Double parton interactions in $\gamma +3$ jet and $\gamma +b/c\mathrm{jet}+2$ jet events in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We determine the fraction of events with double parton (DP) scattering in a single $p\overline{p}$ collision at $\sqrt{s}=1.96\mathrm{TeV}$ in samples of $\gamma +3$ jet and $\gamma +b/c\text{jet}+2$ jet events collected with the D0 detector and corresponding to an integrated luminosity of about $8.7{\mathrm{fb}}^{-1}$. The DP fractions and effective cross sections (${\sigma }_{\text{eff}}$) are measured for both event samples using the same kinematic selections. The measured DP fractions range from 0.21 to 0.17, with effective cross sections in the $\gamma +3$ jet and $\gamma +b/c\text{jet}+2$ jet samples of ${\sigma }_{\text{eff}}^{\text{incl}}=12.7\pm 0.2(\text{stat})\pm 1.3(\text{syst})\mathrm{mb}$ and ${\sigma }_{\text{eff}}^{\text{HF}}=14.6\pm 0.6(\text{stat})\pm 3.2(\text{syst})\mathrm{mb}$, respectively.

Figure 1

Fractional contribution of the Compton-like $qg\to q\gamma$ ($q$ is any quark type) and $bg\to b\gamma$ subprocesses to the associated production of inclusive $\gamma +\text{jet}$ and $\gamma +b$-jet final states as a function of $p_T^{\gamma }$.

Figure 2

Schematic view of the mixing procedure used to prepare the mixdp signal sample. Two combinations are considered: (a) $\gamma +1$ jet and two jets from a dijet event and (b) $\gamma +2$ jets and one jet from a dijet event. The dotted line represents a jet failing the selection requirements since this jet is either not reconstructed or beyond kinematic selection limits.

Figure 3

A possible configuration of photon and jets transverse momenta vectors in $\gamma +3$ jet events. Vectors ${\overrightarrow{P}}_{\text{T}}^1$ and ${\overrightarrow{P}}_{\text{T}}^2$ are the $p_T$-imbalance vectors of $\gamma +\text{jet}$ and dijet pairs.

Figure 4

The $\mathrm{\Delta }S$ distribution in the data, DP and SP models, and the sum of the DP and SP contributions weighted with their fractions (“Total”). Plots (a) and (b) correspond to the inclusive and HF samples, respectively. The lower subplots show the relative difference of the data points with respect to the fitted sum, along with the total uncertainties, i.e., DP fraction and statistical uncertainties from data and MC added in quadrature.

Figure 5

Existing measurements of effective cross section, ${\sigma }_{\text{eff}}$, compared with result presented here (AFS: no uncertainty is reported; UA2: only a lower limit is provided).

Figure 6

The $\mathrm{\Delta }\varphi (\gamma ,\text{jet}1)$ distribution in the SP model extracted from data compared to that in (a) sherpa and (b) pythia. The uncertainties shown are statistical only.

Figure 7

Spectra of the transverse momenta of (a) second and (b) third jets in the sherpa and data SP models. The uncertainties shown are statistical only.