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in photoproduction processes at hera , a quasi - real photon with virtuality @xmath3 is emitted by the incoming electron and interacts with the proton . at leading order ( lo ) in qcd ,
two types of processes are responsible for the production of heavy quarks : the direct photon processes , where the photon participates as a point - like particle , and the resolved photon processes , where the photon acts as a source of partons . in the direct photon - gluon - fusion ( pgf ) process ( fig .
1a ) , the entire photon momentum is involved and the propagator is a spin-@xmath4 quark propagator . in resolved photon processes , a parton from the photon scatters off a parton from the proton ( figs .  1b , 1c and 1d ) , and only a fraction of the photon momentum participates in the hard scatter .
charm quarks present in the parton distributions of the photon , as well as of the proton , lead to processes like @xmath5 , which are called charm - excitation processes ( figs .
1c and 1d ) .
the dominant @xmath6-channel charm - excitation diagram has a spin-@xmath7 gluon propagator ( fig .
at next - to - leading order ( nlo ) in qcd , only the sum of direct and resolved processes is unambiguously defined .    to identify contributions of different charm - production processes and to verify relevant qcd calculations ,
photoproduction of events with a @xmath0 meson and at least two energetic jets has been studied  @xcite .
-5.1 cm    * 3.0 cm ( a)3.8 cm ( b ) *    4.1 cm    * 3.0 cm ( c)3.8 cm ( d ) *
the monte carlo ( mc ) programs pythia  @xcite and herwig  @xcite simulate heavy - quark photoproduction in the framework of the collinear approach using the on - shell lo matrix elements for direct and resolved photon processes ( including charm excitation ) .
higher - order qcd effects are simulated in the leading - logarithmic approximation with initial- and final - state radiation obeying dglap evolution .
the mc program cascade  @xcite simulates heavy - quark photoproduction in the framework of the semi - hard or @xmath8-factorisation approach using the off - shell lo pgf matrix element .
the resolved photon processes are reproduced by the initial - state radiation based on ccfm evolution .
the nlo qcd calculations of differential cross sections for photoproduction of charm dijet events are available  @xcite in the fixed - order scheme assuming no explicit charm - excitation component .
charm photoproduction cross sections are calculated in the framework of the collinear approach using the on - shell matrix elements .
an experimental separation of the direct and resolved processes was obtained by a selection on the variable @xmath9 where @xmath10 is the initial photon energy .
the variable @xmath11 is the fraction of the photon s momentum contributing to the production of the two jets .
the measured @xmath0 photoproduction cross section peaks at @xmath12 , in agreement with the expectation for direct photon processes .
a large cross section is also measured at low @xmath11 , where resolved processes are expected to contribute significantly .
the selection of @xmath13 and @xmath14 was used to obtain samples enriched in direct and resolved photon processes , respectively .
sensitivity to the spin of the propagator in the hard subprocess was obtained by measuring the angle between the jet - jet axis and the beam axis in the dijet rest frame .
this angle , @xmath15 , was reconstructed using @xmath16 the angular dependence of the cross section for processes with a spin-1 gluon propagator is approximately @xmath17 .
this cross section rises more steeply with increasing @xmath18 than that for processes with a spin-@xmath4 quark propagator , where the angular dependence is approximately @xmath19 .
figure  2 shows the differential cross sections as a function of @xmath18 for the resolved- and direct - enriched samples .
the angular distribution of resolved - enriched events exhibits a more rapid rise towards high values of @xmath18 than does the distribution of direct - enriched events .
this observation suggests a large contribution from the @xmath6-channel charm - excitation diagram with a spin-@xmath7 gluon propagator ( fig .
the data are compared to the pythia and herwig predictions normalized to the data .
the mc predictions provide adequate descriptions of the shapes of the data distributions .
the two jets can be distinguished by associating the @xmath0 meson to the closest jet in @xmath20 space and calling this jet 1 in eq .
figure  3 shows the differential cross sections as a function of @xmath21 for the resolved- and direct - enriched samples .
the angular distribution of resolved - enriched events exhibits a large asymmetry with a mild rise towards @xmath22 ( proton direction ) and a strong rise towards @xmath23 ( photon direction ) .
this observation shows that dijet events with @xmath14 are dominantly produced by charm quarks coming from the photon side .
the @xmath21 distribution of direct - enriched events is almost symmetric , as expected for the pgf process .
a slight asymmetry can be explained by the feedthrough from resolved photon processes near @xmath23  @xcite .
the cascade and nlo predictions are compared to the data in fig .
3 . for @xmath14 ,
the cascade prediction describes the data in the photon direction and underestimates the data in the proton direction . for @xmath13 ,
the prediction overestimates the data in all regions of @xmath21 , although the shape is described reasonably well .
the nlo prediction is below the data for @xmath14 and in agreement with the data for @xmath13 .
the shapes are reasonably well described by the nlo predictions .
the measured charm dijet angular distributions show that dijet events at low @xmath11 are dominantly produced by charm quarks coming from the photon side .
the shapes of the measured distributions are described adequately by the lo collinear calculations ( pythia , herwig ) including a large charm - excitation component .
the shapes of the distributions are reasonably well described by the nlo collinear calculations in the fixed - order scheme assuming no explicit charm - excitation component .
the lo @xmath8-factorisation calculations with the initial - state radiation based on the ccfm evolution ( cascade ) also reproduce the shapes reasonably well . however , the nlo and cascade calculations do not reproduce relative contributions of charm dijet events with high and low @xmath11 values .
the nlo prediction is below the data at low @xmath11 and the cascade prediction overestimates the data at high @xmath11 .
dijet angular distributions of photoproduction events in which a @xmath0 meson is produced in association with one of two energetic jets have been measured using an integrated luminosity of @xmath1pb@xmath2 . 
 the results are compared with predictions from leading - order parton - shower monte carlo models and with next - to - leading - order qcd calculations .