Casimir energy in a theory of rigid string with massive ends

The Casimir energy in the theory of a rigid string bearing pointlike masses at the ends is investigated. The system under consideration simulates a gluonic tube with finite thickness connecting massive quarks. The string rigidity and the quark masses contribute additively to the Casimir energy, the latter contribution being the just the same as that of the Nambu-Goto string with massive ends. Account of the string rigidity provides positive contribution to the Casimir energy. However, it is not enough to compensate by itself the negative Casimir energy for the Nambu-Goto string. Combined account only of the transverse gluonic-tube size and the nonvanishing quark masses enables obtaining the positive Casimir energy) i.e. removing the tachyon from the string spectrum