I`ve already asked this in the comments below this article http://profmattstrassler.com/articles-and-posts/some-speculative-theoretical-ideas-for-the-lhc/extra-dimensions/how-to-look-for-signs-of-extra-dimensions/ from Prof. Strassler but did not get a satisfactory answer...
In the article Prof. Strassler explains that a possible sign of extra dimensions at the LHC could be the detection of Kaluza-Klein particles. The energy (or mass squared) spectrum of the corresponding particle tower would have a step size proportional to 1/r (where r is the radius of a compact extra dimension).
Now I`m wondering how such a (hypothetical) KK particle candidate can be told apart from a winding mode particle (with the step size of the energy spectrum proportional to r) which is probably more easily produced depending on the size r of the extra dimension ? By the way what's the actual state of these searches for extra dimensions considering the data already available ?
Considering an extra dimension that is much larger than the particle, the KK modes with the 1/r spectrum arise from the quantized angular momentum a particle can have due to it' movement in the extra dimension. If the extra dimension is smaller the particle can wind around the extra dimension leading to the winding mode particles. For these the energy spectrum is determined by the potential energy of stretching. The spectra of the KK and winding modes are T-dual to each other.