document: Thus, the extension to the charmed analogue Θc(3099) provides an interesting test for the SDO sum rule and lattice calculations [17]. Here, the charm quark is quite heavy so that the constituent-quark picture may fit well and the JW prediction for the parity is expected to be reproduced from QCD. In fact, quenched lattice calculation finds the parity of Θc(3099) to be positive [28]. In the extension to the Θc(3099) sum rules, there are two important aspects, which make this sum rule different from the SDO sum rule. First of all, since the charm quark is too heavy to form quark condensate, it gives non-perturbative effects only by radiating gluons. The quark–gluon mixed condensate 〈s̄gsσ·Gs〉, which was the important contribution in the Θ+ sum rule, is replaced by gluonic operators in the heavy quark expansion that are normally suppressed. Secondly, the charm quark mass has to be kept finite in the OPE, which can be done by using the momentum space expression for the charm-quark propagator. This is different from the light-quark sum rule where the calculation is performed in the coordinate space and all the quark propagators are obtained based on the expansion with the small quark mass. Keeping these two aspects in mind, we construct QCD sum rules for Θc(3099) and see how they are different from the Θ+(1540) sum rule.
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