Abstract
From a study of the lineshape of the $X(3872)$, the LHCb collaboration measures a sizeable negative effective range. This cannot be reconciled with a shallow $D\bar{D}^*$ bound state hypothesis. Based on Weinberg's compositeness criterion, together with a theorem by Smorodinsky, it follows that the $X$ has to have a compact hidden charm structure, most likely a tetraquark, interacting with unbound $D\bar{D}^*$ pairs via short-distance color forces. This conclusion is strengthened by the general pattern recently emerging for exotic mesons.
Highlights
The Xð3872Þ is the most studied among the many exotic hadrons which have been discovered since 2003 [1,2,3,4,5,6,7]
Based on Weinberg’s compositeness criterion, together with a theorem by Smorodinsky, it follows that the X has to have a compact hidden charm structure interacting with unbound DD Ã pairs via short-distance color forces
The case Z 1⁄4 0 can be interpreted as the condition for the particle to be composite, since its field does not appear in the Lagrangian: the state is generated dynamically, and the propagator is saturated by multiparticle contributions
Summary
The Xð3872Þ is the most studied among the many exotic hadrons which have been discovered since 2003 [1,2,3,4,5,6,7]. The physical deuteron results from the interaction of the elementary one with the jnpi pairs In this case, the existence of a bound state generated solely by np interactions is not necessary to explain the dynamics of the system. The case Z 1⁄4 0 can be interpreted as the condition for the particle to be composite, since its field does not appear in the Lagrangian: the state is generated dynamically, and the propagator is saturated by multiparticle contributions This reasoning is compatible with the statements written in the original Weinberg’s paper [13], where it is observed that “an elementary deuteron would have 0 < Z < 1.”3. We reexamine the recent LHCb data, to extract the values of Z and r0
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