Multiple Parton Interactions in Z+jets production at the LHC. A comparison of factorized and non--factorized double parton distribution functions
aa r X i v : . [ h e p - ph ] J a n Preprint typeset in JHEP style - PAPER VERSION
DFTT 21/2010
Multiple Parton Interactions in Z + jets production atthe LHC. A comparison of factorized andnon–factorized double parton distribution functions. Ezio Maina a,b a INFN, Sezione di Torino, Italy, b Dipartimento di Fisica Teorica, Universit`a di Torino, Italy
Abstract:
We examine the contribution of Multiple Parton Interactions to Z + n –jets production atthe LHC, n = 2 , ,
4, where the Z boson is assumed to decay leptonically.We compare the results obtained with the correlated GS09 double parton distributionfunction with those obtained with two instances of fully factorized single parton distributionfunctions: MSTW2008LO and CTEQ6L1.It appears quite feasible to measure the MPI contribution to Z +2/3/4 jets already in thefirst phase of the LHC with a total luminosity of one inverse femtobarn at 7 TeV. If asexpected the trigger threshold for single photons is around 80 GeV, Z + 2–jets productionmay well turn out to be more easily observable than the γ + 3–jets channel. The MPIcross section is dominated by relatively soft events with two jets balancing in transversemomentum. ontents
1. Introduction 12. Calculation 43. Results 64. Conclusions 11
1. Introduction
The QCD–improved Parton Model forms the basis of our understanding of high–energyhadron scattering. In this framework each hadron is described as a collection of essentiallyfree elementary constituents. The interactions between constituents belonging to differentcolliding hadrons are the seeds of the complicated process which eventually leads to theparticles observed in the detector. In this conceptual scheme it is quite natural to envisagethe possibility that more than one pair of partons might interact in a single hadronicimpact. This kind of events are referred to as Multiple Parton Interactions (MPI) whilethose in which only a single pair of partons produce a hard scattering are described asSingle Parton Interactions (SPI).Multiple Parton Interactions have been detected in high transverse momentum hadroncollisions both at the ISR at CERN [1] and at the Tevatron at Fermilab [2, 3, 4]. Themeasured cross sections imply that MPI could provide a non-negligible background to allsort of interesting reactions since MPI rates at the LHC are expected to be large. Atsmaller transverse momentum MPI have been shown to be necessary for the successfuldescription of the underlying event both in Pythia [5, 6, 7] and in Herwig [8, 9]. The widerange of phenomena in which MPI are involved highlights the urgency of a more thoroughunderstanding of these reactions both experimentally and from a theoretical point of view.The theoretical investigation of MPI has a long history [10, 11, 12, 13, 14] and haveexperienced a renewed interest in more recent times [15, 16, 17, 18, 19, 20, 21, 22, 23].The basic formalism can be readily described starting from the standard expressionfor the SPI cross section: σ S ( A ) = X i,j Z F i ( x , t ) σ Aij ( x , y ) F j ( y , t ) dx dy (1.1)where t is the factorization scale which characterizes the interaction and at which theparton distribution functions F i ( x , t ) for parton i to have momentum fraction x are– 1 –valuated. Eq.(1.1) can be rewritten in term of parton distributions which depend on thetransverse coordinates as well as on the longitudinal momentum fraction as: σ S ( A ) = X i,j Z Γ i ( x , b , t ) σ Aij ( x , y )Γ j ( y , b − β, t ) dx dy d b d β (1.2)where β is the usual impact parameter. Making the reasonable assumption that the de-pendence on the momentum fraction and that on the transverse position factorizeΓ i ( x, b ) = F i ( x ) × f ( b ) (1.3)and that the latter is a universal function for all kind of partons fixes the normalization ofthe transverse distribution: Z f ( b ) f ( b − β ) d b d β = Z T ( β ) d β = 1 (1.4)where we have defined the overlap function T ( β ) = R f ( b ) f ( b − β ) d b .Analogously we can write the Double Parton Interaction (DPI) cross section as follows: σ D ( A,B ) = m X i,j,k,l Z Γ i,j ( x , b , t , x , b , t ) σ Ai,k ( x , y ) σ Bj,l ( x , y ) (1.5) × Γ k,l ( y , b − β, t , y , b − β, t ) dx dy d b dx dy d b d β where t and t are the factorization scales of the two scatterings; m is a symmetry factorwhich is equal to one if the reactions A and B are identical and equal to two if they arenot. Separating the transverse part, Γ i,j ( x , b , t , x , b , t ) = F i,j ( x , t , x , t ) × f ( b ) × f ( b ) Eq.(1.5) becomes σ D ( A,B ) = m σ eff X i,j,k,l Z F i,j ( x , t , x , t ) σ Ai,k ( x , y ) σ Bj,l ( x , y ) (1.6) × F k,l ( y , t , y , t ) dx dy dx dy where 1 σ eff = Z T ( β ) d β. (1.7)If one makes the further assumptions that double parton distributions reduce to theproduct of two independent one parton distributions, F i,j = F i × F j , the DPI cross sectioncan be expressed in the simple form σ D ( A,B ) = m σ S ( A ) σ S ( B ) σ eff . (1.8)This last assumption however, even though rather common in the literature and quiteconvenient from a computational point of view, is clearly incorrect. In Ref. [15, 16] it wasshown that correlations between the value of the double distribution functions for differentvalues of the two momentum fractions x , x are to be expected, even under the assumption– 2 –f no correlation at some scale Q , as a consequence of the evolution of the distributionfunctions to a different scale Q , which is determined by an equation analogous to the usualDGLAP equation [24, 25, 26].A large number of studies have evaluated the MPI contribution to several high en-ergy processes [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], including Higgs andelectroweak vector boson production. Other studies [41, 42, 43] have in addition focusedon the differences between final states produced in SPI and in MPI as a tool to reducethe background due to MPI or alternatively to separate MPI processes from SPI onesand gain more detailed experimental information on Multiple Parton Interactions. All theaforementioned studies have assumed complete factorization of double Parton DistributionFunctions (dPDF).In [44] the corrections to the factorized form for the dPDF have been estimated. Theydepend on the factorization scale, being larger at larger scales Q , and on the x range,again being more important at larger momentum fractions. For Q = M W and x ∼ . Q once they are satisfied at an inputscale Q . The GS09 set is based on the MSTW2008LO single Parton Distribution Func-tions (sPDF) [46]. Gaunt and Stirling also provide a program which evolves the dPDF fromthe input scale to any scale and a set of publicly available dPDF grids. In their publishedform the GS09 set deals with the case of two identical scales t and t in the distributionfunctions F i,j , but this limitation has been recently dropped.In Ref. [47] the GS09 dPDF have been employed in a study of same–sign W pairproduction at the LHC, including the background due to W ± Z ( γ ∗ ) production. Fromthe ratio R ≡ σ W + W + σ W − W − /σ W + W − , which is equal to one for factorized dPDF, aviolation of factorization at the 20% to 30% level is reported.In this paper we examine the contribution of MPI to Z + n –jets production at the LHC, n = 2 , ,
4, where the Z boson is assumed to decay leptonically. These processes have theadvantage of a much larger cross section than same–sign W W production and therefore aremore likely to allow detailed studies of MPI at the low luminosity, about 1 fb − , foreseenfor the first two years of operation at the LHC with √ s = 7 TeV. While the cross sectionfor Z + nj is smaller than for W + nj because of the smaller leptonic branching ratio,the former is cleaner from an experimental point of view since isolated, high pT chargedleptons, which are the main tool for W detection, can be copiously produced in B-hadrondecays [48, 49, 50] while no comparable mechanism exists for generating lepton pairs ofmass in the M Z region. As pointed out in [47] Z ( γ ∗ ) + jets production, with one of theleptons undetected, can also mimic W + nj processes. Z + nj production probes initial state parton combinations which are different fromthose probed in W ± W ± processes. The latter, at lowest order, are always initiated byfour–fermion states, mainly u ¯ du ¯ d . The former, on the contrary, typically have at least twogluons in the initial state since the largest component [42, 43] involves a two jet processwhich is dominated by gluon–gluon scattering.– 3 –or comparison we also present the predictions for γ + 3 j production, the reaction fromwhich the most recent and precise estimates of σ eff have been extracted at the Tevatron.This measurement will undoubtedly be performed again at the LHC [51].NLO QCD corrections are or will soon be available for all SPI processes leading to anelectroweak vector boson in association with up to four jets [52, 53, 54, 55, 56, 57, 58, 59].The Drell-Yan cross section is known at NNLO [60]. Measurements at the Tevatron showgood agreement between NLO calculations and data [61, 62]. These new developmentsopen the possibility of validating the predictions using events with large visible energy,where the MPI contribution is small, and then using them for a direct measurement ofthe MPI cross section at smaller total invariant masses in parallel with more data drivenanalysis similar to those of CDF and D0.In the following we compare the results obtained with the GS09 dPDF with thoseobtained with two instances of fully factorized sPDF: MSTW2008LO [46] and CTEQ6L1[63]. Hence we can estimate, even in the absence of a proper dPDF set based on CTEQ6,the dependence of MPI predictions on the choice of PDF, a study that to our knowledgehas not been performed before.We have considered three center of mass energies for the LHC: √ s = 7 TeV, √ s = 10TeV and √ s = 14 TeV. This allows us to study the properties of MPI processes while therelevant range of momentum fractions for the dPDF shifts to smaller values as the energyincreases.Given the strong similarities between the production mechanism of Z + jets , W + jets and γ + jets we expect that the conclusions reached in the present paper for Z + jets production concerning the ratio of the MPI to the SPI contribution, the effect of correlationsin MPI and the dependence on the PDF choice will be applicable also to W + jets and γ + jets production.We will confine ourselves to Double Parton Interactions and neglect Triple and HigherOrder Parton Interactions. Triple Parton Interactions are expected to be significantly lessabundant than Double ones, even though it has been argued that they could be indeeddetected at the LHC [42, 43].In Sect. 2 the main features of the calculation are discussed. Then we present ourresults in Sect. 3. Finally we summarize the main points of our discussion.
2. Calculation
The MPI processes which contribute at leading order to Z + n –jets through Double PartonInteractions are those in which an event producing k jets is superimposed to an eventproducing a Z –boson and ( n − k ) jets, k = 2 , . . . , n .At the Tevatron, CDF [2, 3] has measured σ eff = 14 . ± . +1 . − . mb, a value confirmedby D0 which quotes σ eff = 15 . ± . √ s = 1 . σ LHCeff = 12mb. Treleani then estimates the effect of the removal by CDF of TPI events from theirsample and concludes that the CDF measurement yields σ eff ≈
11 mb at Tevatron energies.– 4 –n the following we use σ eff = 12 . σ eff appears as an overall factor in our results it is easy to take into account a different value.It is worth mentioning that at present there is a discrepancy between the value of σ eff extracted by CDF and D0 and the one which is effectively employed by Pythia whosenormalization is derived mainly from comparisons with small p T data which dominate thetotal cross section. The description of MPI in PYTHIA8 [64] assumes that interactions canoccur at different p T values independently of each other inside inelastic non–diffractiveevents. The expression for a DPI cross section becomes therefore: σ = < f impact > σ · σ /σ ND /k (2.1)where σ ND is the total non–diffractive cross section and f impact is an enhancement/depletionfactor chosen event-by-event to account for correlations introduced by the centrality of thecollision. This quantity is typically averaged during an entire run to calculate < f impact > in Eq. 2.1. Typical values at the center of mass energy of 10 TeV are 1.33 for < f impact > and 51.6 mb for σ ND . Comparing Eq. 2.1 with Eq. 1.8 tells us that PYTHIA8 predicts aneffective σ eff = σ ND / < f impact > which is about a factor three larger than the one actuallymeasured at the Tevatron. I believe that this issue deserves careful consideration and thatnew measurements of high p T MPI reactions would be quite welcome.All samples have been generated with the following cuts: p T j ≥
30 GeV , | η j | ≤ . ,p T ℓ ≥
20 GeV , | η ℓ | ≤ . , (2.2) p T γ ≥
30 GeV , | η γ | ≤ . , ∆ R jj ≥ . , ∆ R jl ≥ . , ∆ R jγ ≥ . j = u, ¯ u, d, ¯ d, s, ¯ s, c, ¯ c, b, ¯ b, g and l = e + , e − , µ − , µ + .The Z + 4–jets sample has been generated with PHANTOM [65, 66, 67], while all othersamples have been produced with
MADEVENT [68, 69]. Both programs generate equal weightevents in the Les Houches Accord File Format [70]. All samples have been generated usingCTEQ6L1 [71] parton distribution functions. The QCD scale (both in α s and in the partondistribution functions) has been taken as Q = n X i =1 p T i , (2.3)where n is the number of final state partons, for all reactions with the exception of q ¯ q → l + l − for which the scale has been set at Q = M Z . The scale in Eq.(2.3) is similar, thoughnot identical, to the scale advocated in Refs. [58, 59] for vector boson plus jets productionat NLO.The results shown in the following under the CTEQ heading have been obtained com-bining at random one event from each of the reactions which together produce the desired– 5 –nal state through MPI. When needed, we have required that each pair of colored par-tons in the final state have a minimum ∆ R separation. This implies that the combinedcross section does not in general correspond to the product of the separate cross sectionsdivided by σ eff because the requirement of a minimum separation for all jet pairs inducesa reduction of the cross section when additional pairs are formed in superimposing events.The results shown under the MSTW and GS09 headings have been obtained througha reweighting procedure by the appropriate ratio of parton distribution functions andcoupling constants. For instance, an event like ( q i ¯ q i → gl + l − ) ⊗ ( gg → gg ), constructedfrom two events generated separately with CTEQ6 PDF, can be transformed in a weightedevent with MSTW2008 PDF multiplying its original weight by R = F MSTW i ( t ) F MSTW ¯ i ( t ) F CTEQ i ( t ) F CTEQ ¯ i ( t ) × α MSTW s ( t ) α CTEQ s ( t ) × F MSTW g ( t ) F MSTW g ( t ) F CTEQ g ( t ) F CTEQ g ( t ) × α MSTW s ( t ) α CTEQ s ( t ) (2.4)where t , t are the factorization scales for q i ¯ q i → gl + l − and gg → gg respectively. Thefactorization scales have been read off from the event files. The second and fourth factorsin Eq.(2.4) take into account the different values of the strong coupling constants for thetwo different sets of PDF: α CTEQ s,LO ( M Z ) = 0 .
130 while α MRST s,LO ( M Z ) = α GS s ( M Z ) = 0 . F ij ( t , t ) wouldappear instead of the uncorrelated product F i ( t ) F j ( t ) and so on. The resulting eventsare no longer unweighted. The error on the cross section introduced by the reweightingprocedure is essentially negligible because of the large size, about 5 × events, of thesamples. Reweighting can also be employed to estimate the sensitivity of our tree levelresults to variations of the scale Eq.(2.3) using a straightforward modification of Eq.(2.4).All results are obtained with the following values for the electroweak input parameters: M Z = 91.188 GeV, M W = 80.40 GeV, G F = 0.116639 × − GeV − .We work at parton level with no showering and hadronization. Color correlationsbetween the two scatterings have been ignored.
3. Results
The total cross sections for SPI and DPI production for Z +2–jets, Z +3–jets and Z +4–jetsare presented in Tab. 1, Tab. 2 and Tab. 3 respectively. In all cases the cuts in Eq.(2.2) havebeen imposed. The analysis has been repeated requiring a larger separation between jets;the results for ∆ R jj = 0 . R jj = 0 . Z boson. The Z → e + e − channel givesthe same result. The possibility of detecting high p T taus has been extensively studied inconnection with the discovery of a light Higgs in Vector Boson Fusion in the τ + τ − channelwith extremely encouraging results [72]. Therefore, the tau decay of the Z can be expectedto contribute significantly to MPI studies.The total cross sections for SPI and DPI production for γ + 3–jets are shown in Tab. 4with increasing jet–jet separation. It should be mentioned however that at the LHC triggerthresholds for single photons are foreseen to be much higher than those for double leptons– 6 –4 TeV 10 TeV 7 TeV Z + 2 j CTEQ MSTW GS09 CTEQ MSTW GS09 CTEQ MSTW GS09∆ R jj = 0 . R jj = 0 . R jj = 0 . Table 1: Z + 2–jets, Z → µ + µ − cross sections in pb. Cuts as in Eq.(2.2) with increasing angularseparation between jets, ∆ R jj .
14 TeV 10 TeV 7 TeV Z + 3 j CTEQ MSTW GS09 CTEQ MSTW GS09 CTEQ MSTW GS09∆ R jj = 0 . R jj = 0 . R jj = 0 . Table 2: Z + 3–jets, Z → µ + µ − cross sections in pb. Cuts as in Eq.(2.2) with increasing angularseparation between jets, ∆ R jj . [73, 74, 75]. While pair of leptons are expected to be triggered on for transverse momenta ofabout 15 GeV, single photons will be detected only when their transverse momenta is largerthan about 80 GeV at the design energy of 14 TeV. At lower energies and instantaneousluminosities the threshold could be smaller. Even at design luminosity and center of massenergy a lower threshold could be allowed with some pre–scaling. Since MPI processesare known to decrease sharply with increasing transverse momenta, we present in Tab. 5the predictions for p T γ ≥
80 GeV while the results in Tab. 4 are mainly intended for lowluminosity data taking.The Single Particle Interaction MSTW results are larger than those obtained with theCTEQ PDF by an amount which varies between 15% for Z +2 j to 27% for Z +4 j , increasingas expected with the power of α s in the amplitude. The Double Particle Interaction MSTWresults are larger than those obtained with the CTEQ PDF by an amount which varies– 7 –4 TeV 10 TeV 7 TeV Z + 4 j CTEQ MSTW GS09 CTEQ MSTW GS09 CTEQ MSTW GS09∆ R jj = 0 . R jj = 0 . R jj = 0 . Table 3: Z + 4–jets, Z → µ + µ − cross sections in pb. Cuts as in Eq.(2.2) with increasing angularseparation between jets, ∆ R jj . between 30% and 90%. The larger shift is due to the smaller scales for the two individualscatterings compared to a single interaction event with the same final state particles. Thepredictions for the GS09 correlated dPDF are larger than those with MSTW uncorrelatedones for √ s = 14 TeV and √ s = 10 TeV while they are smaller for √ s = 7 TeV. Thedifference is at most of 15%. Taking into account the errors in the measurement of σ eff we conclude that the uncertainties due to the choice of PDF and to correlation effects arereasonably under control.These variations should be compared with the uncertainty due to scale variation in PDFand in the strong coupling constant. In order to estimate the latter we have reweighted oursamples changing the scale in Eq.(2.3) by a factor of two in either direction for two limitingcases, namely Z + 2 j production at √ s = 7 TeV and Z + 4 j production at √ s = 14 TeV.In both instances we have used MSTW PDF and ∆ R jj = 0 .
5. For Z + 2 j production at √ s = 7 TeV the cross section changes by +14%/-13% when the scale is halved/doubled;in the case of Z + 4 j production at √ s = 14 TeV the corresponding shifts are +57%/-29%.The processes we are interested in therefore are not overly sensitive to scale variations.The corresponding uncertainty is of the same order than that related to PDF choice.The effects of higher order corrections are more difficult to estimate since no NLOcalculation for MPI processes is available. QCD one loop calculations are available forvector boson production with up to four jets [52, 53, 54, 55, 56, 57, 58, 59] and are typicallyof order 10% with the exception of Drell–Yan inclusive production [76] where they are ofthe order of 50%. NLO corrections for the inclusive jet cross section at the LHC have beenpresented in Ref. [77]. For small transverse momenta, as the ones we are interested in thispaper, they are of the order of 10%.The ratio between the MPI and SPI cross sections increases with the collider energy,that is with decreasing average momentum fractions carried by the incoming partons. Italso increases with the ∆ R jj separation because of the absence of correlations between thefinal state partons originating in the independent scatterings which compose MPI events.– 8 –4 TeV 10 TeV 7 TeV γ + 3 j CTEQ MSTW GS09 CTEQ MSTW GS09 CTEQ MSTW GS09∆ R jj = 0 . R jj = 0 . R jj = 0 . Table 4: γ + 3–jets cross sections in pb. Cuts as in Eq.(2.2) with increasing angular separationbetween jets, ∆ R jj .
14 TeV 10 TeV 7 TeV γ + 3 j CTEQ MSTW GS09 CTEQ MSTW GS09 CTEQ MSTW GS09∆ R jj = 0 . R jj = 0 . R jj = 0 . Table 5: γ + 3–jets cross sections in pb. Cuts as in Eq.(2.2) and p T γ ≥
80 GeV, with increasingangular separation between jets, ∆ R jj . For Z + nj processes and taking ∆ R jj = 0 . √ s = 7 TeV and grows to about 25% at √ s = 14 TeV. The results for γ + 3–jetsshow a similar behaviour with somewhat smaller fractions of MPI events to SPI ones whichhowever depend drastically on the p T γ cut. For p T γ ≥
30 GeV they range between 5 and10% while for p T γ ≥
80 GeV they are at the percent level.If we consider the MPI processes as our signal and the SPI ones as the correspondingbackground, we can estimate the prospect of measuring MPI in a given final state from thestandard S/ √ B significance. Using for S the result obtained with GS09 PDF and for B the result for the MSTW set and assuming a luminosity of one inverse femtobarn at 7 TeV,the significancies extracted from Tabs. 1–3, in the Z → µ + µ − channel alone, are 19/7/5for Z +2/3/4 jets with ∆ R jj = 0 .
7. The corresponding number of expected MPI eventsare 2600/500/140. Therefore it appears quite feasible to measure the MPI contribution to– 9 – φ∆ ( pb ) j j φ ∆ / d σ d TotalSPI CTEQSPI MSTWMPI CTEQMPI MSTWMPI GS j1j2 φ∆ (GeV) vis M100 200 300 400 500 600 700 800 ( pb / G e V ) v i s / d M σ d TotalSPI CTEQSPI MSTWMPI CTEQMPI MSTWMPI GS
Mvis
Figure 1:
On the left: distribution of the angular separation in the transverse plane between thetwo highest p T jets in Z + 4 j events. On the right: distribution of the total visible mass, ( P ni =1 p i ) ,in Z + 2 j events. For both plots √ s = 7 TeV, ∆ R jj = 0 . Z +2/3/4 jets already in the first phase of the LHC.The significance of γ + 3–jets depends on the trigger strategies. If the threshold for sin-gle photon detection can be brought in the 30 GeV range then the much larger productionrate, about ten times that of Z ( µµ ) + 2 j , provides the best opportunity for an early mea-surement of MPI at the LHC. If, on the contrary, the photon trigger cannot substantiallydeviate from about 80 GeV, Z + 2 j production looks more promising than the γ + 3–jetschannel whose significance becomes similar to that of Z + 3 j . Anyway, in order to gobeyond measuring σ eff and start to extract the double parton distribution functions fromthe data, one should measure the MPI fraction of as many channels as possible, exploitingthe fact that different reactions are initiated by different combinations of partons.The contribution to the MPI Z + n –jets cross section due to two jet production inassociation to Z + ( n − φ between the two highest p T jets in Z + 4 j events at √ s = 7 TeV and ∆ R jj = 0 . Z + 2 j production with the same energy and angular separation. It clearly shows that MPI eventsare produced with a smaller center of mass energy than SPI ones. Whether or not thesedifferent kinematical distribution can be exploited to further increase the MPI fractionin the event sample depends on the behaviour of the additional radiation produced inassociation with the hard scattering(s) which is bound to distort both the total visiblemass and the relative orientation of jet pairs. A dependable estimate of these effects requireto pass the hard events to a showering Monte Carlo, keeping in mind the normalizationuncertainties mentioned in Sect. 2.The only MPI mechanism contributing at tree level to γ + 3–jets is the production– 10 – (GeV) jet1 pT50 100 150 200 250 300 ( pb / G e V ) j e t / dpT σ d TotalSPI CTEQSPI MSTWMPI CTEQMPI MSTWMPI GS jet1 pT Figure 2:
Transverse momentum distribution of the hardest jet in γ + 3 j events. √ s = 7 TeV,∆ R jj = 0 . p T γ ≥
80 GeV. of two jets in one scattering and of a photon and a jet in the other. Therefore, when thephoton threshold is large, a jet of comparable transverse momentum is also present. Thisfeature could reasonably be expected to provide an additional tool to significantly reducethe SPI contribution. Unfortunately, as shown in Fig. 2, only a modest reduction can beachieved in this way since the p T spectrum of the highest transverse momentum jet is quitehard in SPI events.
4. Conclusions
In this paper we have estimated the contribution of Multiple Parton Interactions to Z +2 / / γ + 3–jets production, comparing the traditional factorized double par-ton distribution functions, using both MSTW2008LO and CTEQ6L1 PDF, and the newcorrelated set by Gaunt and Stirling.The predictions for the GS09 correlated dPDF differ by at most 15% from those withMSTW uncorrelated distribution functions. The uncertainty due to the choice of PDF isin the 30 to 90% range.It appears quite feasible to measure the MPI contribution to Z +2/3/4 jets alreadyin the first phase of the LHC with a total luminosity of one inverse femtobarn at 7 TeV.If as expected the trigger threshold for single photons is around 80 GeV, the Z + 2–jetsprocess may well turn out to be more easily reachable than the γ + 3–jets channel. It isworth recalling that the results presented here are expected to be valid also for W + 2 / / cknowledgments We wish to express our gratitude to Jonathan Gaunt and James Stirling for providingthe grids and interpolating routines for the PDF set of Ref. [45]. This work has beensupported by MIUR under contract 2008H8F9RA 002 and by the European Community’sMarie-Curie Research Training Network under contract MRTN-CT-2006-035505 ‘Tools andPrecision Calculations for Physics Discoveries at Colliders’
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