Higgs physics: Review of recent results and prospects from ATLAS and CMS
An overview of recent results in Higgs boson physics obtained with the ATLAS and CMS experiments at the Large Hadron Collider located at CERN, Geneva, is presented. The focus is on measurements of the properties of the recently discovered Higgs boson with a mass of about 125 GeV. A brief selection of results in searches for Higgs bosons beyond the Standard Model is given, and prospects of future Higgs boson measurements and searches at the LHC are discussed.
In July 2012, the ATLAS  and CMS  collaborations announced the discovery of a new particle compatible with being the Higgs boson of the Standard Model (SM) [3, 4]. Subsequent measurements of the properties of this particle are all consistent with the SM Higgs boson interpretation. In the following sections, the most recent results from studies of this Higgs boson using the data collected with the ATLAS and CMS experiments are presented. First, the results in various Higgs boson production and decay channels are given, followed by the measurement of Higgs boson properties using a combination of these results. Searches for Higgs bosons predicted by theories beyond the Standard Model (BSM) are briefly summarized and prospects for future Higgs boson property measurements are discussed. Most of the results are based on the full data set recorded in 2011 and 2012 at center-of-mass energies of 7 TeV and 8 TeV, respectively, corresponding to about 25 fb per experiment.
2 Higgs boson search results
The dominant Higgs boson production modes are gluon-gluon fusion (ggF), vector boson fusion (VBF), production in association with a vector boson (, or ), and in association with top quarks (). The five most sensitive Higgs boson decay channels at the LHC are the modes , 4-leptons, , and [5, 6, 7]. Results for these channels are summarized in the following.
The channel is characterized by relatively high total event counts but a low signal-over-background ratio. Furthermore, it offers a high mass resolution () and thus contributes strongly to the Higgs boson mass measurement. The analyses [8, 9] proceed by selecting events with two photons in various categories, aimed at different production modes. This is done by additionally requiring two jets with a high rapidity gap (VBF), additional leptons and in some cases missing energy () or an event topology consistent with an additional top quark pair event (). The final discriminating variable is the estimator. The background, dominantly continuum , +jet and di-jet events, is estimated by fitting the sidebands of the distribution, as illustrated in Fig. 2. The signal is visible on top of the estimated background at GeV.
Both ATLAS and CMS observe slightly more candidate events than expected; however, the measurement is within one Gaussian standard deviation () of the SM expectation. Both experiments measure the signal strength (observed cross section times branching ratio divided by the SM expectation) also individually for the various Higgs boson production modes, see Fig. 2. All values are in agreement with the SM expectation of . The observed signal significance is (expected: ) for CMS and (expected: ) for ATLAS.
The expected rate of lepton events is low compared to the other channels presented here; however, this is compensated by the highest signal-over-background ratio. This channel is further characterized by a high mass resolution () and dominates the Higgs boson mass measurement together with . The analyses [10, 11] first require four light leptons and are then pursued in subchannels depending on the flavor of the two lepton pairs. Like the analysis, it is split in categories targeting different production modes. However, the main sensitivity rests in the jet category aimed at gluon-gluon fusion production. The main background is continuum production which is estimated from simulation and validated in control regions. The combined distribution for ATLAS is shown in Fig. 4. The mass peak at about 125 GeV is clearly visible.
Both the ATLAS and CMS results are in very good agreement with the SM expectation. This is illustrated in Fig. 4 where the signal strength for the ggF and production mode is measured with respect to the VBF and production modes. The observed signal significance is (expected: ) for CMS and (expected: ) for ATLAS.
Higgs boson decays to a boson pair offer a relatively high expected rate but suffer from a high irreducible continuum background which is hard to suppress due to the low resolution, caused by the presence of neutrinos in the most sensitive decay modes. The +jets and top quark pair background is also sizable. The most sensitive subchannel features a final state with low jet multiplicity [12, 13]. Requirements of additional jets or leptons aim to add extra sensitivity by exploiting production modes other than ggF. The distribution in the category “ + 2 (or more) jets” is shown in Fig. 6. This is the category with the highest expected signal purity.
Both the observed ATLAS and CMS rates are within about of the SM expectation. In Fig. 6, the Higgs boson exclusion versus is shown. Visible are both the excess at about 125 GeV and the exclusion of other, heavy SM-like Higgs bosons.
The analyses are among the most complex analyses of LHC data: Six different channels, depending on the combination of lepton decays, are investigated: , , , , and (here, signifies a hadronic lepton decay, and neutrinos are omitted). For all these channels, categories motivated by the production mode can be established: 0/1-jet, boosted (boson candidate with high ), VBF and . CMS has also investigated with . The CMS analysis  which is based on orthogonal selection requirements implements almost one hundred categories. ATLAS  uses only six; however, here, the analysis is based on a Boosted Decision Tree (BDT). Both ATLAS and CMS use sophisticated estimators using kinematic information of the whole decay chain to reconstruct a mass value in spite of the presence of a number of undetected neutrinos. The combined distribution is shown in Fig. 8. The main background is due to events which are estimated by replacing muons in collision data events with simulated leptons.
Both ATLAS and CMS report evidence for decays. ATLAS observes (expected: ), CMS observes (expected: ). This is the first evidence for Higgs boson decays to leptons. The sensitivity is mostly driven by the VBF category, as can be seen in Fig. 8. While the signal strength in ggF is only weakly constrained, VBF/ decays are established at a -level.
The analysis is extremely challenging at the LHC, despite the high expected branching ratio of at GeV. The ggF production is not accessible as the signal cannot be separated from the overwhelming non-resonant background. The situation for VBF production is only marginally better. The main workhorse are thus events; in addition, is also investigated. Both experiments use a BDT-based analysis [17, 18] to isolate the signal from the overwhelming background of , , , and multi-jet events. The distribution after background subtraction is shown in Fig. 10.
Both observed and expected significance by CMS are . ATLAS observes while the expectation is . The non-significant ATLAS deficit is driven by the TeV data. The CMS measurement of the signal strength is shown in Fig. 10.
The channel poses very particular challenges and is thus in most cases not treated in the context of the usual decay mode analyses by ATLAS and CMS. Instead, dedicated analyses and combinations are produced. CMS investigates six different final states , see Fig. 12. The measured combined signal strength is which is about high compared to the SM expectation. The small excess is almost entirely driven by the same-sign two-lepton category. The BDT output for this category is shown in Fig. 12 and illustrates this point. ATLAS investigates and combines  two final states in production, namely and . The combined ATLAS limit on production is in good agreement with the SM.
3 Higgs boson property measurements
The Higgs boson property measurements use the results of the analyses aiming at the various production and decay modes presented in the previous section. For each measurement, the channels sensitive to the property in question are combined. Among the studied properties are mass, width, signal strength (i.e., normalized cross section times branching ratio), coupling strength and tensor coupling structure (CP properties) of the Higgs boson in relation to other SM particles. In addition, differential cross sections allow further insight and additional tests of BSM scenarios.
The Higgs boson mass measurement uses input from the and 4-lepton decay modes. In both channels, the Higgs boson candidate mass can be reconstructed with high precision directly from its visible decay products. The ATLAS measurement , illustrated in Fig. 14, yields . The CMS measurement , see Fig. 14, is consistent with this result: . Historically, there has been a tension between the two ATLAS measurements. However, this tension is gradually decreasing and currently the mass is only about high with respect to the four-lepton mass. The two CMS mass measurements have a tension in the opposite direction, i.e. .
The SM expectation for the Higgs boson width at GeV is about 4 MeV. There are several ways to access the Higgs boson width experimentally. Directly, the width can be measured by analyzing the width of the and distributions. This method is limited by the experimental resolution which is about three orders of magnitude higher than the width predicted by the SM. The direct ATLAS width limits are 5.0 GeV (), 2.6 GeV ( leptons) ; the corresponding CMS limits are 2.4 GeV ()  and 3.4 GeV ( leptons) .
Indirect limits can be obtained by Higgs boson coupling fits (by leaving the invisible width as free fit parameter). However, the most precise indirect measurement is based on the comparison of the on- and off-shell leptons signal strength. The CMS limit on the Higgs width using this technique is 22 MeV (expected: 33 MeV), which corresponds to 5.4 (expected: 8.0) times the SM expectation . ATLAS uses a more flexible model and excludes 5-8 (expected: 7-12) times the SM expectation, depending on the ratio of the leading-order to next-to-leading order cross section for on- and off-shell production .
3.3 Signal strength
The signal strength , defined as measured cross section times branching ratio of a given process divided by the SM expectation, is an important test for the validity of the SM. With the data accumulated in the LHC Run 1, no significant deviation is observed. The combined CMS result is , and the results for each decay channel are consistent with the SM within , see Fig. 18. The ATLAS result is slightly high, . Note that this combined value has not been updated after the release of the most recent results which are summarized in Fig. 18. The ATLAS results for all channels agree with the SM expectation within about .
3.4 Coupling strength
The coupling strength factors are a leading-order-inspired parametrisation of the Higgs boson coupling to a particle or particle class with respect to the SM expectation. is used to denote the ratio of two values and . The measurements are typically a result of a global fit of a large subset of the Higgs boson analyses and due to the large number of free parameters, some assumptions have to be made to obtain sensible results with the data of the LHC run 1. Usual assumptions are those on the Higgs width (to be SM-like) or of a universal coupling strength scaling, e.g. of all fermions or all up-type quarks. An important SM test is the scaling of fermion couplings versus boson couplings, shown in Fig. 20. The result is consistent with the SM expectation . Further tests involve the custodial symmetry ( versus coupling), up- versus down-type quark couplings or lepton versus quark couplings. As shown in Fig. 20, all results agree with the SM prediction .
3.5 Tensor coupling structure
The study of the spin and CP properties of the discovered boson are essential for the claim of the discovery of the first fundamental scalar. To this date, all measurements are in agreement with the SM but since the parameter space of alternative models is continuous in several dimensions, no generic exclusion of e.g. spin-2 models has been possible. However, a large set of the best-motivated models has been tested with the result that the SM hypothesis is favored [26, 27]. This is illustrated in Fig. 21 where measurements of several parameters for the spin-0 case are made and all are found to be consistent with the SM expectation. Today, all alternatives to a spin-0 boson are disfavored and large anomalous contributions to the CP structure of the Higgs boson couplings are excluded. However, small or medium-sized CP-odd or anomalous CP-even admixtures are still feasible.
3.6 Differential cross sections
By the end of LHC Run 1, sufficient data have been collected to allow for the first publications of differential distributions in Higgs boson events, namely in ATLAS studies of the  and leptons  channels. The resulting contributions are compared to predictions of the SM, but model builders can compare them to predictions of any competing models. Some of the aspects which are probed are the jet multiplicity in Higgs boson events (to test the QCD structure of SM calculations and models), see Fig. 23, the transverse momentum of the Higgs boson candidate (to test for BSM effects hidden in loops, e.g. involving top quarks), see Fig. 23, or the difference of the azimuthal angle of two of the jets in the event (to test for effects of an anomalous tensor coupling structure). The results, within large statistical uncertainties, are broadly in line with the SM predictions.
4 BSM Higgs boson searches
The programme of BSM Higgs boson searches at the LHC is very extensive and cannot be presented exhaustively here. In the following, highlights of searches for Higgs bosons predicted by the Minimal Supersymmetric extension of the SM (MSSM) are presented, and other BSM Higgs boson searches are listed and their conclusions are summarized.
4.1 MSSM Higgs boson searches
The MSSM predicts the existence of five Higgs bosons, three of them neutral and a charged pair. The most sensitive search for neutral MSSM Higgs bosons for most of the parameter space is via their decays. The current CMS limit  in the scenario  is shown in Fig. 25. Due to the charged Higgs boson search result, the option to identify the discovered Higgs boson (at ) GeV with the heavy CP-even neutral MSSM Higgs boson has been strongly disfavored. Presently, BR() above about 1% are excluded for GeV. For charged Higgs bosons heavier than the top quark, a sizable region at moderate and high has been excluded .
4.2 Other BSM Higgs boson searches
There is a vast number of BSM Higgs boson searches with ATLAS and CMS in addition to the and searches introduced in the previous section. A non-exhaustive list of these searches is given here:
All searches have in common that no significant deviation from the SM expectation has been found and that the phase space for BSM Higgs bosons has been constrained. However, the higher kinematic reach at TeV and the extension of the current data set by 1-2 orders of magnitude will allow to explore a magnitude scenarios over the next few years.
5 Prospects for Higgs boson searches
The present LHC programme projects the delivery of about 300 fb of data at TeV per experiment by the year 2022. One of the options is that this will be followed by a high-luminosity LHC (HL-LHC), producing 3000 fb of data at TeV until 2035 . In the following, projections of Higgs boson property measurements assuming these conditions are presented. Typically, it is assumed that the detector and reconstruction performance is comparable to that of LHC Run 1 due to improved reconstruction algorithms and detector upgrades countering the effect of an increase in concurrent proton-proton interactions (“pile-up”). Systematic uncertainties are assumed to be similar to the current status (CMS Scenario 1 and ATLAS) or to go down (CMS Scenario 2; by a factor 0.5 for theoretical uncertainties, and by the inverse of the square root of the integrated luminosity for other systematic uncertainties) [66, 67].
5.1 Signal strength and coupling strength projections
The CMS estimate for the first 300 fb is a precision of roughly 10% on the signal strength for the five most sensitive channels, see Fig. 27. The predicted uncertainties are between 6%–14%, with lower values for the bosonic decay modes and higher ones for the fermionic modes, and depending on the scenario . The ATLAS projection for 300 fb is slightly more conservative, expecting a precision of about 10% for the bosonic modes, and about 20% for the fermionic modes. In addition, a precision of about 40% on the rare decay channels and is estimated, see Fig. 27. Sizable improvements with 3000 fb are in particular expected for the , and measurements but the precision for all signal strength measurements is expected to improve significantly .
CMS estimates a precision of 4%–8% on the Higgs boson coupling strength to elementary bosons and the lepton, and of 10%–15% to the bottom and the top quark with 300 fb , as illustrated in Fig. 29. The ATLAS estimates are comparable but in all cases slightly more pessimistic . In Fig. 29, the projected uncertainty for a fit with two free parameters is shown: and . Assuming only these two universal scaling factors, a precision of about 2%–4% on (when is profiled) and of 3%–9% on (when is profiled) can be achieved, depending on the integrated luminosity and the assumptions on theory uncertainties. The potential improvement on the precision of with the HL-LHC is almost a factor of two.
5.2 Double-Higgs production and Higgs self-coupling projections
There are two kinds of contributions to double-Higgs production: With, and without a triple-Higgs vertex. A measurement of the cross section of this process thus allows to draw conclusions about the Higgs self-coupling. Due to the negative interference of these two contributions in the SM, only about 10 signal events are expected in the final state in 3000 fb of data. According to ATLAS projections, the expected significance for production in this channel for the whole HL-LHC data set is about . CMS estimates a relative uncertainty on the cross section measurement of about 60%  for the same final state. As of today it is thus unclear if any meaningful measurement of the Higgs self-coupling at the LHC is possible.
Both ATLAS and CMS offer a rich Higgs physics programme. Following the Higgs boson discovery in 2012, recent years have seen a focus on measuring the properties of this Higgs boson. All measurements so far are consistent with the SM expectation but only the sizable improvements on their precision expected in the near future will allow to distinguish between the SM and many of its alternatives. In searches for BSM Higgs bosons, no evidence for a new state has been found, severely constraining a wide range of BSM models.
-  ATLAS Collaboration JINST 3 S08003
-  CMS Collaboration JINST 3 S08004
-  ATLAS Collaboration Phys.Lett. B716 1–29 (Preprint 1207.7214)
-  CMS Collaboration Phys.Lett. B716 30–61 (Preprint 1207.7235)
-  LHC Higgs Cross Section Working Group, Dittmaier S, Mariotti C, Passarino G and Tanaka R E CERN-2011-002 (Preprint 1101.0593)
-  LHC Higgs Cross Section Working Group, Dittmaier S, Mariotti C, Passarino G and Tanaka R E CERN-2012-002 (Preprint 1201.3084)
-  LHC Higgs Cross Section Working Group, Heinemeyer S, Mariotti C, Passarino G and Tanaka R E CERN-2013-004 (Preprint 1307.1347)
-  CMS Collaboration Eur.Phys.J. C74 3076 (Preprint 1407.0558)
-  ATLAS Collaboration Phys.Rev. D90 112015 (Preprint 1408.7084)
-  ATLAS Collaboration Phys.Rev. D91 012006 (Preprint 1408.5191)
-  CMS Collaboration Phys.Rev. D89 092007 (Preprint 1312.5353)
-  ATLAS Collaboration (Preprint 1412.2641)
-  CMS Collaboration JHEP 1401 096 (Preprint 1312.1129)
-  CMS Collaboration JHEP 1405 104 (Preprint 1401.5041)
-  ATLAS Collaboration ATLAS-CONF-2014-061
-  CMS Collaboration JHEP 1409 087 (Preprint 1408.1682)
-  ATLAS Collaboration (Preprint 1409.6212)
-  CMS Collaboration Phys.Rev. D89 012003 (Preprint 1310.3687)
-  ATLAS Collaboration ATLAS-CONF-2014-043
-  ATLAS Collaboration Phys.Rev. D90 052004 (Preprint 1406.3827)
-  CMS Collaboration CMS-PAS-HIG-14-009
-  CMS Collaboration Phys.Lett. B736 64 (Preprint 1405.3455)
-  ATLAS Collaboration ATLAS-CONF-2014-042
-  ATLAS Collaboration Summary plots from the ATLAS Higgs physics group 10/2014 URL https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummar%yPlots/HIGGS/
-  ATLAS Collaboration Phys.Lett. B726 88–119 (Preprint 1307.1427)
-  CMS Collaboration (Preprint 1411.3441)
-  ATLAS Collaboration Phys.Lett. B726 120–144 (Preprint 1307.1432)
-  ATLAS Collaboration JHEP 1409 112 (Preprint 1407.4222)
-  ATLAS Collaboration Phys.Lett. B738 234–253 (Preprint 1408.3226)
-  CMS Collaboration JHEP 1410 160 (Preprint 1408.3316)
-  ATLAS Collaboration ATLAS-CONF-2014-050
-  Carena M, Heinemeyer S, Stål O, Wagner C and Weiglein G Eur.Phys.J. C73 2552 (Preprint 1302.7033)
-  ATLAS Collaboration Eur.Phys.J. C73 2465 (Preprint 1302.3694)
-  CMS Collaboration CMS-PAS-HIG-13-035
-  CMS Collaboration CMS-PAS-HIG-13-026
-  ATLAS Collaboration ATLAS-CONF-2012-094
-  CMS Collaboration CMS-PAS-HIG-12-011
-  CMS Collaboration Phys.Lett. B722 207–232 (Preprint 1302.2892)
-  ATLAS Collaboration ATLAS-CONF-2013-027
-  ATLAS Collaboration ATLAS-CONF-2012-079
-  ATLAS Collaboration ATLAS-CONF-2011-020
-  CMS Collaboration Phys.Rev.Lett. 109 121801 (Preprint 1206.6326)
-  ATLAS Collaboration ATLAS-CONF-2013-067
-  CMS Collaboration Phys.Rev. D90 112013 (Preprint 1410.2751)
-  ATLAS Collaboration Phys.Rev.Lett. 112 201802 (Preprint 1402.3244)
-  CMS Collaboration Eur.Phys.J. C74 2980 (Preprint 1404.1344)
-  ATLAS Collaboration (Preprint 1412.0237)
-  CMS Collaboration Eur.Phys.J. C72 2189 (Preprint 1207.2666)
-  CMS Collaboration CMS-PAS-HIG-14-005
-  ATLAS Collaboration JHEP 1406 008 (Preprint 1403.6293)
-  CMS Collaboration CMS-PAS-HIG-13-034
-  ATLAS Collaboration Eur.Phys.J. C72 2157 (Preprint 1205.0701)
-  CMS Collaboration Phys.Lett. B725 36–59 (Preprint 1302.1764)
-  ATLAS Collaboration ATLAS-CONF-2011-135
-  ATLAS Collaboration ATLAS-CONF-2014-010
-  ATLAS Collaboration (Preprint 1406.5053)
-  ATLAS Collaboration ATLAS-CONF-2014-005
-  CMS Collaboration CMS-PAS-HIG-14-013
-  CMS Collaboration CMS-PAS-HIG-13-032
-  CMS Collaboration CMS-PAS-HIG-13-010
-  CMS Collaboration CMS-PAS-HIG-14-011
-  ATLAS Collaboration Phys.Rev. D89 032002 (Preprint 1312.1956)
-  ATLAS Collaboration Phys.Rev.Lett. 108 251801 (Preprint 1203.1303)
-  ATLAS Collaboration New J.Phys. 15 043009 (Preprint 1302.4403)
-  ATLAS Collaboration Phys.Lett. B721 32–50 (Preprint 1210.0435)
-  ATLAS Collaboration ATL-PHYS-PUB-2014-016
-  CMS Collaboration CMS-NOTE-13-002 (Preprint 1307.7135)
-  ATLAS Collaboration ATL-PHYS-PUB-2014-019
-  CMS Collaboration Physics Performance for 2nd ECFA workshop 10/2014 URL https://twiki.cern.ch/twiki/pub/CMSPublic/PhysicsResultsFP/EC%FA-CMSPublicResults.pdf