Determination of the fragmentation functions from an NLO QCD analysis of the HERMES data on pion multiplicities

An NLO QCD analysis of the final HERMES data on pion multiplicities is presented and a new set of pion fragmentation functions is extracted from the best fit to the data. We have studied the so-called $[x,z]$ and $[Q^2,z]$ presentations of their data, as given by HERMES, which, in principle, should simply be two different ways of presenting the experimental data. We have based our extraction on an excellent fit to the $[Q^2,z]$ presentation of the data.

Figure 1

Comparison of HERMES $[Q^2,z]$ proton data on ${\pi }^{+}$ (left) and ${\pi }^{-}$ multiplicities (right) with the best NLO fit curves. The error bands (the area between the dot curves) correspond to uncertainty estimates at 68% C.L. The errors of the data are total, statistical and systematic taken in quadrature.

Figure 2

Comparison of HERMES $[Q^2,z]$ deuteron data on ${\pi }^{+}$ (left) and ${\pi }^{-}$ multiplicities (right) with the best NLO fit curves. The error bands (the area between the dot curves) correspond to uncertainty estimates at 68% C.L. The errors of the data are total, statistical and systematic taken in quadrature.

Figure 3

Comparison between our pion FFs at $Q^2=2.5{\mathrm{GeV}}^2$ along with the uncertainty estimates at 68% C.L. (the area between the dashed curves) and those of DSEHS (solid curves). For the gluon fragmentation function the uncertainty corresponding to $\mathrm{\Delta }{\chi }^2=1$ (the black shaded band) is also presented.

Figure 4

Sensitivity of the extracted favored and unfavored FFs (left), and gluon FF (right) to the choice of the set of unpolarized PDFs (see the text). Note the extremely small scale of the vertical axis in Fig. 4 (left).

Figure 5

Comparison of HERMES $[x,z]$ proton data on ${\pi }^{+}$ (left) and ${\pi }^{-}$ multiplicities (right) with the multiplicities at the same kinematic points calculated by our FFs extracted from HERMES $[Q^2,z]$ data (dot curves with the bands corresponding to uncertainty estimates at 68% C.L). The errors of the data are total, statistical and systematic taken in quadrature. The solid curves correspond to the best fit to the cut $[x,z]$ data (see the text).

Figure 6

As in Fig. 5 but for a deuteron target.

Figure 7

Comparison between favored (top) and unfavored (bottom) fragmentation functions extracted from $[Q^2,z]$ (dot curves) and the cut $[x,z]$ HERMES data on multiplicities (solid curves). The dashed curves mark the error bands for FFs determined from the $[Q^2,z]$ data.