Dijet Angular Distributions

Angular distribution of jets are measured to study the distributions of the outgoing partons and to gain understanding of the parton dynamics of the underlying sub-processes. As described in section 2.3 different types of resolved processes are expected to contribute. In the case of excitation diagrams (fig.5c-d) both quark and gluon propagators are possible. In $g-$exchange (fig.5d in section 2.3), the spin$-1$ propagator of the gluon leads to a steeper angular dependence ( $\sigma \sim$ ( $1 -\vert\cos\theta^{*}\vert$)$^{-2}$) than for quark exchange ( $\sigma \sim$ ( $1 -\vert\cos\theta^{*}\vert$)).

Figures 26c-f show the differential cross section $d\sigma/d\cos\theta^{*}$ for both direct ( $x_{\gamma }^{\rm obs} > 0.75$) and resolved enriched ( $x_{\gamma }^{\rm obs} < 0.75$) samples [17]. Here, $\theta^{*}$ is the angle between the charm-jet axis and the $p$-beam direction in the dijet rest frame. The charm jet is identified by association of the $D^*$ meson with the jet using a criterion $R=\sqrt{(\eta^{jet}-\eta^{D^*})^2 + (\phi^{jet}-\phi^{D^*})^2} < 0.6$. Positive (negative) values of $\cos\theta^{*}$ correspond to cases in which the identified charm jet, which is associated to the reconstructed $D^*$ meson, is oriented in the direction of the incoming proton (photon). The shaded areas for $x_{\gamma }^{\rm obs} < 0.75$ and $x_{\gamma }^{\rm obs} > 0.75$ are, respectively, the contamination of the genuine direct and resolved PYTHIA contributions. The measured differential cross sections $d\sigma/d\cos\theta^{*}$ for both samples are significantly different. For $x_{\gamma }^{\rm obs} < 0.75$ a particular enhancement of the cross section for charm jets is seen in the photon direction (negative $\cos\theta^{*}$). In contrast, in the region $x_{\gamma }^{\rm obs} > 0.75$ the angular distributions reveal a much shallower behaviour. The differences provide an indication that a sizable fraction of the resolved photon events proceeds via gluon exchange for which a steep angular distribution is expected.

Figure: Differential cross sections as a function of $\Delta \phi$ for a) a charmed dijet sample from ZEUS [25] in comparison with a massive NLO calculation, b) a $D^*$-jet sample from H1 [9] in comparison with massive (FMNR) and massless (ZMVFNS) NLO calculations.

New preliminary results are available for the angular correlations in azimuth in charmed photoproduction events containing jets. In leading order the $\Delta \phi$ distribution is expected to show a sharp peak at $180^{\circ}$. Contributions from higher orders, i.e. hard gluon radiation, as well as fragmentation and detector resolution effects smear the distributions out. The ZEUS experiment uses a dijet sample to measure the difference $\Delta \phi$ of the two jets [25] while H1 measures the difference between the reconstructed $D^*$ meson and the leading jet which does not belong to the $D^*$ meson [9]. In fig27 the two measurements are shown, revealing similar features. The data have a shallower behaviour in $\Delta \phi$ than the theories, indicating that the theories, at next-to-leading order, can not fully account for the amount of gluon radiation seen in the data.