,17] for pionful approaches
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