Talk presented by Anthony M. Green

Parallel Session: Heavy Quarks IV

Thursday July 1st, 17.20 - 17.40, Pacinotti Room

Can lattice data for two heavy-light mesons be understood in terms of simply two-quark potentials?

Abstract: For particle physicists, the use of simply two-quark potentials in multiquark problems is not a discussion point, since they know (believe) that it is not correct. In spite of this, there are many-body physicists, who still believe (hope) that this is not so. Over the last few years attempts have been made to clarify this situation by comparing the {\em exact} energies of four-quark systems -- as calculated on a lattice -- with standard many-body models using only two-quark potentials[1]. The outcome is that -- "beyond all reasonable doubt" -- the resulting binding energies are grossly overestimated by the models and that a four-quark form factor is necessary. However, this conclusion was based on lattice data for four static quarks in quenched SU(2). In the present work[2] most of these approximations have been removed by using SU(3) with two heavy-light mesons i.e. $Q^2\bar{q}^2$ compared with the earlier $Q^2\bar{Q}^2$. Furthermore, the gauge field is now treated in the unquenched approximation. The corresponding many-body model now needs some additional assumptions before a comparison with the lattice data is possible. Perhaps the most serious is the use of a non-relativistic kinetic energy, even though the light quark mass is approximately that of the strange quark. However, in the binding energy there is a considerable cancellation between the four- and two-quark kinetic energies. Also the model is developed only for the spin-independent contribution to the binding energy. This requires an averaging of the lattice data. Both of these assumptions are not thought to qualitatively effect the outcome. The main defect of the calculation is that, at present, comparison can only be made for small distances between the two static quarks -- the region where lattice data could suffer from a lack of rotational invariance. However, in spite of these shortcomings, the result is that the use of simply two-quark potentials again overestimates the lattice binding by upto a factor of three -- a result that is not expected to be qualitatively changed by other models without multi-quark interactions. Inclusion of a four-quark interaction term can then remove the discrepancy. This conclusion supports (confirms) the earlier result -- with four static quarks in quenched SU(2) -- that four-quark energies cannot be described simply in terms of two-quark potentials and that attempts to do so could lead to a large overestimate of the binding energy.

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