  We present perturbative calculation of the width of the energy profile of
rigid strings up to two loops in D dimensions. The perturbative expansion of
the extrinsic curvature term signifying the rigidity/smoothness of the string
in Polyakov-Kleinert action is taken around the free Nambu-Goto string. The
mean-square width of the string field is derived for open strings with
Dirichlet boundary condition. We compare the broadening of the smooth
Polyakov-Kleinert string to the lattice Mont-Carlo data of the QCD flux tube
just before the deconfinement point and find a good match at the intermediate
and large color source separation.
