Measurement of the differential cross section of photon plus jet production in $p\overline{p}$ collisions at $\sqrt{s}\mathbf{=}1.96\mathrm{TeV}$

We study the process of associated photon and jet production, $p\overline{p}\to \gamma +\mathrm{\text{jet}}+X$, using $8.7{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the D0 detector at the Fermilab Tevatron Collider at a center-of-mass energy $\sqrt{s}=1.96\mathrm{TeV}$. Photons are reconstructed with rapidity $|y^{\gamma }|<1.0$ or $1.5<|y^{\gamma }|<2.5$ and transverse momentum $p_T^{\gamma }>20\mathrm{GeV}$. The highest-$p_T$ jet is required to be in one of four rapidity regions up to $|y^{\mathrm{jet}}|\le 3.2$. For each rapidity configuration we measure the differential cross sections in $p_T^{\gamma }$ separately for events with the same sign ($y^{\gamma }{y}^{\mathrm{jet}}>0$) and opposite signs ($y^{\gamma }{y}^{\mathrm{jet}}\le 0$) of photon and jet rapidities. We compare the measured triple-differential cross sections, ${\mathrm{d}}^3\sigma /\mathrm{d}{p}_T^{\gamma }\mathrm{d}{y}^{\gamma }\mathrm{d}{y}^{\mathrm{jet}}$, to next-to-leading order (NLO) perturbative QCD calculations using different sets of parton distribution functions, and to predictions from the sherpa and pythia Monte Carlo event generators. The NLO calculations are found to be in general agreement with the data but do not describe all kinematic regions.

Figure 1

The fraction of events, estimated using the pythia event generator [18] with the cteq6L PDF set [19], produced via the $qg\to q\gamma$ subprocess relative to the total cross section of the associated production of a direct photon in the forward rapidity region, $1.5<|y^{\gamma }|<2.5$, and a leading jet in one of the four rapidity intervals satisfying $y^{\gamma }{y}^{\mathrm{jet}}>0$. Statistical uncertainties in the predictions (up to 4%) are not shown.

Figure 2

For $\gamma +\mathrm{\text{jet}}$ events, the fraction of the direct (nonfragmentation) photon contribution of the total ($\mathrm{\text{direct}}+\mathrm{\text{fragmentation}}$) cross section, estimated with jetphox [55] for events with forward photons.

Figure 3

Distribution of observed events for $O_{\mathrm{NN}}$ after all selection criteria for the representative bin $50<p_T^{\gamma }<60\mathrm{GeV}$ ($|y^{\gamma }|<1.0$). The distributions for the signal and background templates are shown normalized to their respective fitted fractions. Fits in the other $p_T^{\gamma }$ bins are of similar quality.

Figure 4

Purity of the selected $\gamma +\mathrm{\text{jet}}$ sample as a function of $p_T^{\gamma }$ is shown for events with central photons, either very central or very forward jet rapidities, and either the same sign or opposite signs for the photon and jet rapidities. The solid line shows the fit, and the dashed lines show the total fit uncertainty.

Figure 5

Same as Fig. 4, but for events with forward photons.

Figure 6

Systematic uncertainties on the prompt $\gamma +\mathrm{\text{jet}}$ production cross sections for events with central and forward photons. Same-sign events with $|y^{\gamma }|<1.0$ and $|y^{\mathrm{jet}}|\le 0.8$ (left) or $1.5<|y^{\gamma }|<2.5$ and $2.4<|y^{\mathrm{jet}}|\le 3.2$ (right) are shown as an example. A common normalization uncertainty of 6.8% (11.2%) for events with central (forward) photons, resulting from uncertainties on integrated luminosity, photon selection efficiency, and photon production vertex, is not included in the figures.

Figure 7

The measured differential $\gamma +\mathrm{\text{jet}}$ cross section as a function of $p_T^{\gamma }$ for the four measured jet rapidity intervals, with central photons, $|y^{\gamma }|<1.0$, and forward photons, $1.5<|y^{\gamma }|<2.5$, for same-sign and opposite-sign photon and jet rapidities. For presentation purposes, the cross sections for $|y^{\mathrm{jet}}|\le 0.8$, $0.8<|y^{\mathrm{jet}}|\le 1.6$, $1.6<|y^{\mathrm{jet}}|\le 2.4$, and $2.4<|y^{\mathrm{jet}}|\le 3.2$ are scaled by factors of 5, 1, 0.3 and 0.1, respectively. The data are compared to the NLO QCD predictions using the jetphox package [55] with the CT10 PDF set [56] and ${\mu }_R={\mu }_F={\mu }_f=p_T^{\gamma }$.

Figure 8

Comparison of the same-sign to opposite-sign cross section ratios for events with a central photon and central jet and those with a forward photon and very forward jet.

Figure 9

Ratios of the measured differential cross sections with central photons in each of the four measured jet rapidity intervals to the pQCD NLO prediction using jetphox [55] with the CT10 PDF set and ${\mu }_R={\mu }_F={\mu }_f=p_T^{\gamma }$. The solid vertical line on the points shows the statistical and $p_T$-dependent systematic uncertainties added in quadrature, while the internal line shows the statistical uncertainty. A common 6.8% normalization uncertainty on the data points is not shown. The two dotted lines represent the effect of varying the theoretical scales of jetphox by factors of 2 and 0.5. The shaded region is the CT10 [56] PDF uncertainty. The dashed and solid lines show ratios of the jetphox predictions with the MSTW2008NLO [61] and NNPDFv2.1 [62] to CT10 PDF sets, respectively. The ratios of the predictions from sherpa and pythia to jetphox are shown by the open squares and triangles, respectively.

Figure 10

Same as Fig. 9, but for events with forward photons. A common 11.2% normalization uncertainty on the data points is not shown.