Measuring Di-Higgs Physics via the t t ¯ hh→t t ¯ b b ¯ b b ¯ Channel
MMeasuring Di-Higgs Physics via the t ¯ thh → t ¯ tb ¯ bb ¯ b Channel
Tao Liu ∗ and Hao Zhang † Department of Physics, The Hong Kong University of Science and Technology,Clear Water Bay, Kowloon, Hong Kong, P.R.China Department of Physics, University of California, Santa Barbara, California 93106, USA
The measurement of di-Higgs physics can provide crucial information on electroweak phase transi-tion in the early Universe and significant clues on new physics coupling with the Higgs field directly.This measurement has been suggested to be pursued mainly via the pp → hh production. In thisletter, we propose a new strategy to do that, i.e., via the pp → t ¯ thh production. Because of itspositive correlation with the rescaled tri-Higgs coupling λλ SM (in comparison to a negative one forthe pp → hh production) in the neighborhood of λλ SM ∼
1, the pp → t ¯ thh production complementsthe pp → hh one in measuring di-Higgs physics, particularly for λλ SM >
1, at both the High Lumi-nosity LHC (HL-LHC) and a next-generation pp -collider. As an illustration, we work on the process pp → t ¯ thh → t ¯ tb ¯ bb ¯ b . We show that a statistical significance of > . σ at the HL-LHC, comparable tothat of the pp → hh → b ¯ bγγ channel, and a statistical significance of ∼ σ at a 100 TeV pp -collider,with 3000 fb − of data, are achievable in searching for the di-Higgs production with λλ SM = 1. INTRODUCTION
The measurement of di-Higgs physics plays an im-portant role in particle physics and cosmology. In thestandard model (SM) of particle physics, the Higgs fieldinduces electroweak (EW) phase transition (EWPT) asan order parameter, by interacting with itself, while themeasurement of di-Higgs physics can provide informationin this regard, given the involvement of the tri-Higgs cou-pling λ in the di-Higgs production.This may have important implications in cosmology.As is well known, if the EWPT is of strong enough firstorder, the cosmic baryon asymmetry (CBA) could begenerated via EW baryogenesis. In the SM, however,such an EWPT requires a Higgs boson much lighter than125 GeV, and hence can not be achieved without violat-ing the current experimental bounds. To achieve thisgoal, several mechanisms were introduced in the SM ex-tensions: (1) by introducing loop-corrections mediatedby new scalar particles to the effective Higgs potential;(2) by incorporating nonrenormalizable operators such as | H | Λ in the effective Higgs potential; and (3) by mixingthe Higgs field with a singlet scalar at tree level. No mat-ter in which case, there is a strong correlation betweenthe EWPT dynamics and the tri-Higgs coupling. As be-ing pointed out in [1], at zero temperature, the tri-Higgscoupling favored by the mechanisms (1) and (2) could bea couple of times larger than its SM value λ SM , while thetri-Higgs coupling favored by the mechanism (3) couldbe as small as ∼ . λ SM .In addition to the tri-Higgs coupling, the di-Higgs pro-duction may receive contributions from new physics cou-pling with the Higgs field. The anomalous Higgs-top op-erator t ¯ thh Λ is such an example, which often arises in thelittle Higgs or the composite Higgs models by integratingout a heavy top partner [2, 3]. With an insertion into thegluon fusion loop, this operator can significantly modify the di-Higgs physics [4–6]. The measurement of di-Higgsphysics therefore provides a nice tool to probe both theEWPT and new physics coupling with the Higgs field.Because of this, the discovery of the Higgs boson in2012 [7, 8] immediately motivated a series of studies onthe measurement of di-Higgs physics at Large HadronCollider (LHC) and High Luminosity LHC (HL-LHC) atwhich 300 fb − and 3000 fb − of data are expected to becollected at each of the ATLAS and the CMS detecters,respectively [9–15], and at a next-generation pp -collider[16]. Currently the measurement of di-Higgs physics issuggested to be pursued mainly via: • Channel 1 [9, 11–15, 17]: pp → hh → b ¯ bγγ , b ¯ bτ τ , b ¯ bW W ∗ which provides the best sensitivity so far in measuringdi-Higgs physics, though some preliminary work has alsobeen done on [18] • Channel 2: pp → jjhh (for a recent review, see [19]). The production of bothchannels however has a negative dependence on λλ SM inthe SM neighborhood, with the differential cross sec-tion d ( σ/σ SM ) d ( λ/λ SM ) becoming less and less negative as λλ SM increases [20]. Both effects can suppress their sensitiv-ities in measuring the tri-Higgs coupling, particularly if λλ SM >
1. In addition, in both channels there exists adegeneracy of production cross section with respect to λλ SM . Breaking this degeneracy may further suppress thesensitivities. To explore the di-Higgs physics, therefore,a complementary strategy is needed, particularly in theparameter region with λλ SM > pp -colliders, say, via • Channel 3: pp → t ¯ thh . a r X i v : . [ h e p - ph ] D ec The t ¯ thh production has a cross section monotonicallyincreasing with respect to λλ SM [20], with the d ( σ/σ SM ) d ( λ/λ SM ) becoming more and more positive as λλ SM increases [20],which potentially enables it to fulfill our needs. A com-parison of the cross sections between the pp → hh pro-duction and the pp → t ¯ thh production are provided inTable I. Though its production cross section is an or- TABLE I: A comparison of the next-to-leading order (NLO)cross sections (in fb) of t ¯ thh and hh at pp -colliders [20]. √ s pp → t ¯ thh pp → hh
14 TeV 0 . +2 . . − . − . . +15+2 . − − .
100 TeV ∼ ∼ der smaller than the pp → hh one, the extra t ¯ t in the t ¯ thh events may suppress one order or orders more back-grounds. So, the t ¯ thh production opens a new avenueto measure di-Higgs physics at HL-LHC and a next-generation pp -collider, with the decays hh → b ¯ bb ¯ b , b ¯ bγγ , b ¯ bτ τ , b ¯ bW W ∗ , b ¯ bZZ ∗ , etc.As an illustration, we will focus on the pp → t ¯ thh production with hh → b ¯ bb ¯ b at the HL-LHC, which resultsin a sensitivity comparable to that of the pp → hh → b ¯ bγγ in searching for the SM di-Higgs production, andshortly discuss its sensitivity at a 100 TeV pp -collider.We would emphasize that this doesn’t mean that, for the t ¯ thh production, the hh → b ¯ bb ¯ b has a better sensitivityat a 100 TeV pp -collider, compared to its other decaymodes. ANALYSIS STRATEGY
In the analysis of measuring di-Higgs physics via pp → t ¯ thh → t ¯ tb ¯ bb ¯ b at the HL-LHC, we allow the top pairs todecay either semi-leptonically or leptonically (with (cid:96) = e, µ ). Unless indicated explicitly, the discussions belowon our strategies can be applied to both cases. In theanalyses, the main irreducible backgrounds include • pp → t ¯ tb ¯ bb ¯ b , • pp → t ¯ thb ¯ b, h → b ¯ b , • pp → t ¯ tZb ¯ b, Z → b ¯ b ,and the main reducible backgrounds include • pp → t ¯ tb ¯ bjj , • pp → t ¯ thjj, h → b ¯ b ,According to [21], a 70% b -tagging rate at 14 TeV LHCwill lead to a 2% mistag rate for light jets and a 24%mistag rate for charm jets, with a 50 pile-up assumed. Thus only charm jets will be considered for reduciblebackgrounds. The contributions of pp → t (¯ t ) + b -jets, W ± + b -jets, t ¯ thZ , t ¯ tZZ and t ¯ tZjj to the backgrounds arenegligibly smaller than that of the top-pair plus multi-jets events. So they will not be considered.Our analysis framework is described in the following.We use MadGraph5 [22] to generate leading-order (LO)signal and background events, with the CTEQ6L1 par-ton distribution function (PDF) [23] applied. All of thesignal and background events are showered by Pythia6.4[24]. We use DELPHES 3 [25] for detector simulationsin which the b -tagging efficiency and the mistag rate of c -jets are tuned to be 70% and 24%, respectively. To re-construct the Higgs invariant mass, the energy of b -jetsis rescaled by a factor1 . p p j b T + p (1)with p = 6 . p = − . , which is obtainedfrom the Zb → µ + µ − b process. [Preselection] In the analysis, electrons and muonsare isolated by passing the cut | η (cid:96) | < . , I iso < . . (2)Here I iso is energy accumulation (except the energy ofthe charged target lepton) in a ∆ R = 0 . p (cid:96)T >
20 GeV, and exactly twoisolated opposite-sign charged leptons with p (cid:96)T >
10 GeV,respectively.Jets are reconstructed by using anti- k T algorithm with∆ R = 0 . | η j | < . | η j | < .
5. We require at least 7jets with p jT >
20 GeV in the semi-leptonic top-pair caseand at least 5 jets with p jT >
20 GeV in the di-leptonictop-pair case. In addition, we require at least 5 of thembe tagged as b -jets. A cut for missing transverse energy /E T >
30 GeV is applied in the semi-leptonic top-pair caseand the leptonic top-pair case with a pair of charged lep-tons of the same flavor. In the latter case, we require thedi-lepton invariant mass satisfy | m (cid:96)(cid:96) − m Z | >
10 GeV , (3)with m Z = 91 . Z -boson decay. In the leptonic top-pair case with a pair ofcharged leptons of different flavors (i.e., eµ ), no /E T cutand Z mass window cut will be applied. [Reconstruction of di-Higgs resonances] The twoHiggs resonances are reconstructed by using b -jets in eachevent. Generically there is a combinatorial problem, dueto the fact that top quarks decay into a bottom quark anda W boson. To reconstruct the two Higgs resonances, wechoose a combination (( b , b ) , ( b , b )) among the tagged b -jets which gives the minimum of χ h ≡ (cid:115)(cid:18) m b b − m h σ h (cid:19) + (cid:18) m b b − m h σ h (cid:19) . (4)Here m h = 125 . σ h = 30 GeV are assumed. (GeV) bb m
50 100 150 200 250 E v en t s / G e V hhtt bbbbtt bbcctt hbbtt zbbtt hcctt L dt = 3000 fb ∫
14 TeV LHC,
FIG. 1: The m bb reconstruction for the two b ¯ b pairs whichminimize the χ h in each event after the preselection cut inthe semileptonic top-pair case. All events are required to pass the reconstruction cutof the di-Higgs resonances χ h < . . (5)In addition, one of the two selected b -jet pairs may havean invariant mass close to m h accidentally. In such acase, this cut may lose its effect since the second b -jetpair is allowed to have a relatively large deviation from m h . To increase the cut efficiency, we require (cid:18) m b b − m h σ h (cid:19) and (cid:18) m b b − m h σ h (cid:19) (6)be symmetric and neither of them is allowed to be largerthan 1.9. As a result, all of the signal and backgroundevents surviving of this cut should have two b -jet pairs,with their invariant masses deviating from m h in a com-parable way. [Reconstruction of top quark resonance] To sup-press the backgrounds with no top quarks, we may re-construct one of the top quarks in the signal events. Insemi-leptonic top-pair case, we reconstruct the leptonictop quark by using the charged lepton ( (cid:96) ), missing trans-verse energy ( ν ) and a reconstructed jet ( j ). Here the jet is not necessary to be b -tagged, but it should not beany one among b , b , b and b . The neutrino momen-tum along the beam-line direction is solved by using the W -boson mass-shell equation. Due to smearing effects,an imaginary solution is possible. So we require at leastone real solution. For the events which have two real so-lutions, we use both of them to calculate m j(cid:96)ν . Then allevents are required to pass a top-mass cutmin | m j(cid:96)ν − m t | < , (7)where m t = 173 . W +jets is negligiblysmall due to the suppression by the requirement of atleast seven jets with at least five of them b -tagged in eachevent. So in the next section, we will present the analysisresults, both with and without top-quark reconstruction.As for the di-leptonic top-pair case, the main non-topbackgrounds are Drell-Yan process for the ee and µµ channels, and di-boson+jets for the eµ channel, whichare also sub-dominant. So, no top reconstruction will beapplied in the di-leptonic top-pair case. SIMULATION RESULTS
The cut flows of the signal and the background eventsin the semi-leptonic top-pair and the di-leptonic top-pair cases are summarized in Table II and Table III,respectively. We find that the background contributedby faked c -jets is important and hence is not negligi-ble. The cut flows indicate that a statistical significancesas large as S/ √ B = 2 . σ (no top-quark reconstruction)and S/ √ B = 1 . σ (with top-quark reconstruction) canbe achieved in the semi-leptonic top-pair case. As forthe di-leptonic top-pair case, the statistical significance is S/ √ B = 0 . σ at the HL-LHC. The sensitivities in thesetwo analyses can be combined quadratically, which givesa sensitivity of 2 . σ (no top-quark reconstruction), incomparison to a statistical significance of 2 . σ expectedto be achieved at the HL-LHC via pp → hh → b ¯ bγγ , witha 75% b -tagging efficiency assumed [16]. TABLE II: Cut flows of searching for t ¯ thh → t ¯ tb ¯ bb ¯ b at the HL-LHC via the semi-leptonic top-pair channel. The unit used inthe table is attobarn. √ s = 14 TeV t ¯ thh t ¯ tb ¯ bb ¯ b t ¯ tb ¯ bc ¯ c t ¯ thb ¯ b t ¯ tZb ¯ b t ¯ thc ¯ c Preselection 39.0 390.6 353.1 222.7 126.8 98.2Di-Higgs rec. 33.0 269.3 242.1 171.0 93.5 76.8Top rec. 19.5 160.7 149.0 102.8 54.6 47.1
TABLE III: Cut flows of searching for t ¯ thh → t ¯ tb ¯ bb ¯ b at theHL-LHC via the dileptonic top-pair channel. The unit usedin the table is attobarn. √ s = 14 TeV t ¯ thh t ¯ tb ¯ bb ¯ b t ¯ tb ¯ bc ¯ c t ¯ thb ¯ b t ¯ tZb ¯ b t ¯ thc ¯ c Preselection 4.8 41.6 30.6 22.6 9.7 8.1Di-Higgs rec. 4.1 27.1 20.7 16.8 7.4 6.4
DISCUSSIONS
Leading-order discussions have been pursued, regard-ing the measurement of di-Higgs physics via the t ¯ thh channel. In the illustrational case with pp → t ¯ thh → t ¯ tb ¯ bb ¯ b , we show that a sensitivity comparable to that ofthe pp → hh → b ¯ bγγ channel is achievable in searchingfor the SM di-Higgs production at the HL-LHC, whichis very encouraging. However, we need to note that thedominant backgrounds in this case are t ¯ tb ¯ bb ¯ b and t ¯ tb ¯ bjj ,both of which have a cross section of order α S at treelevel. This may lead to a large theoretical uncertaintyin estimating the backgrounds. A calculation of higher-order corrections therefore is important for suppressingthis uncertainty. Alternatively, a data-driven methodmay help in this regard.At analysis level, a further improvement is certainlypossible. For example, we may introduce color-flow vari-ables such as the “pull angle” of b -jet pairs [26] to recon-struct the di-Higgs resonances, which has been shownto be useful in suppressing combinatorial backgroundsof multiple b-jets in both supersymmetric [27] and non-supersymmetric [28] contexts. In addition, we can ap-ply more advanced analysis tools, such as the tool ofjet-substructure and the multivariate method of BoostDecision Tree, which have been successfully applied formeasuring di-Higgs physics in the channels pp → hh → b ¯ bτ τ [9] and b ¯ bW W [14], respectively.More importantly, the pp → t ¯ thh provides a series ofnew opportunities to study di-Higgs physics at a next-generation pp -collider, with the decays hh → b ¯ bb ¯ b , b ¯ bγγ , b ¯ bτ τ , b ¯ bW W ∗ , b ¯ bZZ ∗ , etc. Though its production crosssection is an order smaller than that of pp → hh , the ex-tra t ¯ t in the t ¯ thh events may suppress one order or ordersmore backgrounds. As an illustration, let’s consider thespecific process pp → t ¯ thh → t ¯ tb ¯ bb ¯ b again at a 100 TeV pp -collider, with t ¯ t decaying semi-leptonically. Note, thisdoesn’t mean that it has a better sensitivity compared tothe other hh decay modes in the pp → t ¯ thh production.In this case, we modify the p T cuts for jets to be p jT > /E T cut to be /E T >
50 GeV, and requireat least one jet with its p T greater than 100 GeV andat least one b -jet with its p T greater than 120 GeV. To reconstruct the di-Higgs resonances, we redefine χ h to be χ h ≡ (cid:20)(cid:18) m b b − m h σ h (cid:19) p + (cid:18) m b b − m h σ h (cid:19) p (cid:21) /p . (8)We require the combination of b -jet pairs with the min-imal χ h satisfy χ h < . p = 1 . χ h > . p = 0 .
2. The latter is applied to avoid acciden-tal “di-Higgs” resonances in the backgrounds. In addi-tion, we require the di-Higgs invariant mass m hh < | ∆ R b b | p − | ∆ R b b | p ) /p < . p = 0 . S/ √ B = 4 . σ (no top-quark reconstruction) and3 . σ (with top-quark reconstruction) for 3ab − of data. TABLE IV: Cut flows of searching for pp → t ¯ thh → t ¯ tb ¯ bb ¯ b atthe 100 TeV pp -collider via the semi-leptonic top-pair chan-nel. The unit used in the table is attobarn. √ s = 100 TeV t ¯ thh t ¯ tb ¯ bb ¯ b t ¯ tb ¯ bc ¯ c t ¯ thb ¯ b t ¯ tZb ¯ b t ¯ thc ¯ c Preselection 830.5 72678.7 13322.6 10231.8 3252.0 1995.7Di-Higgs rec. 608.4 31679.7 6285.2 5689.9 1504.0 1193.3Top rec. 240.1 10384.4 2189.1 2208.6 428.0 384.9
One application of the di-Higgs measurement is toprobe the tri-Higgs coupling. A rough estimation basedon the calculation in [20] gives d ( σ/σ SM ) d ( λ/λ SM ) (cid:12)(cid:12)(cid:12) λλ SM =1 ∼ . pp → t ¯ thh production, in comparison to its value ∼ − . pp → hh production [16], at a 14 TeV pp -collider. According to the analyses above, the SMtri-Higgs coupling can be measured with a statistical ac-curacy of ∼ ∼
70% at a 100TeV pp -collider with 3ab − of data (with the relation inEq. (9) assumed), via the channel pp → t ¯ thh → t ¯ tb ¯ bb ¯ b .Here the former is based on a combination of the semi-leptonic and leptonic t ¯ t decay modes, and the latter isbased on the semi-leptonic one only. Though the ac-curacy of this measurement is lower than what can beachieved at the HL-LHC via the pp → hh → b ¯ bγγ chan-nel, say, ∼
50% [16], we are able to use it to preliminarilyprobe the λλ SM shift required for generating strong enoughfirst-order EWPT in the early Universe [1].The story could be more subtle if λλ SM >
1. Differentfrom the pp → hh (similar for the pp → jjhh ) produc-tion whose cross section negatively depends on λλ SM in theSM neighborhood, the pp → t ¯ thh production has a crosssection monotonically increasing with respect to λλ SM .Any positive shift in λλ SM caused by new physics, suchas the operator | H | Λ used for strengthening the EWPTin the early Universe [1], will lead to a suppression of the pp → hh production, and simultaneously an enhance-ment of the pp → t ¯ thh one, in this neighborhood. Mean-while, the (cid:12)(cid:12)(cid:12) d ( σ/σ SM ) d ( λ/λ SM ) (cid:12)(cid:12)(cid:12) becomes smaller for the pp → hh production and larger for the pp → t ¯ thh production as λλ SM increases, which also leads to a suppression for the pp → hh sensitivity, and a simultaneous enhancementof the pp → t ¯ thh sensitivity, in measuring the tri-Higgscoupling. For example [20], with a shift 0.5 in λλ SM , the pp → t ¯ thh production is enhanced by twice, relative tothe pp → hh one, while the (cid:12)(cid:12)(cid:12) d ( σ/σ SM ) d ( λ/λ SM ) (cid:12)(cid:12)(cid:12) becomes compa-rable for both. This leads to a pp → t ¯ thh → t ¯ tb ¯ bb ¯ b sen-sitivity roughly twice better than the pp → hh → b ¯ bγγ one in measuring the tri-Higgs coupling at the HL-LHC.Even worse, there exists a degeneracy of cross sectionwith respect to λλ SM for the pp → hh production [20].Breaking this degeneracy may further suppress its sen-sitivity. Given these considerations, the pp → t ¯ thh pro-duction may play a crucial role in measuring the tri-Higgscoupling and hence in exploring the CBA puzzle.Another application of the di-Higgs measurement is tosearch for new physics coupling with the Higgs field di-rectly. The t ¯ thh (including t ¯ thh + /E T ) production ex-tensively exists in the scenarios of new physics. Forexample, it can be initiated by the pair production oftop partners, in both supersymmetric (e.g., see [27]) andnon-supersymmetric (e.g., see [28]) contexts. In addition,higher dimensional operators in low-energy effective the-ories may modify the pp → t ¯ thh production. t ¯ thh Λ is suchan example which can contribute via top-quark pair pro-duction [4–6]. However, to achieve the double goals ofmeasuring the tri-Higgs coupling and searching for newphysics coupling with the Higgs field simultaneously, the pp → t ¯ thh events need to be disentangled.Based on the leading-order discussions above, weconclude that the pp → t ¯ thh channel opens a newavenue to measure di-Higgs physics, complementary tothe channels pp → hh, jjhh suggested in the past, atboth the HL-LHC and a next-generation pp -collider.A systematical exploration along this line is definitelyrequired, which we will leave to a future work. [Acknowledgments] T. L. is supported by his start-up fund at the Hong Kong University of Science andTechnology. H. Z. is supported by the U.S. DOE underContracts No. DE-FG02-91ER40618 and de-sc0011702.T. L. would like to thank Jing Shu and Lian-tao Wangfor useful discussions, and to acknowledge the hospital-ity of the Aspen Center for Physics (Simons Foundation),where part of this work was completed. H. Z. would liketo thank Hua Xing Zhu for discussions. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] A. Noble and M. Perelstein, Phys.Rev.
D78 , 063518(2008), arXiv:0711.3018.[2] C. O. Dib, R. Rosenfeld, and A. Zerwekh, JHEP ,074 (2006), hep-ph/0509179.[3] R. Grober and M. Muhlleitner, JHEP , 020 (2011),arXiv:1012.1562.[4] S. Dawson and E. Furlan, Phys.Rev.
D89 , 015012 (2014),arXiv:1310.7593.[5] C.-R. Chen and I. Low (2014), arXiv:1405.7040.[6] C.-Y. Chen, S. Dawson, and I. Lewis, Phys.Rev.
D90 ,035016 (2014), arXiv:1406.3349.[7] G. Aad et al. (ATLAS Collaboration), Phys.Lett.
B716 ,1 (2012), arXiv:1207.7214.[8] S. Chatrchyan et al. (CMS Collaboration), Phys.Lett.
B716 , 30 (2012), arXiv:1207.7235.[9] M. J. Dolan, C. Englert, and M. Spannowsky, JHEP , 112 (2012), arXiv:1206.5001.[10] D. Y. Shao, C. S. Li, H. T. Li, and J. Wang, JHEP ,169 (2013), arXiv:1301.1245.[11] A. J. Barr, M. J. Dolan, C. Englert, and M. Spannowsky,Phys.Lett.
B728 , 308 (2014), arXiv:1309.6318.[12] D. E. Ferreira de Lima, A. Papaefstathiou, and M. Span-nowsky, JHEP , 030 (2014), arXiv:1404.7139.[13] V. Barger, L. L. Everett, C. Jackson, and G. Shaugh-nessy, Phys.Lett.
B728 , 433 (2014), arXiv:1311.2931.[14] A. Papaefstathiou, L. L. Yang, and J. Zurita, Phys.Rev.
D87 , 011301 (2013), arXiv:1209.1489.[15] F. Goertz, A. Papaefstathiou, L. L. Yang, and J. Zurita,JHEP , 016 (2013), arXiv:1301.3492.[16] W. Yao (2013), arXiv:1308.6302.[17] J. Baglio, A. Djouadi, R. Grber, M. Mhlleitner, J. Quevil-lon, et al., JHEP , 151 (2013), 1212.5581.[18] M. J. Dolan, C. Englert, N. Greiner, and M. Spannowsky,Phys.Rev.Lett. , 101802 (2014), arXiv:1310.1084.[19] J. Baglio, Pos
DIS2014 , 120 (2014), arXiv:1407.1045.[20] R. Frederix, S. Frixione, V. Hirschi, F. Maltoni,O. Mattelaer, et al., Phys.Lett.
B732 , 142 (2014),arXiv:1401.7340.[21] CMS Collaboration, (2013), arXiv:1307.7135.[22] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni,et al., JHEP , 079 (2014), arXiv:1405.0301.[23] J. Pumplin, D. Stump, J. Huston, H. Lai, P. M. Nadolsky,et al., JHEP , 012 (2002), hep-ph/0201195.[24] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP ,026 (2006), hep-ph/0603175.[25] J. de Favereau et al. (DELPHES 3), JHEP , 057(2014), arXiv:1307.6346.[26] J. Gallicchio and M. D. Schwartz, Phys.Rev.Lett. ,022001 (2010), arXiv:1001.5027.[27] D. Berenstein, T. Liu, and E. Perkins, Phys.Rev.
D87 ,115004 (2013), arXiv:1211.4288.[28] J. Li, D. Liu, and J. Shu, JHEP1311