Double parton interactions as a background to associated HW production at the Tevatron
aa r X i v : . [ h e p - ph ] M a r Double parton interactions as a background to associated HW production at the Tevatron Dmitry Bandurin , Georgy Golovanov , Nikolai Skachkov Department of Physics, Florida State University, Tallahassee, FL 32306 Joint Institute for Nuclear Research, Dubna, Russia, Joliot-Curie 6, 141980
Abstract
In this paper we study events with W +jets final state, produced in double parton (DP) interactions, as a backgroundto the associated Higgs boson ( H ) and W production, with H → b ¯ b decay, at the Tevatron. We have found that theevent yield from the DP background can be quite sizable, which necessitates a choice of selection criteria to separatethe HW and DP production processes. We suggest a set of variables sensitive to the kinematics of DP and HW events. We show that these variables, being used as an input to the artificial neural network, allow one to significantlyimprove a sensitivity to the Higgs boson production. I. INTRODUCTION
A significant amount of experimental data, ranging from ISR energies [1] through the SPS [2] to the Tevatron[3–8], and even to photoproduction at HERA [9, 10], shows clear evidence of hard jets produced from multiple partoninteractions (MPI). Specifically, in the Tevatron Run I and Run II studies, 4-jet [3] and γ + 3-jet events [4, 7] havebeen considered with jet p T & −
15 GeV, and the fraction of events occurring due to double parton (DP) interactionshave been measured. Those fractions varied depending on the final state and the jet transverse momentum ( p T ) ofthe second parton interaction. The fraction measured using 4-jet final state is found to be 5 .
5% for jet p T >
25 GeV[3]. The fractions obtained from the γ + 3-jet production range from 51 .
3% for the second (ordered in pT ) and thirdjet p T in the interval 5 − [4] to 47% −
22% for the second jet p T within 15 −
30 GeV [7].Those experiments have also measured the effective cross section σ eff , an important parameter that contains in-formation about the parton spatial density inside the (anti)proton: σ eff = 12 . +10 . − . mb in the 4-jet production inCDF [3], σ eff = 14 . ± . +1 . − . mb and σ eff = 16 . ± . ± . γ + 3-jet productions in CDF [4] and D0 [7],respectively. This parameter allows the calculation of a DP cross section σ DP for any pair of partonic processes A and B according to: σ DP ≡ m σ A σ B σ eff . (1)The factor m has a Poissonian nature [11] and should be equal to 1 / A and B ) or gives unity for distinguishable processes. The CDF [4] and D0 [7] experimentsobtained the most accurate results on σ eff with an average value of about σ aveeff = 15 . W +dijet production, as a background to the HW production,with W → lν and H → b ¯ b decays, which is one of the most promising Higgs boson search channels at the Tevatron.An example of a possible DP process with W + b ¯ b production is shown in figure 1. However, in addition to thetwo- b -jet final state produced in the second parton scattering, we also expect significant contribution from final stateswith light+heavy flavor and two light jets. p p Wb b Figure 1: A possible diagram for W + b ¯ b production due to DP scattering. Due to the similarity of HW and HZ final states, we expect that the relative DP background from Z +dijetproduction to the HZ events should be quite close to the HW case. For this reason, we limit our study to DPbackground to the HW events only.This paper is organized as follows. In section II we describe how DP and Higgs boson samples are simulated andselected. In section III we calculate differential cross sections dσ/dM jj (where M jj is the invariant mass of the twoleading jets) and event yields in the HW and DP processes including the jet energy detector smearing and b -jetidentification effects. The rates of events with W +2-jet production due to the DP and conventional single parton(SP) scatterings are compared in section IV. In section V we introduce a set of variables sensitive to the kinematics ofthe signal HW ( Z ) and DP background final states and use them as an input to a dedicated Artificial Neural Network(ANN) to separate the two event types. We make our conclusions in section VI. In this measurement jet p T is raw, i.e. uncorrected for the energy losses [4]. σ/dM jj cross sections for HW, HZ and double parton events 3 II. SIMULATION AND SELECTIONSA. Selections
The current pythia event generator [16] is the best framework to study many effects related to MPI production.It includes a few sophisticated phenomenological models which consider the MPI scatterings with their various cor-relations, including parton momentum and color. The MPI models in pythia
6, have been tuned to experimentalresults, and reproduce many observables in data quite well [11, 17]. pythia
8, which inherited the majority of featuresof its predecessor, also allows the combination of different kinds of parton processes in the first (main) and secondscatterings within kinematic regions of interest. To simulate events for the study we used pythia . The HW production channel simulated with Higgs boson masses of m H = 115 and 150 GeV wasconsidered. The DP scattering was simulated as inclusive q ¯ q → W + X production in the first parton process andinclusive QCD dijet production in the second process. To increase statistics in the selected final states with the cutsabove, the W scattering process is required to have invariant mass 50 < m W <
120 GeV and the minimal allowedparton transverse momentum (ˆ p min ⊥ ) in the dijet process is required to be ˆ p min ⊥ = 10 GeV.The event selection criteria are taken from [18] and applied to both, the HW and DP production events and brieflysummarized below: • The Higgs boson is required to decay into b ¯ b . • The W-boson is selected in the electron and muon decay modes with lepton p T >
15 GeV and pseudorapidity | η | < . . < | η | < . | η | < . • The total vector sum ~p T of neutrinos should be >
20 GeV (an approximate analog of missing E T >
20 GeV in [18]). • At least two jets are required with p T >
20 GeV and | η | < .
5. Jets are found by the D0 Run II midpoint conealgorithm with radius R =0.5 [19]. For this aim we used the fastjet package [20] interfaced to pythia • The scalar sum of the jet transverse momenta ( HT ) is required to be HT >
60 GeV for the 2 jet final state and
HT >
80 GeV for the 3 jet one.
B. Normalizations
The cross sections of the simulated events were normalized to either experimentally measured cross sections or totheoretical NNLO predictions. Specifically, we normalized all the pythia cross sections in the following way: • We simulated dijet events production and calculated cross sections in the dijet mass bins 150 −
175 and 175 − | y | < . . < | y | < . pythia -to-data correction factor (“K-factor”) is about 1.26, approximately valid forboth the dijet mass bins and the two rapidity regions. • We also simulated separately W inclusive production and, from a comparison of its cross section with the D0 andCDF measurements [22, 23], have obtained a pythia -to-data K-factor of about 1.5. • The HW cross section has been normalized to the NNLO predictions [24] with the pythia -to-NNLO K-factor equalto 1.45. • We corrected the effective cross section σ eff used in Tune 2C by a factor 1.6 to match the CDF and D0 measurements[4, 7] with averaged result σ aveeff = 15.5 mb.The uncertainty assigned in our analysis to the K-factors are 10% and 16% to σ aveeff . The latter is due to thedifference between the D0 and CDF σ eff central values ( ∼ ∼ III. dσ/dM jj CROSS SECTIONS FOR HW AND DOUBLE PARTON EVENTSA. HW and DP cross sections
In this section we calculate he differential cross sections dσ/dM jj for the HW and DP ( W +dijet) events selectedaccording to the criteria of section II. To match the detector resolution, the jet transverse momenta p T are smeared This tune was suggested by the pythia authors. The effective cross section σ eff in pythia σ/dM jj cross sections for HW, HZ and double parton events 4using σ p T p T = S √ p T ⊕ C, (2)where S = 0 .
75 and C = 0 .
06 which approximately reproduces the jet p T resolution for the D0 detector [25]. Thedifferential cross sections dσ/dM jj for the HW and DP productions including the smearing effect are shown in figure2. In addition to the total DP cross section, contributions from the main DP scattering subprocesses are also shownin a separate plot. One can see from these two plots that (a) the DP cross section dominates the HW signal by morethan two orders of magnitude, and (b) the DP cross section is caused mainly by the W +2 light jets (stemming from u/d/s -quarks or gluons) production, followed, in the order of importance, by contributions from W + gc , W + gb , andthen by W + c ¯ c and W + b ¯ b events. (GeV) jj M ( pb / G e V ) jj / d M ( D P ) s d -5 -4 -3 -2 -1 =115 GeV) H HW (m =150 GeV) H HW (mDP, W + inclusive dijet (GeV) jj M ( pb / G e V ) jj / d M D P s d -5 -4 -3 -2 -1 W + qq(g) bW + b cW + cW + gb W + gc
DP subprocesses
Figure 2: The differential cross sections in the dijet mass M jj bins for signal HW and background DP events including thejet p T resolution. On the left plot, dotted and dash-dotted red lines correspond to HW events with m ( H ) = 115 and 150GeV,respectively, while the full black line shows the total background from all the DP W +dijet channels. The right plot showscontributions from main parton scattering subprocesses composing the total DP background. B. Account of b -jet identification efficiencies In the signal HW events we have two b jets in the final state. Since the leading DP background is caused by the W +2 light jet events (figure 2), we should expect a significant reduction after requiring of jet b -tagging. To check thisnumerically, we apply a specific b -tagging requirement for the HW and DP events. In our fast MC we cannot checkthe jet b -tagging quality, but we instead use the efficiencies to pass the b -tagging requirements for light ( l ), c and b jets. We take these efficiencies from [26], where they are parametrized as functions of jet p T and η . These efficienciesare used to re-weight events according to the jet flavors. Typical efficiencies are 50 −
70% for b -jets, 8 −
12% for c -jetsand 0 . −
2% for l -jets. The variations reflect dependence on the jet p T , η and tightness of the b -tagging condition. Weconsider a given jet to be a b -jet if it has a b -quark in the jet cone; if the jet does not have a b -quark but has a c -quarkinstead, it is considered to be a c -jet; otherwise it is a light jet. Figure 3 shows the cross sections × b -jet identificationefficiency ( ε jetb − id ) for the DP and HW events, where each of the two jets is required to satisfy the “loose” b -taggingrequirement [26]. This requirement significantly suppresses rates of the DP events. However, the signal rates are alsonoticeably reduced (compare figures 2 and 3). For this reason, in practice, double tagging is usually combined withsingle tagging. For example, in the search for HW signal [18], two cases of the b -tagging are considered: either anevent should contain two jets satisfying “loose” b -tagging requirements or, if it fails, a single jet should satisfy the“tight” requirement. Fractions of background (=data) and the HW events selected with the single b -tagging can betaken from [18]: they are about 85% and 60% correspondingly . The remaining events are with two b -tagged jets. Clearly, here we assume that the jet flavor content of the background events in data and the dijet events from the DP interaction is thesame. However, we believe that for the current level of estimates this assumption should be good enough. σ/dM jj cross sections for HW, HZ and double parton events 5Figure 4 shows the cross sections × ε jetb − id for the DP and HW events where we have combined events with single and (GeV) jj M ( pb / G e V ) jj / d M ( D P ) s * d b - i d j e t e -6 -5 -4 =115 GeV) H HW (m =150 GeV) H HW (mDP, W + inclusive dijet (GeV) jj M ( pb / G e V ) jj / d M D P s * d b - i d j e t e -6 -5 -4 W + qq(g) bW + b cW + cW + gb W + gc
DP subprocesses
Figure 3: The differential cross sections in the dijet mass bins for signal HW and background DP events including the jet p T resolution and requirement of the two jet b -tagging (See also description in the caption to figure 2). double b -tagging according to their fractions mentioned above. We see that while the dominating DP channel is stillcaused by the W +2 light jet production, the relative contribution from W + gb production is now much higher thanin figure 2 (no b -tagging is applied). The W + gb contribution is followed by similar ones from the W + gc and W + b ¯ b events.Figure 5 is complementary to figure 4 and shows the ratios of the HW event yield to the inclusive DP W +dijet onein the dijet mass M jj bins for the events selected by the combined b -tagging. The uncertainty in each bin is causedby the K-factors and effective cross section (section II).One can see that the Higgs boson events with m H = 115 GeV are expected to be suppressed by about a factor 3( S/B ≃ .
35) in the peak position, while the signal events with m H = 150 GeV are suppressed by about a factor 7.It is interesting to compare the total number of the signal events predicted by our fast MC after all selections (figure4) with those in [18] for the integrated luminosity L int = 5 . − . It is obtained by integrating the cross sectionover the whole M jj range (20–400 GeV) and multiplying by L int . In such a way we have found the expected signalstatistics of about 31 (7) events for m H = 115 (150) GeV. According to [18] there should be about 19 ± m H = 115 GeV. Our estimate seems to be in a reasonable agreement if we take into account the effects offinite lepton identification, jet taggability efficiencies, and detector acceptance unaccounted in our fast MC. (GeV) jj M ( pb / G e V ) jj / d M ( D P ) s * d b - i d j e t e -5 -4 -3 =115 GeV) H HW (m =150 GeV) H HW (mDP, W + inclusive dijet (GeV) jj M ( pb / G e V ) jj / d M D P s * d b - i d j e t e -5 -4 -3 W + qq(g) bW + b cW + cW + gb W + gc
DP subprocesses
Figure 4: The differential cross sections in the dijet mass bins for signal HW and background DP events including the jet p T resolution and the combined jet b -tagging efficiency (see also the main text and the caption to figure 2). σ/dM jj cross sections for HW, HZ and double parton events 6 (GeV) jj M
60 80 100 120 140 160 180 200 220 240 r a t i o o f H W / D P eve n t y i e l d s =115 GeV) H HW (m =150 GeV) H HW (m
Figure 5: The ratio of HW signal to DP background event yields with the combined b -tagging (see the main text). IV. COMPARISON OF THE DP AND SP EVENT YIELDS
In this section we compare the event yields dN/dM jj expected for the DP and SP W +2-jet productions. The twoadditional jets in the SP events come from radiation effects in the initial and/or final states. SP events are simulatedusing q ¯ q → W g and qg → W q subprocesses and applying the HW selection criteria from section II. To reproducethe inclusive W +2 jet cross section in data [27], the pythia events are reweighted with a scaling factor depending onthe second jet p T , what increases the pythia W +2 jet cross section in the region 110 < M jj <
160 GeV by about afactor 2. Also, as before, the jet p T is smeared according to the p T resolution, eq. (2) and the events are weightedwith the jet b -tagging efficiencies according to the jet flavors.The estimated total event yields in the whole mass region at L int = 5 . − for SP and DP events are about 5212and 262 events, respectively. The differential ratios of the DP/SP W +2-jet event yields in the M jj bins are shown infigure 6. They are about 5 −
8% for M jj ≃
115 GeV and 3 . −
6% for M jj ≃
150 GeV. (GeV) jj M
80 100 120 140 160 180 200 220 240 r a t i o o f D P / SP eve n t y i e l d s W + 2 jet production
Figure 6: The ratio of the DP to SP event yields for the W +2-jet production. rtificial neural network for DP and HW(Z) separation 7 V. ARTIFICIAL NEURAL NETWORK FOR DP AND HW(Z) SEPARATIONA. Variables
In this section we discuss variables that can be useful to separate the HW ( Z ) signal from the DP W ( Z )+dijetbackground events. Most of these variables are either based on the previous relevant experimental studies [1–7] orhave been suggested in theoretical papers [11, 28–34]. Due to the similarity of HW and HZ events, most of thesevariables should be useful to suppress the DP background events to both the final states (with some exclusions).Definitions of all the variables are summarized below. • The first variable is an azimuthal angle between two p T vectors, where the first one corresponds to the W ( Z ) p T vector, while the second one is a sum of the leading and second jet p T vectors:∆ S ≡ ∆ φ ( ~p T [ V ] , ~p T [jet , jet ]) , (3)where ~p T [ V ] is the transverse momentum vector of V (= W, Z )-boson and ~p T [jet , jet ] = ~p jet T + ~p jet T . For historicalreasons [1–4, 7] we call this angle ∆ S . • The second variable is the difference between the rapidity of the V -boson and the total rapidity of the two-jetsystem: ∆ η (V , jet12) = | η V − ( η jet1 + η jet2 ) | . (4) • The variable ∆ η (V , jet12) can be calculated just for V = Z events, but not for W due to the missing p z informationof the ν . Instead we can use the rapidity of the electron ( e ) η e from the W decay and introduce an analogous variable:∆ η (e , jet12) = | η e − ( η jet1 + η jet2 ) | . (5) • In the case of the W production the azimuthal angle between the electron from the W decay and the leading jet∆ φ (e , jet1) can be considered.Two other variables use angular differences between the first and second jets: • the azimuthal angle between the jets ∆ φ (jet1 , jet2). • the difference between rapidities of the first and second jets ∆ η (jet1 , jet2). • Another variable characterizes the orientation of the two event planes, one contains the beam (proton) axis and V -boson, and the other one contains the two jets [35]:cos ψ ⋆ (V , jet12) = ( ~p V × ~p proton ) · ( ~p jet1 × ~p jet2 ) | ~p V × ~p proton | · | ~p jet1 × ~p jet2 | . (6) • In the case of the W production, we do not have the 3-vector of the W momentum but can use the electron 3-vectorinstead, i.e. we should calculate cos ψ ⋆ ( e, jet12).Three other variables are based on the jet p T : • the total sum of the first and second jet p T : p sum12 T = p jet1 T + p jet2 T . (7) • the relative difference between the first and second jet p T : p diff12 T = ( p jet1 T − p jet2 T ) /p sum12 T . (8) • the total p T sum of all jets, p sumAll T . • Finally, we add the total number of all jets ( p T > N jets .All these 12 variables are shown in figures 7 and 8 for HW and DP W +dijet events. They demonstrate a goodseparation power between the two event types. B. ANN
The variables presented above can be used as input to a dedicated ANN to separate the HW from the DP events.The variable p sumAll T is very correlated with p sum12 T , but the latter is a bit more sensitive to the signal/backgrounddifference. We do not use the dijet mass information to minimize dependence on a specific Higgs boson mass regionbut rather concentrate on other more generic kinematic properties of the two event types.rtificial neural network for DP and HW(Z) separation 8We have chosen the following 9 variables to train the ANN: ∆ S , ∆ η (e , jet12), ∆ φ (e , jet1), ∆ φ (jet1 , jet2),∆ η (jet1 , jet2), cos ψ ⋆ ( e, jet p sum12 T , p diff12 T , and N jets , using the package jetnet [36]. The ANN is trained us-ing the signal HW (simulated with m H = 115 GeV) and background DP events to produce a single output valueequal to zero for the background and unity for the signal events. The DP background events for the training (andlater for testing) purposes are selected around the Higgs boson M jj peak position taking all events within ± σ aroundthe peak. We have trained the ANN using 200,000 the signal and background events and then tested the ANN using50,000 events that have not been used at the training stage. The normalized distributions of the signal and backgroundevents for the ANN output O NN is presented in figure 9. The ANN weights obtained at the training stage, have beenused later to also separate the HW signal simulated with m H = 150 GeV and DP events.Tighter cuts on the ANN output will reject a larger fraction of the DP events. Figure 10 shows the correlationbetween efficiencies to select the background and signal events ( ε ANN b and ε ANN s , respectively) for the two Higgs bosonmasses, m H = 115 GeV and m H = 150 GeV. Selecting 90% (80%) of the signal events with m H = 115 GeV we willkeep only about 24% (13%) of the DP events, while selecting 90% (80%) of the signal events with m H = 150 GeV wewill keep about 9% (4%) of the DP events. C. Results
The built ANN is used to further suppress the DP background, which strongly dominates the signal events evenafter the b-tagging selections (figure 5). The new signal-to-background ratios are shown in two plots of figure 11,corresponding to the choice of the HW signal efficiencies ε ANN s = 90% and 80%. The ratios at ε ANN s = 90% for boththe mass regions, 115 GeV and 150 GeV, are now close to 1 . − .
5. This ratio grows further with ε ANN s = 80%, andreaches about 2.2 at M jj ≃
115 GeV and about 2.7 at M jj ≃
150 GeV.
VI. CONCLUSION
In our current study we have shown that the W +dijet events produced due to the DP scattering can compose aquite sizable background to the associated HW production with H → b ¯ b decay. Its relative fraction with respect tothe traditional background from SP scattering with the W +2-jet final state is found to be 4 −
8% in the dijet massregion 115 < M jj <
150 GeV. We suggest a set of the angular and jet p T variables that are sensitive to the differencebetween the HW and DP kinematics. The neural network built using these variables allows significant suppressionof the DP background to a desirable level. Provided that the overall systematics in the Higgs searches in the HW channel will go down in a time and since every percent of the background events matters, use of the suggested anti-DPneural network should be very helpful. Acknowledgments
The authors thank Wade Fisher and Aurelio Juste for useful discussions and Stephen Mrena for the help with use ofthe pythia S D HW productionDP production (V,jet12) hD (e,jet12) hD (e,jet1) fD (jet1,jet2) hD (jet1,jet2) fD *(V,jet12) y Cos -1 -0.8 -0.6 -0.4-0.2 0 0.2 0.4 0.6 0.8 10.060.080.10.120.140.160.180.20.22 *(e,jet12) y Cos -1 -0.8 -0.6 -0.4-0.2 0 0.2 0.4 0.6 0.8 10.080.10.120.140.160.18
Figure 7: Normalized distributions of the number of HW signal (full red line) and W +dijets background (dashed black line)events over the kinematic variables of section V A (part 1). onclusion 10 sum12T p HW productionDP production diff12T p sumAllT p Njets
Figure 8: Normalized distributions of the number of HW signal (full red line) and W +dijets background (dashed black line)events over the kinematic variables of section V A (part 2). NN O NN / N d N / d O HW productionDP production
Figure 9: The ANN output for the DP and HW ( m H = 115 GeV) events using the 9 input variables described in the text. onclusion 11 (%) ANNs e
65 70 75 80 85 90 95 100 ( % ) ANN b e = 115 GeV H m = 150 GeV H m Figure 10: DP versus HW neural network selection efficiencies. (GeV) jj M
60 80 100 120 140 160 180 200 220 240 r a t i o o f H W / D P eve n t y i e l d s =115 GeV) H HW (m =150 GeV) H HW (m = 0.90
ANNS e (GeV) jj M
60 80 100 120 140 160 180 200 220 240 r a t i o o f H W / D P eve n t y i e l d s =115 GeV) H HW (m =150 GeV) H HW (m = 0.80
ANNS e Figure 11: Ratio of the HW event yields to the DP ones with account of the ANN selection efficiencies taken for the HW events to be 90% on the left and 80% on the right plot. onclusion 12 [1] Axial Field Spectrometer
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