# Presentation: 657323

## Finding the Higgs boson

- Sally Dawson, BNL
- FNAL LHC School, Lecture 2

- Properties of the Higgs boson
- 	Theoretical uncertainties & motivations for   	precision measurements
- Higgs production at the Tevatron and LHC

## Who needs a Higgs?

- Gives masses to W, Z, and fermions in gauge invariant fashion
- Unitarizes VVVV scattering
- (More in Lecture 3)
- Makes precision electroweak data consistent

## But....

- Higgs mechanism doesn’t explain masses or flavor structure
- It accommodates them
- Higgs mass is quadratically sensitive to physics at high scales
- (More in Lecture 3)
- Higgs potential stable only for certain Higgs masses
- (More in Lecture 3)

## Review of Higgs Couplings

- Higgs couples to fermion mass
- Largest coupling is to heaviest fermion
- Top-Higgs coupling plays special role?
- No Higgs coupling to neutrinos

- v=246 GeV

## Review of Higgs Couplings

- Higgs couples to gauge boson masses
- Only free parameter is Higgs mass!
- Everything is calculable....***testable theory***

## Review of Higgs Boson Feynman Rules

- Higgs couples to heavy particles
- No tree level coupling to gluons (g) or photons ()
- Mh2=2v2  large Mh is strong coupling regime

## Higgs Decays

- hff proportional to mf2
- 3 typical of scalar
- (pseudo-scalar decay )

- For Mh<2MW, decays to bb most important

## QCD Corrections to hQQ

- Tree level:
- Add QCD:
- Large logs absorbed into running MS mass:

## Higgs Decays to Gauge Bosons

- h gg sensitive to top loops
- Remember no coupling at tree level
- h   sensitive to W loops, only small contribution from top loops
- h W+W- ffff has sharp threshold at 2 MW, but large branching ratio even for Mh=130 GeV

- Cubic in Mh, so for heavy Higgs, decays to vector boson dominate

## Decays to Gauge Bosons

## Status of Theory for Higgs BRs

- Data points are e+e- ILC at s=350 GeV with L=500 fb-1

**Bands show theory errors**
**Largest source of  uncertainty is b quark mass**

## Total Higgs Width

- Total width sensitive function of Mh
- Small Mh, Higgs is narrower than detector resolution
- As Mh becomes large, width also increases
- No clear resonance
- For Mh 1.4 TeV, tot Mh

*Higgs branching ratios easily computed with HDECAY program to NLO*
*http://mspira.home.cern.ch/mspira/proglist.html*

## Higgs Searches at LEP2

- LEP2 searched for e+e-Zh
- Rate turns on rapidly after threshold, peaks just above threshold, 3/s
- Measure recoil mass of Higgs; ***result independent of Higgs decay pattern***
-     Pe-=s/2(1,0,0,1)
-     Pe+=s/2(1,0,0,-1)
-     PZ=(EZ, pZ)
- Momentum conservation:
-     (Pe-+Pe+-PZ)2=Ph2=Mh2
-      s-2 s EZ+MZ2= Mh2
- LEP2 limit, ***M******h ******> 114.1 GeV***

## Higgs at LEP2

- Higgs decays predominantly to bb
- LEP-2 searched in many channels
- bbjj, bbl+l-, bb, +jj, jjjj,....
- Z branching ratios
- e+e- (3.3%)
- bb (15%)
-  (20%) invisible
- jj (the rest)

## Higgs production at Hadron Colliders

- Many possible production mechanisms; Importance depends on:
- Size of production cross section
- Size of branching ratios to observable channels
- Size of background
- Importance varies with Higgs mass
- Need to see more than one channel to establish Higgs properties and verify that it is a Higgs boson

## Production in Hadron Colliders

- Gluon fusion
- Largest rate for all Mh at LHC
- Gluon-gluon initial state
- Sensitive to top quark Yukawa t
- Lowest order cross section:
- q=4Mq2/Mh2
- Light Quarks:  F1/2(Mb/Mh)2log(Mb/Mh)
- Heavy Quarks: F1/2 -4/3

*Largest contribution *
*is top loop*

*Rapid approach to heavy quark limit*

- In SM, b-quark loops unimportant

## Gluon fusion, continued

- Integrate parton level cross section with gluon parton distribution functions
- z=Mh2/S, S is hadronic center of mass energy
- Rate depends on R, F
- Rate for gluon fusion independent of Mt for Mt >>Mh
- Counts number of heavy fermions

## NNLO, ggh

- Bands show .5Mh < < 2 Mh
- LO and NLO  dependence bands don’t overlap
-  Dependence used as estimate of theoretical uncertainty

- NLO&NNLO results allow improved estimates of theoretical uncertainties

- Rates depend on renormalization scale, s(R), and factorization scale, g(F)

## Higgs production at the LHC

## Vector Boson Fusion

- W+W- X is a real process:
- Rate increases at large s: (1/ MW2 )log(s/MW2)
- Integral of cross section over final state phase space has contribution from W boson propagator:
- Outgoing jets are mostly forward and can be tagged

- Peaks at small 

- Idea:  Look for h decaying to several different channels
- Ratio of decay rates will have smaller systematic errors

## W(Z)-strahlung 

- W(Z)-strahlung (qqWh, Zh) important at Tevatron
- Same couplings as vector boson fusion
- Rate proportional to ***weak*** coupling
- Below 130-140 GeV, look for
- For Mh>140 GeV, look for hW+W-
- Theoretically very clean channel
- NNLO QCD corrections:  KQCD1.3-1.4
- Electroweak corrections known (-5%)
- Small scale dependence (3-5%)
- Small PDF uncertainties

##   tth Production

- Large QCD effects

- tth production unique channel to measure top quark Yukawa coupling
- htt never important
- bbh small in SM, but can be enhanced in SUSY models with large tan 

## Higher order corrections

- QCD effects can be large
- Leading order cross sections have large uncertainties due to:
- Renormalization/factorization scale dependence
- Uncertainties from parton distribution functions (PDFs)
- Important modes have large QCD backgrounds
- Often backgrounds only known to leading order

## PDF uncertainties

- CTEQ6m:  40 PDFs for uncertainty studies
- http://user.pa.msu.edu/wkt/cteq/cteq6pdf.html

***NLO PDFs with NLO cross sections!***

- Smaller PDF uncertainties in vector boson fusion (qq initial channel)

## Production mechanisms at LHC

- Bands show scale dependence

- All important channels calculated to NLO or NNLO

## Comparison of rates at Tevatron

- Luminosity goals for Tevatron: 6-8 fb-1
- Higgs very, very hard at Tevatron

## Higgs at the Tevatron

- Largest rate, ggh, h bb, is overwhelmed by background

- (ggh)1 pb << (bb)

## Higgs at the Tevatron

- Wh, Zh production important for Mh<140 GeV, hbb
- Background from Wbb, Zbb
- One of the few examples where both signal and background known to NLO

***Wh, Zh and background in MCFM Monte Carlo to NLO***
***http:mcfm.fnal.gov***

## Search channels at Tevatron

- For heavier Higgs, look for hW+W-
- Searches for ggh W+W- (dileptons)
- And Wh WW+W- (2 and 3 leptons)

- Requiring leptons reduces backgrounds

## Tevatron Higgs Searches

## Can the Tevatron discover the Higgs?

- 2006

- 2009

- This relies on statistical combination of multiple weak channels

## Search Channels at the LHC

***gg************h*********
- Small BR (10-3 – 10-4)
- Only measurable for Mh < 140 GeV
- Largest Background: QCD continuum production of 
- Also from -jet production, with jet faking , or fragmenting to 0
- Fit background from sidebands of data

- Mh=120 GeV; L=100 fb-1

- S/B = 2.8 to 4.3 

- gghbb has huge QCD bkd: Must use rare decay modes of h

- Gives 1% mass measurement

## tth at the LHC

- ggtth ttbb
- Spectacular signal
- t Wb
- Look for 4 b jets, 2 jets, 1 lepton

- Unique way to measure top quark Yukawa coupling

- Early studies looked promising

## BUT...Large QCD background to tth

- S/B=1/6 for Mh=120 GeV

## Vector Boson Fusion

- Outgoing jets are mostly forward and can be tagged
- Vector boson fusion and QCD background look different

## Vector Boson Fusion

- Identify signal with forward jet tagging and central jet veto
- Large Higgs + 2 jet background from ggggh
- Kinematic cuts effective at identifying signal

**Higgs + 2 jet Production**

- Signal from WBF after cuts

- 

**Rapidity between outgoing jets**

## Vector Boson Fusion for light Higgs

- For Mh = 115 GeV combined significance ~ 5

*Vector boson fusion effective for measuring Higgs couplings*

- Proportional to gWWh and gZZh
- Often assume they are in SU(2) ratio:  gWWh//gZZh=cos2W

## Vector Boson Fusion for Heavy Higgs

- h  ZZ  l+l- l+l-

- Gold-plated

***200 GeV < M******h****** < 600 GeV: ***
**- discovery in h ******** ZZ ******** l****+****l****- ****l****+****l****-**** **
**Background smaller than signal**
**Higgs width larger than experimental resolution** **(M****h**** > 300 GeV)**
- - **confirmation in h ******** ZZ ******** l****+****l****-**** jj**** ****channel**

***M******h****** > 600 GeV:***
**4 lepton channel statistically limited**
**h ******** ZZ ******** l****+****l****-  ******
**h ******** ZZ ******** l****+****l****-**** jj , h ******** WW ******** l ********jj**
-     -150 times larger BR than 4l channel

## If there is a light SM Higgs, we’ll find it at the LHC

- No holes in Mh coverage

**Notes:**
Comment on important of wbf

## If we find a “Higgs-like” object, what then?

- We need to:
- Measure Higgs couplings to fermions & gauge bosons
- Measure Higgs spin/parity
- Reconstruct Higgs potential
- Is it the SM Higgs?
- Reminder: Many models have other signatures:
- New gauge bosons (little Higgs)
- Other new resonances (Extra D)
- Scalar triplets (little Higgs, NMSSM)
- Colored scalars (MSSM)
- etc

## Is it a Higgs?

- How do we know what we’ve found?
- Measure couplings to fermions & gauge bosons
- Measure spin/parity
- Measure self interactions

- Very hard at
-  hadron collider

## Absolute measurements of Higgs couplings

- Ratios of couplings more precisely measured than absolute couplings
- 10-40% measurements of most couplings

**Notes:**
Note LHC numbers normalized to HW coupling

## Can we reconstruct the Higgs potential?

- Fundamental test of model!

- We have no idea how to measure 4

## Reconstructing the Higgs potential

- 3  requires 2 Higgs production
- Mh<140 GeV, hbbbb
- Overwhelming QCD background
- Easier at higher Mh

- Can determine whether 3=0 at 95% cl with 300 fb-1 for 150<Mh<200 GeV

**Notes:**
This is not the best case since br H->bb is smaller at Mh=180 than smaller Mh

Can tell that lambda_3 isn’t zero

## Higgs measurements test model!

- Supersymmetric models are our favorite comparison
- SUSY Higgs sector
- At least 2 Higgs doublets
- SM masses from
-     term not allowed in SUSY models:  Need second Higgs doublet with opposite hypercharge
- 5 physical Higgs: h0,H0,A0,H±

## SUSY Higgs

- General 2 Higgs doublet potential has 6 couplings and a phase
- SUSY Higgs potential has only 2 couplings
- Take these to be ***M******A****** and tan*********
- At tree level Higgs couplings, neutral and charged Higgs masses are predicted
- Lightest Higgs mass has upper limit

## Upper Limit on Higgs Mass in SUSY Models

- Can tune parameters,  but always have upper limit below Mh130 GeV

## Higgs Couplings very different from SM in SUSY Models

- Ratio of h coupling to b’s in SUSY model to that of SM

## MSSM discovery

- For large fraction of MA-tan space, more than one Higgs boson is observable
- For MA, MSSM becomes SM-like
- Plot shows regions where Higgs particles can be observed with > 5

- Need to observe multiple Higgs bosons and measure their couplings

## Limits on SUSY Higgs from LEP

- Mt=169.3,174.3,
- 179.3, 183 GeV

## New Discovery Channels in SUSY

## Conclusion

- The Higgs boson is the final missing link in the SM