# Presentation: 264315

## Higgs Bosons and b Quarks

***Higgs Bosons and b Quarks***

- September, 2007
- Sally Dawson

-  Laura Reina, Chris Jackson, Doreen Wackeroth

## Plan:

- Lightning review of SM Higgs physics
- QCD corrections to bg→bh (review)
- Discussion of gg→bbh vs bg →bh
- MSSM results for bg→bh
- Status of current (Summer, 2007) limits
- Effects of SQCD on bg→bh
- Why are these effects interesting?
- Does the effective Lagrangian approach work here?
- What about decoupling for heavy SUSY particles?

## Precision measurements limit Higgs Mass

- LEP EWWG (July, 2007):
- Mt=170.9  1.8 GeV
- Mh=76+36-24 GeV
- Mh < 144 GeV (one-sided 95% cl)
- Mh < 182 GeV (Precision measurements plus direct search limit)

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

- 2007

## Understanding Higgs Limit

- Theory:  Input MZ, GF, 
- 	→ Predict MW

- Jan, 07

## Producing the Higgs at the Tevatron

- NNLO or NLO rates

- Mh/2 <  < Mh/4

##  SM Higgs at Tevatron

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

*** ******h ******→WW****

## SM Higgs Searches at Tevatron

- LP07

- Summer 2006

- New in 2007 (to be combined)

- 95% cl limit/SM

- Higgs Mass (GeV)

- Higgs Mass (GeV)

- 95% cl limit/SM

## SM Higgs Searches at Tevatron

**Tevatron Observed**

**Tevatron Expected**

- LP07

## 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

## pp  bbh 

- 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)

- This can be a top quark

## General Approach

- NLO total cross section
- NLO corrections contain:
- 	   Renormalize UV divergences (d=4-2)
- 	   Cancel IR divergences in virtual + real contributions
- 	   Check  dependence

- : One loop virtual corrections to

- : One gluon real emission

## Virtual Corrections

- Reduce each diagram in terms of scalar integrals of the form:
- Three external massive particles (keep b mass everywhere)
- Several massive internal propagators
- Finite integrals: use existing libraries/packages
- UV divergent integrals: analytic (easy)
- IR divergent integrals:  analytic (hard)

## Virtual Corrections:  Main Challenge is pentagon diagrams

- Scalar pentagon integrals:  reduced to linear combination of five box scalar integrals (Bern, Dixon, Kosower; Denner)
- Tensor pentagon integrals:  numerical instabilities (due to Gram determinant spurious ingularities) treated both analytically and numerically

- b

- b

- b

- b

- b

- b

- b

- b

- b

- b

- b

- b

## Real Corrections

- Real gluon emission:  IR singularities for 24 process
- Phase Space Slicingisolate the region of phase space where sig0
-                                   sig=2pipj=2EiEg(1-cosig )
- → Two cut-off method:
- s (Eg<ss/2) 	Soft singularities
- c (1-cosig<c) 	Collinear singularities

- b

- b

- b

- b

- b

- b

- Final result is independent of cut-offs

## Two Cutoff Method (s,c):

- In the soft limit (Eg0):
- d(PS)4d(PS)3d(PS)g =

- Divide gluon phase space:

- Eikonal factor contains soft poles:

- soft computed analytically:

## Hard gluon phase space further divided:

- In collinear limit: iig ; pj=zpi, pg=(1-z)pi

- Compute hard/collinear  analytically

-  hard/not collinear is finite:  compute numerically

## Use MS Renormalization

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

*Lore: MS is best!*

- h

- h

- h

## 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

- Scale dependence

- Scheme dependence

## Strong dependence on ptb cuts:

- Suppression of rate at NLO at LHC

## Distributions for bbh production

- Dawson, Jackson, Reina, Wackeroth

- pTb> 20 GeV
- || < 2 (Tevatron), 2.5 (LHC)
- R > 0.4

- Mh=120 GeV

## 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?

## 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

- vs

## Counting Rules with b PDFs:

- (sln(Mh2/mb2))2.4

- s2.01

- s2ln(Mh2/mb2).06

- Reordering of perturbation expansion

## Re-ordering of Perturbation Theory

- 0 b tag process in 5FNS:
- LO:      bb→h     O(s2b2)
- NLO:   Virtual+real corrections    O(s3b2)
- NLO:    bg →bh    O(s2b) , correction of O(1/ b)  to tree level
- NNLO: gg →bbh  O(s2),      correction of O(1/b2)  to tree level
- 1 b tag process in 5FNS:
- LO process is bg→bh:  	Tree level, O(s2b)
- NLO includes new subprocess: gg →bbh, O(1/ b) correction to LO

- b=log(Mh2/mb2)

## 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

## What if only 1 b is tagged?

- 4FNS: gg→bbh

- pTb> 20 GeV
- || < 2 (Tevatron), 2.5 (LHC)
- R > 0.4

## 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

- Higgs plus single b at LHC:

- pTb> 20 GeV
- || <  2.5
- R > 0.4

- NLO

## Higgs in the MSSM

-  MSSM has 2 Higgs doublets: Hd and Hu

-  Physical CP-Even Higgs bosons

- Pseudoscalar, A0, and two charged Higgs, H

## 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**

**Light Higgs**

**Heavy Higgs**

- Decoupling limit

## Large tan    Changes Relative Importance of Production Modes

- Large tan    Changes Relative Importance of Production Modes

- tan ≥ 7,  bb production mode dominates

- h

* *b, t

- Kilgore

***tan************=1***

***tan************=40***

***tan************=7***

## 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!

- *Maximal Mixing

- Mh/H (GeV)

- tan=30

- tan=3

##  Enhancement in MSSM

- Can observe heavy MSSM scalar Higgs boson

- Note log scale!

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

- eff from FeynHiggs with MSUSY=Mg= =M2=1TeV, Ab=At=25 GeV

## bbh in SUSY Models at Tevatron

- Huge enhancements in SUSY

## Comparison of 4FNS and 5FNS

- Assume no b quarks tagged

## Single b tag

- MSSM with Mh=MH=120 GeV, tan  =40

- d/dh (fb/GeV)

- d/dH (pb/GeV)

- LHC

- Tevatron

- h

- H

## Single b tag

- pTh (GeV)

- MSSM with Mh=MH=120 GeV, tan  =40

- pTH (GeV)

- NLO

## bh production at NLO

- Larger rate than bbh process, with 2 b’s tagged
- Extra b tag and Higgs transverse momentum improve detection efficiency from 0-b tag process (bbh)
- h →bb require at least 3 b-tagged jets

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

## MSSM Higgs Searches

- h, H, A  bb (CDF)

- h, H, A  bb (DZero)

- LP2007

***bg******→b*********

## MSSM limits from bg→bh (1 fb-1)

- LP, 2007

- 30 fb-1 CMS expects to get to tan  ~ 15 through bh; h→+,  h→bb

## A Reliable Prediction

- We have bg →bh at QCD NLO
- PDF/scale uncertainties ~ 10%
- Are squark/gluino contributions relevant?
- Important for bb→H, A at LHC
- For some parameters as large as -50% effects
- Squark/gluino effects almost completely described by *Improved Born Approximation*

- Dittmaier et al, hep-ph/0611353

## Higgs Couplings to Fermions

- At tree level, Hd couples to charge -1/3 quarks, and Hu couples to charge 2/3 quarks
- Since up and down quark sectors are diagonalized independently, interactions are flavor diagonal
- Trilinear couplings couple both Higgs to charge -1/3 and charge 2/3 squarks

- Couples “wrong” Higgs

## Effective Lagrangian Approach

-  No tree level Hubb coupling in MSSM, but it arises at 1-loop

-  At tree level, mb =bv1/2
-  At one loop: mb   bv1(1+ mb) /2
-  Yukawa coupling shifted:

## b quarks couple to both Higgs at 1-Loop

- bL

- bR

- x

- hu

- Non-decoupling Effect:

- Assumes Mh << MSUSY

- Haber et al, hep-ph/0007006

## h→bb

- If MA also large, decoupling recovered
- Approach to decoupling slowed for large tan 

## Calculate SUSY QCD Corrections to bg→bh

- Approach 1:  “Improved Born Approximation”
- Approach 2: O(s2) NLO calculation
- Use ghbb as above, so subtract off double counting
- Include all contributions from squark/gluino loops

## IBA (Effective L approach) works

- Note slow approach to decoupling limit for large tan

## Need SQCD for Reliable Predictions

## 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
- SUSY QCD corrections can be the same size as QCD

## Backup

## 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

- LP07

## 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

## W and Top Mass in MSSM

##  SM Higgs, CMS 2007 

- Talk by Stefan Soldner-Rembold, Sergio Bertolucci

## Jan, 2007