· literature i have used the following references to prepare these lectures: Œ lectures from...

Italo-Hellenic School of Physics, Lecce, June 2006

Higgs Physics at the Large Hadron Collider

Michael Kramer

(RWTH Aachen)

Electroweak symmetry breaking

The profile of the Standard Model Higgs boson

Higgs searches at the LHC

Michael Kramer Page 1 Italo-Hellenic School of Physics 2006

Literature

I have used the following references to prepare these lectures:

– Lectures from Maria Laach schools, in particular those by S. Dawson and M.L. Mangano;

– Lectures from previous Lecce schools, in particular those by C. Oleari and D. Zeppenfeld;

– Lectures by D. Ross at the Scottish University Summer School SUSSP57;

– Review articles by: A. Djouadi (hep-ph/0503172), H. Spiesberger, M. Spira, P.M. Zerwas (hep-

ph/9803257); C. Quigg (hep-ph/0404228)

– textbooks, mainly: Peskin & Schroeder, Barger & Phillips.

Introduction: The Standard Model and beyond

The SM Lagrangian is 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

Introduction: The Standard Model and beyond

The SM Lagrangian is 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

sfabcfadegbµgc

ν gdµge

ν + 12

ig2s(qσ

iγµqσ

µ + Ga∂2Ga +

gsfabc∂µGaGbgcµ − ∂ν W

+µ ∂ν W

−µ − M2W

−µ − 1

2∂ν Z0

µ∂ν Z0µ − 1

M2Z0µZ0

µ − 12

∂µAν ∂µAν − 12

∂µH∂µH −

H2 − ∂µφ+∂µφ− − M2φ+φ− − 12

∂µφ0∂µφ0 − 12c2w

Mφ0φ0 − βh[ 2M2

g2+ 2M

gH + 1

2(H2 + φ0φ0 + 2φ+φ−)] +

g2αh − igcw [∂ν Z0

µ(W+µ 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

−µ )−Aν (W

+µ ∂ν W

−µ −W

−µ ∂ν W

+µ )+Aµ(W

+ν ∂ν W

−µ −W

−ν ∂ν W

+µ )]− 1

−µ W

−ν +

g2W+µ W

−ν W

−ν + g2c2w(Z0

µW+µ Z0

ν W−ν − Z0

µZ0µW

−ν ) + g2s2w(AµW

+µ Aν W

−ν − AµAµW

−ν ) +

g2swcw [AµZ0ν (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

Z0µZ0

µH− 12

ig[W+µ (φ0∂µφ−−φ−∂µφ0)−

W−µ (φ0∂µφ+ − φ+∂µφ0)] + 1

+µ (H∂µφ− − φ−∂µH)− W

−µ (H∂µφ+ − φ+∂µH)] + 1

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

Z0µZ0

µ[H2+(φ0)2+2(2s2w−1)2φ+φ−]− 12

g2 s2wcw

Z0µφ0(W

+µ φ−+

W−µ φ+) − 1

2ig2 s2w

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

igswAµ[−(eλγµeλ)+ 23(uλ

jγµuλ

j)− 1

jγµdλ

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

jγµ( 4

3s2w−

1 − γ5)uλj) + (dλ

jγµ(1 − 8

3s2w − γ5)dλ

+µ [(νλγµ(1 + γ5)eλ) + (uλ

jγµ(1 + γ5)Cλκdκ

−µ [(eλγµ(1 +

γ5)νλ) + (dκj

C†λκ

γµ(1 + γ5)uλj)] +

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

M[H(eλeλ) +

iφ0(eλγ5eλ)] +ig

2φ+[−mκ

jCλκ(1 − γ5)dκ

j) + mλ

u(uλj

Cλκ(1 + γ5)dκj] +

2φ−[mλ

†λκ

(1 + γ5)uκj) −

mκu(dλ

†λκ

(1 − γ5)uκj] − g

MH(uλ

j) − g

MH(dλ

Mφ0(uλ

jγ5uλ

j) − ig

Mφ0(dλ

jγ5dλ

j) + X+(∂2 −

M2)X+ + X−(∂2 − M2)X− + X0(∂2 − M2

)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]

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

⇒ violates unitarity

Solution: interaction mediated by heavy vector boson W±

M[νµe− → µ−νe] →GF s

M2W − s

(with MW ≈ 100 GeV)

L =GF√

2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]

M2W − s

L =GF√

2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]

M2W − s

L =GF√

2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]

� ��

� �

M2W − s

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 M2H

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

−MH ∼< 1 TeV

Consider WW → WW

��

�� M → GF M2

−MH ∼< 1 TeV

Consider WW → WW

��

�� M → GF M2

−MH ∼< 1 TeV

Spontaneous symmetry breaking I: 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

)where v =

√−µ2/|λ|

→ spontaneous symmetry breaking

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

MW,Z 6= 0 ⇔ 〈0|X|0〉 6= 0

Φ =1√2

(φ1 + iφ2

φ3 + iφ4

〈Φ〉 =1√2

)where v =

√−µ2/|λ|

� ��

��

� ��

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

MW,Z 6= 0 ⇔ 〈0|X|0〉 6= 0

Φ =1√2

(φ1 + iφ2

φ3 + iφ4

〈Φ〉 =1√2

)where v =

√−µ2/|λ|

� ! "

$ %& '→ 3 Goldstone bosons → mass for W±, Z→ 1 physical scalar (Higgs) particle

Spontaneous symmetry breaking I: U(1)-Example

Or: How to generate masses for gauge bosons without violating gauge invariance?

Recall structure of U(1) local gauge theory with single spin-1 gauge field Aµ:

L = − 1

4FµνFµν where Fµν = ∂νAµ − ∂µAν

→ mass term ∝ m2AµAν not gauge invariant → massless gauge boson A

Possible solution: add complex scalar field φ with charge −e:

L = − 14FµνFµν + |Dµφ|2 − V (φ) where V (φ) = µ2|φ|2 + λ|φ|4

If µ2 > 0: unique minimum at φ = 0 → QED with MA = 0 and Mφ = µ

Reverse sign of µ2 so that V (φ) = −µ2|φ|2 + λ|φ|4

→ minimum of potential at√

−µ2

2λ≡ v√

Expand φ around vacuum expectation value: φ = 12 (v + H + iχ)

⇒ L = − 1

4FµνFµν +

2∂µH∂µH + ∂µχ∂µχ +

2e2v2AµAµ + evAµ∂µχ

−eAµ(χ∂µH − H∂µχ) +1

2e2AµAµ(H2 + χ2) − V (φ)

L = − 1

−µ2

2λ≡ v√

⇒ L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

L = − 1

−µ2

2λ≡ v√

⇒ L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

L = − 1

→ minimum of potential at√−µ2

2λ≡ v√

⇒ L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

L = − 1

→ minimum of potential at√−µ2

2λ≡ v√

⇒ L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

The theory now has:

• a photon of mass MA = ev

• a scalar field H with M 2H = −2µ2 > 0

• a massless scalar field χ (Goldstone boson)

The mixed A − χ propagator can be removed by a gauge transformation:

Aµ → Aµ − 1ev

∂µχ and φ → e−iχv φ (unitary gauge)

→ the χ field has been absorbed by a redefinition of A

(jargon: χ has been “eaten” to give photon mass)

Counting of degrees of freedom:

before symmetry breaking: massless gauge boson (2 dof) and complex scalar (2 dof)

after symmetry breaking: massive gauge boson (3 dof) and physical scalar (1 dof)

L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

The theory now has:

Aµ → Aµ − 1ev

L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

The theory now has:

Aµ → Aµ − 1ev

L = − 1

4FµνFµν +

2e2AµAµ(H2 + χ2) − V (φ)

The theory now has:

Aµ → Aµ − 1ev

Spontaneous symmetry breaking I: the ABEGHHK’tH Mechanism?

John Earman, Philosopher, on the need to choose a specific gauge to suppress Goldstone

bosons and generate masses for gauge bosons:

“A genuine property like mass cannot be gained by eating descriptive fluff,

which is just what gauge is”

The birth of the Higgs boson

Spontaneous symmetry breaking II: superconductivity

Ginzburg-Landau description: Fsuper(B = 0) = Ffree(B = 0) + α|Ψ|2 + β|Ψ|4

T > Tc : α > 0 ⇒ Ψ0 = 0 T < Tc : α < 0 ⇒ Ψ0 6= 0

Microscopic mechanism (Bardeen, Cooper, Schrieffer):electromagnetic gauge invariance is broken by Cooper pairs of electrons with 〈0|ee|0〉 6= 0

Weisskopf, Cornell seminar (recalled by Brout), 1960:

“Particle physicists are so desperate these days that they have to borrow from the new things

coming up in many-body physics - like BCS. Perhaps something will come of it. . . ”

T > Tc : α > 0 ⇒ Ψ0 = 0 T < Tc : α < 0 ⇒ Ψ0 6= 0

Spontaneous symmetry breaking III: chiral symmetry in QCD

For mup,mdown = 0:

LQCD = qLD/ qL + qRD/ qR (qL,R=(1∓γ)q/2)

→ independent left and right rotations permitted: U(2)L⊗U(2)R (chiral) symmetry

Spontaneous breaking of chiral symmetry through quark condensate:

〈0|qq|0〉 ≡ 〈0|qLqR + qRqL|0〉 ' Λ3QCD ' (250 MeV)3 6= 0

→ 3 massless Goldstone bosons: π0, π±

→ dynamical quark masses → heavy nucleons

QCD liteTM (2 massless quarks and gluons)

90% of mass of ordinary matter (without the Higgs particle. . . )

In the real world mup,mdown 6= 0 and chiral symmetry is not exact.

But mup,mdown � ΛQCD and mπ � mproton,neutron,...

For mup,mdown = 0:

Dynamical electroweak symmetry breaking: Technicolour

SSB in condensed matter physics and QCD through fermion condensate

〈0|FF |0〉 6= 0

⇒ EWSB through new strong interactions of new massless fermions (“technicolour”):

〈0|T T |0〉 ' Λ3TC ' (1 TeV)3 6= 0

→ massless technipions → masses for W±, Z via Brout-Englert-Higgs mechanism

→ new bound states (“technihadrons”) with M ≈ 1 TeV

To give masses to the Standard Model quarks and leptons must add interactions between T , q, l

(“extended technicolour”)

Features+ no fundamental scalar needed

+ dynamical generation of hierachy ΛTC/MPlanck ≈ 10−17 through RGE running

− What breaks extended technicolour?

− How to accommodate FCNC and electroweak precision tests? (→ “walking technicolour”)

− How to accomodate the large top quark mass? (→ “topcolour assisted technicolour”)

〈0|FF |0〉 6= 0

〈0|T T |0〉 ' Λ3TC ' (1 TeV)3 6= 0

〈0|FF |0〉 6= 0

〈0|T T |0〉 ' Λ3TC ' (1 TeV)3 6= 0

〈0|FF |0〉 6= 0

〈0|T T |0〉 ' Λ3TC ' (1 TeV)3 6= 0

EWSB: fundamental Higgs boson or fermion condensate?

fundamental Higgs boson

+ simple and predictive

+ consistent with precision data

− no dynamical explanation of EWSB

− fundamental scalar has never been

observed in nature

− Higgs mass unstable under radiative

corrections: why is MHiggs�MPlanck?

(naturalness problem)

fermion condensate

+ analogous to existing mechanisms (BCS, QCD)

+ no fundamental scalar → no naturalness problem

− less predictive (strongly interacting theorie)

− no realistic and compelling models(?)

Michael Peskin, EPS 99:

“The idea that the data drives us to a weak-coupling picture of the Higgs boson was contro-

versial at HEP99. Among the people arguing vocally on the other side were Holger Nielsen

and Gerard ’t Hooft. So if you do not wish to accept this argument, you are in good company

(but still wrong).”

observed in nature

fermion condensate

observed in nature

fermion condensate

Consider first the Higgs kinetic term

L ⊃ |DµΦ|2

with the covariant derivative of the SU(2) × U(1) gauge theory

Dµ = ∂µ + igW

2σiW i

µ + ig′W2

Expanding Φ about its vacuum expectation value

Φ =1√2

the covariant derivative may be written (in unitary gauge)

DµΦ =1√2

(∂µ + i

√2W−

µ√2W+

µ −W 0µ

which leads to

L ⊃ |DµΦ|2 =1

2(∂µH)2 +

g2W v2

4W+µW−

µ +v2

8(gW W 0

µ − g′

W Bµ)2 + interaction terms

Consider first the Higgs kinetic term

L ⊃ |DµΦ|2

with the covariant derivative of the SU(2) × U(1) gauge theory

Dµ = ∂µ + igW

2σiW i

µ + ig′W2

Expanding Φ about its vacuum expectation value

Φ =1√2

the covariant derivative may be written (in unitary gauge)

DµΦ =1√2

(∂µ + i

√2W−

µ√2W+

µ −W 0µ

which leads to

L ⊃ |DµΦ|2 =1

2(∂µH)2 +

g2W v2

4W+µW−

µ +v2

8(gW W 0

µ − g′

W Bµ)2 + interaction terms

L ⊃ |DµΦ|2 =1

2(∂µH)2 +

g2W v2

4W+µW−

µ +v2

8(gW W 0

µ − g′W Bµ)2 + interaction terms

→ massive gauge bosons: W±µ and Zµ = 1√

+g′2W

)(gW W 0

µ − g′W Bµ)

with masses: M±W = 1

2gW v and MZ = 12

√(g2

W + g′2W ) v

Orthogonal superposition to Z : massless photon Aµ = 1√(g2

W+g′2

W)(g′W W 0

µ + gW Bµ)

Introduce the electroweak mixing angle

sin θW =g′

W√(g2

W+ g′2

and cos θW =gW√

+ g′2W

so thatg′W = gW tan θ and MW = MZ cos θW

The Higgs vacuum expectation value can be determined from the Fermi constant GF :

GF√2

=⇒ v =

√1√2GF

≈ 246.22 GeV

L ⊃ |DµΦ|2 =1

2(∂µH)2 +

g2W v2

4W+µW−

µ +v2

8(gW W 0

+g′2W

)(gW W 0

µ − g′W Bµ)

2gW v and MZ = 12

√(g2

W + g′2W ) v

W+g′2

W)(g′W W 0

µ + gW Bµ)

sin θW =g′

W√(g2

W+ g′2

and cos θW =gW√

+ g′2W

GF√2

=⇒ v =

√1√2GF

≈ 246.22 GeV

L ⊃ |DµΦ|2 =1

2(∂µH)2 +

g2W v2

4W+µW−

µ +v2

8(gW W 0

+g′2W

)(gW W 0

µ − g′W Bµ)

2gW v and MZ = 12

√(g2

W + g′2W ) v

W+g′2

W)(g′W W 0

µ + gW Bµ)

sin θW =g′

W√(g2

W+ g′2

and cos θW =gW√

+ g′2W

GF√2

=⇒ v =

√1√2GF

≈ 246.22 GeV

L ⊃ |DµΦ|2 =1

2(∂µH)2 +

g2W v2

4W+µW−

µ +v2

8(gW W 0

+g′2W

)(gW W 0

µ − g′W Bµ)

2gW v and MZ = 12

√(g2

W + g′2W ) v

W+g′2

W)(g′W W 0

µ + gW Bµ)

sin θW =g′

W√(g2

W+ g′2

and cos θW =gW√

+ g′2W

GF√2

=⇒ v =

√1√2GF

≈ 246.22 GeV

The Higgs kinetic termL ⊃ |DµΦ|2

also includes Higgs–gauge-boson interactions:

|DµΦ|2 ⊃(

µ W−µ +g2

8 cos2 θW

ZµZµ

)(H2 + 2vH

= gW MW W+µ W−µH +

2 cos θW

MZZµZµH

µ W−µH2 +g2

8 cos2 θW

ZµZµH2

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

2(0, v)

becomes

2(2λv2)H2 + λvH3 +

4H4 − λ

yielding a Higgs mass

MH = 2λv2

and cubic and quartic Higgs self-couplings.

The Higgs kinetic termL ⊃ |DµΦ|2

also includes Higgs–gauge-boson interactions:

|DµΦ|2 ⊃(

µ W−µ +g2

8 cos2 θW

ZµZµ

)(H2 + 2vH

= gW MW W+µ W−µH +

2 cos θW

MZZµZµH

µ W−µH2 +g2

8 cos2 θW

ZµZµH2

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

2(0, v)

becomes

2(2λv2)H2 + λvH3 +

4H4 − λ

yielding a Higgs mass

MH = 2λv2

and cubic and quartic Higgs self-couplings.

Fermion masses are generated through so-called Yukawa interactions, e.g. for electrons

L ⊃ −Ge liLΦieR + h.c.

which, in unitary gauge, is

L ⊃ −Ge√2

eR + h.c.

This yields an electron mass term

L ⊃ −Gev√2

(eLeR + eReL) =Gev√

The Yukawa coupling Ge is related to the electron mass me by

Ge = gW

me√2MW

There is also an interaction between the electron and the Higgs

L ⊃ −gW

L ⊃ −Ge√2

eR + h.c.

L ⊃ −Gev√2

Ge = gW

me√2MW

L ⊃ −gW

L ⊃ −Ge√2

eR + h.c.

L ⊃ −Gev√2

Ge = gW

me√2MW

L ⊃ −gW

L ⊃ −Ge√2

eR + h.c.

L ⊃ −Gev√2

Ge = gW

me√2MW

L ⊃ −gW

Quark masses are also generated through Yukawa interactions

L ⊃ −GdqiLΦidR + h.c.︸︷︷︸

d-quark mass

−Guεij qiLΦ†juR + h.c.︸︷︷︸

u-quark mass

with masses

md =Gd√

√2GdMW

and mu =Gu√

√2GuMW

There is also an interaction between the quarks and the Higgs:

L ⊃ −gW

uHu − gW

Adding more generations will introduce mixing in the Yukawa interactions, e.g.

L ⊃ −Gds

d-quark mass

u-quark mass

with masses

md =Gd√

√2GdMW

and mu =Gu√

√2GuMW

L ⊃ −gW

uHu − gW

L ⊃ −Gds

d-quark mass

u-quark mass

with masses

md =Gd√

√2GdMW

and mu =Gu√

√2GuMW

L ⊃ −gW

uHu − gW

L ⊃ −Gds

Three-point couplings with Higgs bosons

= igWMWgµν

cos2 θW

MWgµν

3igWM2

Four-point couplings with Higgs bosons

Wgµν

2 cos2 θW

3igWM2

SM Higgs decay modes and branching ratios

[HDECAY: Djouadi, Kalinowski, Spira]

( )) )

*,+ *- -

/ /0 0

1+ 12+ 2

3 34+ 4

5 6 798 :

; < =?>@ A B C D D DE D DF D DG D DH D DC I DC G DC D DC

DJ CDJ D C

DJ D D CDJ D D D C

⇒ dominant decay into

{bb for MH ∼< 130 GeVWW, ZZ for MH ∼> 130 GeV

SM Higgs total decay width

K L9M NOQP R S T

U V W?XY Z [ \ ] ] ]^ ] ]_ ] ]` ] ]a ] ]\ b ]\ ` ]\ ] ]

\ ] ] ]\ ] ]

]c \]c ] \

]c ] ] \

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

fermions: gffH ∝ mf/v

gauge bosons: gV V H ∝ M2V /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

Theoretical constraints on the Higgs boson mass

Hambye, Riesselmann

Running of the Higgs coupling:

dlnµ2=

8π2[λ2 + λG2

t − G4t ]

with λ = M2H/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

Requiring λ(Λ) < ∞ yields

<∼8π2v2

3 ln (Λ2/v2)

Theoretical constraints on the Higgs boson mass

Hambye, Riesselmann Running of the Higgs coupling:

dlnµ2=

8π2[λ2 + λG2

t − G4t ]

with λ = M2H/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

Requiring λ(Λ) < ∞ yields

<∼8π2v2

3 ln (Λ2/v2)

Higgs boson hunting: indirect search

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

∝ m2top ∝ lnMHiggs

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

(1 − M2

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

8π2√

2+ · · ·

The Higgs contribution is screened, depending only logarithmically on MHiggs

∆rHiggs =GF M2

8π2√

1 + 9 sin2 θW

3 cos2 θW

)+ · · ·

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

∝ m2top ∝ lnMHiggs

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

(1 − M2

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

8π2√

2+ · · ·

The Higgs contribution is screened, depending only logarithmically on MHiggs

∆rHiggs =GF M2

8π2√

1 + 9 sin2 θW

3 cos2 θW

)+ · · ·

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 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:

10 102

mH [GeV]

Excluded

High Q2 except mt

68% CL

mt (Tevatron)

10 102

mH [GeV]

Excluded

High Q2 except mt

68% CL

mt (Tevatron)

10 102

mH [GeV]

Excluded

High Q2 except mW/ΓW

68% CL

mW (LEP2 prel., pp−)

⇒ Data consistent with SM

⇒MH < 219 GeV (95% CL)

(LEPEWWG)

10 102

mH [GeV]

Excluded

High Q2 except mW/ΓW

68% CL

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

⇒MH < 219 GeV (95% CL)

(LEPEWWG)

Precision SM measurements are important to constrain the Higgs sector

. . . what we hope to see (maybe?)

(Bentvelsen, Grunewald)

Repeat the electroweak fit with

smaller uncertainties

– δMW = 15 MeV

– δMtop = 1 GeV

– same central values

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

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

Italo-Hellenic School of Physics, Lecce, June 2006

Higgs Physics at the Large Hadron Collider

Michael Kramer

(RWTH Aachen)

Electroweak symmetry breaking

Higgs searches at the LHC

Summary of lecture 1: SM Higgs boson properties

Three-point couplings with Higgs bosons

= igWMWgµν

cos2 θW

MWgµν

3igWM2

Four-point couplings with Higgs bosons

Wgµν

2 cos2 θW

3igWM2

SM Higgs decay modes and branching ratios

[HDECAY: Djouadi, Kalinowski, Spira]

l mm m

n,o np p

r rs s

to tuo u

v vwo w

x y z9{ |

} ~ �?��

��

⇒ dominant decay into

{bb for MH ∼< 130 GeVWW, ZZ for MH ∼> 130 GeV

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

Higgs boson search at the LHC

The days of the Higgs boson are numbered!

mH (GeV)

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

H → ZZ → llνν H → WW → lνjj

H → WW(*) → lνlν

Total significance

∫ L dt = 30 fb-1

(no K-factors)

Higgs boson production at the LHC

σ(pp → H + X) [pb]√s = 14 TeV

NLO / NNLO

gg → H

qq → Hqqqq

_' → HW

qq_ → HZ

gg/qq_ → tt

MH [GeV]

100 200 300 400 500 600 700 800 900 1000

��

� ��

� � �

��

� ��

��

Higgs production cross sections: theoretical status

Higgs production in gluon-gluon fusion ��

− NLO corrections: KNLO ≈ 1.7[Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman]

− NNLO corrections:

KNNLO(mtop � MH) ≈ 2[Harlander, Kilgore; Anastasiou, Melnikov ’02; Ravindran et al. ’03]

→ NNLO scale dependence ∼< 15%

− Soft-gluon summation ≈ 5%[MK, Laenen, Spira; Catani, de Florian, Grazzini]

− Electroweak corrections ≈ 5%[Aglietti, Bonciani, Degrassi, Vicini; Degrassi, Maltoni]

[Harlander, Kilgore ’02]

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

Higgs production in gluon-gluon fusion ¡¢

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

Higgs production in gluon-gluon fusion £¤¥

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

Higgs production in gluon-gluon fusion ¦§¨

100 120 140 160 180 200 220 240 260 280 300

σ(pp → H+X) [pb]

MH [GeV]

LONLONNLO

√s = 14 TeV

Vector boson fusion

− discovery channel & measurement ofHiggs couplings[Zeppenfeld, Kauer, Plehn, Rainwater]

− NLO QCD corrections (cf DIS) ≈ +10%[Han, Valencia, Willenbrock;Figy, Oleari, Zeppenfeld; Berger, Campbell]

Associated VH production

− crucial for Tevatron search (MH ∼< 130 GeV)

− NLO QCD corrections ≈ +(30 − 40)%[Han, Willenbrock]

− NNLO QCD corrections ≈ +10%[Brein, Djouadi, Harlander]

− NLO electroweak corrections ≈ −10%[Ciccolini, Dittmaier, MK]

Vector boson fusion

¯ °¬±

¯ °¬± ³

− discovery channel & measurement ofHiggs couplings[Zeppenfeld, Kauer, Plehn, Rainwater]

− NLO QCD corrections (cf DIS) ≈ +10%[Han, Valencia, Willenbrock;Figy, Oleari, Zeppenfeld; Berger, Campbell]

Associated VH production

´ µ·¶

¸¹¸

º »½¼¾

− crucial for Tevatron search (MH ∼< 130 GeV)

− NLO QCD corrections ≈ +(30 − 40)%[Han, Willenbrock]

− NNLO QCD corrections ≈ +10%[Brein, Djouadi, Harlander]

− NLO electroweak corrections ≈ −10%[Ciccolini, Dittmaier, MK]

Higgs production in association with top quarks

ÀÁÀ

− small cross section but distinctive final state

− direct measurement of top-Higgs Yukawa

coupling

→ need precise theoretical cross section

prediction

− NLO scale dependence ∼< 15%

[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas;

Dawson, Jackson, Orr, Reina, Wackeroth]

[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]

σ(pp → tt_ H + X) [fb]

√s = 14 TeV

MH = 120 GeV

µ0 = mt + MH/2

µ/µ0

0.2 0.5 1 2 5200

ÄÅÄ

coupling

prediction

√s = 14 TeV

MH = 120 GeV

µ0 = mt + MH/2

µ/µ0

0.2 0.5 1 2 5200

ÈÉÈ

coupling

prediction

√s = 14 TeV

MH = 120 GeV

µ0 = mt + MH/2

µ/µ0

0.2 0.5 1 2 5200

ÌÍÌ

coupling

prediction

√s = 14 TeV

MH = 120 GeV

µ0 = mt + MH/2

µ/µ0

0.2 0.5 1 2 5200

ÐÑÐ

coupling

prediction

√s = 14 TeV

MH = 120 GeV

µ0 = mt + MH/2

µ/µ0

0.2 0.5 1 2 5200

0.1 1 1010-7

σjet(ETjet > √s/4)

LHCTevatron

σttbar

σHiggs(MH = 500 GeV)

σjet(ETjet > 100 GeV)

σbbar

√s (TeV)

−→ QCD background: σbb ≈ 108 pb

−→ Higgs signal: σH+X ≈ 10 pb

↪→≈ 3 × 105 Higgs bosons/year

(∫L = 30 fb−1)

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

0.1 1 1010-7

LHCTevatron

σttbar

σbbar

√s (TeV)

(∫L = 30 fb−1)

0.1 1 1010-7

LHCTevatron

σttbar

σbbar

√s (TeV)

(∫L = 30 fb−1)

Inclusive channels

γ, W, Z

– pp → H(→ γγ) + X important for MH ∼< 150 GeV

– pp → H(→ WW ∗ → l+νl−ν) + X important for 140 GeV ∼< MH ∼< 200 GeV

– pp → H(→ ZZ∗ → l+l−l+l−)+X important for MH ∼> 130 GeV and MH 6= 2MW

Associated production

b, τ, γ, W, Z, . . .

jet, top

– pp → ttH(→ bb) + X important for MH ∼< 140 GeV

– pp → qqH(→ ττ, bb, γγ, WW, ZZ) + X important for whole Higgs mass range

Inclusive channels

γ, W, Z

– pp → H(→ γγ) + X important for MH ∼< 150 GeV

– pp → H(→ WW ∗ → l+νl−ν) + X important for 140 GeV ∼< MH ∼< 200 GeV

– pp → H(→ ZZ∗ → l+l−l+l−)+X important for MH ∼> 130 GeV and MH 6= 2MW

Associated production

b, τ, γ, W, Z, . . .

jet, top

– pp → ttH(→ bb) + X important for MH ∼< 140 GeV

– pp → qqH(→ ττ, bb, γγ, WW, ZZ) + X important for whole Higgs mass range

Inclusive search channels: H → γγ

− small branching ratio BR(H → γγ) ≈ 10−3

− large background from QCD processes

+ excellent photon-energy resolution in

CMS and ATLAS

→ Higgs discovery through resonance peak

+ determine background from sideband of data

080 100 120 140

mγγ (GeV)

Higgs signal

HSM γγ

Simulated 2γ mass plotfor 105 pb-1 mH =130 GeV

in the lead tungstate calorimeter

CMS, 105 pb-1

⇒ S/√B = 2.8 to 4.3 σ

(∫L = 30 fb−1

CMS and ATLAS

080 100 120 140

mγγ (GeV)

Higgs signal

HSM γγ

CMS, 105 pb-1

⇒ S/√B = 2.8 to 4.3 σ

(∫L = 30 fb−1

CMS and ATLAS

080 100 120 140

mγγ (GeV)

Higgs signal

HSM γγ

CMS, 105 pb-1

⇒ S/√B = 2.8 to 4.3 σ

(∫L = 30 fb−1

CMS and ATLAS

080 100 120 140

mγγ (GeV)

Higgs signal

HSM γγ

CMS, 105 pb-1

⇒ S/√B = 2.8 to 4.3 σ

(∫L = 30 fb−1

CMS and ATLAS

080 100 120 140

mγγ (GeV)

Higgs signal

HSM γγ

CMS, 105 pb-1

⇒ S/√B = 2.8 to 4.3 σ

(∫L = 30 fb−1

CMS and ATLAS

080 100 120 140

mγγ (GeV)

Higgs signal

HSM γγ

CMS, 105 pb-1

⇒ S/√B = 2.8 to 4.3 σ

(∫L = 30 fb−1

Inclusive search channels: H → WW ∗ → l+νl−ν

− neutrinos in final state

→ no invariant Higgs mass peak

− large background from QCD process

qq → WW

+ exploit lepton rapdity distributions and an-

gular correlations to suppress background(Dittmar, Dreiner)

0 50 100 150 200 250

mT (GeV)

⇒ S/√B = 3 to 15 σ

(∫L = 30 fb−1

qq → WW

0 50 100 150 200 250

mT (GeV)

⇒ S/√B = 3 to 15 σ

(∫L = 30 fb−1

qq → WW

0 50 100 150 200 250

mT (GeV)

⇒ S/√B = 3 to 15 σ

(∫L = 30 fb−1

qq → WW

0 50 100 150 200 250

mT (GeV)

⇒ S/√B = 3 to 15 σ

(∫L = 30 fb−1

Inclusive search channels: H → ZZ∗ → l+l−l+l−

+ most important and clean search channel

for MH > 2MZ

+ only limited background from QCD processes

+ reconstruction of Higgs mass peak

⇒ S/√B ≈ 20 σ

(∫L = 30 fb−1

for 180 GeV ∼> MH ∼< 400 GeV

for MH > 2MZ

⇒ S/√B ≈ 20 σ

(∫L = 30 fb−1

for 180 GeV ∼> MH ∼< 400 GeV

for MH > 2MZ

⇒ S/√B ≈ 20 σ

(∫L = 30 fb−1

for 180 GeV ∼> MH ∼< 400 GeV

for MH > 2MZ

⇒ S/√B ≈ 20 σ

(∫L = 30 fb−1

for 180 GeV ∼> MH ∼< 400 GeV

Associated production: pp → ttH(→ bb)

H0t–,t

[Drollinger, Muller, Denegri]

0 50 100 150 200 250 300minv(j,j) [GeV/c2]

CMS Lint = 30 fb-1

k = 1.5

gen. mH: 115 GeV/c2

const. : 13.63 ± 3.76mean : 110.3 ± 4.14sigma : 14.32 ± 3.70

∆gttH/gttH ≈ 15% (exp.)

− small cross section: σ(ttH)/σ(H + X) ≈ 1/100 → only relevant for MH ∼< 140 GeV

+ distinctive final state: pp → t(→ W +b) t(→ W−b) H(→ bb)

+ cross section ∝ g2ttH → unique way to measure top-Higgs Yukawa coupling

H0t–,t

0 50 100 150 200 250 300minv(j,j) [GeV/c2]

CMS Lint = 30 fb-1

k = 1.5

gen. mH: 115 GeV/c2

const. : 13.63 ± 3.76mean : 110.3 ± 4.14sigma : 14.32 ± 3.70

H0t–,t

0 50 100 150 200 250 300minv(j,j) [GeV/c2]

CMS Lint = 30 fb-1

k = 1.5

gen. mH: 115 GeV/c2

const. : 13.63 ± 3.76mean : 110.3 ± 4.14sigma : 14.32 ± 3.70

Associated production: pp → qqH(→ τ+τ−, bb, γγ, WW, ZZ)

τ, b, γ, W, Z

+ identify signal with forward jet tagging

and central jet veto

+ relevant for many Higgs decay channels

→ measurement of Higgs couplings

H → τ+τ−, bb

H → γγ

H → WW ∗

H → ZZ

MH ∼< 140 GeV

MH ∼< 150 GeV

MH ∼> 130 GeV

MH ∼> 500 GeV

[Eboli, Hagiwara, Kauer, Plehn, Rainwater, Zeppenfeld;Mangano, Moretti, Piccinini,Pittau, Polosa. . . ]

(Asai et al., ATLAS)

-4 -2 0 2 4

τ, b, γ, W, Z

H → τ+τ−, bb

H → γγ

H → WW ∗

H → ZZ

MH ∼< 140 GeV

MH ∼< 150 GeV

MH ∼> 130 GeV

MH ∼> 500 GeV

-4 -2 0 2 4

τ, b, γ, W, Z

H → τ+τ−, bb

H → γγ

H → WW ∗

H → ZZ

MH ∼< 140 GeV

MH ∼< 150 GeV

MH ∼> 130 GeV

MH ∼> 500 GeV

-4 -2 0 2 4

τ, b, γ, W, Z

H → τ+τ−, bb

H → γγ

H → WW ∗

H → ZZ

MH ∼< 140 GeV

MH ∼< 150 GeV

MH ∼> 130 GeV

MH ∼> 500 GeV

-4 -2 0 2 4

Higgs boson search at the LHC: signal significance

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

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

qqH → qq ττ

Total significance

∫ 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 search at the LHC: signal significance

)2(GeV/cHm

100 200 300 500 800

CMSjjνl→WW→qqH, H

ννll→ZZ→qqH, H, NLOννll→WW*/WW→H

4 leptons, NLO→ZZ*/ZZ→H

-τ+τ, γγ →qqH, H inclusive, NLOγγ→H

bb→H, WH, HttCombined channels

Higgs boson search at the Tevatron (revisited)

current∫L = 0.8 fb−1

For MH

< 140 GeV

> 140 GeV

pp→ WH/ZH and H → bb

pp→ H and H → WW

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

The Higgs mass

Expected precision ∆M/M ≈ 10−3 for MHiggs ∼< 500 GeV

The Higgs width

Remember: Ó ÔÖÕ ×ØÚÙ Û Ü Ý

Þ ß àâáã ä å æ ç ç çè ç çé ç çê ç çë ç çæ ì çæ ê çæ ç ç

æ ç ç çæ ç ç

æ çæ

çí æçí ç æ

çí ç ç æ

⇒ measurement of Γ possible only for MH ∼> 200 GeV

The Higgs width

Expected precision ∆Γ/Γ ≈ 5 − 10% for MHiggs ∼> 250 GeV

The Higgs spin and parity quantum numbers

– Discovery of H → γγ ⇒ J 6= 1 and C = +1 (Landau-Yang)

– Angular-correlations, e.g. in H → V V (∗):

θ1θ3

– Angular-correlations in H → V V (∗):

[Choi, Miller, Muhlleitner, Zerwas]

ϕH → ZZ → (f1f

–1)(f2f

MH = 280 GeV

SMpseudoscalar

0 π/2 π 3π/2 2π

The measurement of Higgs couplings:

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

[Zeppenfeld, Kinnunen, Nikitenko, Richter-Was]

Different production and decay channels provide measurements of combinations of

partial decay widths, for example

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

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

Different production and decay channels provide measurements of combinations of

partial decay widths, for example

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

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

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

Partial widths can be extracted with additional theoretical assumptions

[Duhrssen et al.]

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

Recall:

2H2 + λ3vH

3 +λ4

In the SM we have

λ3 = λ4 =M2

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

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

Recall:

2H2 + λ3vH

3 +λ4

In the SM we have

λ3 = λ4 =M2

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

The measurement of λ3 appears to be very difficult

The problem is the low cross section and large backgrounds

− MHiggs ∼< 140 GeV: HH → bbbb

overwhelming QCD background

+ 150 GeV ∼< MHiggs ∼< 140 GeV:

HH → (WW )(WW ) → (jjlν)(jjlν)

→ can determine whether λ3 = 0

[Baur, Plehn, Rainwater]

+ 150 GeV ∼< MHiggs ∼< 140 GeV:

The measurement of λ4 appears to be impossible

Higgs boson physics at the LHC: beware of backgrounds!

Consider Higgs search in pp→ H → WW → lν l′ν ′ channel

– WW pair production is the dominant background: σ× BR ≈ 5 times larger than signal

– a Higgs mass peak cannot be reconstructed from leptonic W decays

⇒ theoretical control of the background is important

experimental selection cuts may enhance the importance of higher-order

corrections for background processes

example: gg → WW → lν l′ν′[Binoth, Ciccolini, Kauer, MK; Duhrssen, Jakobs, van der Bij, Marquard]

νe γ, Z

W+γ, Z, H

→ formally NNLO

→ but enhanced by Higgs search cuts

gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%

νe γ, Z

W+γ, Z, H

→ formally NNLO

gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%

νe γ, Z

W+γ, Z, H

→ formally NNLO

gg qq (NLO) corr.

σtot 54 fb 1373 fb 4%

σbkg 1.39 fb 4.8 fb 30%

Consider search in VBF channel pp→ qqH

– important discovery channel

– provides measurement of HV V couplings

î ïð

î ïð ò

large Higgs + 2 jets background from gg → ggH[Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld]

need additional kinematic cuts

[Del Duca]

ó ôõ

ó ôõ ÷

[Del Duca]

ø ùú

ø ùú ü

[Del Duca]

The hierarchy problem: why is MHiggs � MPlanck?

Quantum corrections to the Higgs mass have quadratic UV divergencies

ý ýþ

ÿ ý ý� → δm2H ∼ α

π(Λ2 + m2

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

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