# Presentation: 153669

## Higgs Bosons and b Quarks

***Higgs Bosons and b Quarks***

- October, 2006
- Sally Dawson

-  Laura Reina, Chris Jackson, Doreen Wackeroth

## Review of Higgs Couplings

- Higgs couples to fermion mass
- Largest coupling is to heaviest fermion
- No Higgs coupling to neutrinos
- Higgs couples to gauge boson masses
- Higgs self-interactions proportional to Mh
- Heavy Higgs implies large 4
- Only free parameter is Higgs mass!
- Everything is calculable....***testable theory***

## Standard Model is Incomplete Without Something like a Higgs boson

- Higgs mechanism gives gauge invariant masses for W, Z
- Higgs mechanism gives fermion masses
- Requires physical, scalar particle, h, with unknown mass
-        Mh is ***ONLY*** unknown parameter of EW sector
- Observables predicted in terms of:
- MZ=91.1875   .0021 GeV
-        GF=1.16639(1)  x 10-5 GeV-2
-        =1/137.0359895(61)
-        Mh
- Higgs and top quark masses enter into quantum corrections
-         Mt2, log(Mh)

## Precision measurements limit Higgs Mass

- New from ICHEP 2006:
- Mt=171.4  2.1 GeV
- Mh=85+39-28 GeV
- Mh < 166 GeV (one-sided 95% cl)
- Mh < 199 GeV (Precision measurements plus direct search limit)

***Best fit in region excluded from direct searches***

- 2006

## SM Production Mechanisms at LHC

- Bands show scale dependence

- All important channels calculated to NLO or NNLO

***Production with b’s very small in SM***

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

- No holes in Mh coverage

- NLO QCD corrections not available for many backgrounds

**Notes:**
Comment on important of wbf

## Comparison of rates at Tevatron

- NNLO or NLO rates

- (ggh)1 pb << (bb)

##  SM Higgs at Tevatron

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

- 120 GeV SM Higgs
-  exclude at 95 % c.l. in 2006
-  3  evidence in 2009

- 2006

- 2009

## Limits understood from BRs

## SM Higgs Limits from the Tevatron

- 2006

## pp  bbh at NLO

- Why is bbh interesting?
- Direct measurement of b quark Yukawa coupling (enhanced in MSSM at large tan )
- Higgs discovery mode in SUSY models at large tan 
- Theoretical questions about b quark parton distribution functions (PDFs)
- Why do NLO corrections?
- Improved theoretical reliability
- Often find large numerical results

##     pp  bbh at NLO in QCD

- Almost identical calculation to pptth calculation
- Dominant contribution at both Tevatron and LHC is gg initial state
- Virtual + real corrections computed numerically using phase space slicing
-  b quark mass included everywhere
- Differences:  closed loops with top quarks,  numerical problems from large log(mb/Mh)

## Strong dependence on ptb cuts:

- Suppression of rate at NLO at LHC

## Residual Scheme Dependence at NLO

- Not obvious what “best” scheme for b mass is
- Cross section proportional to b Yukawa, b2(mb/v)2
- MS vs on-shell definitions of b quark mass
- Pole mass (from  decays): mb=4.62 GeV
- MS mass depends on physical scale:
- Difference between schemes is O(s()4)

- Definition of b mass is numerically important

- bbh production uniquely measures b Yukawa

## Consider hbb

- Compute the (s) corrections:
- Define the running b mass
- Large logarithms absorbed to 2-loops

*Lore: MS is best!*

## New Logs in Production Processes

- At NLO:
- Logs not neatly absorbed into running b mass

-  Mh associated with renormalization of s

- F mb associated with PDFs

## Residual  Scale and Scheme Dependence at NLO

- Large remaining scale/scheme dependence between OS and MS at NLO
- Effect  10-20%

- NLO calculations improve scale dependence
- Scale dependence enters in running of s() and PDFs, g(), as well as s3log() contributions
- Formally, scale dependence is O(s4) but may be numerically large
- Often used as estimate of theoretical uncertainties

- Scale dependence

- Scheme dependence

## Distributions for bbh production

- Not a huge effect in shapes of distributions from NLO corrections

- Dawson, Jackson, Reina, Wackeroth

- Note:  Most of cross section is at low pT

## What is the dominant process for Higgs + b Production?

- Answer depends on whether you tag outgoing b’s

- Is there double counting when including b initial state?

## Collinear Singularities

- gbb splitting
- Singular when b’s are collinear with initial gluon
-  mb regulates singularity

- p

-  p’

- k

- Collinear limit:
- 	p’=(1-z)p
- 	k=zp
- Internal propagator:

## The b quark as a parton

- Phase space factorizes in collinear limit:
- Integration over b phase space gives large log
- Absorb log into b quark distribution
- Altarelli-Parisi evolution of PDFs sums snlnn(2/mb2)
- b quark PDF  sln(2/mb2) relative to gluon PDF

## Two Schemes for PDFs:

- 4 flavor number scheme (also called fixed flavor number scheme)
- No b quarks in initial state
- Lowest order process involving Higgs and b’s is ggbbh
- 5 flavor number scheme (also called variable flavor number scheme)
- Define b quark PDFs (absorbs large logarithms)
- Higgs produced with no pT at lowest order (bb h)
- Higgs pT generated at higher orders in expansion

- Is one scheme intrinsically better?
- Much angst among theory set

- vs

## Counting Rules with b PDFs:

- (sln(Mh2/mb2))2.4

- s2.01

- s2ln(Mh2/mb2).06

*Reordering of perturbation expansion*

## Larger rate if only 1 b is tagged

- SM

## Exclusive cross section for pp bbh: 1 b tag

- Compare *5 flavor number scheme*  (b PDFs) with *4 flavor number scheme*  (no b PDFs) for PDFs
- Consistent results in two schemes

- It doesn’t matter
-  which scheme
-  you use *!*

- This is SM—Note smallness of rates

## What about distributions?Compare 4 and 5 Flavor Number PDF Schemes

- NLO corrrections to gbbh in Monte Carlo program, MCFM

- Higgs plus single b at LHC:

- pTh > 20 GeV

- Apparent singularity at threshold removed by rebinning

- Familiar problem:  requires resummation at threshold

## Inclusive Cross Section for bb h:  0 b tags

- Harlander & Kilgore, hep-ph/0304035

- Campbell et al, hep-ph/0405302

- Almost no scale dependence at NNLO

- bb h vs gg  bbh

- It really doesn’t matter which PDF scheme you use

## Theoretical subtlety

- b Higgs production only phenomenologically relevent in MSSM with large tan 
- Closed fermion loops can be different flavor from produced quark
- In SM, these contributions are important for comparison between 4FNS and 5FNS (they are proportional to Mt/v):  They lower rate at LHC by 10%.
- In MSSM at large tan , closed top loops suppressed by cot  and should be neglected.

## Picture is very different in SUSY Models

- SUSY models have at least two Higgs doublets: H1, H2
- 5 physical Higgs bosons, h0, H0, A0, H
- Tree level potential has 2 free parameters
- Typically pick MA, tan  as parameters
- Predict Mh, MH, MH,  all couplings
- Large corrections O(GFmt2) to predictions

*Gauge Couplings*

***Upper bound on M******h***

- Heinemeyer, Weiglein

## LEP MSSM Higgs Bound

***LEP MSSM Higgs Bound***

- Boundaries of theoretically inaccessible region  (“the nose”) have shifted due to 2- loop calculations of MSSM Higgs mass and larger Mt

## Higgs Couplings very different in MSSM

- Couplings to d, s, b enhanced at large tan 

- Couplings to u, c, t suppressed at large tan 

**SM**

- Spira, Zerwas

**Light Higgs**

**Heavy Higgs**

- Decoupling limit

## Why is large tan  Interesting?

- Brief excursion to SUSY SU(5) unified model
- At GUT scale, b=
- Renormalization group scale couplings from MGUT to MZ
- QCD corrections large and negative
- Balance with large Yukawa couplings
- Get experimental value for mb/m if tan40-50

- Numerology:  Mt/mb  40

## Large tan    Changes Relative Importance of Production Modes

- tan ≥ 7,  bb production mode dominates

- h

* *b, t

- Kilgore

## New Modes important 

- New channels can play a role: Higgs plus jet
- Large tan , b quarks dominate

- Dawson, Field, Smith, hep-ph/0311199

*Note huge enhancement at large tan ***

- b, t

## Production of SUSY Higgs Bosons

-  For large tan , dominant production mechanism is with b’s
-   bbh can be 10x’s SM Higgs rate in SUSY for large tan 

- LHC

- SUSY Higgs are produced with b’s!

## SUSY Rates at the Tevatron

##  Enhancement in MSSM

- Can observe heavy MSSM scalar Higgs boson

- Note log scale!

*This is why the *
* **calculation is*
*interesting!*

## bbh in SUSY Models at Tevatron

- Huge enhancements in SUSY

## Higgs Decays also affected at large tan 

- SM:  Higgs branching rates to bb and +- turn off as rate to W+W- turns on (Mh > 160 GeV)

- MSSM: At large tan , rates to bb and +-  stay large

- SM

- Heavy H0 MSSM BRs

- A0 MSSM BRs

- Rate to bb and +- almost constant in MSSM

## Tevatron SUSY Sensitivies

- Tevatron will be sensitivite to MSSM Higgs for all tan  > 30 and MA < 200 GeV

## bh production at NLO

- Larger rate than 2-b tag process
- Extra b tag and Higgs transverse momentum improve detection efficiency from 0-b tag process (bbh)
- Require at least 3 b-tagged jets
- Look for excess in di-jet mass

- Look for signal in invariant mass spectrum from two leading b-jets
- Main background is QCD b-jets
- Signal acceptance 0.2-1.5%

## New bh, hbb  limit

*** ******D0 search: tag 3 b’s***

- 260 pb-1

- .9 fb-1

- ICHEP, 2006

## Limit on MSSM from bh, hbb 

## bh Production: h+-

- Smaller branching ratio than hbb, but clean signal

## MSSM limits from bh,  h+-

- D0, 340 pb-1, ICHEP 2006

## b Higgs expectations at the LHCfrom bbh,  h+-

*At least 1 b jet tagged*

- CMS Physics TDR, 2006

##  bb h in MSSM

- 5 discovery region

- Dawson, Dicus, Kao, Malhotra, hep-ph/0402172

*Can you use decay h****+****-**?*

- Best channel is bh production

## Conclusions

- In the MSSM Higgs and b quarks go together at large tan 
- Higgs production with b’s is dominant mechanism for tan  > 7
- Theoretical understanding of b PDFs:  compatible answers in 4FNS and 5FNS for PDFs