Problems with the perturbative QCD interpretation of HERMES data on semi-inclusive lepto-production of pions

A theoretical analysis has been performed of the HERMES semi-inclusive deep inelastic data on the difference between $\pi^{+}$ and $\pi^{-}$ multiplicities. It turns out that the application of a standard perturbative QCD analysis, using, as usual, isospin symmetry for the fragmentation functions, leads to a poor description of the deuteron data at small z values. If one allows a breaking of isospin invariance, a good fit to both proton and deuteron data can be achieved for all measured z, but the level of isospin violation, especially at small values of z, is simply not credible. We suspect that the problem is a consequence of using the factorized QCD treatment in a kinematic region where it is unjustified.