physics at the large hadron collider - rwth …mkraemer/lhc-tu.pdftu munchen,¤ mai 2006 physics at...

TU Munchen, Mai 2006

Physics at the Large Hadron Collider

Michael Kramer

(RWTH Aachen)

Mini-Review of the Standard Model

SM physics at hadron colliders: W -boson and top-quark production

Higgs and SUSY searches at the LHC

Michael Kramer TU Munchen, Mai 2006

Literature

I have used the following references to prepare these lectures:

– Lectures from Maria Laach schools, in particular those by S. Dawson, A. Denner,

M.L. Mangano, D. Zeppenfeld and myself (see Maria Laach web pages);

– Lectures by D. Ross, R.K. Ellis and J. Ellis at SUSSP57 “LHC phenomenology”

(published in the IoP Scottish Graduate Series);

– Review articles by: H. Spiesberger, M. Spira, P.M. Zerwas (hep-ph/9803257);

D.E. Soper (hep-ph/0011256); S. Willenbrock (hep-ph/0211067)

– and textbooks, mainly: Peskin & Schroeder, Barger & Phillips, Ellis, Stirling & Webber.


Introduction: Our picture of matter

Pointlike constituents (r < 10−18m):

(u

d

)

L

(s

c

)

L

(b

t

)

L

uR dR cR sR tR bR

(e

νe

)

L

(µ

νµ

)

L

(τ

ντ

)

L

eR {νeR} µR {νµR} τR {ντR}

Few fundamental forces, derived from SU(3)×SU(2)×U(1) gauge symmetryand mediated by

Vector bosons: γ, W±, Z, g

Electroweak symmetry breaking

Higgs mechanism with a Higgs scalar?


Introduction: The Standard Model

The SM Lagrangian is completely determined by

– the particle content

– Poincare invariance

– local gauge invariance under SU(3), SU(2) and U(1)

– renormalizability

– and the mechanism of electroweak symmetry breaking

LSM = −14F a

µνFaµν + iψDψ gauge sector

+ψiλijψjH + h.c. flavour sector

+|DH|2 − V (H) EWSB sector

+NiMijNj ν-mass sector


The SM Lagrangian looks a bit more complicated when you spell it out (typed by T.D.Gutierrez from Diagrammatica by M.Veltman)

LSM = − 12

∂ν gaµ∂ν ga

µ − gsfabc∂µgaν gb

µgcν − 1

4g2

sfabcfadegbµgc

ν gdµge

ν + 12

ig2s(qσ

iγµqσ

j)ga

µ + Ga∂2Ga +

gsfabc∂µGaGbgcµ − ∂ν W

+µ ∂ν W

−µ − M2W

+µ W

−µ − 1

2∂ν Z0

µ∂ν Z0µ − 1

2c2w

M2Z0µZ0

µ − 12

∂µAν ∂µAν − 12

∂µH∂µH −

12

m2h

H2 − ∂µφ+∂µφ− − M2φ+φ− − 12

∂µφ0∂µφ0 − 12c2w

Mφ0φ0 − βh[ 2M2

g2+ 2M

gH + 1

2(H2 + φ0φ0 + 2φ+φ−)] +

2M4

g2αh − igcw [∂ν Z0

µ(W+µ W

−ν − W

+ν W

−µ ) − Z0

ν (W+µ ∂ν W

−µ − W

−µ ∂ν W

+µ ) + Z0

µ(W+ν ∂ν W

−µ − W

−ν ∂ν W

+µ )] −

igsw [∂ν Aµ(W+µ W

−ν −W

+ν W

−µ )−Aν (W

+µ ∂ν W

−µ −W

−µ ∂ν W

+µ )+Aµ(W

+ν ∂ν W

−µ −W

−ν ∂ν W

+µ )]− 1

2g2W

+µ W

−µ W

+ν W

−ν +

12

g2W+µ W

−ν W

+µ W

−ν + g2c2w(Z0

µW+µ Z0

ν W−ν − Z0

µZ0µW

+ν W

−ν ) + g2s2w(AµW

+µ Aν W

−ν − AµAµW

+ν W

−ν ) +

g2swcw [AµZ0ν (W

+µ W

−ν − W

+ν W

−µ ) − 2AµZ0

µW+ν W

−ν ] − gα[H3 + Hφ0φ0 + 2Hφ+φ−] − 1

8g2αh[H4 + (φ0)4 +

4(φ+φ−)2+4(φ0)2φ+φ−+4H2φ+φ−+2(φ0)2H2]−gMW+µ W

−µ H− 1

2g M

c2w

Z0µZ0

µH− 12

ig[W+µ (φ0∂µφ−−φ−∂µφ0)−

W−µ (φ0∂µφ+ − φ+∂µφ0)] + 1

2g[W

+µ (H∂µφ− − φ−∂µH)− W

−µ (H∂µφ+ − φ+∂µH)] + 1

2g 1

cw(Z0

µ(H∂µφ0 − φ0∂µH)−

igs2wcw

MZ0µ(W

+µ φ−−W

−µ φ+)+igswMAµ(W

+µ φ−−W

−µ φ+)−ig

1−2c2w2cw

Z0µ(φ+∂µφ−−φ−∂µφ+)+igswAµ(φ+∂µφ−−

φ−∂µφ+)− 14

g2W+µ W

−µ [H2+(φ0)2+2φ+φ−]− 1

4g2 1

c2w

Z0µZ0

µ[H2+(φ0)2+2(2s2w−1)2φ+φ−]− 12

g2 s2wcw

Z0µφ0(W

+µ φ−+

W−µ φ+) − 1

2ig2 s2w

cwZ0

µH(W+µ φ− − W

−µ φ+) + 1

2g2swAµφ0(W

+µ φ− + W

−µ φ+) + 1

2ig2swAµH(W

+µ φ− − W

−µ φ+) −

g2 swcw

(2c2w − 1)Z0µAµφ+φ− − g1s2wAµAµφ+φ− − eλ(γ∂ + mλ

e )eλ − νλγ∂νλ − uλj(γ∂ + mλ

u)uλj

− dλj(γ∂ + mλ

d)dλ

j+

igswAµ[−(eλγµeλ)+ 23(uλ

jγµuλ

j)− 1

3(dλ

jγµdλ

j)]+

ig4cw

Z0µ[(νλγµ(1+γ5)νλ)+(eλγµ(4s2w−1−γ5)eλ)+(uλ

jγµ( 4

3s2w−

1 − γ5)uλj) + (dλ

jγµ(1 − 8

3s2w − γ5)dλ

j)] +

ig

2√

2W

+µ [(νλγµ(1 + γ5)eλ) + (uλ

jγµ(1 + γ5)Cλκdκ

j)] +

ig

2√

2W

−µ [(eλγµ(1 +

γ5)νλ) + (dκj

C†λκ

γµ(1 + γ5)uλj)] +

ig

2√

2

mλe

M[−φ+(νλ(1 − γ5)eλ) + φ−(eλ(1 + γ5)νλ)] − g

2

mλe

M[H(eλeλ) +

iφ0(eλγ5eλ)] +ig

2M√

2φ+[−mκ

d(uλ

jCλκ(1 − γ5)dκ

j) + mλ

u(uλj

Cλκ(1 + γ5)dκj] +

ig

2M√

2φ−[mλ

d(dλ

jC

†λκ

(1 + γ5)uκj) −

mκu(dλ

jC

†λκ

(1 − γ5)uκj] − g

2

mλu

MH(uλ

juλ

j) − g

2

mλd

MH(dλ

jdλ

j) +

ig2

mλu

Mφ0(uλ

jγ5uλ

j) − ig

2

mλd

Mφ0(dλ

jγ5dλ

j) + X+(∂2 −

M2)X+ + X−(∂2 − M2)X− + X0(∂2 − M2

c2w

)X0 + Y ∂2Y + igcwW+µ (∂µX0X− − ∂µX+X0) + igswW

+µ (∂µY X− −

∂µX+Y ) + igcwW−µ (∂µX−X0 − ∂µX0X+) + igswW

−µ (∂µX−Y − ∂µY X+) + igcwZ0

µ(∂µX+X+ − ∂µX−X−) +

igswAµ(∂µX+X+ − ∂µX−X−) − 12

gM[X+X+H + X−X−H + 1c2w

X0X0H] +1−2c2w2cw

igM[X+X0φ+ −

X−X0φ−] + 12cw

igM[X0X−φ+ − X0X+φ−] + igMsw [X0X−φ+ − X0X+φ−] + 12

igM[X+X+φ0 − X−X−φ0]


Introduction: The Standard Model and beyond

Why do we believe in the Standard Model? . . . because experiment tells us to!

The SM can explain all experimental data up to energies of O(200) GeV!

Why do we not believe in the Standard Model?

The problem of Mass:What is the origin of particle masses? Is it a Higgs boson?

What sets the scale of fermion masses?

The problem of Unification:Is there a simple framework for unifying all particle interactions, a so-called grand unified theory?

The problem of Flavour:Why are there so many types of quarks and leptons?

What is the origin of CP-violation?

Cosmological problems:What is the origin of the baryon-antibaryon asymmetry?

What is the nature of dark matter and dark energy?

The holy grail: How to incorporate gravity?


From WW -scattering to the Higgs boson

Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−νeνµ

L =GF√

2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]

with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)

Fermi theory at high energies: M[νµe− → µ−νe] ∼ GF

2√

2πs (s = E2

scattering)

⇒ violates unitarity

Solution: interaction mediated by heavy vector boson W±

� ��

� ��

� ��

� �

�

M[νµe− → µ−νe] →GF s

2√

2π

M2W

M2W − s

(with MW ≈ 100 GeV)


From WW -scattering to the Higgs boson

Consider WW → WW

��

��

��

�

M[WLWL → WLWL] ∝ s ⇒ violates unitarity

Solution: − strong WW interaction at high energies or

− new scalar particle H with gWWH ∝MW

��

�� M → GF M2

H

4√

2π

Unitarity ⇒ properties of H : − coupling gXXH ∝ particle mass MX

−MH ∼< 1 TeV


Spontaneous symmetry breaking: the ABEGHHK’tH Mechanism

(Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, ’t Hooft)

Generating particle masses requires breaking the gauge symmetry

MW,Z 6= 0 ⇔ 〈0|X|0〉 6= 0

Standard Model: Spontaneous symmetry breaking through scalar isodoublet Φ

Φ =1√2

(φ1 + iφ2

φ3 + iφ4

)with scalar potential V = µ2|Φ|2 + λ|Φ|4

If µ2 < 0 (why?), then the minimum of the potential is at

〈Φ〉 =1√2

(0

v

)where v =

√−µ2/|λ|

→ spontaneous symmetry breaking

� ��

��

� �� → 3 Goldstone bosons → mass for W±, Z→ 1 physical scalar (Higgs) particle


The birth of the Higgs boson


Higgs boson properties

The SM Higgs mechanism is testable because all couplings are known:

fermions: gffH =√

2mf/v

gauge bosons: gV V H = 2MV /v

with vacuum expectation value v2 = 1/√

2GF ≈ (246 GeV)2 (from µ-decay)

The Higgs sector and the properties of the Higgs particle(lifetime, decay branching ratios, cross sections)are fixed in terms of the Higgs boson mass MH .

[Express the Higgs potential in terms of (µ, λ) → (v2, MH)]

Extended Higgs models (eg. 2-Higgs-doublet models like the MSSM) have a morecomplicated structure


Higgs boson hunting: past and present colliders

search at the CERN LEP2 (e+e− collider with√

s ∼< 200 GeV)

e+e− −→/ ZH ⇒MH > 114.4 GeV (95% CL) (LEPHIGGSWG)

search at the Fermilab Tevatron (pp collider with√

s = 2 TeV)

current∫L ≈ 1 fb−1

expectation in 2008:∫L = 4 − 6 fb−1


Indirect search for the Higgs boson

Quantum corrections to precision observables give access to high mass scales:

�

��

��

∝ m2top ∝ lnMHiggs

More precisely: calculate MW from MZ and GF including quantum corrections

M2W

M2Z

(1 − M2

W

M2Z

)=

πα√2GF M2

Z(1 − ∆r)

where the quantum correction ∆r is composed of

∆r = ∆α − cot θW ∆ρtop + ∆rHiggs + · · ·

The leading top contribution is quadratic in mtop:

∆ρtop =3GF m2

top

8π2√

2+ · · ·

The Higgs contribution is screened, depending only logarithmically on MHiggs

∆rHiggs =GF M2

W

8π2√

2

1 + 9 sin2 θW

3 cos2 θW

ln

(M2

Higgs

M2W

)+ · · ·



Indirect top hunting works well:

(C. Quigg, arXiv:hep-ph/0404228)

direct observation: mtop = 172.7 ± 2.9 GeV (CDF & D0)

indirect observation: mtop = 179.4 ± 11 GeV (LEP & SLD)



Indirect Higgs hunting is harder:

80.3

80.4

80.5

10 102

103

mH [GeV]

mW

[G

eV]

Excluded

High Q2 except mW/ΓW

68% CL

mW (LEP2 prel., pp−) ⇒ Data consistent with SM

⇒MH < 207 GeV (95% CL)

(LEPEWWG)



Indirect Higgs hunting is harder:

80.3

80.4

80.5

150 175 200

mH [GeV]114 300 1000

mt [GeV]

mW

[G

eV]

68% CL

∆α

LEP1 and SLDLEP2 and Tevatron (prel.)


Higgs boson hunting

Ellis, Gaillard, Nanopoulos, A Phenomenological Profile of the Higgs Boson, 1976:

“We should perhaps finish with an apologie and a caution. We apologize to experimentalists

for having no idea what is the mass of the Higgs boson. . . and for not being sure of its couplings

to other particles except that they are probably all very small. For these reasons we do not

want to encourage big experimental searches for the Higgs boson. . . ”


The Large Hadron Collider LHC

− pp collider located at CERN

− circumference 27 km

−√s = 14 TeV

− ∫L = 10 − 100 fb−1/year

− in “operation” from April 2007


Higgs boson search at the LHC

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


Part II: SM physics at hadron colliders

• Particle production at hadron colliders: the Drell-Yan process

• W production

• top-quark production


Particle production at hadron colliders

Example: Drell-Yan process

�� "!

##

$%'&%

((& ) *+, -. )+ -/0 1 1

Cross section: σpp→l+l− =∑

q

∫dx1dx2 fq(x1) fq(x2) σqq→l+l−

− fq,q(x) dx: probability to find (anti)quark with momentum fraction x

→ process independent, measured in DIS

− σqq→l+l− : hard scattering cross section

→ calculable in perturbation theory



Factorization is non-trivial beyond leading order

− virtual corrections2

33

45765

→ UV divergences

→ IR divergences

− real corrections

88

9:7;: <

→ IR divergences

→ collinear divergences

UV divergences → renormalization (αs(µren) etc.)

IR divergences → cancel between virtual and real (KLN)

collinear initial state divergences → can be absorbed in pdfs



Initial state collinear singularities, eg.

=

>>>?

@ A B

− process independent divergence in∫dk2

T as k2T → 0

→ absorb singularity in parton densities:

fq(x, µfac) = fq(x) +{divergent part of

∫ µ2fac

0 dk2T

}

Hadron collider cross section

σ =∫dx1f

Pi (x1, µF )

∫dx2f

Pj (x2, µF )

×∑

n

αns (µR)Cn(µR, µF ) + O(ΛQCD/Q)

(Altarelli, Ellis, Martinelli ’78; Collins, Soper, Sterman ’82-’84 and many others)

Interactions between spectator partons → underlying event and/ or multiple hard scattering



Scale dependence

σ =

∫dx1f

Pi (x1, µF )

∫dx2f

Pj (x2, µF )

×∑

n

αns (µR) Cn(µR, µF )

finite order in perturbation theory

→ artificial µ-dependence:

dσ

d ln µ2=

d

d ln µ2

N∑

n=0

αB+ns (µ) Cn(µ)

= O(αs(µ)N+1)

⇒ scale dependence ∼ theoretical

uncertainty due to HO corrections

Example: rapidity distribution in pp → W +X

[Anastasiou, Dixon, Melnikov, Petriello ’03]

⇒ significant reduction of µ dependence at

(N)NLO


Global PDF fits

10-3 10-2 10-1 10010-4

10-3

10-2

10-1

100

101

c

b

g

d x

f(x,

Q2 )

u

MRSTQED04proton pdfsQ2 = 20 GeV2

x

γp

sea quarks


PDF uncertainties

[Martin, Roberts, Stirling, Thorne ’03]

2.50

2.55

2.60

2.65

2.70

2.75

2.80

W @ Tevatron

NLO

Q2cut = 7 GeV2

Q2cut = 10 GeV2

NNLO

xcut = 0 0.0002 0.001 0.0025 0.005 0.01

σ W .

Blν

(nb)

MRST NLO and NNLO partons

→ ∆ pdf ∼< 5% (CTEQ, MRST, Alekhin,...)


Cross section compilation

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)


σW


σbbar

σtot

σ (n

b)

√s (TeV)

even

ts/s

ec f

or L

= 1

033 c

m-2

s-1


We will have a closer look at

• W production

• top-quark production


W -boson production at hadron colliders

measurement of MW and ΓW

→ precision test of SM

σW as a (parton) luminosity monitor

e.g. δσ(pp → W+W−)

σ(pp → W±) ∼< 1%?

CED

FGH

I JKD

Anticipated experimental accuracy:

uncertainty now Tevatron Run II LHC

δ sin2 θeff(×105) 17 78 14-20

δMW [MeV] 34 27 15

δmt [GeV] 5.1 2.7 1.0

δMH/MH [%] (from all data) 58 35 18


W -mass measurement

Consider u(pu) + d(pd) → l+(pl) + νl(pν)

LEM

NOP

Q RSM

Using the couplings from the electroweak Langrangian one obtains

∑|M(ud → l+νl)|2 = 16(

√2GF M2

W )2|Vud|2(pu · pl)

2

((pu + pd)2 − M2W )2 + M2

W Γ2W

If we define Θ∗ to be the l+ polar angle in the W + rest frame, then

(pu · pl)2 =

M2W

16(1 + cos2 Θ∗)

and1

σ

dσ

d cosΘ∗=

3

8(1 + cos2 Θ∗)


W -mass measurement

If the W has zero transverse momentum the polar angle is given in terms of the lepton transverse

momentum, pTl:

cos Θ∗ =

√1 − 4p2

Tl

M2W

so that1

σ

dσ

dp2T,l

=3

M2W

1 − 2p2Tl/M

2W√

1 − 4p2Tl/M

2W

The pTl distribution is strongly peaked at pTl = MW /2 (Jacobian peak).

The peak is smeared out by the finite W width and non-zero W transverse momentum. Therefore, in

praxis, one uses the transverse mass

M2T = 2|pTl||pTν |(1 − cos ∆ϕlν)

which is less sensitive to the W transverse momentum. At LO, one has |pTl| = |pTν | = p∗,

∆ϕlν = π and so MT = 2|pTl|. The transverse mass distribution therefore also has a Jacobian

peak, at MT = MW .


W -mass measurement

Transverse mass(GeV)40 50 60 70 80 90 100 110 120

Eve

nts

0

1000

2000

3000

4000

5000

6000

7000

Transverse Mass - W CandidateDataPMCS+QCDQCD bkg

D0 Run II Preliminary

Transverse Mass - W Candidate

W-Boson Mass [GeV]

mW [GeV]80 80.2 80.4 80.6

χ2/DoF: 0.3 / 1

TEVATRON 80.452 ± 0.059

LEP2 80.412 ± 0.042

Average 80.425 ± 0.034

NuTeV 80.136 ± 0.084

LEP1/SLD 80.363 ± 0.032

LEP1/SLD/mt 80.373 ± 0.023


W -mass measurements at the Tevatron and the LHC

Expectations for Tevatron run II

• statistical uncertainty δMW ' 15 MeV per channel and

experiment for∫L = 2 fb−1

• overall uncertainty δMW ' 40 MeV per channel and ex-

periment for∫L = 2 fb−1

0

0.05

0.1

0.15

0.2

0.25

0 0.005 0.01 0.015 0.02

Statistical UncertaintiesRun1, CDF & D0

δW(G

eV/c

2)

1/sqrt (#W)

δW (GeV/c2)= 800 + 330 L (pb -1)

Expectations for the LHC

• statistical uncertainty δMW < 2 MeV for∫L = 10 fb−1

• overall uncertainty δMW ' 20 MeV may be reached if

lepton energy and momentum scales are known to 0.02%.

main theoretical uncertainties from PDFs and multi-photon radiation effects


Search for extra gauge bosons W′, Z′

Many new physics models (eg. SO(10) GUTs) predict an extended gauge group and addtional

heavy gauge bosons W ′ and/or Z ′.

Assuming SM-like couplings, the LHC can discover W ′ and/or Z ′ with masses up to ' 6 TeV

here: 4 TeV W ′ → signal above MT ' 2.3 TeV

For∫L = 100 fb−1 expect

160 signal and 13 background events.


Top-quark physics

Why is the top quark an interesting object to study?

– The top quark mass is a crucial input for electroweak precision tests.

– mtop � mb,c,s,u,d,τ,µ,e,ν : Is the top in some way exotic?

– The top quark may be a window to new physics:

it couples strongly to scalars (like the Higgs);

the top quark mass may be important for testing grand unified theories.

– Events containing top quarks are background for new physics signals.


Top-quark production at hadron colliders

The top-quark is mainly produced through quark-antiquark annihilation and gluon-

gluon fusion:q

q

t

t

g

g

t

t

+

g

g

t

t

+

g

g

t

t

Top quark production at the Tevatron/LHC is dominated by qq/gg initial states:

σNLO (pb) qq → tt gg → tt

Tevatron (√s = 1.8 TeV pp) 4.87 ± 10% 90% 10%

Tevatron (√s = 2.0 TeV pp) 6.70 ± 10% 85% 15%

LHC (√s = 14 TeV pp) 803 ± 15% 10% 90%


Top-quark production at hadron colliders

NLO corrections are important (as usual):

Scale dependence

– R.K.Ellis, St Andrews, August 2003 – 30


Top-quark decays

The dominant decay of the top-quark is t→ Wb

t

q

W

= −i g

2√

2|Vtq|γµ(1 − γ5)

so that

Γ =GF M2

t

8π√

2|Vtb|2

(1 − M2

W

M2t

)(1 +

2M2W

M2t

)' |Vtb|2 × 1.42 GeV

Unitarity of the CKM matrix |Vtb|2 + |Vcb|2 + |Vub|2 = 1 implies |Vtb| ≈ 1

→ Top-quark lifetime τt ' 5 × 10−25 sec

Typical QCD time scale for hadron formation τQCD ' 3 × 10−24 sec

→ The top quark decays before it can form bound states


Top-quark cross sections at the Tevatron

)2Top Mass (GeV/c166 168 170 172 174 176 178 180

) (pb

)t t

→ p(pσ

0

2

4

6

8

10

12Cacciari et al. JHEP 0404:068 (2004)

uncertainty±Cacciari et al. Kidonakis,Vogt PIM PRD 68 114014 (2003)Kidonakis,Vogt 1PI

-1 production cross section for 200 pbtPreliminary CDF combined t@ Summer 2005 CDF+D0 combined top quark mass

) (pb)t t→ p(pσ0 2 4 6 8 10 12 14

0

8Cacciari et al. JHEP 0404:068 (2004)

Kidonakis,Vogt PRD 68 114014 (2003)

2=175 GeV/ctAssume m

CDF Run 2 Preliminary

Combined 0.4 0.4±0.7±0.6± 7.1)-1(L= 350pb(lumi.)±(syst.)±(stat.)

All-hadronic: Vertex Tag 0.4 0.5± 2.2

3.3± 1.7 1.7± 8.0 )-1(L= 311pb

MET+Jets: Vertex Tag 0.3 0.4± 0.9

1.3± 1.2 1.2± 6.1 )-1(L= 311pb

Lepton+Jets: Vertex Tag 0.5 0.5± 0.8

1.1± 0.9 0.9± 8.9 )-1(L= 318pb

Lepton+Jets: Soft Muon Tag 0.3 0.3± 1.0

1.3± 3.3 3.3± 5.3 )-1(L= 193pb

Lepton+Jets: Kinematic ANN 0.3 0.4± 0.9

0.9± 0.8 0.8± 6.3 )-1(L= 347pb

Dilepton: Combined 0.4 0.4± 1.1

1.6± 2.1 2.4± 7.0 )-1(L= 200pb


Top-mass measurement at the Tevatron

Mtop [GeV/c2]

Mass of the Top Quark (*Preliminary)Measurement Mtop [GeV/c2]

CDF-I di-l 167.4 ± 11.4

D∅-I di-l 168.4 ± 12.8

CDF-II di-l* 165.3 ± 7.3

CDF-I l+j 176.1 ± 7.3

D∅-I l+j 180.1 ± 5.3

CDF-II l+j* 173.5 ± 4.1

D∅-II l+j* 169.5 ± 4.7

CDF-I all-j 186.0 ± 11.5

χ2 / dof = 6.5 / 7

Tevatron Run-I/II* 172.7 ± 2.9

150 170 190

Tevatron run II goal: δmtop = 2 GeV with∫L = 4 − 9 fb−1


Top physics at the LHC

The top cross section at the LHC is σtt ' 800 pb → O(107) events in the first year

Physics goals:

• δmtop = 1 GeV with∫L = 100 fb−1

• Observation of single top production with∫L = 30 fb−1

• test of quantum numbers

• sensitivity to rare (BSM) decay modes


Precision physics at the LHC

Precision calculations at hadron colliders require

– the calculation of QCD corrections at (N)NLO;

– the inclusion of electroweak corrections;

– the resummation of large logarithmic corrections;

– the precision determination of input pdfs;

– matching of fixed order calculations with parton showers & hadronization.


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


Part III

Higgs boson production & search at the LHC

Physics beyond the SM: SUSY particle production & search at the LHC


Recap: Higgs boson properties

The SM Higgs mechanism is testable because all couplings are known:

fermions: gffH =√

2mf/v

gauge bosons: gV V H = 2MV /v

with vacuum expectation value v2 = 1/√

2GF ≈ (246 GeV)2 (from µ-decay)

The Higgs sector and the properties of the Higgs particle(lifetime, decay branching ratios, cross sections)are fixed in terms of the Higgs boson mass MH .

[Express the Higgs potential in terms of (µ, λ) → (v2, MH)]

Extended Higgs models (eg. 2-Higgs-doublet models like the MSSM) have a morecomplicated structure


Recap: Higgs boson mass

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

T

UWVUYX

TZ

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

Electroweak precision tests[

\[

provide an upper limit on the SM Higgs mass: MH < 207 GeV (95% CL)


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


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


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

]^_

_` ab

cc

cc

` ab ]

` a b

cdc

e fg]

__

^d^

]


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)].


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


LHCTevatron

σttbar


σZ



σW


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


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


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]


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: ∆M/M ≈ 10−3 (for MHiggs ∼< 500 GeV)

– lifetime: direct measurement of Γtot only for MHiggs ∼> 300 GeV

– couplings to gauge bosons and fermions:ratios of couplings can be measured with an accuracy of 10-40%

– external quantum numbers (spin,parity):decay angular distributions can distinguish between spin S = 0, 1 and even or odd parity

(for MHiggs ∼< 250 GeV)

– Higgs self-couplings:Recall: V =

M2H

2 H2 + λ3vH3 + λ4

4 H4 SM: λ3 = λ4 =M2

H

2v2

With∫L = 300 fb−1 can show that λ3 6= 0 if 150 GeV ∼< MHiggs ∼< 200 GeV

λ4 appears to be hopeless


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)


The hierarchy problem: why is MHiggs � MPlanck?

Quantum corrections to the Higgs mass have quadratic UV divergencies

h hi j h hk → 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

Schmaltz




l lm n l lo → δm2

H ∼ απ(Λ2 + m2

F )



The new physics needs to

– stabilize the hierarchy MPlanck �MHiggs

– decouple from electroweak precision tests

Most popular candidates:

– Supersymmetry

– Technicolour

– Extra dimensions

– Little Higgs models




p pq r p ps → δm2H ∼ α

π(Λ2 + m2

F )



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

t tuv w t txy → δm2

H ∼ −απ(Λ2 + m2

F )

δm2H ∼ α

π(m2

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


The naturalness argument revisited

Are the Λ2 divergences relevant for physics or are they an artefact of perturbation

theory and/or the regularization scheme? (Veltman)

An even bigger naturalness problem:

The Higgs potential V = µ2|φ|2 +λ|φ|4 expanded around the vaccum state 〈Φ〉 = 1/√

2(0, v)

becomes

V =1

2(2λv2)H2 + λvH3 +

λ

4H4 − λ

4v4

Identifying M2H = 2λv2 there is a constant term of the form:

%H =v2M2

H

8→ vacuum energy density

With v2 = 1/√

2GF ≈ (246 GeV)2 and MH > 114 GeV one finds

%H > 108 GeV4

while from observations

%vac < 10−46 GeV4


The naturalness argument revisited

If %vac = %H = 108 GeV4 then the universe would be the size of a


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(H0

2

H−2

)(H+

1

H01

) (H0

2

H−2

)(H+

1

H01

)


SUSY particle production at hadron colliders

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 symme try and SUSY

example: gluonµ, a

p, i

q, j

squark

squark

= −i gs (Ta)ij(p + q)µ

→ no new coupling!

SUSY particles should be produced copiously at hadron colliders through QCD processes, e.g.

g

g


SUSY particle production at the LHC

Cross section predictions

[Prospino: Beenakker, MK, Plehn, Spira, Zerwas]

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


Squark and gluino cross section 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


LHCTevatron

σttbar


σZ



σW


σbbar

σtot

σ (n

b)

√s (TeV)

even

ts/s

ec f

or L

= 1

033 c

m-2

s-1

−→ SUSY signal:

σ(qq + gg + gq) ≈ 2 nb (Mq,g ≈ 300 GeV)

↪→≈ 108squarks & gluinos/year (∫L = 30 fb−1)


SUSY searches at hadron colliders

Distinctive signature due to cascade decays:

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

D_D

_204

7.c.

1

q

q

q

q

q~

~

~

~

—

—

—b

b

l+

l+

g

~g

W— W+t

t

t1

ν

χ1

~χ10

~χ20

Gluino/squark production event topology al lowing sparticle mass reconstruction

3 isolated leptons+ 2 b-jets+ 4 jets

+ Etmiss

~l

+

l-

Such cascade decays allow to reconstructsleptons, neutralinos, squarks, gluinos...in favorable cases with %level mass resolutions

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


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?


SUSY searches at the LHC

Hans-Peter Nilles, Physics Reports 110, 1984:

“Experiments within the next 5-10 years will enable us to decide whether su-

persymmetry, as a solution of the naturalness problem of the weak interaction

is a myth or reality”

Hans-Peter Nilles, private communication, quoted from hep-ex/9907042

“One should not give up yet. . . ”

“Perhaps a correct statement is: it will always take 5-10 years to discover

SUSY.”


A crucial test of the MSSM: 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 is a generic prediction of SUSY models.


A crucial test of SUSY models: the light Higgs

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


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


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

Exciting times ahead. . .


physics at the large hadron collider - rwth …mkraemer/lhc-tu.pdftu munchen,¤ mai 2006 physics at...

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