Asymmetric flux tube

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Abstract
We consider a relativistic flux tube with arbitrary mass spinless quarks at the ends. In the unequal-mass case the additional constraint that the center of momentum is fixed must be included. An analytic classical circular solution is found and is used as a correspondence limit. The quantized equations for mesons at rest are constructed and solved. A comparison is made with all available spin-averaged heavy-light and heavy-heavy states. We find evidence for running of the heavy quark masses as well as the short range coupling constant.