Higgs Bosons and b Quarks

1
Higgs Bosons and b Quarks

• November, 2007
• U.C. Irvine
• Sally Dawson

Laura Reina, Chris Jackson, Doreen Wackeroth
2
Plan

• Lightning review of SM Higgs physics
• Discussion of gg?bbh vs bg ?bh
• Emphasize understanding of theoretical
  assumptions
• MSSM results for bg?bh
• Status of current (Summer, 2007) limits
• Effects of squark/gluino loops on bg?bh
• Why are these effects interesting?

3
Precision measurements limit Higgs Mass

• LEP EWWG (July, 2007)
• Mt170.9 ? 1.8 GeV
• Mh7636-24 GeV
• Mh lt 144 GeV (one-sided 95 cl)
• Mh lt 182 GeV (Precision measurements plus direct
  search limit)

2007
Best fit in region excluded from direct searches
Higgs mass limit only holds in SM
4
Precision Measurements in the SM

• At tree level, muon decay related to input
  parameters
• One loop corrections included in parameter ?r
• Where

??
e
?
W
?e
5
Understanding Higgs Limit
Theory Input MZ, GF, ?, Mh ? Predict MW
Jan, 07
6
Limits on Higgs Mass ASSUME Standard Model

• Its easy to construct a model which evades Higgs
  mass limits
• All you need is large ?? ??T

7
SM Isnt the Only theory That Fits Precision
Measurements

• Slight preference for MSSM over SM

8
Producing the Higgs at the Tevatron

• Theory uncertainties small
• Bands are scale uncertainties
• PDF uncertainties 10

NNLO or NLO rates
Mh/2 lt ? lt Mh/4
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Limits understood from Branching Ratios

• Bands are theory errors, mostly from mb

• Tevatron searches Mh lt 140 GeV, qq?Wh, h ?bb
• Mh larger, gg ?h, h ?WW

10
SM Higgs Searches at Tevatron
Tevatron Expected
Tevatron Observed
LP07
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How close will they get?

• Its not just luminosity

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CDF/DO Projections
FNAL PAC, Nov. 07
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SM Production Mechanisms at LHC
Bands show scale dependence
All important channels calculated to NLO or NNLO
Production with bs very small in SM
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SM Higgs, CMS 2007

• Includes radiative corrections

• Higgs bs arent discovery mode for SM Higgs

• Note h??? lack of tth

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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

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Which b mass?

• ?(bbh)?(mb/v)2
• Pole mass (from ? decays) mb4.62 GeV
• MS bar mass

• Makes a big numerical difference which b mass you
  use

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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
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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
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General Approach

• NLO total cross section
• NLO corrections contain
• ? Renormalize UV divergences (d4-2?)
• ? Cancel IR divergences in virtual real
  contributions
• ? Check ? dependence

One loop virtual corrections to
One gluon real emission
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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)

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Virtual Corrections Main Challenge is pentagon
diagrams
b
b
b

• 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
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Real Corrections

• Real gluon emission IR singularities for 2?4
  process
• Phase Space Slicing?isolate the region of phase
  space where sig?0
• 
  sig2pi?pj2EiEg(1-?cos?ig )
• ? Two cut-off method
• ?s (Eglt?s?s/2) Soft singularities
• ?c (1-cos?iglt?c) Collinear singularities

b
b
b
b
b
b
Final result is independent of cut-offs
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Two Cutoff Method (?s,?c)
Divide gluon phase space
In the soft limit (Eg?0) d(PS)4?d(PS)3d(PS)g
Eikonal factor contains soft poles
?soft computed analytically
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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
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Scale and Scheme Dependence at NLO

• 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

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

Scheme dependence
Scale dependence
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What is the dominant process for Higgs b
Production?

• Answer depends on whether you tag outgoing bs

• Is there double counting when including b initial
  state?

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The b quark as a parton

• Absorb collinear logs in b quark distributions
• Altarelli-Parisi evolution of PDFs sums
  ?snlnn(?2/mb2)
• b quark PDF ??sln(?2/mb2) relative to gluon PDF
• Have to be careful about double counting

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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 bs 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
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Counting Rules with b PDFs
Reordering of perturbation expansion
(?sln(Mh2/mb2))2?.4
?s2ln(Mh2/mb2)?.06
?s2?.01
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Re-ordering of Perturbation Theory

• 0 b tag process in 5FNS
• LO bb?h O(?s2?b2)
• NLO Virtualreal 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

?blog(Mh2/mb2)
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Inclusive Cross Section for bb? h 0 b tags
Almost no scale dependence at NNLO
bb? h vs gg ? bbh
It really doesnt matter which PDF scheme you use
Harlander Kilgore, hep-ph/0304035
Campbell et al, hep-ph/0405302
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What if only 1 b is tagged?
4FNS gg?bbh
This is most important process experimentally
pTbgt 20 GeV ? lt 2 (Tevatron), 2.5 (LHC) ?R gt 0.4
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What about distributions?Compare 4 and 5 Flavor
Number PDF Schemes
Higgs plus single b at LHC
NLO
pTbgt 20 GeV ? lt 2.5 ?R gt 0.4
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Good Theoretical Understanding of Uncertainties
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Higgs in the MSSM

• MSSM has 2 Higgs doublets Hd and Hu

• Physical CP-Even Higgs bosons

• Pseudoscalar, A0, and two charged Higgs, H?

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Higgs Couplings very different in MSSM
Light Higgs
Heavy Higgs
Couplings to d, s, b enhanced at large tan ?
SM
Couplings to u, c, t suppressed at large tan ?
Decoupling limit
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Large tan ? Changes Relative Importance of
Production Modes
b, t
h
tan?1
tan?40
tan?7
tan? 7, bb production mode dominates
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Production of SUSY Higgs Bosons

• Large tan ?, dominant production mechanism is
  with bs
• bbh can be 10xs SM Higgs rate for large tan ?

LHC
tan?30
tan?3
Mh/H (GeV)
SUSY Higgs are produced with bs!
Maximal Mixing
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Enhancement in MSSM
Note log scale!
This is why the calculation is interesting!
?eff from FeynHiggs with MSUSYMg ?M21TeV,
AbAt25 GeV

• Can observe heavy MSSM scalar Higgs boson

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Single b tag
d?/d?h (fb/GeV)
d?/d?H (pb/GeV)
LHC
Tevatron
?h
?H
MSSM with MhMH120 GeV, tan ?40
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Single b tag
NLO
pTh (GeV)
pTH (GeV)
MSSM with MhMH120 GeV, tan ?40
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Higgs Decays also affected at large tan ?

• SM Higgs branching rates to bb and ??- turn
  off as rate to WW- turns on (Mh gt 160 GeV)

• MSSM At large tan ?, rates to bb and ??- stay
  large

Heavy H0 MSSM BRs
Rate to bb and ??- almost constant in MSSM
A0 MSSM BRs
SM
43
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
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A Reliable Prediction

• We have bg ?bh at QCD NLO
• PDF/scale/scheme uncertainties 10-20
• 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
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Higgs Couplings to Fermions in MSSM

• 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
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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

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b quarks couple to both Higgs at 1-Loop
Assumes Mh ltlt MSUSY
hu
x
bL
bR
Non-decoupling Effect
Haber et al, hep-ph/0007006
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h?bb

• If MA also large, decoupling recovered
• Approach to decoupling slowed for large tan ?

Contributions of squark and gluino loops will be
important
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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

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Need SQCD for Reliable Predictions
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Squark/gluino loops important for large tan ? and
small MSUSY

• Note slow approach to decoupling limit for large
  tan?

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gb?b?
Dawson, Jackson, hep-ph/0709.4519
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Can gb?b? jet be useful?

• LHC

More soon..
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Conclusions

• In the MSSM Higgs and b quarks go together at
  large tan ?
• Higgs production with bs is dominant mechanism
  for tan ? gt 7
• Theoretical understanding of b PDFs compatible
  answers in 4FNS and 5FNS for PDFs
• SUSY QCD corrections can be the same size as QCD
  corrections

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Jan, 2007