Multiple parton interaction studies at DØ

We present the results of studies of multiparton interactions done by the DØ collaboration using the Fermilab Tevatron at a center of mass energy of 1.96 TeV. Three analyses are presented, involving three distinct final signatures: (a) a photon with at least 3 jets (γ + 3jets), (b) a photon with a bottom or charm quark tagged jet and at least 2 other jets (γ + b/c + 2jets), and (c) two J/ψ mesons. The fraction of photon + jet events initiated by double parton scattering is about 20%, while the fraction for events in which two J/ψ mesons were produced is 30 ± 10. While the two measurements are statistically compatible, the difference might indicate differences in the quark and gluon distribution within a nucleon. This speculation originates from the fact that photon + jet events are created by collisions with quarks in the initial states, while J/ψ events are produced preferentially by a gluonic initial state.


Introduction
One way that scientists can look for highbackground decay modes of rare objects is by means of associated production. As an example, at the Fermilab Tevatron, the search for the Higgs boson decaying into bottom quarks was pursued by searching for events in which both a Higgs boson (H) and an electroweak boson (W/Z) were produced in tandem. This associated production greatly improved the signal to noise ratio for this search. However, there are other ways in which H/Z or H/W events might be produced. One such way is in the case when one pair of partons from the parent beam particles creates a Higgs boson, while another pair of partons generates an electroweak boson. Unless multiparton interactions are included in our simulations, the background for these rare associatedproduction processes will be systematically underestimated.
The DØ collaboration has an established history investigating multiparton interactions [1 -2]. This proceeding extends those studies into physical processes in which heavy flavour quarks are produced [3 -4].

DØ Detector
The D0 detector is a general purpose detector described in detail elsewhere [5]. The sub-detectors used in this analysis to select events at the trigger level and to reconstruct muons are the muon and the central tracking systems. The central tracking system, used to reconstruct charged particle tracks, consists of the silicon microstrip tracker (SMT) [6] and a central fiber tracker (CFT) detector both placed inside a 1.9 T solenoidal magnet. The solenoidal magnet is located inside the central calorimeter, which is surrounded by the muon detector [7]. The muon detector consists of three layers of drift tubes and three layers of plastic scintillators, one inside surrounding 1.9 T toroidal magnets and two outside.
The luminosity of colliding beams is measured using plastic scintillator arrays installed in front of the two end calorimeter cryostats [8].

Phenomenological Overview
The double parton cross section for processes A and B can be denoted σDP. The single parton cross sections are denoted σA and σB. A phenomenological parameter, σeff, characterizes the size of the effective interaction region.
This parameter contains information on the spatial distribution of partons. If the spatial distribution of partons is uniform within a nucleon, then σeff is large and σDP is small. Conversely, if the distribution of partons is correlated and compact, then σeff is small and σDP is large.
The correlation between these cross sections is given by σDP = (σA × σB)/σeff. The phenomenological parameter σeff is directly related to the parton spatial density via 2 and ( ) is the density of partons in transverse space. Thus by measuring σeff, we can estimate ( ).

γ + 3 jet and γ + b/c + dijet events
Jets were reconstructed using a cone-based jet finding algorithm, using R = 0.5 [9]. Multivariate techniques were used to identify photons [10] and to tag bottom and charm quark jets [11]. Once these were identified, two very similar analyses were performed.
For both analyses, the following selection criteria were applied. For photons, we require the transverse momentum > 26 GeV and the pseudorapidity | | < 1.0 or 1.5 < | | < 2.5. For the jets, we require at least 3 jets with > 15 GeV and | | < 2.5. The transverse momentum of the second leading jet is required to be 15 < 2 < 35 GeV. In addition, to ensure good isolation, we require topological cuts of Δ ( , ) > 0.7 and Δ ( , ) > 1.0, where Δ = �Δ 2 + Δ 2 , and Δ is the azimuthal angular distribution between two objects. The first analysis is an inclusive one. Events with at least one photon and at least three jets were used. The transverse momentum vectors of the photon and leading jet were added 1 = + 1 , as were the second and third leading jet 2 = 2 + 3 .
Using these two combined vectors, the azimuthal angle between the two was determined Δ = Δ (1,2). In events in which all four objects originated from the scattering of a single pair of partons, the distribution of ∆S should peak near π radians. In contrast, for events in which the objects were created from the collision of two completely independent pairs of partons, the azimuthal angle of the scatters should be independent, resulting in a flat distribution. Figure 1 shows how the vectors 1 and 2 are defined. Figure 2 demonstrates the expected correlations between vectors 1 and 2. By fitting data to templates similar to those shown in figure 2, it is possible to extract the fraction of events caused by multiple parton scattering.   While the first analysis was inclusive, requiring only a photon and three jets, the second analysis tagged the leading jet as including a bottom or charm quark. The extracted results are given in Table 1.
We can see from Table 1 that the values for both the multiparton fraction and σeff are independent of whether the leading jet is tagged with a heavy flavour quark or not.

Multiple parton interactions in double J/ψ events
Events in which two J/ψ mesons were made were also studied to determine the fraction of events in which multiple parton interactions occurred. The data set was comprised of 8.1 fb -1 of data. The data was triggered using a logical OR of all low transverse momentum dimuon triggers. The cuts required at least four muons with transverse momentum and pseudorapidity requirements. If | | < 1.35, > 2 GeV; while if 1.35 < | | < 2.0, > 4 GeV. All reconstructed J/ψ candidates were required to have / > 4.0 GeV and | | < 2.0. Event selections were imposed that required the outer muon detector and inner tracker to have matched tracks. The muon track was required to have at least 3 hits and requirements were imposed to insure that the muons originated from the reconstructed collision vertex. Along with timing requirements, this reduced the impact of muons originating from cosmic rays. Finally, the mass of oppositely signed dimuons was required to be in the range 2.85 < < 3.35 GeV. The fraction of J/ψ mesons originating from the primary vertex was determined by fitting the twodimensional proper decay length = / / / , where is the two-dimensional decay length and / is the world averaged mass of the J/ψ as reported by the Particle Data Group. We find that the fraction of events with promptly produced single J/ψ mesons was 0.814 ± 0.009, while the fraction of promptly produced double J/ψ mesons was 0.604 ± 0.084.
Initial acceptance and selection efficiencies were determined using Monte Carlo simulation. These initial numbers were adjusted by data/Monte Carlo correction factors that depended on both transverse momentum and pseudorapidity. These corrections were small (of order 10%). From the data and these corrections, we were able to determine that the single J/ψ production cross section was 22.9 ± 4.6 (stat.) ± 3.7 (syst.) nb. This measurement can be compared to an analytic prediction of the cross section, using the "kT factorization." This prediction was 23.0 ± 8.6 nb. The theoretical uncertainties stem from uncertainties in the gluon parton distribution function and from varying the renormalization and factorization by a factor of 2.
The double J/ψ cross section was extracted in a similar way, with the additional selection requirement that two J/ψ mesons were produced. To extract the double and single parton scattering production mechanisms, the absolute value of the difference between the pseudorapidities of the two J/ψ mesons was used. A representative example is given in figure 3.
Using the extracted fractions of single and double parton production of two J/ψ mesons, it was possible to extract the respective cross sections and fraction of events from each mechanism. The fraction of double J/ψ production from multiple parton scattering is 0.3 ± 0.1.
For single parton production, we measured σSP = 112.0 ± 9.8 (stat) ± 29.8 (syst) fb. This is in contrast a predicted cross section using kT factorization of 55.1 [+28.  This discrepancy of a factor of two is not significant, but may have an explanation. A recent NLO calculation at LHC energies [12] has become available. For a selection of / > 4 GeV, the predicted NLO calculation is about a factor of two larger than the corresponding LO calculation. While a Tevatron calculation is not available, one could expect that a similar difference should be true for Tevatron conditions. The cross section for double J/ψ production via two independent parton scattering was measured to be σDP = 56.6 ± 5.8 (stat) ± 23.2 (syst) fb. The predicted cross section using the kT factorization is 17.6 ± 13 fb.

Summary and Discussion
The phenomenological parameter σeff in double J/ψ production was measured to be 5.0 ± 2.8 mb, while the same parameter for γ + 3 jet events was 12.7 ± 1.3 mb. These two measurements are consistent within two standard deviations, but it is true that central values are noticeably different. Is there a possible cause?
One possible explanation might be that the initial state in double J/ψ production is dominated by gluons, while the associated production of γ + 3 jet events is dominated by a quark and antiquark initial state. If this is relevant, then it is possible that the measured σeff difference could indicate a smaller average distance between adjacent gluons than between adjacent quarks, or between a quark and a gluon, in transverse space. This speculation is in qualitative agreement with the pion cloud model that predicts a smaller gluonic transverse size than for singlet quarks.