Parton Distributions and Event Generators
aa r X i v : . [ h e p - ph ] N ov Parton Distributions and Event Generators
Stefano Carrazza, Stefano Forte
Dipartimento di Fisica, Universit`a di Milano and INFN, Sezione di Milano, ViaCeloria 16, I-20133 Milano, Italy
Juan Rojo
PH Department, TH Unit, CERN, CH-1211 Geneva 23, SwitzerlandWe present the implementation within the
Pythia8 event generatorof a set of parton distributions based on NNPDF methodology. We con-struct a set of leading-order parton distributions with QED corrections,NNPDF2.3QED LO set, based on the same data as the previous NNPDF2.3NLO and NNLO PDF sets. We compare this PDF set to its higher-ordercounterparts, we discuss its implementation as an internal set in
Pythia8 ,and we use it to study some of the phenomenological implications of photon-initiated contributions for dilepton production at hadron colliders.
1. PDFs and event generators
The needs of physics at the LHC require an increasingly accurate controlof the parton substructure of the nucleon: for example, this is a necessaryingredient in the accurate determination of Higgs couplings [1, 2], whichin turn is essential both for precision determination of Standard Model pa-rameters and for indirect searches for New Physics. Current sets of partondistributions [3] are based on increasingly refined theory, use an increasinglywide dataset (now also extended to LHC data) and attempt to arrive at anestimation of uncertainties which is as reliable as possible. An importantingredient in achieving all of these goals is the integration of parton distri-butions within Monte Carlo event generators [4]. Indeed, parton showeringand hadronization are necessary in order to bridge perturbative QCD cal-culation with the quantities which are actually measured in experiments, allthe more so as less inclusive observables are considered, even though alsofor observable which are in principle inclusive (such as the production ofgauge bosons) comparisons are best made between theoretical predictions,and data collected in an experimental fiducial region.Whereas next-to-leading (NLO) order Monte Carlo tools play an in-creasingly important role, leading-order (LO) Monte Carlo simulations aretill commonly used in a variety of applications. Furthermore, both LO andNLO Monte Carlo event generators typically rely on leading-order PDFs forthe description of multiple-parton interactions and the underlying event, sothat in fact generators which include a hadronization model, such as
Pythia (and specifically its current version,
Pythia8 [5]) are tuned using one ormore ‘native’ PDF setsIn this short contribution, we will discuss the NNPDF2.3QED LO PDFset, and its implementation within
Pythia8 : this is a PDF set which is basedon the successful NNPDF methodology, which strives to minimize theoret-ical bias and construct statistically reliable parton distributions, recentlyused to produce a first global set of PDFs using LHC data, NNPDF2.3 [6].This PDF set was subsequently used to construct a first set of PDFs withQED corrections and a photon distribution determined by experimentaldata, NNPDF2.3QED [7]. Recent general reviews of parton distributionsare presented in Refs. [8, 9, 3].
2. The NNPDF2.3QED LO parton set
The NLO and NNLO NNPDF2.3QED PDF sets were recently presentedin [7]. In these sets, the evolution of quark and gluon PDFs is consistentlyperformed using combined QCD ⊗ QED evolution equations, and the photonPDF γ ( x, Q ) is determined from LHC vector boson production and deep-inelastic scattering data. In order to construct a corresponding leading-orderset, NNPDF2.3QED LO, we start from the NNPDF2.1LO PDF sets [10],with two different values of α s ( M Z ): 0.119 and 0.130. Note that in Ref. [10]further LO sets were constructed, NNPDF2.1 LO* in which the momentumsum rule was not imposed; however, this choice, sometimes advocated, didnot turn out to be especially advantageous, hence we will not discuss thesesets further.The NNPDF2.3QED LO set is constructed by combining the PDFs fromthe NNPDF2.1 LO set with the photon PDF from the NNPDF2.3QED NLOset at Q = 2 GeV , and then evolving upwards this boundary conditionwith combined LO QCD ⊗ QED evolution equations, including O ( α s ) and O ( α ), but not O ( αα s ) terms. This procedure (which clearly retains LOQED+QCD accuracy) is justified because of the very mild correlation be-tween the photon and the other PDFs, and the large uncertainty on thephoton PDF itself [7]. The set of PDFs thus obtained is then also evolveddown to Q = 1 GeV : whereas leading-twist perturbative QCD might notbe accurate in this region, low-scale PDFs are necessary for tunes of theunderlying event and minimum bias physics in shower Monte Carlos.The combined QCD ⊗ QED evolution has been performed with the
APFEL package [11]. Among the various forms of the solution to the evolutionquation, differing by O ( αα s ) terms which are beyond our accuracy, we usethe so-called QECDS [11] solution, which was also used for the constructionof the NNPDF2.3QED NLO and NNLO sets. Strict positivity of all LOPDFs has been imposed in the relevant range of x and Q .In Fig. 1 we show the gluon PDF in the LO, NLO and NNLO NNPDF2.3QEDfits. The much larger small- x gluon is a well-known feature of LO PDF sets,due to the need to compensate for missing NLO terms when fitting deep-inelastic structure function data. It is an important ingredient for tunes ofsoft QCD dynamics at hadron colliders.In Fig. 2 we also show the photon PDF at Q = 10 GeV , at LO, NLOand NNLO. The small differences seen arise due to the different evolutionof quarks and gluons and their mixing with the photon through evolutionequations. x -6 -5 -4 -3 -2 -1
10 105101520 = 0.119 s α NNPDF2.3QED LO, = 0.119 s α NNPDF2.3QED NLO, = 0.119 s α NNPDF2.3QED NNLO, ) = 2 GeV xg(x,Q Fig. 1. The gluon PDF at LO, NLO and NNLO in the NNPDF2.3QED sets.
Finally, in Fig. 3 we compare the gluon PDF in the LO sets correspond-ing to the two different values of α s ( M Z ) = 0 .
119 and 0 . α s at LO, the smaller value is more accurate at higherscale, and the larger value at low scales. Reassuringly, in the small x ≤ − ,relevant for tunes of soft physics at hadron colliders, the two sets turn outto agree within their large uncertainties.
3. Implementation in
Pythia8 and phenomenological implica-tions
The NNPDF2.3QED LO sets, with two different α s values, togetherwith their NLO and NNLO counterparts, have been implemented as internal -5 -4 -3 -2 -1
10 100.050.10.150.20.250.3 = 0.119 s α NNPDF2.3QED LO, = 0.119 s α NNPDF2.3QED NLO, = 0.119 s α NNPDF2.3QED NNLO, ) GeV = 10 (x,Q γ x Fig. 2. The photon PDF at LO, NLO and NNLO in the NNPDF2.3QED sets. x -6 -5 -4 -3 -2 -1
10 105101520 = 0.119 s α NNPDF2.3QED LO, = 0.130 s α NNPDF2.3QED LO, ) = 1 GeV xg(x,Q Fig. 3. The small- x gluon PDFs in the NNPDF2.3QED LO set for α s = 0 .
119 and0.130.
PDF sets in
Pythia8 [5] starting with v8.180 , and there is ongoing workby the
Pythia8 authors towards providing a complete new tune based onNNPDF2.3QED LO, including all the relevant constraints from LHC andprevious lower-energy colliders [12].For the time being, we will illustrate some of the phenomenological im-plications of the NNPDF2.3QED LO set by generating events with
Pythia8 for processes in which photon-initiated contributions are substantial. As aase study, we consider dilepton production at the LHC 14TeV. Relatedstudies were presented in the original NNPDF2.3QED paper [7] but wererestricted to the parton level, while now we include the effects of the initialstate parton shower and underlying event with the standard
Pythia8 tune.The QED shower option of
Pythia8 is turned off. We generate events for q ¯ q → γ ∗ /Z → l + l − and for γγ → l + l − , and compare the relative contri-butions of the two different initial states. We consider both electrons andmuons in the final state.The invariant mass distributions of the dilepton pair at the LHC 14TeV, without any kinematical cut, is shown in Fig. 4, in the Z peak massregion. We shown separately the contributions from the q ¯ q and γγ initiatedsubprocesses (though experimentally they cannot be separated, as they leadto the same final state). Is clear that in this region the q ¯ q contribution ismuch larger, while the γγ contribution is at the permille level. The total(leading order) cross section, including branching fractions, is found to bearound 3.2 nb, in agreement with MCFM when run with the same inputPDF set. We conclude that photon-initiated contributions are generally notrequired in the Z peak region, except perhaps for high precision studies, suchas the determination of the W boson mass, where a permille accuracy inthe distributions is required [13]. Invariant Mass of the Dilepton Pair ( GeV )
70 75 80 85 90 95 100 105 110 115 ( nb / G e V ) ll / d M σ d -5 -4 -3 -2 -1 LHC 14 TeV initial stateqq initial state γγ Dilepton production in Pythia8 with NNPDF2.3 LO QED
Fig. 4. Invariant mass distributions of the dilepton pair at the LHC 14 TeV, com-puted with NNPDF2.3QED LO and
Pythia8 . The contribution from the q ¯ q and γγ initiated subprocess are separately shown. No kinematical cuts have been applied. The situation is quite different if we consider the high-mass tail. In Fig. 5e show the region of dilepton invariant masses M ll between 1 TeV and 2.5TeV. We have applied realistic kinematical cuts based on the typical ATLASand CMS acceptances, namely, we require p T,l ≥
25 GeV and | η l | ≤ .
5. Itis clear that now the photon-initiated contributions to the event yields arerather more significant, ranging from 10% at low masses to up to 50% athigh masses. Therefore, photon-induced contributions are an importantbackground for New Physics searches in electroweak production at highinvariant masses.
Invariant Mass of the Dilepton Pair ( GeV ) ( f b / G e V ) ll / d M σ d -5 -4 -3 -2 -1 initial stateqq initial state γγ LHC 14 TeV > 25 GeV
T,l | < 2.5, p l η | Dilepton production in Pythia8 with NNPDF2.3 LO QED
Fig. 5. Same as Fig. 4 but now in the high dilepton mass region. Realistic kine-matical cuts have been applied to the events, see text.
In order to disentangle the two contributions, or to provide a measure-ment which is especially sensitive to the photon PDF, one may look at therapidity distribution of the dilepton system. This is shown in Fig. 6 forfixed dilepton invariant mass of 2 TeV, at LHC 14 TeV, using the samekinematical cuts as before. It is clear that for a q ¯ q initial state, the dileptonsystem tends to be produced more centrally (due to the s -channel exchangeof the Z boson) while for a γγ initial state, the system is more broadly dis-tributed in rapidity ( t -channel exchange). Indeed, for the bins with largerrapidity the contribution from γγ diagrams becomes larger than that of q ¯ q contributions.All this suggest that a measurement of the rapidity distribution of high-mass Drell-Yan pairs, with a cut excluding the central region to enhance the γγ contribution, might be a good way to isolate and eventually pin downthe photon contribution to gauge boson production. apidity of the Dilepton Pair -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 ( f b ) ll η / d σ d -5 -4 -3 -2 -1 LHC 14 TeV > 25 GeV
T,l = 2 TeV, p ll M initial stateqq initial state γγ Dilepton production in Pythia8 with NNPDF2.3 LO QED
Fig. 6. The rapidity distribution of the dilepton system at LHC 14 TeV and for thesame kinematical cuts as in Fig. 5.
4. Using the NNPDF2.3QED LO sets
The NNPDF2.3QED LO sets can be obtained from the NNPDF website http://nnpdf.hepforge.org/html/nnpdf23qed/nnpdf23qed.html together with the corresponding
C/C++ stand-alone code. They can be usedtogether with the
LHAPDF5.9.0 interface, and they will also be available ina future release of
LHAPDF6 . They are now also available as an stand-aloneinternal PDF set in
Pythia8 . For consistency of notation, the NNPDF2.1LOPDF set (without QED corrections) will henceforth be equivalently referredto as NNPDF2.3 LO.
Acknowledgments:
We are grateful to T. Sjostrand and P. Skands fortheir help with the implementation of the NNPDF2.3 sets in
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