Problems with the perturbative QCD interpretation of HERMES data on semi-inclusive leptoproduction 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.

Figure 1

Comparison between the LO QCD nonsinglet fragmentation functions $z{D}_{u_v}^{{\pi }^{+}}(z,Q^2)$ extracted from the differences of the pion multiplicities. Full squares (open circles) correspond to the data using a proton (deuteron) target, respectively.

Figure 2

Comparison between the data and the best fit curves (black solid lines) obtained from a combined NLO QCD fit to the proton and deutron data on the differences of the pion multiplicities. The dashed curves correspond to the separate fits to the proton and deuteron data. The errors of the data are combined statistical and systematic.

Figure 3

The nonsinglet fragmentation function $z{D}_u^{({\pi }^{+}-{\pi }^{-})}(z)$ at $Q^2=2.5{\mathrm{GeV}}^2$ extracted from NLO QCD fits to (a) proton, (b) deuteron and (c) proton and deuteron data on the differences of pion multiplicities.

Figure 4

Comparison between the LO and NLO nonsinglet fragmentation functions $D_{u_v}^{{\pi }^{+}}(Q^2)$ at the different $z$ bins. For details see the text.

Figure 5

Comparison between the data and the best fit curves (dashed lines) obtained from a combined NLO QCD fit to the proton and deuteron data on the differences of pion multiplicities without $SU(2)$ symmetry. The solid curves correspond to the $SU(2)$ symmetric fit to the same data.

Figure 6

Nonsinglet fragmentation functions $z{D}_u^{({\pi }^{+}-{\pi }^{-})}(z)$ and $z{D}_d^{({\pi }^{+}-{\pi }^{-})}(z)$ at $Q^2=2.5{\mathrm{GeV}}^2$ together with their error bands extracted from a NLO QCD combined fit to proton and deuteron data on the differences of pion multiplicities.

Figure 7

Comparison between nonsinglet fragmentation function $z{D}_u^{({\pi }^{+}-{\pi }^{-})}(z)$ extracted from the fit to proton and deuteron data on the differences of the pion multiplicities and that one constructed from favored $z{D}_u^{\pi +}$ and unfavored $z{D}_u^{\pi -}$ fragmentation functions determined from a NLO combined fit to proton and deuteron data on pion multiplicities themselves.

Figure 8

Comparison between our NLO nonsinglet fragmentation function $z{D}_u^{({\pi }^{+}-{\pi }^{-})}(z)$ extracted from the fit to proton and deuteron data on the differences of the pion multiplicities and those of HKNS and DSS constructed from their favored $z{D}_u^{\pi +}$ and unfavored $z{D}_u^{\pi -}$ NLO fragmentation functions.