aa r X i v : . [ h e p - ph ] A p r Higgs at LHC
S. Bolognesi ( ) , G. Bozzi ( ) and A. Di Simone ( ) ( ) Universit`a di Torino and INFN Sezione di Torino, Via P. Giuria 1, I-10125 TORINO, Italy ( ) Institut f¨ur Theoretische Physik, Universit¨at Karlsruhe, P.O.Box 6980, D-76128 Karlsruhe,Germany ( ) INFN Sezione di Tor Vergata, Via Ricerca Scientifica 1, I-00133 Roma, Italy
Summary. — An overview of recent theoretical results on the Higgs boson andits discovery strategy at ATLAS [1] and CMS [2] will be presented, focusing on themain Higgs analysis effective with low integrated luminosity ( <
30 fb − ).PACS – Standard Model Higgs Boson.
1. – Introduction
One of the main tasks of the Large Hadron Collider (LHC) will be the search forthe Higgs particle [3], which is responsible for the electroweak symmetry breaking ofthe Standard Model (SM). A lower limit m H >
114 GeV was put on the Higgs mass bythe non-observation of the so-called ”Higgs-strahlung” process e + e − → HZ at LEP [4].Since radiative corrections to electroweak observables vary with m H , a global χ -fit ofhigh-precision electroweak measurements performed at lepton and hadron colliders allowsan indirect measure of the Higgs mass: the upper limit m H <
160 GeV has been obtainedat 95% confidence level (∆ χ =2.7)[5].A considerable effort has been devoted in recent years to improve the theoreticalpredictions both for the production mechanisms and the main background processes,hopefully leading to an overall improvement of the search strategies at the LHC.This brief review is intended to summarize the status of the QCD corrections to Higgsboson production and decay at the LHC, and to present the main discovery strategies atATLAS and CMS.
2. – Higgs production at the LHC
In fig. 1 (left), taken from [6], the relevant cross sections for Higgs production atthe LHC are shown as a function of the Higgs mass. The results refer to fully inclusivecross sections and no acceptance cuts or branching ratios are applied. In this section, wedescribe the state-of-the-art of theoretical calculations for the main production channels. S. BOLOGNESI, G. BOZZI and
A. DI SIMONE -2 -3 bb_ WW ττ gg ZZcc_ Z γγγ
120 140 160 180 200100 mH (GeV/c )SM Higgs branching ratios (HDECAY) Fig. 1. – Higgs production cross sections (left) and branching ratios (right) at the LHC (from[6]) as function of Higgs mass. .1. Gluon fusion . – At the LHC, mainly because of the large gluon luminosity, thedominant production channel over the entire mass range will be the gluon fusion process gg → H , where the Higgs couples to gluons through a heavy-quark loop. The totalcross section at leading-order (LO) in QCD perturbation theory ( O ( α s )) was computedmore than 30 years ago [7]. The next-to-leading order (NLO) corrections [8, 9, 10] yielda K-factor of about 80-100%, thus making a NNLO calculation explicitly needed. Thecomplexity involved with the heavy-quark loop makes the computation of higher-ordercorrections extremely difficult. Considerable simplifications arise in the large- m t limit( m t ≫ m H ), where it is possible to introduce an effective lagrangian [11] directly couplingthe Higgs to gluons: L eff = −
14 [1 − α s π Hv (1 + ∆)] Tr G µν G µν , (1) where the coefficient ∆ is known up to O ( α s ) [12]. It was shown [13] that NLOcalculations based on the effective lagrangian approximate the full NLO result within10% up to m H =1 TeV. The reason for the high accuracy of this approximation is thefact that the Higgs particle is predominantly produced in association with partons ofrelatively low transverse-momenta, which are unable to resolve the heavy-quark loop[14]. The next-to-next-to-leading order (NNLO) corrections have been evaluated in thelarge- m t limit [14, 15, 16, 17]. In the case of a light Higgs boson ( m H ∼ LL level [19], providing a further 7-8%increase w.r.t. NNLO and reducing scale dependence to less than 4%. Also the NLO
IGGS AT LHC EW contributions have been computed [20], showing a 5-8% effect below the m H = 2 m W threshold.Realistic experimental analysis, including exact kinematics of the final states, areonly possible if reliable theoretical predictions for the Higgs differential ( q T and y ) dis-tributions are available. The most advanced predictions at present are the NNLO fullyexclusive distribution [21] and the parton level event generator (including Higgs decays) HNNLO [22]. In the region of small transverse-momentum, in addition to these fixed-orderresults, q T -resummation has been performed at the NNLL level with inclusion of the ra-pidity dependence[23], while joint (threshold and q T ) resummation has been performedat the full NLL level [24], leading to very precise predictions and to an overall excellentconvergence of the perturbative result. .2. Vector boson fusion (VBF) . – This production mechanism occurs as the scatteringbetween two (anti)quarks with weak boson ( W or Z ) exchange in the t-channel and withthe Higgs boson radiated off the weak-boson propagator. Even though the Higgs VBFproduction cross section is somewhat smaller ( ∼ • since the parton distribution functions (pdfs) of the incoming valence quarks peakat values of the momentum fractions x ∼ • the large weak boson mass provides a natural cutoff on its propagator: as a con-sequence, the jets from the two outgoing quarks are produced with a transverseenergy of the order of a fraction of the weak boson mass and thus with a large ra-pidity interval between them (typically one at forward and the other at backwardrapidity); • since the exchanged weak boson is colourless, no further hadronic production oc-curs in the rapidity interval between the quark jets (except for the Higgs decayproducts).The LO partonic cross section can be found in [25]. Gluon radiation can only occur asbremsstrahlung off the quark legs: NLO corrections to Higgs production via VBF havebeen computed for the total cross section [26] and for Higgs production in associationwith two jets [27]. They have been found to be typically modest (5-10%) and the scaleuncertainty is at the percent level, mainly because of the good precision to which thevalence quark pdfs in the intermediate-x regions are known. .3. Associated production with top . – The Higgs boson is radiated off one of the twotops in the q ¯ q, gg s-channel or off the top propagator in the gg t-channel at LO. Thischannel can be important in the low-mass region (provided a good b -tagging and a highluminosity are reached), where it allows to search for H → b ¯ b decay and can be usefulto measure the t ¯ tH Yukawa coupling. The QCD corrections to the LO cross section(computed in [28]) involve the computation of massive pentagons and enhance the crosssection by ∼ ∼
15% [29].
3. – Low Higgs mass searches
In fig. 1 (right) the branching ratios are shown as function of the Higgs mass forthe low-intermediate Higgs mass region 100 GeV < m H <
200 GeV, favourite by the
S. BOLOGNESI, G. BOZZI and
A. DI SIMONE electroweak precision measurements [5]. Unfortunately, the low Higgs mass region is themost challenging for the Higgs detection because the biggest Higgs branching ratios (BR)are into heavy quarks or τ leptons [30], which are difficult to be disentangled from thehuge QCD background.For very low Higgs mass ( m H ∼
120 GeV) the H → b ¯ b decay channel (BR ∼ t ¯ t . The request of two additional topquarks helps to cut the huge amount of b ¯ b QCD background but it makes the final statevery complex ( bbbbW W ).For Higgs mass up to 130 GeV the most promising decays are into photons and τ leptons.Both the channels have high background rate due to fakes, therefore they are also studiedin the VBF production of the Higgs to achieve a better significance. The decay H → γγ is known up to 3-loop QCD [32], while the irreducible pp → γγ background is available atNLO in the program DIPHOX [33], which also includes all relevant photon fragmentationeffects. The loop-mediated process gg → γγ contributes about 30% to the backgroundand has been calculated at O ( α s ) [34]. .1. t ¯ tH → t ¯ tb ¯ b . – ATLAS and CMS study this channel in all the combinations ofthe W decays: b ¯ bb ¯ blνlν with σ ∼ b ¯ bb ¯ blνjj with σ ∼ b ¯ bb ¯ bjjjj with σ ∼ l stays for e or µ . These final states involve many systematics ( e.g. ,effect of alignment on b -tagging, jet and missing energy calibration) which need to bemeasured from the data using dedicated control samples. Moreover, in addition to thephysics QCD background ( t ¯ t +jets with σ ∼
350 pb, t ¯ tb ¯ b with σ ∼ b -jets coming from theHiggs decay.Both the experiments quote a quite low significance for the Higgs discovery in thischannel with 30 fb − : the most recent results are from CMS [36] and indicate a sig-nificance smaller than 1 for the combined analysis, considering all the systematics; theATLAS analysis is quite old, it relays on a fast simulation of the detector and it quotesa significance of about 2-3 for the semileptonic final state only [35].However the analysis of this channel suffers of some drawbacks which can be solvedin the future. The low trigger efficiency (mainly in the fully hadronic final state) canbe raised with a dedicated, more complex trigger menu. The b -tagging performances areoptimal for jets with p T ∼
80 GeV, while this channel contains many low p T jets. Onthis kind of jets also the reconstruction and calibration performances are quite low, asshown in fig. 2 (left). Both these aspects, the b -tagging and the jet measurement, can beimproved exploiting a particle-flow approach to the jet reconstruction. .2. H → γγ . – The branching ratio for this decay channel is actually very low (0.2%for m H = 130 GeV). On the other hand, the final state is very clean, thus allowing abigger suppression of the backgrounds. Reconstruction of the primary vertex is crucialfor this analysis. ATLAS and CMS have different approaches to the problem, which takeinto account the different electromagnetic calorimetry used by the experiments.ATLAS can use the longitudinal granularity of its EM calorimeter to reconstruct thedirection of the photons, thus achieving a precision on the z coordinate of the primaryvertex of 1 . p T tracks reconstructed in the inner detector can be in-cluded in the fit to improve the precision, leading to a precision of about 40 µ m.In CMS, where there is no longitudinal segmentation of the calorimeter, only the recon- IGGS AT LHC M(bb) (GeV)0 50 100 150 200 250 A r b i t r a r y un i t s / ndf χ ± ± ± Higgs invariant mass, GeV120 125 130 135 140 E ve n t s With correctionNo correction
Fig. 2. – Left: reconstructed Higgs mass in the channel t ¯ tH → b ¯ bb ¯ blνlν in CMS. The jets arecalibrated using the PTDR II recommandation 1 settings and they are matched ( R < .
3) tothe Monte Carlo b partons from Higgs. Right: effect of the primary vertex reconstruction inCMS for the H → γγ channel. The dashed line shows the reconstructed Higgs mass when novertex correction is applied. structed tracks can be used to fit the primary vertex, and the resulting precision is 5 mm(in a low luminosity scenario). Fig. 2 (right) shows the effect of vertex reconstructionon the reconstructed Higgs mass. If proper vertex position is calculated from the tracks,the number of events inside a window of 5 GeV around the peak increases of about 15%.Together with vertex reconstruction, γ/π and γ /jet discrimination play an importantrole in the analysis for this decay channel, since they are crucial in rejecting the highreducible background. The signal cross section is about 86 fb at m H = 130 GeV, thusbeing three orders of magnitude below the cross section for γ +jet final state from back-ground processes, and a factor 10 below the one for jet+jet final state. This calls forsevere requirements in terms of jet and π rejection.CMS will use isolation contraints against jets, while π rejection will be based on a neuralnetwork using as input several variables related to shower shapes, plus the informationfrom pre-shower detectors in the endcaps. An extensive use of the calorimeter trans-verse granularity, of hadronic leakage and shower shape parameters, will allow ATLASto achieve a total rejection factor of about 3000 for γ efficiency of 80%.Given the amount of material in the inner trackers of the two experiments, photon con-versions are not negligible in these studies, but must be recovered by means of dedicatedreconstruction algorithms.Signal significances can be improved using associated production studies, or more ad-vanced analysis techniques (neural networks, likelihood, categories) and both ATLASand CMS are exploring several possibilities.Expected signal significances ( m H = 130 GeV) at 30 fb − are 6.0 (cut based) and 8.2(neural network) for CMS [41] and 6.3 (cut based) for ATLAS. .3. H → τ τ . – The high background rate for this final state makes it impossible tostudy the gg production channel. Both experiments are thus focusing on VBF productionwhere the additional jets in the final state allow to improve significantly the signal overbackground ratio, compensating for the smaller production cross section: σ ∼
80 fb at
S. BOLOGNESI, G. BOZZI and
A. DI SIMONE
Signal Efficiency
Signal Efficiency B ack g r ound E ff i c i e n cy QCD Z+2/3jets+2jet t EW 2 WbWb fi ttW+3/4jets Fig. 3. – Left: CMS results for central jet veto on the VBF H → τ τ channel. Background vssignal ( m H = 135 GeV) efficiencies for different threshold values (10, 15, 20, ..., 45 GeV) [42].Right: invariant mass of the two Z bosons for the H → ZZ → l channel as expected in theATLAS experiment. Signal and main backgrounds are shown. m H = 135 GeV. All possible final states (lepton-lepton, lepton-hadron, hadron-hadron)are presently under study in ATLAS, while CMS focused on the recent past only on the lh decay channel.The irreducible background for this decay channel comes from Zjj (QCD and elec-troweak) processes. In addition, several reducible backgrounds need to be taken intoaccount, such as QCD multijet, W +jet, Z/γ +jet, t ¯ t .For leptonic and semi-leptonic final states, trigger menus based on single leptons andsingle leptons plus τ s will be used, while for the fully hadronic decay channel, the mostpromising trigger configuration is τ plus missing E T .The VBF production channel allows for Forward Jet Tagging, where the event is searchedthrough looking for the two additional quark initiated jets, which are typically located inopposite hemispheres and have high p T values. Both the experiments use similar tech-niques, looking for the two highest p T jets and requesting that they have opposite η sign.Another important characteristic of VBF events is the absence of jets in the centralrapidity region. This can be exploited implementing a Central Jet Veto, which rejectsevents with jets in the central region of the detector (apart from the jets identified as τ s). Fig. 3 (left) shows the background vs signal selection efficiencies for different valuesof the threshold applied on the jet energy in the central jet veto.Expected signal significance ( m H = 130 GeV) at 30 fb − is 4.4 ( lh final state) and 5.7( lh plus ll ) for ATLAS [43] and 3.98 ( lh final state) for CMS [42].
4. – H → V V channels
In the high mass region ( m H >
150 GeV) the most promising channels are the oneswith the Higgs decaying into two vector bosons (
W W or ZZ ). Their effectiveness ofcourse follows very closely the shape of the branching ratio curves. At about 160 GeVthe most interesting channel is W W , while for heavier higgses, ZZ becomes dominantonce the threshold for the on-shell production of the second Z is approached. For m H >
350 GeV, the t ¯ t channel becomes available, and the discovery potential for these channelsis thus reduced.The theoretical cross sections for these decay channels are known at 3-loop QCD for IGGS AT LHC H → V V [37] and 2-loop QCD for H → t ¯ t [38]. The backgrounds to the H → V V decay channel are also known at NLO QCD for
W W → lνlν, ZZ → l [39] and for V V production via VBF [40].Moreover, the VBF production channel (
V V → V V ) is interesting per se, since it is apowerful probe of the electroweak symmetry breaking mechanism. In these processes,either the Higgs is found in the s-channel, or unitarity is violated in SM at the TeV scaleand new physics must appear. .1. H → ZZ → l . – These processes are very interesting over a wide mass range,mainly for their very clean signature and quite high production cross section ( ∼
38 fb − at m H = 135 GeV). The most critical region is 125-150 GeV, where one of the Z bosonsis off-shell, leading to low- p T leptons which make the analysis more difficult.The irreducible background ZZ ∗ /γ ∗ → l has a cross section of the order of tens of fband it gives the biggest contribution to background after analysis selection. In addition,reducible background comes from Zbb and t ¯ t processes, where the needed rejection factorsof ∼ and ∼ respectively are achieved using lepton isolation and impact parametercuts.The crucial point of the analysis is lepton identification and reconstruction and actuallythe main systematic effects are expected to arise from lepton energy scale/resolution andlepton identification efficiency. In order to keep these effects under control, both ATLASand CMS plan to measure lepton performance from data using Z → l events.Reconstructed invariant mass of the ZZ pair is shown in fig. 3 (right) for signal and themain backgrounds. .2. H → W W → lνlν . – This fully leptonic final state ( σ ∼ φ ( ll )). In the SM the Higgs boson has 0 spinso the lepton (left-handed) and the anti-lepton (right-handed) tends to go in the samedirection and ∆ φ ( ll ) is small. This is a good assumption only for not too high Higgs mass(below 200-250 GeV), otherwise the big boost of the W bosons pushes the two chargedleptons into opposite directions.Because of the absence of an Higgs peak, a careful strategy for background normal-ization from real data is needed. The rate of the main backgrounds ( t ¯ t with σ ∼
86 pb,
W W with σ ∼
12 pb, in the fully leptonic final states) in the signal region is extrapolatedfrom dedicated control regions, using a rescaling factor evaluated from Monte Carlo.A detailed study of the impact of theoretical uncertainties (mainly due to the gg → W W description and double top with single top interference) on this procedure has been car-ried out in the ATLAS collaboration [44], showing an uncertainty of about 5% and 10%respectively on
W W and t ¯ t rate in the signal region. Given these systematics, a Higgsdiscovery at m H ∼
160 GeV would require less than 2 fb − .A similar study from the CMS collaboration [45] also takes into account the exper-imental systematics (due to lepton identification, b -tagging, calorimetry energy scaleand jet energy scale) on the background normalization procedure, showing that 2 fb − (10 fb − ) should be enough for a Higgs discovery at 155 GeV < m H <
170 GeV(150 GeV < m H <
180 GeV).The most recent progesses on this channel concern the strategies to measure theinteresting detector performances directly from data: the lepton identification efficiencycan be extrapolated from the efficiency computed on single Z sample exploiting the tag- S. BOLOGNESI, G. BOZZI and
A. DI SIMONE ,GeV/c A M
100 200 300 400 500 600 700 800 b t an -1 CMS, 30 fb = h,H,A f , f bb fi pp scenario maxh m = 1 TeV/c SUSY M = 200 GeV/c M = 200 GeV/c m = 800 GeV/c gluino m SUSY = 2 M t Stop mix: X m e fittfif + j e t mfittfif e+jet fittfif - j e t + j e t , f b fittfif mmfif ,GeV/c A M
100 200 300 400 500 600 700 800 b t an CMS scenario maxh m = 1 TeV/c SUSY M = 200 GeV/c M = 200 GeV/c m = 800 GeV/c gluino m SUSY = 2 M t Stop mix: X =115 GeV/c h m - , c u t s , f b ggfi h - , op t ., f b ggfi h -1 l+jet, 30 and 60 fb fittfi qqh, h -1 l+jet, 30 and 60 fb fittfi qqH, H Fig. 4. – Left: 5 σ discovery regions in CMS with 30 fb − for the neutral Higgs bosons ( φ = h, H, A ) produced in association with b quarks and decaying into τ τ and µµ in the m maxh scenario. Right: 5 σ discovery regions in CMS with 30 fb − for the light neutral Higgs boson( h ) decaying into γγ and for the light and heavy Higgs bosons ( h and H ) produced in VBF anddecaying into τ τ → l +jet in the m maxh scenario. and-probe technique; to evaluate the impact of the W +jets background, the lepton fakerate can be measured from QCD multi-jets events; finally, the systematics on the missingenergy can be estimated from the W mass measurement or by comparing W and Z withone lepton artificially removed.
5. – Higgs in the MSSM model
The light neutral Higgs boson ( h ) has a similar behavior to the SM Higgs, the mosteffective channel being H → τ τ .The heavier neutral Higgs bosons ( A , H ) are studied in different channels, dependingon the tan β value. For low tan β , the gg fusion production is usually considered withpeculiar Higgs decay channels like A → Zh → llbb or A/H → χ χ → l + /E T . For hightan β , the associated Higgs production with b ¯ b is studied with the Higgs decaying into τ τ or µµ (with quite low BR but much clean). The 5 σ discovery regions with 30 fb − for the three neutral Higgs bosons at CMS are shown in fig. 4.Finally the charged Higgs bosons ( H + , H − ) are studied in different channels dependingon their mass. If m H < m t then the most promising channel is tt → tbH → tbτ ν . For m H > m t , gg → tbH and gb → tH are the main production mechanisms and H → tb and H → τ ν (with lower BR but more clean) are the best decay channels. All these finalstates are very crowded, therefore they suffer from combinatorial background in additionto big QCD background (mainly t ¯ t +(b)jets and W +(b)jets).
6. – Combined results
In fig. 5 the combined results of the two experiments for the Higgs discovery (orexclusion) are shown [46]. The low Higgs mass region is the most complex case becauseit requires the combination of several channels ( H → τ τ , H → γγ and possibly H → bb ).The region 150 GeV < m H <
500 GeV is the most favourable one, exploiting the cleanchannels H → ZZ → l in quite all this mass range except for m H ∼
160 GeV, where
IGGS AT LHC Fig. 5. – Luminosity needed for the Higgs discovery and exclusion at 95% C.L. as a function ofthe Higgs mass, combining the results from ATLAS and CMS. the H → W W → lνlν decay channel dominates.However, before a Higgs discovery can be claimed, some effort will be necessary tounderstand the detector systematics (mainly regarding jets, γ fake rate, missing energy)and to perform a careful measurement of the multi-jets background cross sections (likeQCD jets, V +jets, V V +jets, t ¯ t +jets, b ¯ b +jets). REFERENCES[1]
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