Charmed meson production in deep inelastic scattering

Charmed meson production in semi-inclusive deep inelastic scattering is investigated in the color-dipole formalism. The transverse momentum distributions are calculated. We find good agreement with the H1 data using a hard fragmentation function.

Figure 1

Kinematics of one-particle semi-inclusive scattering. The reaction plane in $(e,e^{\prime }h)$-scattering is defined by the initial and final momenta of the lepton $(\overrightarrow{k},{\overrightarrow{k}}^{\prime })$. The produced hadron ${\overrightarrow{p}}_h$ and photon momenta $\overrightarrow{q}$ define a second plane.

Figure 2

Boson-gluon-fusion graphs. Figure 2a shows $i{M}_1$, Fig. 2b $i{M}_2$.

Figure 3

The ratio of the cross section $d\sigma ({\gamma }^{*}p\to cX)/d{p}_c^{\perp 2}$ in $r^2$-approximation over the same cross section calculated with the full GBW cross section $\sigma (r)$ is shown as a function of the transverse momentum of the charm quark $p_c^{\perp 2}$.

Figure 4

The charm quark production cross section ${\gamma }^{*}p\to cX$ induced by transverse and longitudinal photons for $Q^2=2{\mathrm{GeV}}^2$ and $W^2=200{\mathrm{GeV}}^2$. The transverse photon cross section is dominating over the whole transverse momentum region.

Figure 5

The Peterson fragmentation function with ${ϵ}_c=0.05$ for charm quarks and ${ϵ}_b=0.006$ for bottom quarks in the leading-log approximation. The bottom quark fragmentation is harder since the bottom quark mass is about 3.5 times higher than the charm quark mass. Both curves are normalized to unity.

Figure 6

The longitudinal heavy meson production cross section ${\gamma }^{*}p\to h(Q)X$ induced by longitudinal photons as a function of the transverse momentum of the meson. The two $ϵ$ parameters correspond to charm (${ϵ}_c=0.05$) and bottom quark (${ϵ}_b=0.006$) fragmentation. For comparison we also show the transverse quark production cross section without fragmentation.

Figure 7

Theoretical cross section $d\sigma (ep\to D^{+}X)/d{Q}^2$ with branching ratio $f_c^{D^{+}}=0.202$ plotted against experimental data from Ref. 14. Note, the experimental lower cut for the transverse momentum is $p_{D,\min }^{\perp }=2.5\mathrm{GeV}$.

Figure 8

Theoretical cross section $d\sigma (ep\to D^{+}X)/d\eta$ with branching ratio $f_c^{D^{+}}=0.202$ plotted against experimental data from Ref. 14.

Figure 9

Theoretical cross section $d\sigma (ep\to D^{*+}X)/d{p}_D^{\perp }$ with branching ratio $f_c^{D^{*+}}=0.263$ plotted against experimental data from Ref. 17.

Figure 10

Relating transverse momenta relative to the electron beam line, $p_D^{{\perp }^{\prime }}$, and to the virtual photon direction $p_D^{\perp }$ for a small rotation of the $z$ axis.