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Decoding the Higgs boson

Paul Grannis

Escolo Swieca, Campos do Jordao

Jan. 19 – 23, 2009

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The Higgs as giver of mass Before the arrival of the star physicist, the room

is filled with quietly chattering students (i.e. the vacuum) The star (Prof. Higgs)

arrives and moves across the room, attracting questioners, thus gaining mass (e.g. slowing down).

The same thing occurs if a juicy rumor is introduced. The physicists cluster to discuss the rumor and become a ‘composite Higgs’.

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Courtesy D.J. Miller

So what is this mysterious ‘Higgs’?

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Higgs -- outline

Phenomenology of the SM Higgs boson

Extension to Supersymmetric Higgs

Status of Tevatron SM Higgs

Prospects for LHC SM and Susy Higgs search

What the ILC will add to understanding the Higgs

More exotic Higgs possibilities

A case study: search for Z ( ) H ( bb)

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The Higgs boson and Electroweak Symmetry Breaking (EWSB)

We see that something breaks the symmetry of the Electroweak interaction into distinct EM and Weak pieces, yielding massive W and Z bosons (and massive fermions). It may be the SM Higgs mechanism, or it may be due to some more complex theory, but in all Beyond the SM extensions there is something that plays the role of the Higgs and that induces the breaking of EM and Weak symmetry.

The most pressing job of experiment over the coming decade is to find the source of EWSB, and if it is related to a particle, to explore the properties of that state.

The underlying fundamental question is:

“What is the nature of the physics of EWSB”.

We believe this is a question that will be answered by the tools we now have in hand or will soon build.

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Theory constraints on MH

The SM Higgs could in principle have any mass (MH = 4v2), but some values make no sense.

At some high mass scale , the SM will become self-inconsistent for most MH, so new physics must set in at that scale.

The value of limiting is determined by the Higgs mass. If MH is too large, the Higgs self coupling blows up at a scale less than the Planck scale. If MH is too small, the Higgs potential develops a false vacuum (second minimum) at scale and thus new physics must enter to keep the EW scale fixed at v = 246 GeV.

Thus the SM bears the seeds of its own destruction as a complete theory (breaks down below the Planck scale) unless 150 < MH < 180 GeV.

We need MH < 1 TeV to avoid a violation of unitarity, for example in the 2-body scattering amplitude for WL WL.

Divergent Higgs self coupling

False vacuum

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Higgs production

In the SM, the Higgs boson has couplings proportional to mass. Thus production processes involving virtual W, Z and top quarks dominate. In hadron-hadron collisions (Tevatron and LHC) the dominant processes are:

Note already there are some differences between the Tevatron and LHC: LHC has valence quarks in both beam particles (pp), whereas Tevatron has valence quark and antiquark (pbar p). So the LHC relies on antiquarks from the sea, whereas the Tevatron has valence antiquarks available. Moreover, at √s ≈ MH, the parton x (pparton/pproton) required is lower at LHC (higher pproton), in a region that is more dominated by gluon content than at the Tevatron. For these reasons, the relative importance of the processes are different at LHC than at the Tevatron.

q

q

W/ZW/Z

H

tg

gH

qq’

q’q

W

W

H

gluon-gluon fusion (gg)

associated VH production (V=W/Z)

vector boson fusion (VBF)

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Summary of tree level cross sections at Tevatron and LHC:

gg

gg

VBF

VBF

VH

VH

SM Higgs production

Show for Tevatron only to MH = 200 GeV (lower energy than LHC). Cross sections at LHC are ~50X those at Tevatron. gg fusion is largest at both machines, but VBF rivals gg at large Higgs mass for LHC. At Tevatron, associated VH production is closer to gg fusion (due to valence antiquarks in antiprotons). Backgrounds also vary from Tevatron to LHC: For example the QCD production of W+2 b-quark jets is a dominant background for the WH process, and this cross section grows rapidly with √s .

Tevatron LHC

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SM Higgs decays

Again the Higgs coupling to mass dictates the branching ratio pattern. In first approximation, the Higgs decays to the heaviest available particles, so as MH increases, the BR pattern changes drastically and as a result the experimental signatures are strongly dependent on MH.

t

g

gH

The gg decay is the inverse of the gg production: a Higgs decay through a quark loop to two gluons. Measuring this rate is of interest in directly measuring the gg fusion cross section.

Warning: if there is Susy, then Higgs can decay into sparticles as soon as it is energetically possible, and BR pattern will change.

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SM Higgs experimentThe Higgs enters in loops in higher order corrections to

the properties of W, Z and top quarks, and thus precision measurement of these quantities give indirect limits on the Higgs within a model context.

Measurements of top quark mass and W boson mass further constrain the Higgs to be light. In fact the 1 ellipse is outside the allowed MH space, in the region preferred by Susy!

Plotting the 2 for a fit to all data with MH as a free parameter gives a preferred value at MH = 84 +34/-

26 GeV, with a 95% CL upper limit of 154 GeV. The yellow band shows the region excluded by direct search at LEP, MH > 114.4 GeV. When this exclusion is taken into account, the upper limit (95% CL) is 185 GeV. This assumes that the SM is correct!

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Susy HiggsIn supersymmetry, the Higgs sector is more complex. In the simplest Susy models we start with two complex Higgs doublets, each with charged and neutral components. One doublet contributes to the up-type fermions and the other to down-type fermions. Vacuum expectation values: <X

† X> = vX2/2 (X=Up or Down)

Define the ratio of expectation values as vu/vd = tan

After EWSB absorbs 3 Goldstone boson dof’s for longitudinal W & Z states, there are 5 physical Higgs boson states remaining. Two, like the SM Higgs, are scalars (JP=0+) called h and H (h by definition is the lighter). One is a pseudoscalar (JP=0) called A. The remaining two are charged, H±. LEP limits MA > 88 GeV.

At tree level, the Susy higgs sector is controlled by one Higgs mass (MA) and tan. All Susy Higgs masses are given (at tree level) by these two parameters (not undetermined as in SM).

For MA >>MZ (tree level):

In particular, note that h is bounded from above.

Couplings of Susy Higgs and W/Z are also specified by tan, SM constants and angle = mixing angle taking the CP-even Higgs states (h,H) from the basis of the complex doublets to the mass eigenstate basis.

Mh2 ≈ MZ

2 cos2 2MH

2 ≈ MA2 + MZ

2 sin2 2MH±

2 ≈ MA2 + MW

2

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Radiative corrections alter this relatively simple picture: Susy higgs masses are modified depending on the values of squark masses and their mixings, and supersymmetry Higgsino mass parameter . The lightest Susy higgs mass can rise to 130 GeV.

Susy Higgs

The Susy higgs masses are determined by tan and MA: For large MA (> MZ) as is thought likely, the A, H, H± masses are nearly degenerate. This regime is called the decoupling regime in which h behaves just like the SM Higgs. Hbb and Abb couplings ~ tan making H/A cross sections relatively large (enhanced cross sections for Hbb, H) at large tan.

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Tevatron Higgs searchesFor low mass (MH< 135 GeV) the dominant decay is H → bb. Although

the dominant production process is gg fusion, a final state with just bb is swamped by background from QCD production of bb pairs. Thus the most promising approach makes use of VH (V=W or Z) where the additional V boson costs about a factor of 10 in cross section but has lower backgrounds if V decays to leptons. In practice this search is subdivided experimentally into several channels: VH productionWH: W→e, , and H→bbWH: W→qq and H→ZH: Z→ee, , or and H → bb ZH: Z→qq and H→ At the upper end of the low mass region WH : W→l and H→WW* (both W’s to l), so 3 lepton final states.Some sensitivity from ttH: H → bb (4 b final state) gg fusion the low background H → , and H()+2jets VBF H()+2 jets.

The most sensitive of these channels for low mass are Z()H(bb) and W(l) H(bb).

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Tevatron Higgs searches

Observed limits vary between 3X to 8X SM expectation. Not all channels are included here.

MH

Compute expected limit (relative to SM prediction) and observed limit as a function of MH. Green band gives ±1 range for expected limits. Yellow band is ±1.

Limits are improving faster than 1/√L. This indicates that as time goes on, the experiments are becoming more clever in analysis techniques (and adding new search channels).

1-3fb-1/ analysis

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At high mass (140<MH<180 GeV) at the Tevatron where the H → WW* branching ratio becomes large, the Tevatron experiments become sensitive to the gg fusion reaction with the leptonic decays of the two W’s (so far, ee, e). The WH (H →WW) channel also contributes here. The SM Higgs is now ruled out at 95% CL for MH = 170 GeV, and at 90% CL, excluded for 165<MH<175 GeV.

This is the first new direct exclusion since the close of LEP (summer – northern hemisphere 2008).

Tevatron Higgs searches

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The Tevatron is expected to run until September 2010; discussions are underway to extend for a year due to delay in LHC and the Tevatron sensitivity to low mass Higgs.

Higgs searches continue to gain sensitivity faster than L-1/2 due to improvements in algorithms and adding new channels.

Tevatron Higgs searches

The expected available data set of 6.8 fb-1 per experiment (to Sept. 2010) will allow exclusion at 95% CL over almost the full range of Higgs mass up to 180 GeV.

3 evidence can be achieved at low mass (<120 GeV) and 155 < MH < 175 GeV.An additional year would bring about 2fb-1 more per experiment and give good prospect for seeing evidence of 115 GeV Higgs

Luminosity needed for 95% exclusion and for 3 evidence vs. MH

8.8 fb-1 (2011)

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LHC Higgs searchesAt the LHC, the dominant Higgs cross sections are gg fusion (gg H) and vector boson fusion (qq W*W*qq Hqq). Associated VH production is relatively less important (no valence quarks).

Tag jets Higgs decay

products

qq’

q’q

W

W

HVector boson fusion:

Central region is relatively free from jet activity so a jet veto will be effective. Higgs tt

Rapidity distribution of jets in tt and Higgs signal events:

tg

gHgluon gluon

fusion:

No other high pT activity in the event so all the discrimination must be obtained from the Higgs decay. For most decay channels, this is hard.

Two spectator jets (relatively forward, unlike major backgrounds)

ln tan

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For these gg/VBF reactions with no real vector boson in the final state, the decays of H bb are extremely difficult to separate from the large multijet QCD backgrounds.

In the case that MH is large (>140 GeV), the gg/VBF production with decays H WW/ZZ offer very clean signatures. In this case (not favored for SM Higgs or the light Susy h!), the golden channel H ZZ with both Z ll gives excellent mass resolution, and by measuring the angular correlations for the final leptons, information on JP.

For smaller MH, the LHC experiments rely on the subdominant decay H (BR ~ few 10-3). The backgrounds from QCD processes are moderately high, but the excellent energy resolution for ’s permits good background rejection.

t

H

mass peaks for several hypothesized Higgs masses

For VBF, H also looks feasible.

LHC Higgs searches

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LHC Higgs searchesPutting together all the search channels, we find that the LHC can cover the full range of possible Higgs masses from 115 to 1000 GeV. Plot shows the significance achieved in 30 fb-1 in 1 experiment.

– 5 discovery – 95% CL exclusion

CMS and ATLAS

1 fb-1

10 fb-1

0.1 fb-1

MH

At the LEP exclusion point (114 GeV), need about 5 fb-1 for discovery and 1.5 fb-1 for exclusion. At the optimum mass (~160 GeV), need 0.4 fb-1 and 0.14 fb-1.

Note: at Lt= 1033 fb-1, get about 4 fb-1/year, so achieving discovery of low mass Higgs will take several years of good running. (ultimate LHC goal is Lt = 1034 fb-1)

Note: Tevatron is now ruling out SM Higgs around 170 GeV.

Luminosity needed for

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Higgs mass determination: For either the or ZZ decay modes, the limiting factor for mass determination is the EM calorimeter calibration:

M/M ~ 0.1%

LHC Higgs studies

Quantum numbers: to be the SM Higgs, we require JP = 0+. For the decay mode H ZZ, this can be done by examining the correlation of the decay planes of the two Z’s. If MH < 140 GeV, determining spin parity will be very difficult.

Higgs couplings: LHC experiments will not be able to measure absolute couplings. Ratios of couplings for Z/W/top at the 20% level are feasible for the higher Higgs masses with 300 fb-1. The Higgs self coupling is probably out of reach (6000 fb-1 needed for MH=165 GeV and worse elsewhere).

The LHC will give us discovery of the SM Higgs (and in most cases some of the Susy Higgs), but the exploration of its properties will be difficult. However, one should not under estimate the cleverness of experimenters with real data in hand.

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LHC Susy Higgs

Recall that the main parameters controlling the Susy Higgs sector are tan and MA, with subdominant radiative effects from the squark sector.

We would like to observe all 5 Susy Higgs (h, H, A, H±). Strategies depend quite sensitively to values of tan and MA due to changes in production and decay mechanisms, so one has to do many analyses.

An example: Produce A/H and observe in decay to . For large tan and 120 < MA < 200 GeV, LHC has discovery potential.

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LHC Susy HiggsAnother example: Search for H± decays to or tb.

The orange region represents the state of the Tevatron searches. LHC expands this range considerably to lower tan and higher MA. H± mass

tan

Can have CP violation in MSSM higgs sector if the trilinear couplings are complex. The h, H, A mix to H1, H2, H3 similarly to neutrino mixing.

In case of maximal coupling phases, LHC can see at least one Higgs eigenstate.

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LHC Susy Higgs

4 Higgs observable3 Higgs observable2 Higgs observable

1 Higgs observable

A, H, H cross-sections ~ tan2

- best sensitivity from A/H , H (not easy the first year ....)

- A/H experimentally easier (esp. at the beginning)

Here only SM-like h observable

Summary for the number of observed Susy (CP conserving) Higgs in 300 fb-1 as a function of tan and MA (maximal mixing in squark sector scenario). See all 4 Susy Higgs in rather small region of parameter space. In some of parameter space see only the h. Other squark sector parameters give similar but somewhat different results.

Direct observation of the full MSSM higgs sector particles is by no means assured.

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ILC HiggsAt lepton-lepton colliders (e.g. ILC), Higgs production is much simpler. One knows the initial state parton energies and polarizations. The dominant production is e+e → Z/* → ZH (Higgstrahlung), but VBF processes are also important. ZHH production reveals the Higgs self coupling.

For ZH production, it is not necessary to observe the Higgs directly. The mass recoiling from the Z can be determined from the Z decays to dileptons, so the Higgs is observed without bias (even if it decays to invisible particles, e.g. H → two LSPs.Higgs inferred from recoil to

the Z(fb)

qq

WW tt

RR

Zh

HA~ ~ ~ ~

ECM

ECM =500 GeV

103

106

1

L = 1x1034 cm-2s-1 for 107 sec. year gives 100 fb-1/year

Typical XS of 10 – 104 fb give O(103 – 106) events/yr

ZH cross section is large (>1% of total annihilation cross section)

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Spin of H can be done through measurements of the cross section energy dependence just above threshold.

= cm production angle;

= fermion decay angle in Z frame

Angular distributions of the Z/H reveal the parity. JP = 0+ JP = 0

d/dcos sin2 (1 - sin2 )

d/dcossin2 (1 +/- cos )2

Possible CP even and odd admixtures can be determined.

ILC Higgs quantum numbers

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ILC Higgs BRs

One of the most important measurements for the Higgs sector is the determination of its decay BRs. In the SM, the couplings are just proportional to mass.

As we noted, the LHC will not do a good job on this. At the ILC, with its unbiassed sample of Higgs, cleaner environment, better vertex detectors (can get closer to interaction point), these BRs can be measured at the several % level.Errors show

ILC precision

Ratio of cross sections for VBF involving WW or ZZ determine the HWW and HZZ couplings to ~1-2% and allow tests of quantum corrections.

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The BRs are a sensitive measure of what theory is responsible for the ‘Higgs’ that is observed. The pattern of couplings and total width tell us what kind of model is responsible for EWSB.

supersymmetry

Higgs-radion mixing (extra dimensions)

baryogenesis

ILC Higgs BRs

Shown here are ratios of couplings to those in the SM for the fermion or boson pairs named in the legend. Error bars indicate ILC precision. We see that to discriminate model classes, BR measurements at the few % level are necessary.

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uncertainty = 20 – 30% in 1000 fb-1. Not easy!

In my view, observation of a light Higgs at LHC provides much of the justification needed to proceed to build a lepton collider with energy sufficient to produce ZH and study the higgs exhaustively.

ILC Higgs self couplingMeasuring the Higgs self coupling (rate of ZHH production) gives the term in the potential. Comparing with from Higgs self coupling with that from the Higgs mass determination is an important cross check of the theory.

Cross section is low; final state is qqbbbb so is complex. Excellent mass resolution and b-quark identification are needed.

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It is likely that the Susy H, A, H± are too massive to be produced in 500 GeV e+e collisions. If they are light enough, ILC will do very well in measuring their properties. However, accurate measure of BRs for the low mass h can tell us the value of MA up to about 700 GeV.

e+e- → H A → 4 b jets signal is striking, if above threshold. H & A are nearly degenerate. This plot (MH/A = 450 GeV; 50 fb-1; ECM=1 TeV) demonstrates that backgrounds are not a problem. Widths ~ tan2 and are measurable for tan > 10.

A job for the Collider: it could produce CP even and odd states separately via → H0 or A0 using polarized ’s. Linear polarizations of the two ’s parallel accesses H; polarizations perpendicular accesses A. (Recall the Yang theorem for determining the parity of the 0 .) Since it is an s-channel production of a single Higgs, can reach higher masses in than from e+e- .

ILC Susy HiggsSM value (decoupling limit)

b

c

g

W

Possible BR measurements

Allowed MA

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Other Higgs possibilities

Some models provide a more complex Higgs sector:

Extra dimension models provide a scalar ‘radion’ due to fluctuations in brane metric, which has Higgs like properties and can interfere with a SM Higgs. (lecture on Alternate Models)

Some models postulate Higgs bosons that give mass to gauge bosons but not fermions (Fermiphobic Higgs with only H 2 bosons).

With more than two complex scalar doublets, more than the 5 Susy Higgs states can occur, including distinctive doubly charged Higgs states, H++ .

In Susy models, it is possible that the dominant decays of Higgs could be to invisible particles H LSP pair, thus making it very hard to see at LHC, but visible in ILC through Higgs recoil against a Z.

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A real world Higgs searchTake as a case study, a Tevatron (DØ) search for associated ZH

production with Z , H bb (the most sensitive single channel for low mass Higgs)

Final state is 2 b-jets, missing ET (MET) with other particles from spectator quark fragmentation, extra interactions, gluon radiation etc.

The primary backgrounds are (1) W+2 bjets with W l and the lepton not seen,

(2) W+2 light jets with W l, light jets faking b-jets and the lepton not seen,

(3) ttbar ,

(4) Z+2 jets,

(5) di-boson production (WW, WZ, ZZ) e.g. ZZ with 1 Z and 1 Zbb, AND

(6) multijet QCD production with enough mismeasurement to give fake MET.

Trigger on large MET and acoplanar jets.

Event pre-selection: no observed e or

2 or 3 jets pT > 20 GeV within good coverage of detector; leading jets not back to back in . Jets must have enough reconstructed tracks to allow for b-tagging in final selection.

MET> 50 GeV; require MET in calorimeter to be roughly aligned with MET from tracks (suppress bad measurement of jet in calorimeter).

jet1

jet2

MET

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Z()H(bb)Final selection:

Require that at least two jets are b-tagged with silicon vertex detector using decay length, decay length significance, vertex mass, impact parameter to identify a secondary vertex displaced from the primary interaction (neural network). One jet must pass loose tagging requirement and the second a tight cut.

Background simulations:

Use LO event generator (ALPGEN) for dominant ttbar and V+jets backgrounds; LO generator PYTHIA for dibosons.

Correct cross sections to NLO using data reweightings to get kinematic distributions right and NLO QCD calculations for normalization.

Multijet background is determined directly from data using events in which the MET in calorimeter and tracking system do not agree.

primary vertex

secondary vertex

secondary vertex

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Dijet mass

MET Dijet separation

Before b-tagging

(Higgs sig X500)

After b-tagging

(Higgs sig X10)

Z()H(bb) Compare data and MC for many kinematic distributions to validate analysis

Data well modelled by MC

Signal is small (x500 and x10 in plots)

Dominant background before b-tagging is W+light parton jets

Dominant background after b-tagging is W/Z+bb and ttbar

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Cannot cut on a single variable to distinguish signal and background – cutting sequentially reduces acceptance too much. Thus go to a multivariate technique where a large number of variables, each with some degree of signal/background discrimination are fed to an artificial intelligence learning algorithm that recognizes the magnitudes AND correlations of the variables for signal and background samples. Neural networks are often used; this analysis uses a Boosted Decision Tree (BDT).

Z()H(bb)

In the BDT, samples of MC signal and background are split into to two branches at successive ‘nodes’ based on the most discriminating variable at that node. Branching continues until the sample population reaches a minimum size, or no further signal/background separation, at a ‘leaf’. The purity (signal/background) at each leaf is computed. Iterate the tree with weights (boosting) to help reclassify mis-assigned signal and background. The final discriminant is the sum of probabilities for being signal like over all leaves.

Decision tree output for 115 GeV Higgs (signalX25= red line), data (points) and background expectations (histogram). Signal and background are reasonably well separated in this variable.

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Use the BDT output to form a negative log likelihood ratio that subjects prediction for signal (S) and background (B) to agreement with data (D).

Run thousands of simulated experiments (Poisson statistics), varying all the parameters (e.g. jet energy scale) within their Gaussian errors, obeying correlations. For the ensemble of simulated experiments (a) assuming no signal and (b) signal + background, determine the expected distributions of LLR. For data, compute the LLR value and calculate the probability that data is more likely than the distribution of signal+bknd or bknd only distributions by integrating the LLR to the right (more background-like than data).Define the integrals as CLB (background only) and CLSB (signal + background).

CLS = 1 – CLSB/CLB gives the confidence level that a signal is present. The CLB term is present to guard against cases where the result resembles neither background only or signal + background. Artificially inflate the signal until CLS = 0.95 for 95% CL limit.

Signal like

Bknd like

Z()H(bb)

Product is over all bins of BDT histogram for all analysis subsets (#jets)

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Z()H(bb)The resulting expected LLR values as a function of Higgs mass for the ensembles of pseudodata for S and S+B are shown by the dotted lines. Separation of these indicates the sensitivity.

The observed LLR values are shown by the solid line. In this case, the observed LLRs are more background-like than signal like. The green and yellow bands give the ±1 and ±2 ranges for the expected LLRB.

More signal like

Limit on SM Higgs cross section obtained from the Z()H(bb) channel as a function of MH, plotted normalized to the SM cross section. At MH=115 GeV, set a limit at about 7.5X SM. As MH increases, Higgs decreases, making the limit ratios worse.

Combine these results with all the other DØ and CDF limits to get the Tevatron limit plots shown earlier.

More bkgd like

Clearly the distinction of S and S+B is weak, so to get limits, scale up the signal.

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Higgs summary

The SM Higgs is expected below ~180 GeV; the lightest Susy Higgs should be < 130 GeV. To retain unitarity, the Higgs must lie below ~1 TeV.

The Tevatron may find evidence for Higgs below ~120 GeV; the LHC should discover the Higgs at any mass.

Detailed exploration of the SM Higgs sector – quantum numbers, decay branching ratios, couplings can be done with the ILC.

LHC should see the lightest Susy Higgs, maybe some others. If ILC can see the heavy Susy Higgs, will give full description of properties.

Experiments are demonstrating the ability to dig Higgs signals out even in for challenging signatures.