QCD radiation effects on the signal at the LHC
Abstract:
The discovery of a Standard Model Higgs boson is possible when experimental cuts are applied which increase the ratio of signal and background crosssections. In this paper we study the signal crosssection at the LHC which requires a selection of Higgs bosons with small transverse momentum. We compare predictions for the efficiency of the experimental cuts from a NNLO QCD calculation, a calculation of the resummation of logarithms in the transverse momentum of the Higgs boson at NNLL, and the event generator MC@NLO. We also investigate the impact of various jetalgorithms, the underlying event and hadronization on the signal crosssection.
CavendishHEP08/01
1 Introduction
Physical processes at collider experiments can be simulated using flexible event generators such as PYTHIA [1] and HERWIG [2]. In this approach, the momenta of partons in hard scattering processes are distributed among hadrons using an approximate probabilistic algorithm for parton branching and hadronization. Traditionally, event generators compute the hard scattering partonic crosssection at leading order in fixed order perturbation theory which yields only a rough estimate.
Crosssections for the hard interaction of three or four particles can be computed routinely through nexttoleading order (NLO) in the expansion. The results from NLO QCD calculations and parton shower event generators are often combined with an empiric method. First the efficiency of the experimental cuts and normalized differential distributions are computed with parton shower event generators. Then, they are multiplied with the result for the total crosssection from the NLO calculation ^{1}^{1}1Note that differential “factors” to reproduce bin integrated differential distributions at higher orders in perturbation theory are also used [3, 4].. However, it is now understood how to combine parton shower generators and NLO results with theoretically sound methods so that (i) leading logarithms are resummed with the parton shower, and (ii) all differential crosssections are exactly accurate through NLO upon an expansion of the Sudakov factors in [5, 6].
Fixed order perturbative computations have now advanced beyond the next to leading order, and there are two hadron collider processes which are known through nexttonexttoleading order (NNLO) in . The NNLO total crosssection of the DrellYan process [7, 8] is the most precise theoretical prediction for a hadron collider observable with a scale variation uncertainty of about . The total crosssection for Higgs boson production is also known at NNLO [8, 9, 10, 11, 12]. For the LHC, the NLO [13, 14] and NNLO corrections are both important and increase the LO result by about and respectively. The perturbative series converges slowly and the remaining theoretical uncertainty is about [15, 8, 9, 10, 11, 12].
In Higgs boson [16, 17, 18] and electroweak gauge boson [19, 20, 21, 22] production there exist novel differential crosssection calculations at NNLO [16, 17, 19, 20, 21, 22, 18] ^{2}^{2}2In nonhadronic collisions the state of the art at NNLO is fully differential crosssections for [23, 24, 25].. The crosssections with arbitrary experimental cuts applied at the parton level can be computed exactly at this order in pertubration theory for the two processes. It is very instructive to compare the efficiencies of experimental cuts from the newly available fully differential NNLO calculations, merged NLO and partonshower calculations with MC@NLO, and simple leading order event generators. This is valuable in order to estimate the inherent theoretical uncertainties of the above approaches.
Such a comparison can be made for the DrellYan process with the results from Refs. [21, 22, 26], as well as discussed in Ref. [21]. MC@NLO and the NNLO MonteCarlo FEWZ [21, 22] predict very similar experimental efficiencies for the entire kinematic range where the NNLO prediction retains its phenomenal scale variation of about . Significant differences, however, arise when the experimental cuts suppress contributions from the twoloop matrix elements.
A similar comparison [27] between MC@NLO and the NNLO partonic MonteCarlo FEHiP has been made for the Higgs boson diphoton signal at the LHC. The signal crosssection is known with a scale uncertainty of about at NNLO [17]. Besides a relatively large perturbative correction from NLO to NNLO of about , the efficiency of the experimental cuts turns out to be very similar in MC@NLO and NNLO [27].
A challenging channel for the Higgs boson discovery at the LHC is . This channel is contaminated by background processes, and , with much larger crosssections. For a Higgs boson with a mass close to the Wpair threshold, the crosssections for all other discovery signals are suppressed. In this case, the process becomes the only viable channel for the Higgs boson to be discovered at the LHC. It is thus indispensable to achieve a very good signal to background (S/B) ratio. An optimized selection of Wpair events [28] is then required. If appropriate cuts are applied, as in Refs. [29, 30, 31, 32], a discovery of a Standard Model Higgs boson with a mass close to the threshold should be achieved with an integrated luminosity of a few at the LHC.
The decay mode was recently implemented in the NNLO MonteCarlo FEHiP [17] and a calculation of the crosssection with the experimental cuts of Ref. [29, 30] was performed in Ref. [33]. The very good agreement of the MC@NLO and NNLO calculations for the efficiency of the experimental cuts in the diphoton signal [27, 17, 5] does not guarantee that a similarly good agreement will be found in the channel. In this paper, we will compare the NNLO predictions from Ref. [33] with resummation calculations and event generators.
In the channel, the experimental cuts select events “democratically”, irrespectively of the transverse momentum of the jets associated with the Higgs boson production. The event selection in the channel [30, 31] imposes an explicit jetveto and other cuts which reject events with large transverse momentum for the Higgs boson. This may turn out to be problematic for an agreement in experimental efficiencies between MC@NLO and NNLO for two reasons. First, the NNLO/NLO factor is sensitive to the cutoffs imposed on the [34, 16, 17]; this effect is treated only in the parton shower approximation in MC@NLO. Second, by selecting events with low , multiple gluon radiation effects which are not included in the fixed order NNLO calculation may be important.
The resummation through nexttonexttoleading logarithms (NNLL) of is now achieved [35, 36, 37]. The resummed spectrum, after matching to fixed order, integrates to the NNLO total crosssection. This calculation takes into account consistently both multiple gluon radiation effects at low transverse momentum and fixed order high transverse momentum contributions.
A theoretical prediction for the signal crosssection cannot be made directly from the spectrum, since the experimental cuts restrict many phasespace variables. The crosssection must therefore be computed using fully differential MonteCarlo programs. However, we will use the resummation calculation of the spectrum [38, 36, 37] to validate fixed order MonteCarlo’s and parton shower event generators in the low kinematic region, which is favored by the experimental selection cuts.
We first compare in Section 2 the theoretical calculations from the NNLL resummation [38], MC@NLO [5] and NNLO [33] for the spectrum. Then we compare in Section 3 the MC@NLO [5], HERWIG [2] and NNLO [33] MonteCarlo predictions for kinematic distributions of variables which are restricted by the experimental selection.^{3}^{3}3In the case of MC@NLO and HERWIG, we use a modified version of HERWIG with the correct decay angular correlations. We perform a similar comparison for the signal crosssections when all cuts are applied. We find a good agreement for the efficiencies of experimental cuts and normalized kinematic distributions. This gives us confidence that the selection of events for the signal crosssection does not invalidate the approximations in the used MonteCarlo programs.
In Section 4 we study the sensitivity of the signal crosssection with all experimental cuts applied to the choice of jet algorithm. We find a mild change on the crosssection () by using the SISCone or the algorithm. We also study the effect of hadronization (using the model in HERWIG [2]) and of the underlying event (using the JIMMY model [39]). We find that proposed experimental cuts render the crosssection sensitive to these effects at the level of up to . The changes to the crosssection are with opposite signs and the combined effect is rather mild.
2 Integrating over the transverse momentum of the Higgs boson
In this Section we compare fixed order [17] and parton shower calculations [2, 5] against the theoretical predictions for the transverse momentum spectrum of the Higgs boson from resummation [38]. Fixed order perturbation theory is invalid for small values of . Nevertheless, observables can be reliably computed if their definition allows for an integration over a sufficiently large range in values. Here, we study the cumulative crosssection
(1) 
This observable mimics the effect of selection cuts with a cutoff on the maximum Higgs transverse momentum. Since in the transverse plane the Higgs boson balances the associated jet radiation, the crosssection with a jetveto is similar to the crosssection with a veto on high values of .
In Fig. 1 we plot the crosssection in the fixed NLO and NNLO expansion. As in all plots of this paper, we show the scale variation in the interval . The fixed order crosssections at NLO and NNLO become negative and tend to infinity when the cutoff is small (below ). For such small values of perturbation theory breaks down. We observe that for larger cutoffs (above and up to ) the NLO and NNLO results are in very good agreement. The NNLO crosssection increases however faster than NLO with higher cutoffs leading to the known by larger NNLO result with respect to NLO for the total crosssection [8, 9, 10]. The analyses in Ref. [29, 30] show that a better S/B ratio is achieved if stricter than 40 cutoffs are used for the jet transverse momenta; for cutoff values in between and we observe large perturbative corrections.
In Fig. 2 we compare the fixed NLO result with the resummed NLL spectrum from Ref. [38] and with MC@NLO [5] without hadronization and underlying event. We find that for the parton shower or the NLL resummation change significantly the integrated NLO distribution. All results converge for higher and higher cutoffs and agree with each other for the fully inclusive crosssection. Notably, the MC@NLO and the NLL resummation are in a rather good agreement with each other within the uncertainties from scale variation.
Differences between crosssection predictions with fixed order perturbation theory and resummation are expected to become smaller when the fixed order calculations are extended to higher orders.
In [33] it was found that the average of the Higgs boson, when discovery selection cuts are applied, can be as low as . This leads to the question whether the NNLO result, unlike the NLO result, is a reliable prediction for such small values of the average . In Fig. 3 we compare the integrated distribution at NNLO against the resummed NNLL spectrum. We find a very good agreement between the two approaches for surprisingly low values of . We conclude that higher than NNLO perturbative contributions, which are accounted for with the resummation, remain small for the integrated spectrum, when the maximum Higgs transverse momentum is restricted even down to .
We have now validated the NNLO perturbative calculation [33] in a challenging case for fixed order perturbation theory which similarly emerges, due to the jetveto and other cuts favoring small values, in the search for a Higgs boson in the decay channel. However, the simulation of processes at NNLO is only performed at the parton level. We would like to investigate whether parton shower MonteCarlo programs, which can also model nonperturbative effects and are computationally more flexible than NNLO MonteCarlo’s, provide realistic estimates of the signal crosssection.
We first discuss the problem of the normalization of the event generators. Parton shower MonteCarlo programs predict the same total crosssection as the crosssection for their encoded partonic hard scattering at fixed order in perturbation theory. Therefore, HERWIG predicts the Higgs boson total crosssection with LO accuracy (underestimating it by a factor of ) and MC@NLO provides NLO precision (underestimating the total crosssection by a factor of ). A matching of parton showers to NNLO fixed order calculations is not yet developed. Following a practical approach, we will validate whether the efficiency of experimental cuts and normalized differential distributions are in agreement with the NNLO calculations of Ref. [33]. We will then rescale the predictions of the MC@NLO and HERWIG event generators with a global factor in order to reproduce the fixed order result for the total crosssection. We will denote that the results of the MonteCarlo have been multiplied with a factor using the notation .
Now we will test how well event generators agree with resummation results for the spectrum. In Fig. 4 we compare the integrated spectrum of MC@NLO and HERWIG against the resummed NNLL prediction. We observe that both generators are in very good agreement with the NNLL spectrum. This is especially surprising for HERWIG which aims to describe the salient physics features of the process. Note, however, that MC@NLO gives slightly larger and HERWIG slightly smaller values than the NNLL resummation [38].
Before we conclude our analysis of the integrated distribution we wish to comment further on the scale variation of the fixed order results. In Fig. 1 we find a with no scale variation. A similar behavior is also observed for the accepted crosssection with all experimental cuts [29, 30] in Ref. [33]. It is therefore necessary to investigate in better detail the variation of the NNLO result. We show the value of the crosssection at NNLO for , varying independently the renormalization and factorization scales (the errors correspond to the numerical integration):
The crosssection is more sensitive to independent variations of the renormalization and factorization scales; however, this variation is significantly smaller than in the total crosssection. A detailed study of the crosssection when all experimental discovery cuts are applied, which shows a similar scalevariation pattern, has been made in Ref. [33].
Summarizing, in this Section we found that the integrated spectrum is predicted reliably at NNLO for the kinematic range of which is relevant in the search . On the contrary, the NLO fixed order calculation is unreliable. We have also established that for the same observable, MC@NLO and HERWIG are in a very good agreement with the resummed NNLL spectrum when they are normalized to a common NNLO total crosssection.
3 Kinematic distributions and signal crosssection
The main backgrounds for the process are and . These backgrounds are sufficiently suppressed to allow for the discovery of a Higgs boson with a combination of experimental cuts [29, 30], exploiting the spincorrelations in the decay of the Higgs boson and the high average transverse momentum of jets in toppair events. In Ref. [33], the signal crosssection with these cuts was computed at NNLO. In this section we will compare the NNLO results of Ref. [33] with MC@NLO. The public version of MC@NLO includes only partial spincorrelations for the decay. Here, the full spincorrelations for the decay of the Higgs boson have been implemented in MC@NLO. All the results of this paper correspond to a Standard Model Higgs boson mass of .
In Figs. 58 we present the crosssections when a single cut is applied on

, the invariant mass of the charged lepton pair,

, the angle between the two charged leptons in the plane transverse to the beam axis,

, the transverse momentum of the harder lepton, and

, the missing transverse energy.
The four distributions show an excellent agreement for the efficiencies among NNLO and MC@NLO. This is a remarkable result and could not have been easily foreseen; there is a significant change in the shape of the , , and distributions from NLO to NNLO, as seen in Ref. [33].
A crucial experimental cut for suppressing the toppair contribution to the background is a jetveto. We veto events which have a transverse momentum of the leading jet in the central rapidity region () that is larger than . For the jet definition we use here a algorithm with a jetradius parameter ; later we will also use a cone algorithm (SISCone [40]). The two algorithms are identical for the LO and NLO calculation where only up to one parton can be present in the final state, if the same jetradius is used. They differ, however, in the parton shower calculations (MC@NLO and HERWIG) and at NNLO as more partons are generated. In the envisaged experimental analysis a jetveto with a rather small value of is considered. We will investigate whether the NNLO and MC@NLO predictions are consistent with each other for such small values of the jetveto.
The good agreement of the integrated distribution between NNLO, MC@NLO and NNLL resummation suggests that a good agreement between MC@NLO and the NNLO crosssections with a jetveto may also hold. The jetveto crosssection should be qualitatively similar to the crosssection with a cutoff on the since at NLO the Higgs transverse momentum corresponds exactly to the transverse momentum of the additional jet. However, the two cuts are not exactly the same and they compare only qualitatively. The jetveto applies only at central rapidities; in addition, beyond NLO the is not the same variable as the maximum transverse momentum of the jets.
In Fig. 9 we present the crosssection with a jetveto applied. Indeed, we find a very good agreement between the NNLO result and MC@NLO (rescaled with the appropriate NNLO/NLO factor for the total crosssection).
In Table 1 we list the crosssection after all signal cuts as described in Ref. [33] are applied. We have used both the and SISCone algorithm of Ref. [40] and their implementation from Ref. [41]. The jet radius in the azimuthrapidity plane was set to and the merging parameter for the SISCone algorithm to ^{4}^{4}4The merging parameter defines, how much two separate protojets need to overlap in order to be merged into one jet.. The two algorithms yield formally identical results for the fixed order calculation through NLO and indistinguishable results at NNLO within our MonteCarlo integration precision ^{5}^{5}5We thank Gavin Salam for pointing out to us that the SISCone and algorithms are formally different already at NNLO.. In the first section of the Table we present the results obtained using a fixedorder LO computation and the LO+partonshower event generator HERWIG. We find a much larger fixed order result than when a parton shower is added. At fixed leading order all events have a Higgs boson with zero transverse momentum, and the jetveto rejects none of the events. On the contrary, HERWIG generates a large fraction of events with .
[]  

jet algorithm  SISCone  SISCone  
LO  
HERWIG  
NLO  
MC@NLO  
(HERWIG)  
NNLO  
(MC@NLO)  
(HERWIG) 
In the second section of Table 1 we present the results obtained using a fixedorder NLO computation, the event generator MC@NLO and HERWIG after we have rescaled it with an inclusive NLO/LO factor. While in MC@NLO and fixed order (LO, NLO and NNLO) we can set the renormalization and factorization scales for the hard scattering at will, we use HERWIG at the default scale since this affects the triggering of the hadronization procedure. We then rescale the HERWIG result using a factor, taking the NLO fixed order result to be at the scale or . The NLO result is quite different from the one obtained with MC@NLO. We can attribute this failure of the NLO computation to the poor modeling of the low region, as is shown in Fig 2.
In the last part of Table 1 we present the results obtained using a fixedorder NNLO computation and the results from MC@NLO and HERWIG, rescaled to the NNLO total crosssection. The NNLO result and the rescaled MC@NLO give consistent results, albeit with different behavior when varying the renormalization and factorization scales. A detailed analysis of the NNLO scale dependence when all cuts are applied can be found in Ref. [33].
We note that for all the results of this section we use MC@NLO and HERWIG at the parton level, switching off the hadronization and without using a model for the underlying event. We observe that the algorithm gives larger crosssections than the SISCone algorithm for MC@NLO and HERWIG; as mentioned before, the results for the two algorithms are very similar at fixed order through NNLO (within our integration precision). Additionally MC@NLO gives slightly smaller values for the crosssections than HERWIG.
We have established in this section that the efficiency of experimental cuts computed with MC@NLO and HERWIG is similar to the efficiency obtained at NNLO. There are rather dramatic changes in differential distributions when going from NLO to NNLO [33]. It is only at NNLO that the fixed order calculation is consistent with the parton shower efficiency of the experimental cuts. In the following Section we will study the dependence of the crosssection on effects that are not captured by the fixed order NNLO calculation. We will study the effect of hadronization and of the underlying event. We will also investigate further the differences in the crosssection due to the two different jet algorithms.
4 Jet algorithms, hadronization and the underlying event
In this Section we perform a study of the signal crosssection with all cuts applied using MC@NLO. We will analyze the impact of different jet clustering methods, hadronization and the underlying event.
In Fig. 10 we plot the crosssection using MC@NLO as a function of the value for the and the SISCone algorithm with a jetradius and . The clustering is applied to all final state particles before hadronization.
We find that for small values of the jetveto parameter the choice of the jet clustering method is more significant. For a jetveto at the choice of jetalgorithm changes the crosssection by with MC@NLO. A similarly large variation of is observed when we vary the jetradius from to . For a jet veto value larger than about the sensitivity of the crosssection to the choice of the jetalgorithm or the jetradius falls below .
We now study the effect of hadronization as it is modeled in HERWIG and of the underlying event as implemented in JIMMY [39]. In Fig. 11 we present the relative difference of the crosssection with respect to the partonic crosssection when the hadronization or/and the underlying event models are switched on. We have used here the SISCone algorithm with a merging parameter and two values for the jetradius R=0.4 (left) and R=0.7 (right). We apply the signal cuts set to the values which are used in Ref. [33]. We vary, however, the allowed maximum value of . Of interest are values of the jetveto between 25 and 40 , which are envisaged in the Higgs boson search.
Qualitatively, we anticipate that the hadronization and the underlying event change the partonic crosssection with opposite signs (we refer the reader to the recent analysis in Ref. [42] for a detailed study). Hadronization reduces the average of (gluonic) jets by roughly . The underlying event increases the jet by roughly at the LHC. The slope of the partonic crosssection with the jetveto cutoffs (Fig. 9) is large for small values of the jetveto. The shifts from hadronization and the underlying event can therefore induce significant changes to the crosssection. A jetveto after hadronization corresponds to a looser effective jetveto at the parton level. We therefore anticipate the crosssection to increase by switching on the hadronization model. Similarly, we anticipate a decrease of the crosssection due to the underlying event.
The trends can be verified in Fig. 11. A smaller jetradius increases the impact of hadronization and decreases the impact of the underlying event. The two effects are not linearly additive. However, we find that a cancelation between the two effects, which varies according to the jetradius, takes place. For a jet veto and a radius , the hadronization shift is about and the underlying event shift is . For a larger radius , the two shifts are and correspondingly.
In Fig. 12 we show the effects of hadronization and the underlying event for the algorithm. We find the same features qualitatively for the two effects as in the SISCone algorithm. We note however, that the algorithm shows an overall reduced sensitivity.
5 Conclusions
In this paper we have studied QCD effects for the process . This process is of particular interest at the LHC since it is possible that for a range of mass values of the Higgs boson, this channel is the only viable one for a discovery.
The crosssection with all envisaged experimental cuts applied was computed in an earlier publication [33] at NNLO in QCD. In this paper we compared these NNLO results with the leading order event generator HERWIG [2] and the event generator MC@NLO [5] which performs a matching of HERWIG with NLO fixed order perturbation theory. We found very good agreement in efficiencies of all experimental cuts that are relevant in the search for the Higgs boson. This is rather spectacular given that there are significant corrections in the total crosssection and the shape of kinematic distributions from NLO to NNLO.
The experimental cuts select events with small transverse momentum of the Higgs boson. This is important in order to reduce the selection of events from topquark production, which is a major background. We have compared a NNLO computation and the result of NNLL resummation [38] for the cumulative distribution. We found that NNLL resummation does not induce significant corrections with respect to the NNLO calculation for the kinematic range which is favoured by the selection cuts. We have also found that, within the uncertainty from scale variations, MC@NLO and HERWIG are in very good agreement with the NNLL result. On the contrary, fixed order NLO perturbation theory provides a rather poor approximation for the required distributions and efficiencies.
Finally, we investigated the magnitude of effects due to hadronization, the underlying event, and the choice of jet algorithms. For typical choices of parameters and cutoffs in the experimental cuts we find a mild dependence of the crosssection on these effects. In this paper we did not examine a variety of remaining uncertainties, such as uncertainties in the parton densities, which may be relevant at a precision level of 10%. Studies of electroweak corrections can be found in Refs. [43, 44, 45] and of the backgroundsignal interference in Ref. [46].
The results and comparisons made in this paper provide a firm validation of the fixed order NNLO results and the event generator tools which are available for simulating the process at the LHC.
Acknowledgements
We thank Michael Dittmar, Stefano Frixione, Massimiliano Grazzini and
Giulia Zanderighi for useful discussions and suggestions.
This research was supported by the Swiss
National Science Foundation under contracts 200021117873
and 200020113378/1.
We thank Gavin Salam
for pointing out to us that the SISCone and
algorithms are formally different at NNLO.
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