Resolving the Higgs-Gluon Coupling with Jets
Malte Buschmann, Christoph Englert, Dorival Goncalves, Tilman Plehn, Michael Spannowsky
IIPPP/14/50DCPT/14/100
Resolving the Higgs–Gluon Coupling with Jets
Malte Buschmann , , Christoph Englert , Dorival Gon¸calves , Tilman Plehn , Michael Spannowsky Institut f¨ur Theoretische Physik, Universit¨at Heidelberg, Germany Institute for Particle Physics Phenomenology,Department of Physics, Durham University, United Kingdom and SUPA, School of Physics and Astronomy, University of Glasgow, United Kingdom
In the Standard Model the Higgs coupling to gluons is almost entirely induced by top quark loops.We derive the logarithmic structure of Higgs production in association with two jets. Just like in theone-jet case the transverse momentum distributions exhibit logarithms of the top quark mass andcan be used to test the nature of the loop–induced Higgs coupling to gluons. Using Higgs decaysto W bosons and to tau leptons we show how the corresponding analyses hugely benefit from thesecond jet in the relevant signal rate as well as in the background rejection.
Contents
I. Introduction II. Top mass effects
III. Signal–background analyses H → W W decays 8 H → τ τ decays 9 IV. Conclusions Acknowledgments References a r X i v : . [ h e p - ph ] M a y I. INTRODUCTION
After the recent discovery of a light, narrow, and likely fundamental Higgs boson [1, 2], one of the main tasksof the upcoming LHC runs will be to study the properties of this new particle. An interesting aspect of theHiggs discovery is that it largely relies on higher dimensional Higgs interactions which in the Standard Model areinduced by loops of heavy quarks and gauge bosons. While this indirect information on Higgs coupling structuresis complemented by precise tree–level information in the Higgs–gauge sector, our understanding of Higgs couplingsto fermions largely relies on these loop effects.This shortcoming is most obvious in our currently very limited and model–dependent understanding of the topYukawa coupling [3–6]. A measurement of the top Yukawa coupling from associated Higgs and top productionwith a proper reconstruction of the heavy states will be challenging even in the upcoming LHC run [7–9]. Thislimitation is in stark contrast with our theoretical interest, where a measurement of the large top Yukawa couplingis crucial to extrapolate our understanding of the Higgs mechanism from LHC energy scales to more fundamental,high energies [10]. Beyond the Standard Model this large size of the top Yukawa suggests that any new physicsstabilizing the scalar Higgs mass should include a top partner, which in turn can contribute to the loop–inducedHiggs couplings to gluons and photons [11].To disentangle the Standard Model contribution for example to the Higgs–gluon coupling from new physicseffects we can use a particular feature of the Standard Model loops: in the presence of a Yukawa coupling theassociated dimension-6 operators no longer decouple. Instead, they induce a dimension-6 operator with a couplingstrengths which approaches a finite value in the limit of large top masses. In this low energy limit the interactionsbetween any number of gluons and any number of Higgs bosons is given by a simple effective Lagrangian [12, 13].While this approximation provides a very good prediction of the inclusive Higgs production rate it leads to O (10%)deviations in most distributions for the gg → H production process [14–16] and fails quite spectacularly for Higgspair production [17]. Turning this argument around, we can use kinematic distributions in Higgs productionprocesses to test our assumption that the Higgs–gluon interactions are induced by heavy quarks.Physics beyond the Standard Model might also exhibit non–decoupling effects in the effective Higgs couplings.One such example is a fourth generation of chiral fermions, where the effects from new physics are of the samesize as the Standard Model prediction. Because they are not described by a small parameter such scenarios arelargely ruled out altogether. In new physics extensions which do decouple, the characteristic small parameter istypically the ratio of the electroweak scale to the new physics mass scale. This mass ratio is constrained to bebelow O (1 / ∗ . Itis well known that the correlations of the two initial state radiation jets reflect the higher dimensional structure ofthe Higgs coupling to gluons or any other hard process [26]. In this study we will use the two hard jets to extractthe top mass dependence of the Higgs–gluon coupling.First, we will show that the logarithmic top mass dependence in the VBF topology is the same as for Higgsproduction with a single jet. Adding a second hard jet to the hard process [27] shifts a sizeable number of Higgsevents from phase space regions which are not sensitive to top mass effects to regions which are sensitive. Wewill find that the sensitivity of the VBF topology to top mass effects should exceed the sensitivity of the Higgs–plus–one–jet channel. Moreover, the VBF topology allows for a much improved background suppression in the H → τ τ and H → W W channels. This way, a second hard jet is not just an improvement of a dominant 1-jetanalysis; the 2-jet hard process is more sensitive to top mass effects, the correlations of the second hard jet andthe logarithmic top mass dependence are not covered by a parton shower description, and the second hard jetmakes a big difference in the background rejection. ∗ We will refer to this process as vector boson fusion (VBF) and neglect the numerically small weak boson fusion contributions.Moreover, we do not require the usual forward tagging jets, but two hard jets defining the hard process together with the Higgs.
II. TOP MASS EFFECTS
The main production process responsible for the Higgs discovery is gluon fusion, mediated by the Higgs couplingto a pair of gluons. This interaction does not exist at tree level, i.e. , as part of the renormalizable dimension-4Lagrangian. It is induced by heavy quarks, in the Standard Model dominantly via top quark loop [12, 13], L ggH ⊃ g ggH Hv G µν G µν g ggH v = − i α s π v τ [1 + (1 − τ ) f ( τ )] f ( τ ) on-shell = (cid:32) arcsin (cid:114) τ (cid:33) τ →∞ = 1 τ + 13 τ + O (cid:18) τ (cid:19) , (1)all in terms of τ = 4 m t /m H >
1. Barring prefactors the function f corresponds to the scalar three–point functionfor a closed top loop. In the usual kinematic configuration for single Higgs production the coupling g ggH dependsonly on the top and Higgs masses, as indicated above. Once it appears as part of a more complex Feynmandiagram the coupling g ggH will depend on the momenta of all three external states as well as on the top mass.This will become our main reason to define the hard process including two hard jets rather than one jet plus aparton shower.In the simple low energy limit the interaction vertices between any number of gluons and any number of Higgsbosons can be described by the Lagrangian L ggH = α s π log (cid:18) Hv (cid:19) G µν G µν ⊃ α s π Hv G µν G µν . (2)The top Yukawa coupling in the top loop violates the decoupling theorem, so the interaction approaches a finitelimit [12]. This non–decoupling property in combination with the absence of a dimension-4 Higgs coupling togluons is unique to the dimension-6 operators mediating the Higgs couplings to gluons and photons, which are toa large degree responsible for the Higgs discovery [2].One question which we have to answer based on LHC measurements is if the top Yukawa coupling is in-deed responsible for the observed Higgs–gluon coupling, or if other top partners contribute to the correspondingdimension-6 operator. In two different conventions the relevant part of the Higgs interaction Lagrangian includinga finite top mass and free couplings reads L int ⊃ (cid:104) κ t g ggH + κ g α s π (cid:105) Hv G µν G µν − κ t m t v H (¯ t R t L + h.c.) Refs. [24]= (1 + ∆ t + ∆ g ) g ggH Hv G µν G µν − (1 + ∆ t ) m t v H (¯ t R t L + h.c.) SFitter [3] . (3)We show the SFitter conventions to indicate that the parameters κ t and κ g are indeed part of the usual LHCcoupling analyses. The new aspect is to extract them from distributions rather than rates. As alluded to above,the dimension-6 operator is defined not only without any reference to the top mass, but also with the entiremomentum dependence arising from the gluon field strengths. One physics scenario which could serve as anultraviolet extension of Eq.(3) would be the Standard Model with an extended Higgs sector and an unobservedtop partner [3, 21]. Throughout this paper we will rely on two reference points unless otherwise mentioned,( κ t , κ g ) SM = (1 ,
0) and ( κ t , κ g ) BSM = (0 . , . . (4)In the second point the contributions from a top partner to a good approximation compensate for the reducedtop Yukawa in the Higgs–gluon coupling, leaving the observed Higgs cross section at the LHC unchanged. Figure 1: Sample Feynman diagrams for the processes qq → Hgg and gq → Hgq , indicating the cuts which contribute toabsorptive parts.
280 300 320 340 360 380 400 420 440 460 -1 HEFTSM qq HEFT qq SM GeVfb
Hjj dm s d [GeV] Hjj m300 350 400 4500.81
SM/HEFT
280 300 320 340 360 380 400 420 440 460 HEFTSM gq HEFT gq SM GeVfb Hj dm s d [GeV] Hj m300 350 400 4500.911.1 SM/HEFT
Figure 2: Differential distributions for m Hjj (left) and for m Hj (right) for the Hjj process. The Standard Model curves(SM) include the full top mass dependence while the low energy effective field theory approximation (HEFT) relies on theapproximation in Eq.(2). The index ‘qq’ (‘gq’) indicates Feynman diagrams with an incoming quark pair (gluon-quark).We assume √ S = 13 TeV. Absorptive terms
Absorptive terms in the top loop inducing the effective Higgs–gluon coupling are well known from the behaviorof the cross section as a function of the (formerly unknown) Higgs mass [13, 16]. At m H = 2 m t the formula for thescalar integral given in Eq.(1) develops an imaginary absorptive part, leading to a kink in the LHC cross section.Given the now fixed Higgs mass of 126 GeV the question is how we can search for such effects at the LHC. Forexample, in Higgs production in association with two jets the same absorptive parts should appear in the loopintegrals shown in Fig. 1, m Hg = 2 m t and m Hgg = 2 m t . (5)To illustrate the size of such absorptive effects we study the process pp → Hjj at parton level in Fig. 2. It includesthe loop–induced gggH interaction which indeed shows an absorptive part around m Hj ∼
350 GeV, as indicatedin Eq.(5). We see that these absorptive parts are very small for both distributions and will hardly allow us tomake a qualitative statement about the origin of the effective Higgs–gluon coupling, not even talking about ameasurement of κ t and κ g . Top–induced logarithms
Higgs production in association with a hard jet probes a logarithmic top mass dependence of the loop–inducedcoupling [19, 20]. This effect has recently been transformed into a proposed experimental separation of the couplingmodifications κ t and κ g in this production channel [21–24]. In the high energy limit, or for small top and Higgsmasses, the leading term of the matrix element for the partonic subprocess gg → Hg scales like |M Hj | ∝ m t log p T m t . (6)The transverse momentum constitutes the external energy scale in the limit of p T (cid:29) m H , m t . If the effectiveHiggs–gluon coupling is not induced by the top quark this logarithm does not occur.Next, we look at the logarithmic structure for the more complex final state of Higgs production in associationwith two jets. In the presence of several external mass scales it is not clear which final–state invariant drives thelogarithmic top mass dependence. The simplest subprocess q ¯ q → q ¯ qH only probes the effective ggH coupling,but with two off-shell gluons at sizeable virtualities. In terms of the virtualities of Q , > t -channel gluons the corresponding scalar three point function scales like |M Hjj | ∝ m t ( Q − Q ) (cid:18) log Q m t − log Q m t (cid:19) Q (cid:29) Q = m t Q log Q m t . (7) -7 -6 -5
10 [GeV] Q0 200 400 600 800 1000 [ G e V ] T , j p -7 -6 -5
10 [GeV] Q0 200 400 600 800 1000 [ G e V ] T , H p Q0 200 400 600 800 1000 [ G e V ] T , j p Q0 200 400 600 800 1000 [ G e V ] T , H p Figure 3: Left to right: correlation plots for the leading p T,j vs Q and p T,H vs Q for Hjj production in the StandardModel, κ t,g = (1 , κ t,g = (0 . , . In the collinear limit the virtuality of the incoming parton splitting is linked to the transverse momentum of theforward tagging jet through a simple linear transformation. Logarithms in the virtuality can be directly translatedinto logarithms of the transverse momentum, independent if they are scaling logarithms which get absorbed intothe parton densities or if they affect the hard process [28].In the limit of one significantly harder tagging jet Q (cid:29) Q recoiling against the Higgs boson the diagrams inthe vector boson fusion topology scale like |M Hjj | ∝ m t log p T,j m t ∼ m t log p T,H m t . (8)In this step we assume a linear relation between the virtuality and the transverse momentum of the additionaljets [28]. In the left panel of Fig. 3 we show the correlation between the leading p T,j and the correspondinggluon virtuality for the SM hypothesis and clearly see the expected correlation with p T,j > Q . Away from thediagonal we only find events with p T,j < Q , in agreement with the kinematic considerations of Ref. [28]. Thispattern gets transferred to the transverse momentum of the recoiling Higgs. In the right two panels we showthe same kinematic correlation for the ratio SM/BSM. We see the same increase of the dimension-6 operatorsat larger transverse momenta as in the Hj channel [21–24]. For given p T,j values this ratio is independent ofthe virtuality. This means that while the virtuality is fixed by the steep gluonic parton densities the top masslogarithm feeds on the transverse momentum and the jet momentum in the beam direction.After ensuring that the top mass logarithms in Hj and Hjj have the same origin we can compare their numericalimpact. In Fig. 4 we show the dependence of the Hj and Hjj production rates on the transverse momentum of theleading tagging jet and the Higgs, based on the
Mcfm [29] and
Vbfnlo [30] implementations. We have validated
Figure 4: Parton–level p T,H (left) and p T,j (right) distributions for Hj and Hjj production. The red curve correspondsto the Standard Model κ t,g = (1 , κ t,g = (0 . , . √ S = 13 TeV.
200 400 600 800 1000 1200 1400 1600 1800 2000 -1 BSMSM GeVfb jj dm s d [GeV] jj m500 1000 1500 200011.52 BSM/SM -1 BSMSM GeVfb z,j dp s d [GeV] z,j p0 200 400 600 800 100011.52 BSM/SM -1 BSMSM GeVfb z,H dp s d [GeV] z,H p0 200 400 600 800 100011.52 BSM/SM
Figure 5: Parton–level m jj (left), p z,j (center) and p z,H (right) distributions for Hjj production. this modified
Mcfm dimension-6 setup against an independent implementation based on
Vbfnlo . We comparethe prediction of the Standard Model κ t,g = (1 , κ t,g = (0 . , . Hjj production process includes one–loop triangle, box and pentagon contributions, which cannot beseparated. However, the different qq , gq and gg initial states offer a handle to determine the size of their relativecontributions. For the qq and gq initial states we have triangle and box diagrams, and the gg initial state willinclude pentagons. For all initial states we find an enhanced dimension-6 BSM component at large Higgs and jettransverse momenta. The effect is strongest for incoming quarks and less pronounced for pure gluon amplitudes.This confirms our original assumption that the top mass logarithm arises from the VBF topology with an effectivetriangular ggH interaction for all initial states. This topology is approximately added to the Hj simulation oncewe include a parton shower to simulate initial state radiation. However, if both jets are hard the VBF topologyis correctly described by the appropriate hard process, which includes the Higgs as well as two jets.The comparison of the Hj and the Hjj channels in Fig.4 also shows that for one recoiling jet most of the crosssection comes from phase space regions which do not resolve the effective Higgs–gluon coupling. In comparison,for two hard jets recoiling against the boosted Higgs the drop in the total cross section appears exclusively inthe insensitive regime, while even in terms of absolute event numbers the sensitivity to the top mass logarithmincreases. If indeed the hard
Hjj process is numerically more relevant in the high- p T regime than the hard Hj process we need to worry about even more jets. We can only speculate about this, but from the above observationthat the top mass logarithm arises from the VBF topology the third jet would be most helpful if arising from afinal state splitting. Such configurations should be reasonably well described by the final state parton shower.After isolating the top mass logarithm in the transverse momentum spectra for Hjj production given by Eq.(8)we need to sadly convince ourselves that there are no additional top mass logarithms in this process. For example,there could be very promising logarithms in the largest momentum scale, i.e. log m jj /m t . In Fig. 5 we show the m jj distribution as well as the leading p z,j and p z,H distributions for Hjj production. For the top–induced couplingand the dimension-6 coupling they are perfectly aligned, indicating that none of these observables are affected bytop mass logarithms. The top mass dependence really only appears in the transverse momentum spectra. In thefollowing we will focus on the transverse momentum of the Higgs, while eventually an experimental analysis couldinclude both, p T,H and the leading p T,j . Including the interference
Based on the interaction Lagrangian in Eq.(3) we can easily translate the modified coupling strengths intodifferential or total LHC cross sections. For simplicity, we keep all other tree–level Higgs interactions unchanged,so the expected slight shift in the photon–Higgs coupling will be of no phenomenological relevance. The matrixelement for Higgs production in gluon fusion is based on the HG µν G µν interaction and will consist of two terms, M = κ t M t + κ g M g , (9) [GeV] T,H p0 200 400 600 800 1000 -5 -4 -3 -2 -1 T,H /dp tt s d T,H /dp tg s d T,H /dp gg s d T,H /dp tt s d T,H /dp tg s d T,H /dp gg s d[fb/GeV] MCFM Hj inclusiveVBFNLO Hjj inclusive Figure 6: Transverse momentum distribution for Hj production (based on Mcfm ) and
Hjj production (based on
Vbfnlo ).Both codes use
Pythia8 for the parton shower. The top–induced and dimension-6 contributions as well as their interferenceare defined in Eq.(10). We assume √ S = 13 TeV and for technical reasons include a decay H → τ τ with minimal cuts. where the index g indicates the dimension-6 operator contribution and all prefactors except for the κ j are absorbedin the definitions of M j . For the matrix element squared and any kinematic distributions this means dσd O = κ t dσ tt d O + κ t κ g dσ tg d O + κ g dσ gg d O , (10)where for small deviations from the Standard Model the last term will be numerically irrelevant. In Fig. 6 wepresent the three transverse momentum distributions for the Higgs, on which we will rely for the remaininganalysis. To be consistent, we use Mcfm + Pythia8 [29, 31] for the hard Hj production process with the scalechoice µ F = µ R = m H + p T,j and
Vbfnlo + Pythia8 [30, 31] for the hard
Hjj production process with thescale choice µ F = µ R = m H + p T,j + p T,j . For example the slight broadening of the low- p T peaks comparedto Fig. 4 is due to parton shower effects and this scale choice. The full simulation confirms that the Hj processhas a larger total rate than the Hjj process, but this additional Hj rate is concentrated at small transversemomenta and does not carry information on the Higgs–gluon coupling. For p T,H >
300 GeV the parton showeris expected to underestimate additional jet radiation off the Hj process and cannot be expected to reflect thetop mass logarithms; hence, the Hjj process gives a larger relevant number of events to probe the Higgs–gluonvertex. This is universally true for all three contributions defined in Eq.(10).
III. SIGNAL–BACKGROUND ANALYSES
Following the results in the last section the key question becomes how much, in addition to the increase in thenumber of relevant signal events, the background rejection benefits from the additional jet in the hard process.As simple examples we consider the two most promising Higgs decay channels, H → W W and H → τ τ in thefully leptonic decay modes at the LHC with √ S = 13 TeV.The signal events are generated with Mcfm [29] for the Hj process and with Vbfnlo [30] for the
Hjj process,respectively. They are showered with
Pythia8 [31]. Both generators provide results for finite top mass, κ t,g =(1 , κ t,g = (0 , κ t vs κ g range we expand bothimplementations including the complete interference structure given in Eq.(10). Because there are no next–to–leading order (NLO) computations available for either of the two channels with full top mass dependence, wescale our total cross sections to the corresponding NLO rates in the heavy top limit. For a consistent scale choicewe apply a flat correction of K Hj ∼ . K Hjj ∼ . t ¯ t +jets and W W +jets background are generated with the
PowhegBox [33], showered with a vetoed
Pythia8 shower [31]. We also include the Z +jets background from Sherpa + BlackHat [34] merged at next–to–leading order with up to three hard jets. In all background processes we enforce top, W , and Z decaysto charged leptons, i.e. muons, electrons or taus. Jets are defined using the anti- k T algorithm implemented in Fastjet [35] with R = 0 . p T,j >
40 GeV and | y j | < . . (11)If explicitly shown, the one or two recoil jets are defined as the hardest jets fulfilling this requirement. Throughoutwe smear the missing energy vector using a gaussian. For the leptons we require two isolated opposite sign leptonswith p T,(cid:96) >
20 GeV and | y (cid:96) | < . , (12)where the isolation criterion is a hadronic energy deposition E T, had < E T,(cid:96) /
10 within a cone of size R = 0 .
2. Tosuppress the top background we require zero b -tags with a flat tagging efficiency of 70% and a mistag rate of 2%.Our simulation of the top pair background should be taken with a grain of salt, because there are many ways offurther suppressing this background based on the underlying jet structure [36]. Note that the focus of this signaland background analysis is not to estimate a realistic target for the measurement of κ t and κ g , but to see howthe Hjj process compares with the Hj process [21–24]. H → W W decays
As the first signature, we show how we can probe the structure of the Higgs–gluon coupling in
Hjj productionbased on leptonic H → W W decays. To estimate the additional benefit of including the second jet we compare thesignal–to–background ratios
S/B for Higgs production with one and two hard jets. For the
W W decay channelthe main backgrounds are
W W +jets and t ¯ t +jets production. We start with the basic cuts shown in the first linesof Tab. I.Aside from the missing weak boson fusion characteristics they are similar to the known analysis techniquesfor Higgs production in association with two jets. Obviously, we do not apply a stiff m jj cut to reduce QCDbackgrounds as well as gluon fusion Higgs production. The transverse mass of the W W system is defined as m T = ( E (cid:96)(cid:96)T + / E T ) − | (cid:126)p (cid:96)(cid:96)T + / (cid:126)E T | with E (cid:96)(cid:96)T = (cid:113) | (cid:126)p (cid:96)(cid:96)T | + m (cid:96)(cid:96) . (13)The p T,H cut extracts events which are sensitive to the logarithmic dependence on the top mass. The numbersshown for the Hj process are in good agreement with the findings of Ref. [21]. As expected from Fig. 6 thenumber of signal events in the Hjj process exceeds the corresponding number in the Hj channel by a factor oftwo. Moreover, in particular the W W +jets background is reduced by the required second hard jet.In addition, we can use the second jet to define additional observables which can in turn be used to suppressbackgrounds. Two choices, namely the azimuthal angle between the tagging jets [26] and the ratio of transversemomenta of the two jets, are shown in Fig. 7. It is interesting to notice that the usual application of the azimuthalangle between the tagging jets relies on the forward jet kinematics, while in this analysis the tagging jets are hardand relatively central. First, we see that the boosted Higgs configuration forces the two recoil jets for the Higgssignal and the
W W background to move close to each other in the azimuthal plane. In addition, two jets recoilingagainst one Higgs boson prefers more balanced jet momenta than the recoil against two independently produced Hj → ( W W ) j inclusive Hjj → ( W W ) jj inclusivecuts H +jets W W +jets t ¯ t +jets H +jets W W +jets t ¯ t +jets p T,j >
40 GeV, | y j | < . p T,(cid:96) >
20 GeV, | y (cid:96) | < . N b = 0 33.3 515 4920 15.2 87.4 1690 m (cid:96)(cid:96) ∈ [10 ,
60] GeV 28.3 106 1060 13.0 17.2 351/ E T >
45 GeV 21.4 92.9 930 10.6 15.9 309∆ φ (cid:96)(cid:96) < . m T <
125 GeV 14.2 26.6 220 8.09 6.14 76.2 p T,H >
300 GeV 0.59 2.73 5.18 1.06 1.39 3.28∆ φ jj < . p T,j /p T,j < . H +jets, W W +jets and t ¯ t +jets. All rates are given in fb. +jets WW fi H+jetsttWW+jets jj fD d s d s jj fD +jets WW fi H+jetsttWW+jets
T,j2 /p T,j1 dp s d s T,j2 /p T,j1 p Figure 7: Normalized ∆ φ jj (left) and p T,j /p T,j (right) distributions for the H → W W signal and the dominant back-grounds. All universal cuts listed in Tab I are already applied. W bosons. This again supports our earlier conclusion that the underlying hard process indeed includes two hardjets. Cutting on both jet–jet correlations we can reduce the W W background to the
Hjj signal to roughly a fifthof the corresponding Hj background, for similar signal rates in the boosted phase space region. H → τ τ decays As an alternative decay signature we also study
Hjj production with a purely leptonic H → τ τ decay. Becausethe leptonic W W and τ τ decay channels have a similar detector signature and main backgrounds are t ¯ t +jets and W W +jets we stick to a similar initial analysis strategy, now shown in Tab. II. Instead of the transverse mass cutwe compute m ττ in the collinear approximation [19], m ττ = m vis √ x x with x , = p vis1 , p vis1 , + p miss1 , , (14)where m vis and p vis are the invariant mass and total momentum of the visible tau decay products. The variable p miss is the neutrino momentum reconstructed in the collinear approximation. Using this approximation we require | m ττ − m H | <
20 GeV with x , ∈ [0 . , . (15)This large mass window should include the vast majority of signal events while we will see that it is still sufficientto control the backgrounds. By imposing p T,H ∼ p T,(cid:96) + p T,(cid:96) + / p T >
300 GeV (16) Hj → ( τ τ ) j inclusive Hjj → ( τ τ ) jj inclusivecuts H +jets Z/γ ∗ +jets W W +jets t ¯ t +jets H +jets Z/γ ∗ +jets W W +jets t ¯ t +jets p T,j >
40 GeV, | y j | < . p T,(cid:96) >
20 GeV, | y (cid:96) | < . N b = 0 9.21 148221 515 4920 4.50 23218 87.4 1690 m (cid:96)(cid:96) ∈ [10 ,
60] GeV 6.59 10466 179 1616 3.41 1832 28.3 541 m (cid:96)(cid:96) (cid:48) ∈ [10 , E T >
45 GeV 6.24 38.1 166 1616 3.31 0.65 27.0 541 | m ττ − m H | <
20 GeV 5.88 2.84 6.28 45.9 3.10 0.11 1.18 16.0 p T,H >
300 GeV 0.23 0.013 0.40 0.87 0.41 0.004 0.20 0.56∆ φ jj < . p T,j /p T,j < . H +jets, Z/γ ∗ +jets, W W +jets and t ¯ t +jets. All rates are given in fb. +jets WW fi H+jetsttWW+jets jj fD d s d s jj fD +jets WW fi H+jetsttWW+jets
T,j2 /p T,j1 dp s d s T,j2 /p T,j1 p Figure 8: Normalized ∆ φ jj (left) and p T,j /p T,j (right) distributions for the H → τ τ signal and the dominant backgrounds.All universal cuts listed in Tab II are already applied. we ensure perfect kinematical conditions to apply the collinear approximation. Similar to the W W channel wethen use the second jet to further suppress the backgrounds, see Fig. 8. As for the
W W case we see that forsimilar event numbers in the top–mass–sensitive region the backgrounds in the
Hjj analysis are something like afactor 1/5 smaller than for the Hj case.Combining the different p T,H bins into a shape analysis allows us to extract information on the parameters κ t and κ g introduced in Eq.(3). To estimate the power of the Hjj analysis we evaluate the p T,H distributionusing the CL s method. The Standard Model κ tg = (1 ,
0) defines the null hypothesis, to be compared with theBSM parameter point κ tg = (0 . , . O (20%) [30]. We also show results for the leading p T,j distribution, indicating that the Higgs transversemomentum is the best–suited single observable for the
Hjj analysis. Unlike for the Hj analysis we find that theleptonic W W and τ τ decays are similarly promising.As indicated by Fig. 9, excluding small deviations of the Higgs–top and Higgs–gluon from their Standard Modelvalues couplings remains a challenge for the upcoming LHC runs. To accumulate the best sensitivity possibleit will be necessary to combine all available channels. However, cleanly separating the leptonic H → τ τ and H → W W decays in Hj production is kinematically very difficult [21]. In this study we now find that Hjj production with a decay H → W W is almost as sensitive as the corresponding τ τ decay channel, so with fullcontrol over the additional one or two jets a combination of the two decay channels seems possible. ] -1 L [fb500 1000 1500 2000 2500 3000 s C L T,H
Exclusion plot based on p95% exclusion s s tg k WW fi H ] -1 L [fb500 1000 1500 2000 2500 3000 s C L T,j
Exclusion plot based on p95% exclusion s s tg k WW fi H ] -1 L [fb500 1000 1500 2000 2500 3000 s C L T,H
Exclusion plot based on p95% exclusion s s tg k tt fi H Figure 9: Confidence level for separating the BSM hypotheses κ t,g = (0 . , .
3) from the Standard Model. We show resultsfor H → W W decays based on the transverse momentum of the Higgs (left) and the hardest jet (center). For the H → τ τ decays (right) we limit ourselves to the more promising case of the Higgs transverse momentum. IV. CONCLUSIONS
We have shown that the extraction of the top mass dependence in the effective Higgs–gluon coupling at theLHC benefits from a second jet, i.e. a hard process consisting of the Higgs plus two jets. As two robust examplesignatures we consider purely leptonic Higgs decays to W bosons and τ leptons. Higgs production with two hardjets should not be considered a correction to Higgs production plus one jet in the boosted regime, because in thecorresponding analysis we find:1. the divergence structure of the Hjj process is given by a similar logarithm as the Hj case; numerically, theVBF topology with two hard jets radiated off the initial state partons dominates the top mass dependenceat large transverse momenta.2. adding a second hard jet moves a large fraction of signal events from top–mass–insensitive phase spaceregions to top–mass–sensitive configurations. For large transverse momenta of the Higgs boson the Hjj production process even contributes more signal events than the Hj process.3. a second fully correlated jet described by the hard matrix element can be used to reduce the backgroundsby roughly a factor 1/5 for a similar number of signal events, compared to the same analysis with only onehard jet.4. both, the H → W W and H → τ τ signatures appear feasible when combined with the Hjj productionprocess.Given the statistical limitation of this detailed study of the Higgs–gluon coupling and its underlying loop structurethe
Hjj channel should be a very useful additional handle. Obviously, a fully merged analysis of the Hj and Hjj channels including the complete Higgs–gluon coupling structure will combine the two available channels forexample in the p T,H distribution.
Acknowledgments
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