Precision SM physics at the LHC

. . . what we hope to see

(Bentvelsen, Grunewald)

Repeat the electroweak fit

changing the uncertainties

– δMW = 15 MeV

– δMtop = 1 GeV

– same central values

Michael Kramer Page 1 Herbstschule Maria Laach, September 2005

Herbstschule Maria Laach, September 2005

Physics at the Large Hadron Collider

Michael Kramer

(RWTH Aachen)

Lecture 1: Review of the Standard Model

Lecture 2: SM physics at hadron colliders

Lecture 3: Higgs and SUSY searches at the LHC

Michael Kramer Page 2 Herbstschule Maria Laach, September 2005

Introduction: The Higgs boson

The Higgs mechanism is testable becauseall couplings are known:

− fermions: gffH =√

2mf/v

− gauge bosons: gV V H = 2MV /v

with vacuum expectation value

v2 = 1/√

2GF ≈ (246 GeV)2

The Higgs sector and the properties of theHiggs particle (lifetime, decay branching ratios,

cross sections) are fixed in terms of theHiggs boson mass MH .Express Higgs potential in terms of (µ, λ) → (v2, MH)

Michael Kramer Page 3 Herbstschule Maria Laach, September 2005

Higgs boson mass

Higgs search at LEP in associated ZH production e+e− → Z∗ → ZH

�

������

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provide a lower limit on the SM Higgs mass: MH > 114.4 GeV (95% CL)

Electroweak precision tests�

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provide an upper limit on the SM Higgs mass: MH < 219 GeV (95% CL)

Michael Kramer Page 4 Herbstschule Maria Laach, September 2005

Higgs boson mass

Theoretical constraints

Hambye, Riesselmann

0

Landau Pole

Vacuum Instability

Running of the Higgs coupling:

dλ

dlnµ2=

3

8π2[λ2 + λG2

t − G4t ]

with λ = M2

H/v2 and Gt =√

2mt/v.

For MH > mt one has dλ/dlnµ2∼λ2

and thus

λ(µ2) =λ(v2)

1 −3λ(v2)8π2 ln µ2

v2

Requiring λ(Λ) < ∞ yields

M2H

<∼

8π2v2

3 ln (Λ2/v2)

Michael Kramer Page 5 Herbstschule Maria Laach, September 2005

Higgs boson decays

Higgs decay modes and branching ratios

[HDECAY: Spira et al.]

BR(H)

bb_

τ+τ−

cc_

gg

WW

ZZ

tt-

γγ Zγ

MH [GeV]50 100 200 500 1000

10-3

10-2

10-1

1

102

103

⇒ dominant decay into

bb for MH ∼< 130 GeV

WW, ZZ for MH ∼> 130 GeV

Michael Kramer Page 6 Herbstschule Maria Laach, September 2005

Higgs boson decays

Higgs decay width

Γ(H) [GeV]

MH [GeV]50 100 200 500 1000

10-3

10-2

10-1

1

10

10 2

102

103

→ direct measurement of Γ only for MHiggs ∼> 300 GeV

Michael Kramer Page 7 Herbstschule Maria Laach, September 2005

Higgs boson production at the LHC

σ(pp → H + X) [pb]√s = 14 TeV

NLO / NNLO

MRST

gg → H (NNLO)

qq → Hqqqq

_' → HW

qq_ → HZ

gg/qq_ → tt

_H (NLO)

MH [GeV]

10-4

10-3

10-2

10-1

1

10

10 2

100 200 300 400 500 600 700 800 900 1000

�

�

� �

��

��

� �

� �

���

� ��

��

�

Michael Kramer Page 8 Herbstschule Maria Laach, September 2005

Higgs boson production at the LHC

Precision calculations are needed for signal and background processes

– for Higgs discovery in WW decay channels (no reconstruction of mass peak possible)

– for a reliable determination of the discovery/exclusion significance

– for a precise measurement of the Higgs couplings

↪→ test of the Higgs mechanism↪→ discrimination between SM and BSM (eg. SUSY)

Recent progress for SM Higgs production includes– NNLO QCD calculations for pp → H

[Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, Smith, van Neerven; Anastasiou, Melnikov, Petriello; . . . (02-04)]

– NNLO QCD calculations for pp → HZ, HW[Brein, Djouadi, Harlander (04)]

– (N)NLO QCD calculations for pp → QQH[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas; Dawson, Jackson, Orr, Reina, Wackeroth; Harlander, Kilgore;Campbell, Ellis, Maltoni, Willenbrock; . . . (01-05)]

– NLO QCD calculations for pp → qqH[Figy, Oleari, Zeppenfeld; Berger, Campbell (03-04)]

– NLO EWK calculations for pp → HZ, HW[Ciccolini, Dittmaier, MK (03)]

– (N)NLL resummation for pp → H[Kulesza, Sterman, Vogelsang; Berger, Qiu; Catani, de Florian, Grazzini; . . . (03-04)]

– matching of NLO calculation with parton shower MC Herwig for pp → H[Frixione, Webber (04)];

– NNLO splitting functions and PDF fits, error estimates for PDF fits[Moch, Vermaseren, Vogt; MRST; CTEQ (02-05)].

Michael Kramer Page 9 Herbstschule Maria Laach, September 2005

Higgs boson production at the LHC

Higgs production in gluon-gluon fusion

��

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− NLO corrections: KNLO ≈ 1.7

− NNLO corrections:

KNNLO(mtop � MH) ≈ 2

→ NNLO scale dependence ∼< 15%

[Harlander, Kilgore ’02]

1

10

102

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

Michael Kramer Page 10 Herbstschule Maria Laach, September 2005

Higgs boson search at the LHC

0.1 1 1010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

σjet(ETjet > √s/4)

LHCTevatron

σttbar

σHiggs(MH = 500 GeV)

σZ

σjet(ETjet > 100 GeV)

σHiggs(MH = 150 GeV)

σW

σjet(ETjet > √s/20)

σbbar

σtot

σ (n

b)

√s (TeV)

even

ts/s

ec f

or L

= 1

033 c

m-2

s-1

−→ QCD background: σbb ≈ 108 pb

−→ Higgs signal: σH+X ≈ 10 pb

↪→≈ 3 × 105 Higgs bosons/year

(∫L = 30 fb−1)

−→ Higgs-search through associate production or/and through rare decays

Michael Kramer Page 11 Herbstschule Maria Laach, September 2005

Higgs boson search at the LHC: signal significance

The days of the Higgs boson are numbered!

1

10

10 2

102

103

mH (GeV)

Sig

nal s

igni

fican

ce H → γ γ ttH (H → bb) H → ZZ(*) → 4 l

H → ZZ → llνν H → WW → lνjj

H → WW(*) → lνlν

Total significance

5 σ

∫ L dt = 30 fb-1

(no K-factors)

ATLAS

Michael Kramer Page 12 Herbstschule Maria Laach, September 2005

Higgs boson search at the LHC: signal significance

1

10

10 2

100 120 140 160 180 200 mH (GeV/c2)

Sig

nal s

igni

fican

ce H → γ γ ttH (H → bb) H → ZZ(*) → 4 l H → WW(*) → lνlν qqH → qq WW(*)

qqH → qq ττ

Total significance

5 σ

∫ L dt = 30 fb-1

(no K-factors)ATLAS

MH ∼< 2MZ →

gg → H (H → γγ, ZZ∗, WW (∗))

gg/qq → ttH (H → bb, ττ)

qq → qqH (H → γγ, WW ∗, ττ)

qq′ → WH (H → γγ)

MH ∼> 2MZ →

{gg → H (H → ZZ, WW )

qq → qqH (H → ZZ, WW )

[ + diffractive Higgs production]

Michael Kramer Page 13 Herbstschule Maria Laach, September 2005

Higgs boson search at the Tevatron

search at the Fermilab Tevatron

current∫L = 0.8 fb−1

expectation in 2008:∫L = 4 − 6 fb−1

For MH

< 140 GeV

> 140 GeV

use

pp → WH/ZH and H → bb

pp → H and H → WW

Michael Kramer Page 14 Herbstschule Maria Laach, September 2005

Higgs boson physics at the LHC: the Higgs profile

To test the Higgs mechanism we have to determine the profile of the Higgs boson:

– mass and lifetime

– external quantum numbers

– couplings to gauge bosons and fermions

– Higgs self-couplings

Michael Kramer Page 15 Herbstschule Maria Laach, September 2005

Higgs boson physics at the LHC: the Higgs profile

The Higgs mass

The expected precision on MHiggs at the LHC is ∆M/M ≈ 10−3 (for MHiggs ∼< 500 GeV)

Michael Kramer Page 16 Herbstschule Maria Laach, September 2005

Higgs boson physics at the LHC: the Higgs profile

The measurement of Higgs couplings:

The LHC measures σ(pp → H) × BR(H → X) = σ(pp → H) × Γ(H → X)/Γtot

Different production and decay channels provide measurements of combinations of partial decay

widths

Xγ =ΓW Γγ

Γtotfrom qq → qqH, H → γγ Yγ =

ΓgΓγ

Γtotfrom gg → H → γγ

Xτ =ΓW Γτ

Γtotfrom qq → qqH, H → ττ YZ =

ΓgΓZ

Γtotfrom gg → H → ZZ(∗)

XW =Γ2

W

Γtotfrom qq → qqH, H → WW (∗) YW =

ΓgΓW

Γtotfrom gg → H → WW (∗)

Problem: no direct measurement of Γtot

no observation of some decay modes (e.g. H → gg)

→ consider ratios of X or Y ’s

Michael Kramer Page 17 Herbstschule Maria Laach, September 2005

Higgs boson physics at the LHC: the Higgs profile

Ratios of Higgs couplings can be measured with an accuracy of 10-40%:

Michael Kramer Page 18 Herbstschule Maria Laach, September 2005

Higgs boson physics at the LHC: the Higgs profile

Reconstructing the Higgs potential at the LHC is difficult (impossible)

Recall:

V =M2

H

2H2 + λ3vH3 +

λ4

4H4

In the SM we have

λ3 = λ4 =M2

H

2v2

To determine λ3 and λ4 need to measure multi-Higgs production, e.g.

g

g

H

H

H

g

g

H

H

H

H

The measurement of λ3 appears to be very difficult, the measurement of λ4 impos-sible(?)

Michael Kramer Page 19 Herbstschule Maria Laach, September 2005

Higgs boson physics at the LHC: summary

The LHC will find the (or a?) Higgs boson (or something similar).

The LHC will measure some of the Higgs boson properties.

For a more precise and model independent determination of decay widths

and a measurement of quantum numbers we will need the ILC.

Higgs physics is exciting:

– reveals the mechanism of electroweak symmetry breaking

– points towards physics beyond the SM (hierarchy problem)

Michael Kramer Page 20 Herbstschule Maria Laach, September 2005

The hierarchy problem: why is MHiggs � MPlanck?

Quantum corrections to the Higgs mass have quadratic UV divergencies

� ��

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→ δm2H ∼ α

π(Λ2 + m2

F )

The cutoff Λ represents the scale up to which the Standard Model remains valid.

→ need Λ of O(1 TeV) to avoid unnaturally large corrections

In comparison: δme ∼ απme ln(Λ/me) ≈ 0.25me

→ electron mass is stabilized (“protected”) by the chiral symmetry

An elegant way to solve the hierarchy problem is to introduce an additional symmetry that

transforms fermions into bosons and vice versa: supersymmetry

Quantum corrections due to superparticles cancel the quadratic UV divergences

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→ δm2H ∼ −α

π(Λ2 + m2

F )

δm2H ∼ α

π(m2

F − m2F ) → no fine-tuning if m ∼< O(1 TeV)

Michael Kramer Page 21 Herbstschule Maria Laach, September 2005

The Minimal Supersymmetric Standard Model

The MSSM particle spectrum

Gauge Bosons S = 1 Gauginos S = 1/2

gluon, W±, Z, γ gluino, W , Z, γ

Fermions S = 1/2 Sfermions S = 0(

uL

dL

)(νe

L

eL

) (uL

dL

)(νe

L

eL

)

uR, dR, eR uR, dR, eR

Higgs Higgsinos(

H02

H−

2

)(H+

1

H01

) (H0

2

H−

2

)(H+

1

H01

)

Michael Kramer Page 22 Herbstschule Maria Laach, September 2005

SUSY particle production at the LHC

In the MSSM one imposes a symmetryR = (−1)3B+L+2S

{= +1 SM

= −1 SUSYto avoid proton decay

→ SUSY particles produced pairwise

→ lightest SUSY particle stable (dark matter candidate)

The interactions of MSSM particles are determined by gauge symmetry and SUSY

example: gluonµ, a

p, i

q, j

squark

squark

= −i gs (Ta)ij(p + q)µ

→ no new coupling!

SUSY particles would be produced copiously at the LHC through QCD processes, e.g.

g

g

Michael Kramer Page 23 Herbstschule Maria Laach, September 2005

SUSY particle production at the LHC

Cross section predictions

10-2

10-1

1

10

10 2

10 3

100 150 200 250 300 350 400 450 500

⇑

⇑ ⇑ ⇑

⇑

⇑⇑

χ2oχ1

+

t1t−1

qq−

gg

νν−

χ2og

χ2oq

NLOLO

√S = 14 TeV

m [GeV]

σtot[pb]: pp → gg, qq−, t1t

−1, χ2

oχ1+, νν

−, χ2

og, χ2oq

e.g. σ(pp → gg) ≈ 1 pb for Mgluino = 1 TeV → 104 events/year

Michael Kramer Page 24 Herbstschule Maria Laach, September 2005

SUSY searches at the LHC

Distinctive signature due to cascade decays:

multiple jets (and/or leptons) with large amount of missing energy

g

q

χ0

2, χ±

1

χ01

l

(high-pT ) jets

high-pT jets

jets and/or leptons

missing ET

(GeV)effM

0 500 1000 1500 2000 2500

-1E

vent

s/50

GeV

/10

fb

10

102

103

104

105

→ discovery reach for squarks and gluinos: Mq,g ∼< 2.5 TeV

Michael Kramer Page 25 Herbstschule Maria Laach, September 2005

SUSY searches at the LHC

SUSY is broken: SUSY-masses 6= SM-masses

L = L(SUSY) + L(SUSY-breaking)

“soft-breaking”-terms: → 124 parameters in the MSSM

(SUSY is not to blame. The large number of the MSSM parameters is a consequence of our

ignorance of the dynamics of SUSY-breaking)

⇒ What is the mechanism of SUSY-breaking?

The bottom-up approach: Measure the parameters of the SUSY Lagrangian at the

LHC and test models of SUSY breaking.

Will the accuracy of SUSY measurements at the LHC be sufficient to discriminate

among different models of SUSY-breaking?

Michael Kramer Page 26 Herbstschule Maria Laach, September 2005

A crucial test of SUSY models: the light Higgs

MSSM Higgs sector: two Higgs doublets to give mass to up- and down-quarks

→ 5 physical states: h, H , A, H±

The MSSM Higgs sector determined by tan β = v2/v1 and MA.

The couplings in the Higgs potential and the gauge couplings are related by super-

symmetry. At tree level one finds Mh ≤ MZ . This relation is modified by radiative

corrections so that

Mh ∼< 130 GeV (in the MSSM)

The existence of a light Higgs boson with mass Mh ∼< 200 GeV is a generic

prediction of SUSY models.

Michael Kramer Page 27 Herbstschule Maria Laach, September 2005

A crucial test of SUSY models: the light Higgs

One of the SUSY Higgs bosons will be seen at the LHC

Michael Kramer Page 28 Herbstschule Maria Laach, September 2005

A crucial test of SUSY models: the light Higgs

but it may look like the SM Higgs. . .

Consider

σMSSM(gg→h→γγ)

σSM(gg→h→γγ)

→ differences ∼< 10%

Needs precision measure-

ments & calculations for

production cross sections

and b ranching ratios

[Dedes, Heinemeyer, Su, Weiglein]

0 200 400 600 800 1000 1200 1400 1600 1800 20000

10

20

30

40

50

60

MA (GeV)

tanβ

mSUGRA gg−>h−>γγ

< 0.50.5−0.80.8−1.01.0−1.21.2−1.5>1.5

Michael Kramer Page 29 Herbstschule Maria Laach, September 2005

Summary

The LHC will find a Higgs boson or something that does its job

The LHC should find signatures of BSM physics (SUSY?)

Fundamental questions:

– How is SUSY broken?

– Does SUSY provide a viable dark matter candidate?

→ link between collider physics and cosmology

Exploring BSM physics may be difficult and will require in put from

– collider physics

– low energy physics (g − 2, B decays, EDMs, ...)

– ν physics

– astroparticle physics (cosmic rays, ...)

– cosmology

Michael Kramer Page 30 Herbstschule Maria Laach, September 2005