Powheg-Pythia matching scheme effects in NLO simulation of dijet events
MMCnet-16-34
Powheg–Pythia matching scheme effects in
NLO simulation of dijet events
Andy Buckley
School of Physics & Astronomy, Glasgow University, UK
Debottam Bakshi Gupta
Department of Physics, Louisiana Tech University, USA
December 21, 2017
One of the most important developments in Monte Carlo simulation of collider events forthe LHC has been the arrival of schemes and codes for matching of parton showers to matrixelements calculated at next-to-leading order in the QCD coupling. The P
OWHEG scheme, andparticularly its implementation in the P
OWHEG -B OX code, has attracted most attention due toease of use and effective portability between parton shower algorithms.But formal accuracy to NLO does not guarantee predictivity, and the beyond-fixed-ordercorrections associated with the shower may be large. Further, there are open questions overwhich is the “best” variant of the P OWHEG matching procedure to use, and how to evaluatesystematic uncertainties due to the degrees of freedom in the scheme.In this paper we empirically explore the scheme variations allowed in P
YTHIA
OWHEG -B OX dijet events, demonstrating the effects of both discrete and continuous freedomsin emission vetoing details for both tuning to data and for estimation of systematic uncertaintiesfrom the matching and parton shower aspects of the P OWHEG -B OX +P YTHIA
Introduction
One of the most important recent developments in Monte Carlo simulation of collider eventshas been the arrival of schemes and codes for consistent parton-shower dressing of partonichard process matrix elements calculated at next-to-leading order in the QCD coupling.It is now possible to simulate fully exclusive event generation in which the parton shower(PS) is smoothly matched to matrix element (ME) calculations significantly improved overthe leading-order Born level, and the modelling further improved by non-perturbative mod-elling aspects such as hadronization and multiple partonic interactions (MPI). Tools provid-ing these improvements include both “multi-leg LO”, exemplified by the Alpgen [1], Mad-Graph [2], and Sherpa 1 [3] codes; the “single-emission NLO” codes such as P
OWHEG -B OX [4] December 21, 2017 a r X i v : . [ h e p - ph ] D ec nd (a)MC@NLO [5, 6]; and the latest generation in which both modes are combined intoshower-matched multi-leg NLO: Sherpa 2 and MadGraph5-aMC@NLO [7].While the technical and bookkeeping details in these algorithms for combination of different-multiplicity matrix elements and parton showers are formidable, and their availability hasrevolutionised the approaches taken to physics analysis during the LHC era, there remainconstant questions about how to evaluate the uncertainties in the methods. Which generatorconfiguration choices are absolute and unambiguous, and which have degrees of freedom whichcan be exploited either for more accurate data-description (of primary interest to new physicssearch analyses) or to construct a theory systematic uncertainty in comparisons of QCD theoryto data (the “Standard Model analysis” attitude). Despite the confidence-inspiring “NLO” labelon many modern showering generators, there are in practice many freedoms in matching matrixelements to shower generators.The P OWHEG scheme, in particular its implementation in the P
OWHEG -B OX code [4], hasattracted most attention due to its ease of use and formal lack of dependence on the detailsof the parton shower used. But formal accuracy to NLO does not guarantee predictivity, andthe beyond-fixed-order corrections induced by the shower procedure may be large. Further,questions remain over which is the “best” variant of the P OWHEG matching procedure to use, andhow to evaluate systematic uncertainties due to the degrees of freedom in the scheme. Since theextra parton production in P
OWHEG real-emission events suppresses the phase space for partonshower emission, use of such ME–PS matching can lead to underestimation of total systematicuncertainties unless the matching itself is considered as a potential source of uncertainty inaddition to the P
OWHEG matrix element scales and the (suppressed) P
YTHIA parton showers.In this paper we empirically explore the scheme variations allowed in P
YTHIA
OWHEG -B OX dijet [9] events, demonstrating the potentially disastrous effects of “reasonable”matching choices and the remaining tuning freedom for optimal data description. The original and simplest approach to showering P
OWHEG events is to start parton showerevolution at the characteristic scale declared by the input event. Since the P
OWHEG formalismworks via a shower-like Sudakov form factor, and both P
OWHEG -B OX and the P YTHIA partonshowers produce emissions ordered in relative transverse momentum, this approach seemsintuitively correct. But in fact the definition of “relative transverse momentum” is not quitethe same between the two codes and hence this approach may double-count some phase-spaceregions, and fail to cover others entirely.P
YTHIA ’s answer to this is to provide machinery for “shower vetoing”, i.e. to propose partonshower emissions over all permitted phase space (including above the input event scale, up to2he beam energy threshold) according to P
YTHIA ’s emission-hardness definition, but to vetoany proposal whose P
OWHEG definition of “hardness” is above the threshold declared by orcalculated from the input event. This machinery is most easily accessed via the main31 P YTHIA
OWHEG method itself does not prescribe exactly whatform of vetoing variable should be used. P
YTHIA
OWHEG -hardness scales to be used in the shower-emission vetoing. These arecontrolled via the configuration flags pTdef , pTemt , and pThard , which respectively determinethe variable(s) to be used to define “hardness” in the P OWHEG shower-veto procedure, thepartons to be used in computing their values, and the cut value(s) to be used in applying thathardness veto to the calculated hardness variables.The available variations of these scale calculations range from comparison of the matchedemission against only a limited subset of event particles at one extreme, to comparison with allavailable particles at the other. This typically produces a spectrum of scale values to characterise ashower emission, from maximal scales at one end to minimal scales at the other, with a spectrumof in-between values from hybrid approaches. The effect on shower emission vetoing dependson the combination of the scale calculated for each proposed shower emission and the scalethreshold determined from the input event.Testing all options of all three scales simultaneously would produce 50 or so predictions tobe compared and disambiguated: not a pleasant task for either us or the reader! So we insteadtake a divide-and-conquer approach, first focusing on the pTemt scale alone since it has beenobserved to produce large effects in many observables. We then proceed via a reduced set ofpreferred pTemt schemes, on which to study further variations.In all the following comparisons and discussion the combination of scale calculation schemesare represented by an integer tuple
HED = ( pThard , pTemt , pTdef ) . The default P YTHIA OWHEG matching configuration is
HED =
201 in this notation.
All the plots shown in this study were computed using ATLAS and CMS jet analyses encodedin the Rivet 2.4 [10] analysis system. All such available analyses at the time of the study used pp events with √ s = OWHEG -B OX v2 r3144 and processed in parallel through P YTHIA main31 example program, default tune & PDF, and HepMC event record output [12].The full set of Rivet analyses used is listed in Table 1, giving a comprehensive view of theeffects of matching scheme variations across the public LHC measurements of hadronic jetproduction. For obvious reasons of space and exposition, in this paper we only show a small3 b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
Data b POWHEG+Py
POWHEG+Py
POWHEG+Py − − − ATLAS inclusive jet cross-section, | y | < R = d σ / d p T d y [ p b / G e V ] . . . . . . . . . . p T [GeV] M C / D a t a (a) b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py . . . . . . . ATLAS inclusive jet multiplicity ratio N / N − R = σ N / σ N − . . . N jet M C / D a t a (b) Figure 1:
Observables showing the effect of pTemt variation. The 3-digit tuple used in the plot legendsrepresents the P
YTHIA HED flag combination as described in the text. representative subset of these plots, but all 920 (!) have been considered in the discussion ofobserved effects. pTemt
In Figure 1 we show the effects of varying the pTemt scale calculation; for clarity only thecombinations with the main31 default pTdef = pThard = pTemt effects by far dwarf those from the two remaining degrees of freedom.The values 0–2 of pTemt have the following meanings, relating to the “hardness” of a proposedshower emission, to be compared to the vetoing hardness cut specified by the P OWHEG methodand the hard-process event kinematics: hardness calculated for the emitted parton only, with respect to the radiating parton only, andrecoil effects are neglected; hardness calculated for the emitted parton, computed with respect to all partons (initial andfinal), and the minimum such value is used; hardness calculated for all final-state partons, computed with respect to all other partons,and the minimum value used.Scheme 0 is the hardness definition used by the P OWHEG -B OX itself, in the hard process eventssupplied to P YTHIA , and is hence a priori expected to give the best matching. Since the other4ivet analysis name Description & citation
ATLAS analyses
ATLAS 2014 I1326641
ATLAS 2014 I1325553
Inclusive jet cross-section [14]
ATLAS 2014 I1307243
Jet vetoes and azimuthal decorrelations in dijet events [15]
ATLAS 2014 I1268975
High-mass dijet cross-section [16]
ATLAS 2012 I1183818
Pseudorapidity dependence of total transverse energy [17]
ATLAS 2012 I1119557
Jet shapes and jet masses [18]
ATLAS 2012 I1082936
Inclusive jet and dijet cross-sections [19]
ATLAS 2011 S9128077
Multi-jet cross-sections [20]
ATLAS 2011 S9126244
Dijet production with central jet veto [21]
ATLAS 2011 S8971293
Dijet azimuthal decorrelations [22]
ATLAS 2011 S8924791
Jet shapes [23]
ATLAS 2010 S8817804
Inclusive jet cross-section + dijet mass and χ spectra [24] CMS analyses
CMS 2014 I1298810
Ratios of jet p T spectra [25] CMS 2013 I1224539 DIJET
Jet mass measurement in dijet events [26]
CMS 2013 I1208923
Jet p T and dijet mass [27] CMS 2012 I1184941
Inclusive dijet production as a function of ξ [28] CMS 2012 I1090423
Dijet angular distributions [29]
CMS 2012 I1087342
Forward and forward + central jets [30]
CMS 2011 S9215166
Forward energy flow in dijet events [31]
CMS 2011 S9088458
Ratio of 3-jet over 2-jet cross-sections [32]
CMS 2011 S9086218
Inclusive jet cross-section [33]
CMS 2011 S8968497
Dijet angular distributions [34]
CMS 2011 S8950903
Dijet azimuthal decorrelations [35]
Table 1:
List of Rivet analyses used for the jet observables studied in this paper. All analyses wereperformed on pp data at √ s = p T distribution of inclusive jets in the most central rapidity binas measured by ATLAS in 7 TeV pp collisions [14], where the effect of using a non-default pTemt scheme is a cross-section overestimation by factors of 50–300. The P OWHEG matching detailscan hence be exceedingly important, potentially more-so than standard systematic variations onmatrix element scales and PDFs. The right-hand plot shows the effect of pTemt on jet multiplicityratios: a much smaller effect, but still a source of significant mismodelling.It is clear that these are huge effects, utterly incompatible with the data. The only viablecombinations of
HED parameters have pTemt =
0, i.e. the largest of the possible values for theP
OWHEG hardness scales since pTemt = pTemt = YTHIA shower emissions would result in lessemission-vetoing and hence harder distribution tails.In fact, details like jet vetos, jet shapes, and E T flow can be moderately well described by theconfigurations which produce such large jet mass and p T tails. This makes sense for single-jetquantities which are at first-order independent of overall event activity, but is less obvious forthe global event variables. It is clear, though, that from the available options the pTemt = pTdef and pThard schemes, is potentially disturbing. The default pTemt = OWHEG , but since there is no unambiguously correct calculation schemethere must be residual uncertainty over how large the effects of much more subtle variations inscale calculation could be. Given the obvious sensitivity of observables to this matching schemedetail, it will be interesting to explore whether minor refinements to the P
YTHIA scale calculationcan produce more reasonable variations, particularly one which might correct for the systematicundershooting of multi-jet mass measurements. pThard and pTdef
Having established that only the pTemt = pThard ∈ {
1, 2 } and pTdef ∈ {
1, 2 } ;explicitly, the HED tuples 201 (the P
YTHIA main31 example program setting), 101, 202, and 102.The pThard flag distinguishes between two methods for recalculation of the P OWHEG veto scale(as opposed to using the
SCALUP value specified in the LHE file): a value of 1 considers the p T of6 b b b b b b b b b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py − − ATLAS -jet cross-section, R = (cid:12)(cid:12) Y ∗ (cid:12)(cid:12) < d σ / d m jjj / d (cid:12)(cid:12) Y ∗ (cid:12)(cid:12) [ p b / G e V ]
400 600 800 1000 1200 14000 . . . . . . m jjj [GeV] M C / D a t a (a) b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py . . . . . . . . . ATLAS gap fraction vs. leading-dijet mean p T G a p f r a c t i o n . . . . p T [GeV] M C / D a t a (b) b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py . . . . . ATLAS h N jets in rapidity interval i vs. ∆ y h N j e t s i n r a p i d i t y i n t e r v a l i . . . . . . . . ∆ y M C / D a t a (c) b b b b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py . . . . . . . ATLAS gap fraction vs. p T for 1.0 < | ∆ y leadjet | < G a p f r a c t i o n
50 100 150 200 250 300 350 400 450 5000 . . . . . . . . p T [GeV] M C / D a t a (d) Figure 2:
Observables showing the effects of pThard and pTdef variations, with pTemt =
0. The 3-digittuple used in the plot legends represents the P
YTHIA HED flag combination as described inthe text.
OWHEG emitted parton relative to all other partons, while a value of 2 uses the minimal p T of all final state partons relative to all other partons. The pTdef flag switches between using theP OWHEG -B OX or P YTHIA p T ” in the veto scale calculation.These variations are shown in Figures 2 to 4. The most distinctive feature of these histogramsshown in these figures is that there are two consistent groups of MC curves in all cases: the 201& 101 combinations together, and the 102 & 202 combinations together. It is hence clear that the pTdef mode (the 3rd component of the HED tuple) has a stronger effect than pThard on theseobservables – the question is whether there is a clear preference for either grouping, and thenwhether there is distinguishing power between the finer pThard splitting within the preferredgroup.All the (ATLAS) plots in Figure 2 favour the pTdef = OWHEG -B OX p T definition), in particular in the dijet rapidity gap analysis where description of small rapiditygaps and gaps between high mean- p T dijet systems is significantly better than the pTdef = | η | , and both models converge to the same (poor)description at high rapidity; the pTdef = pTdef = shape of the data. Interestingly, dijet azimuthal decorrelation data prefers the pTdef = YTHIA p T ” treatment at the high-decorrelation (left-hand) end of the spectrum but this region ofthe observable is expected to be affected by multiple extra emissions and hence the performanceof the single-emission P OWHEG scheme is not clearly relevant. The 3-to-2 jet ratio also somewhatprefers the P
YTHIA p T scheme, but both schemes lie within the experimental error bars, as theydo for inclusive jet multiplicity modelling.Finally, in Figure 4 we again see mixed results: CMS’ characterisations of the 3-to-2 jet ratio anddijet decorrelations also prefer pTdef =
2, but the distribution of groomed jet masses exhibits aslight preference for the pTdef = OWHEG -B OX p T scheme.The consistent trend throughout these observables is that the P OWHEG -B OX p T definitionproduces more radiation, and hence larger n -jet masses, lower rapidity gap fractions, more jetdecorrelation, and more 3-jet events. Some of these effects increase compatibility with data, whileothers prefer less radiation, as produced by using the P YTHIA p T definition.There is no clear “best” choice of pTdef scheme from the available observables, nor a consistentpreference for either pThard scheme within the pTdef groupings. P YTHIA ’s default
HED =
201 configuration is certainly viable based on this comparison, but a pTdef flip to the 202configuration may be a preferable choice if jet multiplicities are more important than theirrelative kinematics (e.g. the multi-jet masses) for the application at hand.8 b b b b b
Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py . . ATLAS transverse region E ⊥ density for dijet events h d ∑ E ⊥ / d η d φ i [ G e V ] . . . . . . . . . . . | η | M C / D a t a (a) b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py − − ATLAS dijet azimuthal decorrelation for 160 < p max ⊥ /GeV < / σ d σ / d ∆ φ [ π / r a d ] . . . . . . . . . . . ∆ φ [rad/ π ] M C / D a t a (b) b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py − ATLAS -to- jet ratio for p jets ⊥ >
60 GeV, R = [ d σ / d H ( ) T ] ≥ / [ d σ / d H ( ) T ] ≥
200 400 600 800 1000 12000 . . . . . . . . H ( ) T [GeV] M C / D a t a (c) b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py ATLAS inclusive jet multiplicity, R = σ [ p b ] . . . . . . . . N jet M C / D a t a (d) Figure 3:
Observables showing the effect of pThard and pTdef variations. The 3-digit tuple used in theplot legends represents the P
YTHIA HED flag combination as described in the text. b b b b b b b b b b b b b b b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py . . . . . . . . . CMS -jet to -jet cross-section ratio vs. H T R . . . . . . . . . . . . H T [TeV] M C / D a t a (a) b b b b b b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py − − CMS dijet azimuthal decorrelation, 80 < p leading T <
110 GeV σ d σ d ∆ φ [ r a d − ] . . . . . . . . . . . . . . ∆ φ [rad] M C / D a t a (b) b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py − − − CMS ungroomed jet mass in dijets, ( p T + p T ) /2 = – GeV / σ d σ ) / d ( m + m ) [ / G e V ] . . . . . . ( m + m ) /2 [GeV] M C / D a t a (c) b b b b b b b b b b b b b b b Data b POWHEG+Py
POWHEG+Py
POWHEG+Py
POWHEG+Py − − − CMS pruned jet mass in dijet events, ( p T + p T ) /2 = – GeV / σ d σ ) / d ( m + m ) [ / G e V ] . . . . . . . . ( m + m ) /2 [GeV] M C / D a t a (d) Figure 4:
Observables showing the effect of pThard and pTdef variations. The 3-digit tuple used in theplot legends represents the P
YTHIA HED flag combination as described in the text.
10e note that since the majority of these predictions fall within the experimental uncertaintiesand are hence viable competing models, but there are significant differences between them insidethe experimental bands, pTdef variations may be a useful handle through which to estimatesystematics uncertainties in P
OWHEG +P YTHIA matched simulations. α S dependence of matched observables We conclude this short exploration of formal freedoms in P
OWHEG +P YTHIA
NLO matchingby studying the effect of different forms of the running strong coupling α S ( Q ) in the partonshower. The P OWHEG matrix element necessarily uses an NLO α S running with fixed value α S ( M Z ) ∼ α S should itself use such a coupling.But a counter-argument is that the parton shower, as an iterated approximation to the trueQCD matrix elements for many-emission evolution, requires a large α S value to compensate formissing physics. This argument is formally expressed in the proposal for “CMW scaling” [36]of a “natural” α S , in which its divergence scale Λ QCD is scaled up by an N F -dependent factorbetween 1.5 and 1.7. Such a scaling increases the effective α S ( M Z ) of a “bare” NLO strongcoupling. And empirically a fairly large α S is found to be preferred in MC tuning [37, 38, 39], inparticular for description of final-state effects like jet shapes and masses. These large couplingscan become as dramatic as α S ( M Z ) ∼ α S running is more appropriate in P OWHEG matching is also an open questionwith arguments possible in both directions.Since several arguments can be made for using α S ( M Z ) values between 0.12 and 0.14 (respec-tively, consistency, CMW, and naked pragmatism), rather than explicitly perform CMW or similarscalings, we have explored 6 configurations with α S ( M Z ) ∈ { } (”NLO-like”, ”LO-like” and ”enhanced LO”, respectively), and 1-loop and 2-loop running in each. Observablesdemonstrating these variations, each using 10M events with identical α S configurations in ISRand FSR showers, can be found in Figures 5 and 6.In Figure 5 all variations are grouped tightly within the experimental uncertainty band, but aclear trend of higher α S producing lower cross-sections is visible. A similar effect is visible in thedijet cross-section as a function of dijet mass, with all bins favouring a strong α S ( M Z ) = p T spectra. The samestrong α S settings are slightly but consistently preferred by the 3/2 jet ratio data, and thetransverse energy flow also favours a large coupling, although not quite so extreme: either 1-loop α S ( M Z ) = α S ( M Z ) = Or themselves , since P YTHIA ’s initial- and final-state showers can have separate couplings, and both participate inNLO matching. b b b b b b b b b b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . − − − ATLAS inclusive jet p T cross-section, anti- k t . ( | y | < d σ / d p ⊥ d y [ p b / G e V ]
100 200 300 400 500 600 700 800 900 10000 . . . . . . . p ⊥ [GeV] M C / D a t a (a) b b b b b b b b b b b b b b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . ATLAS dijet mass cross-section, anti- k t . (2.0 ≤ y ∗ < d σ / d m d y ∗ [ p b / T e V ] . . . . . . . . . . . . . . . . m [TeV] M C / D a t a (b) b b b b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . − ATLAS -to- jet ratio for p jets ⊥ >
60 GeV ( R = [ d σ / d p l e a d ⊥ ] ≥ / [ d σ / d p l e a d ⊥ ] ≥
100 200 300 400 500 600 700 8000 . . . . . . p ⊥ (leading jet) [GeV] M C / D a t a (c) b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . . . . ATLAS transverse region E ⊥ density for dijet events h d ∑ E ⊥ d η d φ i [ G e V ] . . . . . . . . . . . | η | M C / D a t a (d) Figure 5:
Observables showing the effect of α S variation, in tandem for P YTHIA ’s ISR and FSR partonshowers. The legend indicates the values of α S ( M Z ) used to fix the running coupling, andwhether a 1-loop or 2-loop β -function is being used. S ( M Z ) have a similar magnitude of effect to the switches between 1-loop (“LO”) and 2-loop(“NLO”) running.This is interesting: there is a fairly strong preference across much “ISR-influenced” data fora large shower coupling with α S ( M Z ) ∼ OWHEG -matched simulation. Moregenerally, α S variations on this scale again provide useful coverage of experimental error bandsand are hence a useful systematic handle on P OWHEG simulation.But FSR-dominated jet shapes and masses usually have a strong preference (if only due to thenarrowness of jet shape experimental uncertainty bands) for a slightly smaller α S ( M Z ) ∼ α S ( M Z ) ∼ α S ( M Z ) ∼ α S ( M Z ) to the default 0.13 andvarying the other, and vice versa, with results shown in Figure 6.The results are illuminating: while as usual changes in the ISR shower have little effect on jetmasses, they also have no effect on jet p T – a classic “ISR” observable. This pattern was repeatedfor all “ISR observables”, with virtually zero effect of the ISR shower coupling in all cases. Theonly variable to exhibit ISR shower sensitivity is the soft-QCD-dominated transverse energyflow, which is equally determined by ISR and FSR showering. While na¨ıvely counter-intuitive,this makes perfect sense: the P OWHEG hard process is providing almost all the ISR effects, andleaving little phase space for the initial-state shower to produce effects on hard jet observables.These plots hence illustrate that the FSR shower configuration can have significant effects uponP
OWHEG matching, and that there is a tension between the higher FSR α S desired to describe3/2 jet ratios and multi-jet mass spectra, and the slightly lower values to describe intra-jet effectssuch as single-jet masses. In this note we have explored several freedoms in P
YTHIA
OWHEG -B OX MC generator. Thesehave included discrete options for defining and calculating the P
OWHEG emission vetoing scale,and the continuous freedom to vary the strong coupling in P
YTHIA ’s parton showers.All these freedoms are permitted within the fixed-order accuracy of the P
OWHEG method, butit is clear that some will be better choices than others. We have hence considered the full set of7 TeV pp data analyses available from the ATLAS and CMS collaborations, via the Rivet analysissystem, to determine both whether there is an unambiguously preferred interpretation of theP OWHEG matching scheme, and whether “reasonable” variations on the nominal scheme can be13 b b b b
Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . . . . . ATLAS high- p T jet mass, R = p T >
300 GeV, | η | < / N · d N / d M [ G e V − ]
20 40 60 80 100 120 1400 . . . . . . . . . . Jet mass [GeV] M C / D a t a (a) b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . . . . . ATLAS high- p T jet mass, R = p T >
300 GeV, | η | < / N · d N / d M [ G e V − ]
20 40 60 80 100 120 1400 . . . . . . . . . . Jet mass [GeV] M C / D a t a (b) b b b b b b b b b b b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . − − − − ATLAS incl. jet p T cross-section, anti- k t . ( | y | < d σ / d p ⊥ d y [ p b / G e V ]
200 400 600 800 1000 1200 14000 . . . . . . . . . . p ⊥ [GeV] M C / D a t a (c) b b b b b b b b b b b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . − − − − ATLAS incl. jet p T cross-section, anti- k t . ( | y | < d σ / d p ⊥ d y [ p b / G e V ]
200 400 600 800 1000 1200 14000 . . . . . . . . . . p ⊥ [GeV] M C / D a t a (d) b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . . . . ATLAS transverse region E ⊥ density for dijet events h d ∑ E ⊥ d η d φ i [ G e V ] . . . . . . . . . . . . . . . | η | M C / D a t a (e) b b b b b b Data b POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . POW+Py α s . . . . ATLAS transverse region E ⊥ density for dijet events h d ∑ E ⊥ d η d φ i [ G e V ] . . . . . . . . . . . . . . . | η | M C / D a t a (f) Figure 6:
Observables showing the effect of α S variation. The legend indicates the values of α S ( M Z ) usedto fix the running coupling, and whether a 1-loop or 2-loop β -function is being used. The left-hand column is for variation of the ISR shower α S only, and the right-hand column for variationof the FSR α S only. Due to P OWHEG matching, the ISR shower has essentially no effect, even on“ISR observables”. sed to estimate systematic uncertainties from the matching, to be combined with fixed-orderscale uncertainties.We conclude that the default P
YTHIA main31 ” matching configuration is a viable matchingscheme but it is not unique in this. The calculation of the “hardness” of a proposed partonshower emission must necessarily be chosen to match that used in the P OWHEG hard process,on pain of huge data/MC discrepancies – but there is much less clarity about the choice of p T definition to be used in the scale calculation and (less importantly) the approach taken torecalculate the P OWHEG
ME event’s veto scale. The data suggests that in observables concernedmore with jet multiplicity than kinematics, an alternative p T definition may perform better, andthat in general variations of p T definition may be a useful handle on P OWHEG –P YTHIA matchinguncertainty.Variations of the strong coupling in the P
YTHIA α S ( M Z ) values also gave good coverage of the experimental data uncertainties,and provide an alternative route for systematics evaluation. Interestingly, the P OWHEG matchinghas been seen to almost completely eliminate sensitivity to the P
YTHIA initial-state partonshower in inter-jet observables like jet p T and multi-jet masses – the final-state shower, oftencaricatured as only affecting intra-jet observables like jet shapes and masses, is responsible foralmost all shower effects on observables, even those dominated by ISR. Obviously this simplyreflects the fact that P OWHEG vetoing constrains the emission phase space of the initial-stateshower far more than the final-state one, but it may have implications for NLO-matched showergenerator tuning, e.g. using the FSR coupling to optimise “ISR observables” and the ISR showerfreedom to purely improve the description of soft effects like underlying event and transverseenergy flow.
Acknowledgements
This work was supported by the European Union Marie Curie Research Training NetworkMCnetITN, under contract PITN-GA-2012-315877. Our thanks to Stefan Prestel for several usefuldiscussions, insights into the P
YTHIA matching options, and admirable tenacity in awaiting theoverdue completion of this paper!
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