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Using the Polchinski-Strominger effective string theory in covariant gauge, we compute the mass of a rotating string in D dimensions with large angular momenta J, in one or two planes, in fixed ratio, up to and including first subleading order in the large J expansion. This constitutes a first-principles calculation of the value for the order J^0 contribution to the mass-squared of a meson on the leading Regge trajectory in planar QCD with bosonic quarks. For open strings with Neumann boundarydoi:10.1103/physrevlett.114.111601 pmid:25839257 fatcat:lrobbjun3fhivgeeoqzkuhvycq