The Higgs Boson discovery

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Karl Jakobs and Chris Seez (2015), Scholarpedia, 10(9):32413. doi:10.4249/scholarpedia.32413 revision #151683 [link to/cite this article]
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Curator: Chris Seez


The Higgs boson discovery was announced by the ATLAS and CMS collaborations on 4th July 2012. Evidence for a new particle with the mass of about 125 GeV and the properties of the Standard Model Higgs boson was present in the three decay modes H → ZZ* → ℓℓ ℓℓ, H → γγ, and H → WW* → ℓν ℓν in both experiments.


Contents

Introduction

The Standard Model of particle physics takes quarks and leptons to be fundamental, elementary particles, and describes the forces that govern their interactions as mediated through the exchange of further elementary particles. The exchanged particles are photons in the case of the electromagnetic interaction, W and Z bosons in the case of the weak interaction, and gluons in the case of the strong interaction. After the discovery of the W and Z bosons in the early 1980s, the elucidation of the mechanism by which they acquire mass became an important goal for particle physics. Within the Standard Model the W and Z bosons have masses generated via the symmetry breaking Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, proposed in 1964 and giving rise to a massive scalar particle, the Standard Model Higgs boson.


The Large Hadron Collider

The Large Hadron Collider (LHC) was built at CERN in the 27-kilometre LEP tunnel with the aim of probing the TeV energy scale. A key element in the scientific goals of the LHC was the elucidation of the electroweak symmetry breaking mechanism and the search for the Higgs boson postulated in the Standard Model. The LHC is designed to accelerate and collide protons at a centre-of-mass energy of 14 TeV, and to achieve an instantaneous luminosity exceeding 1034 cm-2s-1 with the counter-rotating proton bunches separated by 25 ns, resulting in a bunch crossing rate of 40 MHz.

Stable operation of the LHC began in 2010 at a centre-of-mass energy of 7 TeV. In 2011 the number of bunches in the beams was increased to 1380, corresponding to a bunch separation of 50 ns, and significantly increasing the luminosity. In 2012 the centre-of-mass energy was raised to 8 TeV, and the luminosity was further increased during the course of the year, reaching peak luminosities of up to 7 \( \cdot \) 1033 cm-2s-1.

Luminosity

The instantaneous luminosity, \(\mathcal{L}\), provides a measure of the beam intensity and depends on the number of particles in the circulating beams and how closely they are squeezed in space at the collision point. The usual unit of measurement is cm-2s-1. The cross section of a process, σ, multiplied by the instantaneous luminosity, then gives the rate of interactions, \( \dot N = \mathcal{L} \sigma \). For example, the Higgs boson production cross section multiplied by the instantaneous luminosity yields the expected production rate of Higgs bosons, i.e. the number of Higgs bosons produced per second.

The integrated luminosity is the instantaneous luminosity integrated over time. The data collected by the ATLAS and CMS experiments in 2011 and in the first months of data taking in 2012, and used in the analyses that resulted in the first observation of the Higgs boson, corresponded to slightly more than 5 inverse femtobarns (fb-1 = 10-39 cm-2) in each year for each experiment. This integrated luminosity resulted in about 1015 proton-proton collisions at the centre of each detector.


Pileup

An event recorded by a detector may contain signals from more than one proton-proton collision and from several bunch crossings. This effect is known as pileup. The high intensity of the proton beams results in multiple proton-proton collisions occurring during each bunch crossing. The average number of interactions per bunch crossing was about 10 in 2011 and increased to about 20 in 2012. Advances in understanding of the performance of the detectors, and improved analysis techniques, were used to associate tracks and energy deposits to the different interactions, thereby mitigating the effects of the harsher environment, as the LHC instantaneous luminosity increased.


Experimental variables

The pseudorapidity, η, is defined as η=−ln[tan(θ/2)], where θ is the polar angle measured from the anticlockwise beam direction. The azimuthal angle, measured about the axis defined by the beam directions, is denoted by \(\phi\). The transverse momentum, pT, denotes the component of momentum perpendicular to the beam axis.

Given the relativistic energy-momentum relation \( E = \sqrt{p^2c^2+m^2c^4}\) and using the Natural Unit system, as commonly used in particle physics, where the speed of light in vacuum c is set to 1, masses and momenta are expressed in units of energy, as eV (electron-volts) or keV, MeV, GeV, or TeV.


The ATLAS and CMS experiments

Figure 1: View of the completed ATLAS detector in its underground cavern. On the left, the coils of the superconducting toroidal magnet system and muon detectors in the barrel region are visible, with the cryostat of the endcap calorimeters in the centre. The detector is an open position. Visible are the endcap toroid (moved out of its position) and the large muon detector system in the endcap region on the right. February 2008 (Photograph © 2008 CERN).
Figure 2: Installation of the CMS detector in the underground cavern. On the left is the barrel, with the superconducting coil surrounded by the iron yoke instrumented with the four muon stations. On the right is one of the two endcaps. In the completed detector, the vacuum pipe for the colliding beams passes through the axis of the solenoid, and is surrounded by silicon pixel and strip detectors, the electromagnetic calorimeter, and the hadron calorimeter (Photograph © 2008 CERN)

ATLAS and CMS were designed as general-purpose detectors, having the capability to identify and precisely reconstruct muons, electrons, photons, hadronic jets, and the imbalance of momentum transverse to the direction of the beams. The latter is used to measure the missing transverse momentum, ETmiss, carried away by weakly interacting particles. The two detectors are composed of subdetector systems employing different technologies, and requiring different methods of calibration and reconstruction. They are thus somewhat complementary and to some extent subject to different experimental sources of systematic uncertainty.

The design of the ATLAS experiment is based on the use of a toroidal magnet system for its muon spectrometer. The toroidal magnet system comprises three large air-core superconducting magnets, each with eight coils, equipped with precision tracking chambers, and fast detectors for triggering. The inner detector, surrounding the beam pipe, consists of a silicon pixel detector, a silicon microstrip detector, and a straw-tube transition radiation tracker. The inner detector is surrounded by a thin superconducting solenoid that provides a 2 T magnetic field, and by high-granularity liquid-argon (LAr) sampling electromagnetic calorimetry. An iron/scintillator-tile calorimeter gives hadronic coverage in the central pseudorapidity range (|η| < 1.7), while a LAr hadronic endcap calorimeter provides coverage over 1.5 < |η| < 3.2. The forward regions (3.2 < |η| < 4.9) are instrumented with LAr calorimeters for both electromagnetic and hadronic measurements. Figure 1 shows a photograph of the ATLAS detector.

The central feature of the CMS experiment is a superconducting solenoid, which provides an axial magnetic field of 3.8 T. The bore of the solenoid is instrumented with both the central tracker and the calorimeters. The steel flux return yoke outside the solenoid hosts gas ionization detectors used to identify and reconstruct muons. Charged-particle trajectories are measured by a silicon pixel and strip tracker, with full azimuthal coverage within |η| < 2.5. A lead tungstate crystal electromagnetic calorimeter (ECAL) and a brass/scintillator hadron calorimeter (HCAL) surround the tracking volume and cover the region |η| < 3. The ECAL barrel extends to |η| < 1.48 while the ECAL endcaps cover the region 1.48 < |η| < 3.0. A lead/silicon-strip preshower detector is located in front of the ECAL endcap in the region 1.65 < |η| < 2.6. The preshower detector includes two planes of silicon sensors measuring the x and y coordinates of the impinging particles. A steel/quartz-fibre Cherenkov forward calorimeter extends the calorimetric coverage to |η| < 5.0. A photograph of the CMS detector is shown in Figure 2.


Higgs boson production at the LHC

Since the strength of the Higgs boson interaction with Standard Model particles depends on their mass, the production of Higgs bosons at the LHC predominantly involves the massive vector bosons W and Z, and heavy fermions. These massive particles may be conceived as being produced via radiation processes from the incoming quarks or gluons in the colliding protons. Due to the large abundance of gluons the most important production process for the Standard Model Higgs boson at the LHC is gluon fusion, where the Higgs boson is produced out of two gluons via a quantum loop process involving top quarks (Figure 3a). This production process has the largest cross section at the LHC. The second most important process is the radiation of W or Z bosons from incoming quarks, which fuse to produce a Higgs boson, as shown in Figure 3b. This process is referred to as vector-boson fusion (VBF) in the following. There exist two additional significant contributions, generally referred to as the associated production of a Higgs boson with a vector boson (W or Z) (Figure 3c), and with a t\(\bar{\mathrm{t}}\) pair (Figure 3d).

Figure 3: Lowest-order Feynman diagrams for the dominant production mechanisms of a Higgs boson at hadron colliders: (a) gluon fusion, (b) vector-boson fusion, (c) Higgs-strahlung or associated WH or ZH production, and (d) associated t\(\bar{\mathrm{t}}\)H production.
Figure 4: The predicted cross sections for the production of the Standard Model Higgs boson in proton-proton collisions, σ (pp → H +X), via the various production processes (gluon fusion (blue), vector-boson fusion (red), associated production, WH (green) and ZH (grey), and t\(\bar{\mathrm{t}}\)H (purple)) at a centre-of-mass energy of 8 TeV. For each process the included quantum corrections are indicated. The bands display the current level of theoretical uncertainties (from LHC Higgs Cross Section Working group (2011, 2012, 2013)).

In parallel with the experimental efforts to build the LHC and its detectors, precise theoretical calculations for the Higgs boson production cross sections have been performed (LHC Higgs Cross Section Working group, 2011, 2012, 2013). They are relevant for comparing observed event yields with the expectations for a Standard Model Higgs boson. The cross sections are calculated in a perturbative approach based on quantum field theory. For precise calculations, higher-order quantum corrections resulting from the strong (QCD) and the electroweak interactions need to be taken into account, in addition to the leading-order contributions shown in Figure 3. Some of these corrections are large, e.g. the next-to-leading order (NLO) QCD correction for the gluon-fusion process increases the cross section by about a factor of two (LHC Higgs Cross Section Working group, 2011, 2012, 2013). For the other processes these NLO corrections are more modest and the cross sections are increased by typically 10-20%. Enormous progress has been achieved in the precision of the predictions over the past decades. Next-to-next-to-leading order QCD corrections (NNLO) are available for the vector-boson fusion and associated WH and ZH production processes. For the gluon-fusion process even the NNNLO contributions have meanwhile (2015) been calculated (Anastasiou et al., 2015) . Likewise, NLO electroweak corrections have been included in the calculations. These efforts have made it possible to reduce the theoretical uncertainties for all production processes to below 10-15%.

The predicted production cross sections for a Standard Model Higgs boson at a centre-of-mass energy of 8 TeV are shown in Figure 4 as a function of the Higgs boson mass. The gluon-fusion process is dominant over the entire mass range. The bands represent the estimate of the remaining theoretical uncertainties, which largely result from missing higher order quantum corrections, beyond those considered, and from uncertainties in the parton-distribution functions, which define the flux of incoming quarks and gluons in the proton.


Higgs boson decays

Figure 5: Predictions for the branching fractions of a Higgs boson as a function of its mass (adapted from LHC Higgs Cross Section Working group (2011, 2012, 2013)).

Once produced, the Higgs boson decays promptly – the lifetime for mH=125 GeV is about 10-22 seconds. The predicted decay branching fractions depend on the Higgs boson interaction strength with the particles into which it decays. For the Standard Model Higgs boson, this interaction strength depends on the particle masses. The calculated branching fractions, including both QCD and electroweak corrections, are shown in Figure 5 as a function of the Higgs boson mass. When kinematically accessible (mH > 2 mW, or 2 mZ), decays of the Higgs boson into pairs of vector bosons, WW or ZZ, predominate. For mH > 2 mt the branching fraction into t\(\bar{\mathrm{t}}\) can reach up to 20%. Other fermionic decays only become significant for Higgs boson masses below 2 mW, with H → b\(\bar{\mathrm{b}}\) being the largest.

For a Higgs boson with a mass of 125 GeV the phenomenology is particularly rich since many different decay modes are available. At that mass the branching fractions for H → b\(\bar{\mathrm{b}}\) and H → ττ reach about 56.9% and 6.2%, respectively. Because of the values of the vector-boson masses, decays into two real massive vector bosons are impossible, but decays into one real and one virtual boson can occur. A Higgs boson may therefore decay into lower mass virtual W* and Z* bosons (the * indicates virtual particles) which serve as mediators and decay promptly. For m= 125 GeV, the branching fractions for decays into WW* and ZZ* are predicted to be 22.3% and 2.8%, respectively. In addition, decays into two photons may occur with a branching fraction of 0.23%. Similar to the production via massless gluons, decays into massless photons are only possible via quantum-loop processes involving heavy charged particles, like W bosons and top quarks, that couple to both photons and the Higgs boson.


Strategies for Higgs boson searches at the LHC

Figure 6: Production cross sections (left hand scale) and production rates at a luminosity of 1033 cm-2 s-1 (right hand scale) for several important processes as a function of the centre-of-mass energy, \(\sqrt{s}\). In the energy regime of the Tevatron the proton-antiproton cross section is given, whereas in the energy regime of the LHC the proton-proton cross section is given, and thus there are small discontinuities at \(\sqrt{s}\approx 4\) TeV (from Stirling (2012)).

The Higgs boson production cross section at the LHC is relatively small compared to those of other processes. Quark-quark (qq), quark-gluon (qg), and gluon-gluon (gg) scattering with large momentum transfer result in the production of jets with large transverse momenta (pT). The production of W and Z bosons and the production of top-quark pairs are several orders of magnitude larger than Higgs boson production. These processes lead to severe backgrounds in the Higgs boson search. In Figure 6 the production cross sections, σ, (scale on the left hand side) and the expected production rates for a luminosity of 1033 cm-2 s-1 (scale on the right hand side), are shown for several important processes as a function of the centre-of-mass energy of proton-(anti)proton collisions.

As can been seen from the figure the production of a Higgs boson with a mass of 125 GeV at \(\sqrt{s}\) = 8 TeV is about seven orders of magnitude smaller than the production of b\(\bar{\mathrm{b}}\) pairs (indicated by σb). The production of these b\(\bar{\mathrm{b}}\) pairs only constitutes a fraction of the inclusive pair production of jets resulting from qq, qg and gg scattering. In the data sample collected by the ATLAS and CMS experiments until June 2012 about 200 000 Higgs bosons with a mass of 125 GeV were expected to be produced in each experiment. This number can be compared with the number of inelastic proton-proton collisions that took place during the same time, about 1015, of which about 1011 were recorded by the experiments.

Given these harsh background conditions, the detection of the Higgs boson at hadron colliders can only be accomplished if non-hadronic final states are considered. Final state leptons, photons and missing transverse energy provide important signatures to discriminate Higgs boson decays against such backgrounds, thus emphasising some of the decay modes shown in Figure 5. At the time of discovery, a few decay modes, resulting in distinctive final states, were used to search for the Higgs boson at the LHC.

Two of the most sensitive channels are the decay into two Z bosons, which in turn each decay into an oppositely charged pair of leptons (ℓ = electron or muon, denoted as the H → ZZ(*) → ℓℓℓℓ channel) and the decay into two photons (denoted as the H → γγ channel). An additional sensitive decay mode involves two W bosons, each decaying into an electron or a muon and neutrinos (denoted as H → WW(*) → ℓνℓν). The neutrinos leave the experiments undetected and lead to an ETmiss signature in addition to the two charged leptons.

In the H → γγ and H → ZZ(*) → ℓℓℓℓ channels the Higgs boson invariant mass can be reconstructed with good precision (1–2%), and the Higgs boson appears as a sharp resonance (in the low mass region the width is dominated by the detector resolution) on top of continuous backgrounds, which are dominated by direct γγ and ZZ* production, respectively. Due to the neutrinos in the final state, no mass peak can be reconstructed in the H → WW* → ℓνℓν channel, and Higgs boson production manifests itself as a broad peak in the dilepton mass, or transverse mass (see below) distributions.

From the fermionic decays, only the modes H → ττ and H → b\(\bar{\mathrm{b}}\) were used, and they did not contribute significantly to the discovery. Due to the large background from jet production, it is not possible to identify the H → b\(\bar{\mathrm{b}}\) decay when the Higgs boson is produced by gluon-fusion, and additional distinctive signatures are required. These can be obtained from the decays of the vector bosons or top quarks accompanying associatively produced Higgs bosons (WH, ZH or t\(\bar{\mathrm{t}}\)H). Given the lower production cross sections, higher integrated luminosities are required to reach sensitivities for these processes.

The background rates and signal efficiencies in the analyses described below were estimated from the data as far as possible. To supplement this, Monte Carlo simulations of the production of the Standard Model signal and relevant background processes were performed. These simulations included modelling of the pileup conditions as observed in the data, and a detailed simulation of the detectors and their performance.


Towards the Higgs boson discovery

With the start of data taking at the LHC in 2010, at a centre-of-mass energy of 7 TeV, an entirely new window was opened for searches for new physics up to the TeV scale. Sensitivity to a Standard Model Higgs boson was achieved with data taken during the year 2011. By summer 2011, the ATLAS and CMS experiments reported exclusion limits on the existence of the Higgs boson, for certain ranges of masses, tighter than those achieved in previous searches at the Large Electron Positron collider (LEP) at CERN, and at the Tevatron at the US research laboratory Fermilab. Based on the data set collected during the year 2011, a Standard Model Higgs boson could be excluded in the high mass range up to masses of about 600 GeV, leaving only a small mass window below 127 GeV open. In 2012 the higher centre-of-mass energy of 8 TeV led to an increase of the cross section for producing a light Higgs boson by about 25%. During the first months of running the accumulated integrated luminosity exceeded that collected in 2011, so that in combination with the excellent performance of the detectors, sensitivity for discovery was reached.


Discovery of the Higgs boson

On 4th July 2012 the ATLAS and CMS collaborations announced the discovery of a new particle with a mass of about 125 GeV and the properties of the Standard Model Higgs boson. Evidence for this particle was present in the three bosonic decay modes H → ZZ* → 4ℓ, H → γγ, and H → WW* → ℓν ℓν in both experiments (ATLAS Collaboration 2012, CMS Collaboration 2012) .


The H → ZZ* → 4ℓ signal

Figure 7: A candidate event for a Higgs boson decay via two Z bosons into two electrons (tracks in the inner detector and energy deposits in the calorimeter (in green)) and two muons (tracks in the inner detector and in the muon spectrometer (in red)) in the ATLAS experiment. https://twiki.cern.ch/twiki/bin/view/AtlasPublic/EventDisplaysFromHiggsSearches#H_ZZ_2e_2

The decay channel H → ZZ* → 4ℓ provides a clean signature, but due to the small branching fractions of the decay chain, the yield of signal events is small. Higgs boson candidates are sought by selecting two pairs of isolated leptons, each of which comprises two leptons with the same flavour and opposite charge. The four decay channels considered are µ+µ- µ+µ- (4µ), e+e- µ+µ- (2e2µ), µ+µ- e+e- (2µ2e) and e+e- e+e- (4e), where the first pair is defined to be the one with the dilepton invariant mass closest to the Z-boson mass. The largest background comes from continuum (Z/γ*)(Z*/γ*) production, referred to as ZZ* production in the following. For the mass range around 125 GeV there are additional backgrounds from the production of Z+jets, including Zb\(\bar{\mathrm{b}}\), and t\(\bar{\mathrm{t}}\) pairs. For these backgrounds two isolated leptons emerge from Z → ℓℓ or from the decay chain t → Wb → ℓνb, respectively. In addition, two further leptons may originate from the decays of the fragmentation products of the heavy b-quarks or jets might be misidentified as leptons. These leptons are less isolated and, when arising from b-quarks, do not originate from the primary interaction point (where decays of the Higgs and Z bosons take place). These backgrounds are referred to as reducible backgrounds in the following.

A candidate from the ATLAS experiment for a Higgs boson decay via the 4ℓ mode with two identified electrons and two identified muons is shown in Figure 7.

Both collaborations have performed the H → ZZ* → 4ℓ search for mH hypotheses in the mass range 110-600 GeV. Calorimeter and track-isolation requirements together with impact-parameter requirements were used to suppress the reducible background down to, or below, the level of the irreducible ZZ* continuum background. The residual Z+jets and t\(\bar{\mathrm{t}}\) backgrounds, which have an impact mostly for low invariant four-lepton masses, were estimated from control regions in the data.

The irreducible ZZ* background was predicted using Monte Carlo simulation. The events were categorised according to their lepton-flavour combination. Relative mass resolutions of approximately 1.5% in the four-muon channel and 2% in the four-electron channel were achieved at m~ 125 GeV. After final selection requirements, the signal-to-background ratio is found to be about two in the signal mass window 120-130 GeV.

The invariant mass of the four leptons provides a powerful discriminating variable, which is complemented by kinematic information on the H → ZZ* → 4ℓ decay, contained in the invariant masses of the two-lepton pairs and the decay angles characterising the decay topology in the rest frame of the four-lepton system.

The observed and expected mass distributions for events after the full selection are displayed in Figure 8.

Terminology used in the data analysis

The reconstructed location of the proton-proton interaction is referred to as the primary vertex — charged particle tracks reconstructed in the tracking devices converge at this point. A secondary vertex occurs when a particle originating from the interaction decays after travelling some distance from the primary vertex. The impact parameter of a recontructed charged particle track is its distance of closest approach to the primary vertex. The magnitude of the impact parameter can be used to discriminate between the tracks of particles which originated in the interaction and those of particles produced from the decay of a relatively long-lived product of the interaction (for example a b-hadron) even if it is not possible to reconstruct a secondary vertex.

Leptons and photons originating from a hard interaction, or from the decay chain of a particle, such as a Z boson or Higgs boson, directly produced in a hard interaction are not (except by chance) closely accompanied by other particles — they are isolated. Many lepton and photon candidates reconstructed in the detector do not originate directly from the hard interaction, but come from the constituents of the jets of particles formed by the hadronization of gluons or quarks. These candidates tend not to be isolated — they are surrounded by other particles from the jet. A measure of how many particles, or how much energy, surrounds a candidate lepton or photon can be used to determine whether it is probable that it emerged directly from the hard interaction, or more likely that it originated in a jet fragment.

Events selected so as to have negligible probability of containing signal events constitute a control sample, and the selection requirements define a control region in parameter space. The control sample in the control region contains only background events and can be used to estimate the number of background events expected in the region of the signal, provided the effect of whatever distinguishes the control region from the signal region is sufficiently well understood.

For both experiments, an excess of events is present in the mass region around 125 GeV. In the ATLAS experiment 4.9 events are expected from Standard Model background processes in the mass window 120-130 GeV, whereas 13 events are observed in the data. The corresponding numbers for the CMS experiment in the mass window 121.5-130.5 GeV are 3.8 events expected from background processes, compared to 9 events observed. More details about the observed and expected numbers of events, their uncertainties and the split in the various four-lepton channels are given in Table 1 for the ATLAS and in Table 2 for the CMS experiment.


Figure 8: Distributions of the invariant mass of selected events with two pairs of electrons or muons (each pair of opposite charge) measured by the ATLAS (left) and CMS (right) experiments (from ATLAS Collaboration (2012) and CMS Collaboration (2012) ). The inset plot shows the result of applying a tight selection on a kinematic discriminant constructed to separate signal and background.
Table 1: The numbers of expected signal (mH = 125 GeV) and background events (separated into the irreducible ZZ* and reducible components) expected by the ATLAS experiment in the H → ZZ* → 4ℓ analysis, together with the numbers of observed events in the data, in a window of size ±5 GeV around 125 GeV, for the combined √s =7 TeV and √s =8 TeV data (adapted from ATLAS Collaboration (2012) ).
4e 2e2µ / 2µ2e
Signal 0.90 ± 0.14 2.29 ± 0.33 2.09 ± 0.30
ZZ* background 0.44 ± 0.04 0.80 ± 0.05 1.12 ± 0.05
Z+jets, t\(\bar{\mathrm{t}}\) background 1.09 ± 0.20 1.27 ± 0.19 0.13 ± 0.04
Observed 2 5 6


Table 2: The numbers of selected events, compared to the expected background yields and expected numbers of signal events (mH = 125 GeV) in the mass region 121.5 < m4ℓ < 130.5 GeV for each final state in the H → ZZ* → 4ℓ analysis of the CMS experiment, for the combined √s =7 TeV and √s =8 TeV data (adapted from CMS Collaboration (2012)).
4e 2e2µ / 2µ2e
Signal 1.36 ± 0.22 3.44 ± 0.44 2.74 ± 0.32
Total background 0.7 ± 0.2 1.9 ± 0.3 1.3 ± 0.1
Observed 1 5 3


In order to quantify these excesses, the probabilities for the background-only hypotheses were calculated. The minimum local p-values in the data of the ATLAS and CMS experiments occur at 125.0 GeV and 125.6 GeV, respectively, and have an observed (expected) significance of 3.6 (2.7) σ and 3.2 (3.8) σ, respectively.


p-value

The local p-value is defined to give the probability of a background fluctuation. It measures the consistency of the data with the background-only hypothesis (null-hypothesis), and its significance may be expressed in terms of standard deviations of a Gaussian distribution – thus a local p-value having a significance of 5σ means a deviation of five standard deviations from the background-only hypothesis, and corresponds to a probability of about 1 in 3·106. The convention in particle physics is to claim discovery when 5σ is reached.

The probability that an excess of events observed anywhere within an extended search range is due to a background fluctuation is termed the global p-value, and is larger than the local p-value — this fact is often referred to as the look-elsewhere effect.


The Η→γγ signal

Figure 9: Candidate event for a Higgs boson decay into two photons (no tracks in the inner detector and energy deposits in the calorimeter (in green)) in the CMS experiment. (CMS-PHO-EVENTS-2012-003)

The search for the Standard Model Higgs boson decaying to two photons involves detecting a narrow peak above a background diphoton invariant mass spectrum. The background spectrum results from processes involving two prompt photons, with a further, reducible contribution from pp → γ+jet and dijet processes where at least one of the objects reconstructed as a photon originates in a jet. The Higgs boson decay to two photons proceeds via loop diagrams containing charged particles. The W boson loop and the top quark loop diagrams dominate the decay amplitude, but contribute with opposite sign. The Standard Model branching fraction is small, having a maximum value of 0.23% at mH ≈ 125 GeV and falling steeply above 150 GeV. Despite the small branching fraction and the presence of a large background, the Standard Model Higgs boson signal significance expected in this decay mode is one of the highest among all the decay modes in the mass range 110 < mH < 150 GeV.

Figure 10: Weighted distributions of the invariant mass of photon pairs measured by the ATLAS (left) and CMS (right) experiments. The distributions are obtained by summing the invariant mass distributions of all of the event categories, with each event being weighted by S/B (ATLAS) or S/(S+B) (CMS), where S and B and the number of signal and background events, respectively, within a window (of width ±2 times the mass resolution) about the signal mass. The insert shows the unweighted distribution (from ATLAS Collaboration (2012) and CMS Collaboration (2012) ).

Events containing diphotons are collected by both experiments using diphoton triggers. Further selection requirements are applied to suppress the reducible background contribution from photons originating in jets. The photon showers are required to be located within fiducial regions of the calorimeters that exclude the barrel/endcap transition, and to satisfy requirements on their transverse momenta. Requirements are made on the shapes of the showers in the calorimeter cells or crystals, and on the isolation of the photons from other activity in the detectors.

There are many interactions for each bunch crossing, whose longitudinal position along the beam axis has a RMS spread of about 5 cm. The diphoton interaction vertex is assigned using multiple sources of information combined in a global likelihood (ATLAS) or using a boosted decision tree (BDT) (Hoecker et al., 2007) (CMS). Both analyses take account of the ΣpT2 of the charged particle tracks associated with reconstructed vertices, and the direction of electrons reconstructed in the tracking detectors and associated with converted photon showers. The analysis of the ATLAS experiment additionally considers the directions of the photon showers reconstructed in the calorimeter using its longitudinal granularity. That of the CMS experiment additionally examines the correlation between the kinematic properties of the charged particle tracks associated with the reconstructed vertices, with those of the diphoton system.

Both ATLAS and CMS enhance the sensitivity of their analyses by subdividing the selected diphoton events into mutually exclusive categories, where the categorization is based upon criteria sensitive to the diphoton mass resolution, and to the probability that an event is signal rather than background. The ATLAS classification is based on the location of the photons in the calorimeter, whether they are tagged as having converted in the material in front of the calorimeter, by the presence of a reconstructed electron track, and pTt, the component of the diphoton transverse momentum that is orthogonal to the axis defined by the difference between the photon momenta. The CMS classification is based on the output of a BDT which is trained to give a high value for signal-like events and for events with good diphoton invariant mass resolution.

Events in which a dijet is present, in addition to the diphoton, and satisfies selection criteria chosen to be consistent with the characteristics of signal events produced by the vector-boson fusion process, are placed in dijet categories. For the analysis of the 8 TeV dataset CMS uses two dijet categories with differing levels of selection stringency. Both analyses published tables listing the categories and indicating the numbers of events expected from a Standard Model Higgs boson signal in each category, the mass resolution expected in each category, and information about the numbers of events present in the data (ATLAS Collaboration 2012 , CMS Collaboration 2012) . Some important numbers from these tables are reproduced in Table 3 and Table 4.


Table 3: Numbers of events in the data (ND) and expected numbers of signal events (NS) for mH = 126.5 GeV from the H→γγ analysis in the ATLAS experiment, for each category in the mass range 100–160 GeV, separately for the data taken at √s =7 TeV and √s =8 TeV. The mass resolution, measured by the full-width-at-half-maximum (FWHM), is also given for the data taken at √s = 8 TeV. The statistical uncertainties on NS and FWHM are less than 1% (adapted from ATLAS Collaboration (2012) ).
√s = 7 TeV, 4.8 fb-1 √s = 8 TeV, 5.8 fb-1
Category ND NS ND NS FWHM [GEV]
Unconverted, central, low pTt 2054 10.5 2945 14.2 3.4
Unconverted, central, high pTt 97 1.5 173 2.5 3.2
Unconverted, rest, low pTt 7129 21.6 12136 30.9 3.7
Unconverted, rest, high pTt 444 2.8 785 5.2 3.6
Converted, central, low pTt 1493 6.7 2015 8.9 3.9
Converted, central, high pTt 77 1.0 113 1.6 3.5
Converted, rest, low pTt 8313 21.1 11099 26.9 4.5
Converted, rest, high pTt 501 2.7 706 4.5 3.9
Converted, transition region 3591 9.5 5140 12.8 6.1
2-jet 89 2.2 139 3.0 3.7
All categories (inclusive) 23788 79.6 35251 110.5 3.9


Table 4: Expected numbers of Standard Model (SM) Higgs boson events (mH = 125 GeV) and estimated background (at mγγ = 125 GeV) for all event categories of the 7 and 8 TeV data sets in the H→γγ analysis of the CMS experiment. There are two dijet-tagged categories for the 8 TeV, and for both data sets the remaining untagged events are separated into four categories labelled here BDT 0–3, BDT 0 having the largest expected signal-to-background ratio (adapted from CMS Collaboration (2012) ). The mass resolution is given as full-width-at-half maximum (FWHM) divided by 2.35.
Event categories SM Higgs boson expected signal (mH = 125 GeV) Background
mγγ = 125 GeV
(events / GeV)
Events FWHM/
2.35 (GeV)
7 TeV, 5.1 fb-1 BDT 0 3.2 1.14 \( 3.3 \pm 0.4 \)
BDT 1 16.3 1.08 \( 37.5 \pm 1.3 \)
BDT 2 21.5 1.32 \( 74.8 \pm 1.9 \)
BDT 3 32.8 2.07 \( 193.6 \pm 3.0 \)
Dijet tag 2.9 1.37 \( 1.7 \pm 0.2 \)
8 TeV, 5.3 fb-1 BDT 0 6.1 1.23 \( 7.4 \pm 0.6 \)
BDT 1 21.0 1.31 \( 54.7 \pm 1.5 \)
BDT 2 30.2 1.55 \( 115.2 \pm 2.3 \)
BDT 3 40.0 2.35 \( 256.5 \pm 3.4 \)
Dijet tight 2.6 1.57 \( 1.3 \pm 0.2 \)
Dijet loose 3.0 1.48 \( 3.7 \pm 0.4 \)


For the statistical analysis of the data, the sum of a signal mass peak and a background distribution is fitted to the diphoton invariant mass distribution. The fits are performed for a range of Higgs boson mass hypotheses, 110 < mH < 150 GeV, over the diphoton mass ranges 100 < mγγ < 160 GeV (ATLAS), and 100 < mγγ < 180 GeV (CMS). The shape of the invariant mass distribution of the signals is obtained from detailed simulation for each of the categories. It is parameterized, either by a Crystal Ball function (ATLAS) or a sum of Gaussian functions (CMS). The background in the different categories is modelled by parametric functions. Various tests are made to determine the potential bias resulting from the choice of background fit functions. These tests involve either pseudo-experiments, or large samples of simulated events complemented by data-driven estimates. CMS uses polynomials (in the Bernstein basis) with degree ranging from 3 to 5 depending on category. ATLAS uses Bernstein polynomials of degree 4, exponentials of a polynomial of degree 2, and plain exponential functions, depending on the category.

The analyses of both collaborations found a statistically significant excess of events near mγγ = 125 GeV as shown in Figure 10.

The H → WW* → ℓνℓν signal

The decay mode H → WW* → ℓνℓν has the highest sensitivity for a Standard Model-like Higgs boson for masses around the WW threshold of 160 GeV. Based on searches in this channel, mass regions could be excluded by both the Tevatron and the LHC experiments already in summer 2011. However, this channel is more challenging in the low-mass region around 125 GeV since the expected signal rates are small due to the reduced H → WW* branching fraction.

Figure 11: Distribution of the transverse mass, \(m_T\), in the 0- and 1-jet channels as measured by the ATLAS experiment (left) and the distribution of the invariant mass of the two leptons in the CMS experiments (right) (from ATLAS Collaboration (2012) and CMS Collaboration (2012) ).

The presence of neutrinos makes the reconstruction of a narrow mass peak impossible, and evidence for a signal must be extracted from an excess of events above the expected backgrounds. Usually, the WW transverse mass (mT), computed from the leptons and the missing transverse momentum,

\( m_T = \sqrt{(E_T^{\ell\ell}+E_T^{miss})^2 -|{\bf p}_T^{\ell\ell}+{\bf p}_T^{miss}|^2} \),

where \( E_T^{\ell\ell} = \sqrt{|{\bf p}_T^{\ell\ell}|^2 +m_{\ell\ell}^2} \) and \( |{\bf p}_T^{miss}|=E_T^{miss} \) is used to discriminate between signal and background. The WW, t\(\bar{\mathrm{t}}\) and single-top production processes constitute severe backgrounds and the signal significance depends critically on their absolute knowledge.

In order to optimise the sensitivity, both collaborations subdivided the events into categories according to the lepton final state (ee, eµ, µµ) and jet multiplicity. Typical selection requirements are the presence of two isolated high-pT leptons with a small azimuthal angular separation and a significant missing transverse energy. The first requirement is motivated by the decay characteristics of a spin-0 boson decaying into two W bosons with their subsequent decay W → ℓν. The weak decays of the W-bosons imply a correlation between the directions of the charged leptons, which can be exploited to reject the WW background. These correlations lead to the use of quantities such as the dilepton invariant mass, mℓℓ, and the angular separation, \(\Delta\phi_{\ell\ell}\), in the selection criteria. The different jet categories are sensitive to different Higgs boson production mechanisms, and show very different background compositions. The 0-jet category has non-resonant WW production as major background, while the 2-jet category, sensitive to Higgs production via vector-boson fusion, is dominated by t\(\bar{\mathrm{t}}\) background. The distributions of two discriminating variables, the transverse mass and the invariant mass of the two leptons, as measured in July 2012, after the application of all final selection criteria, are shown in Figure 11.

Excesses of events above the expectations from Standard Model processes excluding Higgs boson production are visible. Details about the observed and expected numbers of events, their uncertainties and the split in the various categories are given in Table 5 for the ATLAS and in Table 6 for the CMS experiment.

A shallow minimum of the local p-value appears at 125.0 GeV, with a local observed (expected) significance of 2.8 (2.3) σ in the ATLAS and 1.6 (2.4) σ in the CMS analysis.


Table 5: The expected numbers of signal (mH = 125 GeV) and background events (for the dominant WW* and the total background) after all selections, including a cut on the transverse mass of 0.75 mH < mT < mH for mH = 125 GeV in the ATLAS experiment. The observed numbers of events in data are also displayed. The eμ and μe channels are combined. The uncertainties shown are the combination of the statistical and all systematic uncertainties, taking into account the constraints from control samples (adapted from ATLAS Collaboration (2012) ).
0-jet 1-jet 2-jet
Signal eµ, µe 20 ± 4 5 ± 2 0.34 ± 0.07
WW* background 101 ± 13 12 ± 5  0.10 ± 0.14
Total background 142 ± 16 26 ± 6 0.35 ± 0.18
Observed 185 38 0


Table 6: Observed numbers of events, background estimates, and signal predictions for mH = 125 GeV in each category of the WW analysis of the 8 TeV data set in the CMS experiment. All the selection requirements have been applied. The combined experimental and theoretical, systematic and statistical uncertainties are shown (adapted from CMS Collaboration (2012) ).
0-jet 1-jet 2-jet
Signal eµ, µe 23.9 ± 5.2 10.3 ± 3.0 1.5 ± 0.2
WW* background 87.6 ± 9.5 19.5 ± 3.7 0.4 ± 0.1
Total background 124.2 ± 12.4 61.7 ± 7.0 4.1 ± 1.9
Observed 158 54 6
Signal ee, µµ 14.9 ± 3.3 4.4 ± 1.3 0.8 ± 0.1
WW* background 60.4 ± 6.7 9.7 ± 1.9 0.3 ± 0.1
Total background 115.5 ± 15.0 33.1 ± 5.7   5.4 ± 2.2
Observed 123 43 7


Search for ττ and b\(\bar{\mathrm{b}}\) decays

In addition to the searches for the decays to bosons, both experiments also performed searches for the fermionic decays to a (particle-antiparticle) pair of τ leptons or b quarks and reported on them in their papers detailing the discovery, but only CMS included them in the combined result presented at that time. These decay channels require a larger data sample to produce statistically significant measurements.

The τ leptons are identified by their visible decay products, either electrons or muons (leptonic decays), or hadrons (semi-hadronic decays). The searches are for an excess of events in the ditau invariant mass distribution, in the range 110 < mττ < 150 GeV (ATLAS) and 110 < mττ < 145 GeV (CMS). Since at least one neutrino is present in all τ decays, complete reconstruction of the invariant mass is not possible and the expected signal is a broad enhancement in excess of the expected background, rather than a resonance peak. The background is estimated mainly through the use of control samples in data. The different τ decay channels are analysed separately, and classified according to the number of jets and the amount of ETmiss in the event. The results in the individual categories are combined to give the final result.

For mH < 135 GeV the Standard Model Higgs boson decay to b\(\bar{\mathrm{b}}\) has the largest branching fraction of all decays, but the background from b-quark production is formidable, and the searches are restricted to Higgs bosons produced in association with a W or Z boson which is observed by its leptonic decay. This restriction greatly improves the signal-to-background ratio. The b-quark jets are identified by the presence of secondary vertices, and the requirement of a high pT on the dijet system significantly reduces the background. The dominant backgrounds are estimated from data, and the remaining backgrounds from simulation studies.

In the Higgs boson discovery analyses no statistically significant enhancement over the expected background was observed in either of the two fermionic decay channels.


Combined significances

Figure 12: The observed local p-value as a function of mH (solid line) and the expectation with its ±1σ band assuming the presence of a Standard Model Higgs boson at that mass (dashed line) from the combination of the ZZ*, γγ and WW* channels by the ATLAS experiment. The horizontal dashed lines indicate the p-values corresponding to significances of 1 to 6σ (from ATLAS Collaboration (2012) ).
Figure 13: Best-fit signal strength as a function of mH as determined by the CMS experiment from the combination of the ZZ*, γγ, WW*, ττ and b\(\bar{\mathrm{b}}\) (VH, H → b\(\bar{\mathrm{b}}\)) channels. Around the fitted signal strength µ = σ/σSM the ±1σ uncertainty band is shown (from CMS Collaboration (2012) ).

In Summer 2012, the ATLAS and CMS experiments observed an excess of events near mH = 125 GeV in the H → ZZ* → 4ℓ and H → γγ channels. These excesses were confirmed by the sensitive, but low-resolution, H → WW* → ℓνℓν channel.

The significances of the signals seen by the two experiments are summarized in Table 7 and Table 8.

Table 7: Characterisation of the excess in the H → ZZ* →4ℓ, H → γγ and H → WW* → ℓνℓν channels and the combination of all channels for the ATLAS experiment. The mass value mmax for which the local significance is maximal, the maximum observed local significance, σ, and the best fit value of the signal strength parameter, μ, (see text) at mH = 126 GeV, and its uncertainty, are shown (adapted from ATLAS Collaboration (2012) ).
Search channel mmax (GeV) σ (observed) µ (mH = 126 GeV)
H → ZZ* → 4ℓ 125.0 3.6 1.2 \( \pm \) 0.6
H → γγ 126.5 4.5 1.8 \( \pm \) 0.5
H → WW* → ℓνℓν 125.0 2.8 1.3 \( \pm \) 0.5
Combined 126.5 6.0 1.4 \( \pm \) 0.3


Table 8: The expected and observed local p-values, expressed as the corresponding number of standard deviations of the expected and observed excess from the background-only hypothesis, for mH = 125.5 GeV, for various combinations of decay modes for the CMS experiment (from CMS Collaboration (2012) ).
Decay mode / combination (σ) expected (σ) observed
γγ 2.8 4.1
ZZ 3.8 3.2
ττ + b\(\bar{\mathrm{b}}\) 2.4 0.5
γγ + ZZ 4.7 5.0
γγ + ZZ + WW 5.2 5.1
γγ + ZZ + WW + ττ + b\(\bar{\mathrm{b}}\) 5.8 5.0


The observed local p-value from the combination of all channels in the ATLAS experiment is shown as a function of mH in Figure 12 for the low mass range. The largest local significance was found for a Standard Model Higgs-boson mass hypothesis of mH = 126.5 GeV, where it reaches 6.0 σ, with an expected value in the presence of a Standard Model Higgs boson signal at that mass of 4.9 σ. A compatible picture was observed in the CMS experiment with an observed (expected) local significance of 5.0 (5.8) σ at a mass near 125 GeV.

A first test of the compatibility of the observed signal with the Standard Model Higgs boson was provided by the examination of the best-fit value of the common signal strength µ = σ/σSM, defined as the ratio between the fitted cross section and the expectation for a Standard Model Higgs boson. It was obtained by a combination of all channels. The result of a scan of the fitted values of µ as a function of mH for the CMS experiment is shown in Figure 13. The observed value for the excess at mH = 125.5 GeV is 0.87 ± 0.23. The corresponding value determined by the ATLAS collaboration is 1.40 ± 0.30 at a mass of 126.0 GeV.


Summary

The results presented by the ATLAS Collaboration (2012) and the CMS Collaboration (2012) summarised above, provided conclusive evidence for the discovery of a new particle with a mass around 125 GeV in the data taken by the ATLAS and CMS experiments. The measured signal strength was found to be consistent with the one expected for the production of the Higgs boson of the Standard Model.

The decays to pairs of vector bosons with a net electric charge of zero identified the new particle as a neutral boson. The observation in the diphoton channel excluded the spin-1 hypothesis for the production of an on-shell resonance by virtue of the Landau-Yang theorem. Although these results were compatible with the interpretation in terms of the Standard Model Higgs boson, a wide range of other interpretations was possible as well.

At the end of the first LHC operation period (2010 – 2012) about 2.5 times more data had been collected by each of the experiments than was used for the discovery of the Higgs boson. Using this data, evidence for the Higgs boson was seen in many individual production and decay modes, including the Standard Model predicted decays into fermions. Extensive searches were made for deviations from the Standard Model predictions, but in general the measured signal strengths were broadly consistent with expectations, and tests of angular distributions indicated that the particle discovered is a scalar, as expected. A combined measurement of the mass of the Higgs boson by the two experiments (ATLAS and CMS Collaborations, 2015) obtained the result mH = 125.09 ± 0.21 (stat.) ± 0.11 (syst.) GeV.


References

  • ATLAS Collaboration, (2012). Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716: 29. doi:10.1016/j.physletb.2012.08.020.
  • CMS Collaboration, (2012). Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716: 31. doi:10.1016/j.physletb.2012.08.021.
  • Hoecker, A et al. (2007). TVMA: Toolkit for Multivariate Data Analysis, PoS ACAT 040: 0. arXiv:physics/0703039 and references therein
  • Reports of the Higgs Cross Section Working Group and references therein
    • LHC Higgs Cross SectionWorking Group, “Handbook of LHC Higgs cross sections: 1. Inclusive observables”, CERN Report CERN-2011-002, 2011 (see http://cds.cern.ch/record/1318996)
    • LHC Higgs Cross SectionWorking Group, “Handbook of LHC Higgs cross sections: 2. Differential Distributions”, CERN Report CERN-2012-002, 2012 (see http://cds.cern.ch/record/1416519)
    • LHC Higgs Cross SectionWorking Group, “Handbook of LHC Higgs cross sections: 3. Higgs Properties”, CERN Report CERN-2013-004, 2013 (see http://cds.cern.ch/record/1559921)


Further reading

Books on Particle Physics

  • Francis Halzen and Alan D. Martin, Quarks & Leptons - An introductory course in modern particle physics, John Wiley & Sons, ISBN 978-0471887416
  • I.J.R. Aitchison and A.J.C. Hey, Gauge Theories in Particle Physics, IoP Publishing, ISBN 0-85274-329-7


Books on Data Analysis and Statistical Methods

  • Data Analysis in High Energy Physics, Ed. O. Behnke, K. Kröninger, G. Schott and T. Schörner-Sadenius, WILEY-VCH, ISBN 978-3-527-41058-3
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