Higgs bosons and Supersymmetry

1. The Higgs mechanism in the Standard Model— The story so far— The SM Higgs boson at the LHC— Problems with the SM Higgs boson

2. Supersymmetry— Surpassing Poincare— Supersymmetry motivations— The MSSM

3. Conclusions & Summary

D.J. Miller, Edinburgh, July 2, 2004 page 1 of 25

1. Electroweak Symmetry Breaking in the Standard Model

1. Electroweak Symmetry Breaking in the Standard Model

Observation:

• Weak nuclear force mediated by W± and Z bosons

MW = 80.423± 0.039GeV MZ = 91.1876± 0.0021GeV

• W couples only to left–handed fermions

• Fermions have non-zero masses

Theory:

We would like to describe electroweak physics by an SU(2)L⊗U(1)Y gauge theory.

Chiral theory ⇒ { Left–handed fermions are SU(2) doubletsright–handed fermions are SU(2) singlets

There are two problems with this, both concerning mass:

• gauge symmetry ⇒ massless gauge bosons• SU(2)L forbids m(ψLψR + ψRψL) terms ⇒ massless fermions

D.J. Miller, Edinburgh, July 2, 2004 page 2 of 25

1. Electroweak Symmetry Breaking in the Standard Model

Higgs Mechanism

Introduce new SU(2) doublet scalar field (φ) with potential

V (φ) = λ|φ|4 − µ2|φ|2Minimum of the potential is not at zero

〈φ〉 = 1√2

(

0v

)

with v =

√

µ2

λ

Electroweak symmetry is broken

Interactions with scalar field provide:

• Gauge boson masses

MW =1

2gv MZ =

1

2

√

g2 + g′2v

• Fermion masses

Yf ψRψLφ −→ mf = Yfv/√

2

4 degrees of freedom., 3 become longitudinal components of W and Z,

one left over the Higgs boson

D.J. Miller, Edinburgh, July 2, 2004 page 3 of 25

1. Electroweak Symmetry Breaking in the Standard Model

The Higgs boson mass is not predicted in the SM

LEP limits (e+e− → ZH) ⇒ MH > 114.4 GeV at 95% C.L.

Electroweak Precision tests:

0

1

2

3

4

5

6

10020 400

mH [GeV]

∆χ2

Excluded Preliminary

∆αhad =∆α(5)

0.02761±0.000360.02747±0.00012incl. low Q2 data

Theory uncertainty

MH = 96+60−38 GeV MH < 219 GeV at 95% C.L.

D.J. Miller, Edinburgh, July 2, 2004 page 4 of 25

1. Electroweak Symmetry Breaking in the Standard Model

Sensitivity |∂Otheo/∂logMH|/σmeas

Winter 2004

ΓZΓZ

σhadσ0

RlR0

AfbA0,l

Al(Pτ)Al(Pτ)

RbR0

RcR0

AfbA0,b

AfbA0,c

AbAb

AcAc

Al(SLD)Al(SLD)

sin2θeffsin2θlept(Qfb)

mWmW

ΓWΓW

QW(Cs)QW(Cs)

sin2θ−−(e−e−)sin2θMS

sin2θW(νN)sin2θW(νN)

gL(νN)g2

gR(νN)g2

0

24

0 1 2 3 4 5

MH [GeV]

Summer 2003

ΓZ [GeV]ΓZ [GeV]σhad [nb]σ0

RlR0

AfbA0,l

Al(Pτ)Al(Pτ)

RbR0

RcR0

AfbA0,b

AfbA0,c

AbAb

AcAc

Al(SLD)Al(SLD)

sin2θeffsin2θlept(Qfb)

mW [GeV]mW

ΓW [GeV]ΓW

sin2θW(νN)sin2θW(νN)

QW(Cs)QW(Cs)

0

21

10 102

103

logarithmic sensitivity to MH [c.f. top mass]

Not clear how to combine different measurements

&%'$

NuTeV

D.J. Miller, Edinburgh, July 2, 2004 page 5 of 25

1. Electroweak Symmetry Breaking in the Standard Model

• The Large Hadron Collider (LHC) will switch on in 2007

main goal: discover the mechanism of Electroweak Symmetry Breaking

Guaranteed to see something

WW scattering at LHC will violate unitarity without Higgs boson(or something else)

H

+W

-W

+W

-W

⇒M2H .

8π√

25GF

. (780 GeV)2

D.J. Miller, Edinburgh, July 2, 2004 page 6 of 25

1. Electroweak Symmetry Breaking in the Standard Model

SM Higgs production at the LHC

σ(pp→H+X) [pb]√s = 14 TeV

Mt = 175 GeV

CTEQ4Mgg→H

qq→Hqqqq_’→HW

qq_→HZ

gg,qq_→Htt

_

gg,qq_→Hbb

_

MH [GeV]0 200 400 600 800 1000

10-4

10-3

10-2

10-1

1

10

10 2

0 100 200 300 400 500 600 700 800 900 1000

Main production channel is gg → H�

��

��

��

��+

�� ���

��

D.J. Miller, Edinburgh, July 2, 2004 page 7 of 25

1. Electroweak Symmetry Breaking in the Standard Model

SM Higgs branching ratios

D.J. Miller, Edinburgh, July 2, 2004 page 8 of 25

1. Electroweak Symmetry Breaking in the Standard Model

1

10

10 2

102

103

mH (GeV)

Sig

nal s

igni

fican

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

H → ZZ → llνν H → WW → lνjj

H → WW(*) → lνlν WH → WWW(*)

Total significance

5 σ

∫ L dt = 100 fb-1

(no K-factors)

ATLAS

D.J. Miller, Edinburgh, July 2, 2004 page 9 of 25

1. Electroweak Symmetry Breaking in the Standard Model

Is the Standard Model valid to all energies?

V (φ) = λ(φ†φ)2 − µ2(φ†φ) MH =√

2λ(v2)v

Coupling λ runs with energy, t ≡ logQ2/v2:

dλdt

= 316π2(4λ

2 + λm2t v

2 −m4t v

4/4)

• Triviality upper bound on MH

Large λ: λ(Q2) ≈ λ(v2)/(1− 3λ(v2)4π2 logQ2/v2) <∞

−→M2H ≤ 8π2v2/3 log Q2

v2

[this triviality problem is endemic to scalar theories]

• Vacuum stability lower bound on MH

Small λ: large mt pulls λ(Q2) < 0

−→ electroweak vacuum unstable

D.J. Miller, Edinburgh, July 2, 2004 page 10 of 25

1. Electroweak Symmetry Breaking in the Standard Model

If no new physics up to MGUT ≈ 1016 GeV

⇒MH ≈ 130–170 GeV

Fits well with Electroweak precision tests...

D.J. Miller, Edinburgh, July 2, 2004 page 11 of 25

1. Electroweak Symmetry Breaking in the Standard Model

The Hierarchy Problem

The Standard Model (SM) has a fundamental flaw:

The parameters of the model must be fine tuned

The Higgs mass gains corrections from fermion loops

H

f

H

Quadratic divergence:

δM2H = −2

|λf |216π2Λ

2 + ...

Λ ∼ Scale of new physics ∼ 1016 GeV (?)

⇒ δM2H ∼ 1030 GeV !

must arrange for parameters to cancel to one part in 1026

Is this a hint that new physics will be seen at the LHC?

D.J. Miller, Edinburgh, July 2, 2004 page 12 of 25

2. Supersymmetry

2. Supersymmetry

The new physics most favoured by theorists is Supersymmetry

— a symmetry between particles with different spins

Coleman-Mandula theorem:

Most general symmetries of the S matrix are• boosts, rotations and translations of the Poincare group• symmetries of compact Lie groups (e.g. U(1), SU(2), E6...)

But they didn’t consider groups with anti-commuting generators

Supersymmetry enlarges the Poincare group by introducing new fermioniccoordinates of space-time, θ, θ [anticommuting Weyl spinors]

fields φ(x)−→promoted

superfields Ψ(x, θ, θ)

D.J. Miller, Edinburgh, July 2, 2004 page 13 of 25

2. Supersymmetry

Expand superfields in powers of θ and θ:

Since θ only has two components, terms like θθθ must vanish

θαθβ = −θβθα

e.g. a chiral superfield (DαΨ = 0)

Ψ(x, θ, θ) = φ(x) + θψ(x) + θθF (x) [xµ = xµ + iθσµθ]

��

��

���

scalar

6

fermion@

@@

@@

@I

auxilliary field

Supersymmetry is just a rotation in the new enlarged space-time (x, θ, θ)

quarks, leptons ←→ squarks, sleptonsgauge bosons ←→ gauginosHiggs bosons ←→ higgsinos } neutralinos & charginos

“extra” particles are just different facets of the known SM particles

D.J. Miller, Edinburgh, July 2, 2004 page 14 of 25

2. Supersymmetry

The Hierarchy Problem Revisited

H

f

H

H H

f~

δM2H = +2

|λf |216π2Λ

2 + ... δM2H = −2

λf16π2Λ

2 + ...

Supersymmetry ⇒ |λf |2 = λf

quadratic divergence cancels (to all orders in perturbation theory)

⇒ Higgs mass stabilized!

D.J. Miller, Edinburgh, July 2, 2004 page 15 of 25

2. Supersymmetry

Supersymmetry breaking

Clearly supersymmetry is not a true symmetry of nature

— it must be broken

How supersymmetry is broken is not known but it might go something like this...

Hidden Sector Visible Sector

Exact Supersymmetry

E

Gauge theory becomesstrongly interactingCondensates form 〈FF 〉

-gravity

Gravitational interactions with hiddensector produce soft supersymmetry

breaking terms:M2

Λ

MPlanck

φ†φ

?

logarithmic running

Low energy softly broken supersymmetry

6

D.J. Miller, Edinburgh, July 2, 2004 page 16 of 25

2. Supersymmetry

More motivations for Supersymmetry

♦ Local supersymmetry Supergravity

♦ An essential ingredient of String Theory

Both of the above very exciting but only imply SuSy at some (high?) scaleThey are no motivation for low (TeV) scale SuSy

♦ Gauge coupling unification

If we want to unify the 3 forces atMGUT, need to unify their couplings

Supersymmetry more compatiblewith gauge unification

Desert between MEW ≈ 103 GeVand MGUT ≈ 1016 GeV

2 4 6 8 10 12 14 16 18Log10(Q/1 GeV)

0

10

20

30

40

50

60

α−1

α1−1

α2−1

α3−1

SM

SuSy

D.J. Miller, Edinburgh, July 2, 2004 page 17 of 25

2. Supersymmetry

♦ “Natural” mechanism of electroweak symmetry breaking

16π2 d

dtM2

Hu≈ 6h2

t (M2Hu

+M2Q3

+M3u3)− 6g22M

22 −

6

5g21M

21

[t = log QMGUT

]

large top mass pulls M2Hu< 0,

breaking Electroweak Symmetry

Explains why we have a“mexican hat” potential

[Still doesn’t explain whyMH(MGUT)�MGUT]

2

Hu

Hd

B~

L~

W~

g~qL~

tL~

tR~

qR~

4 6 8

Run

ning

Mas

s (G

eV)

M0

m1/2

10Log10Q (GeV)

12 14 165–97

8303A15

600

400

200

0

–200

µ + M0

22

D.J. Miller, Edinburgh, July 2, 2004 page 18 of 25

2. Supersymmetry

♦ Dark Matter

Supersymmetry allows lepton and baryon number violating interactions

⇒ Proton decay!

u

d

u

b~

-e

u

u

Bλ Lλ

Observation: life-time of the proton > 1032 years

D.J. Miller, Edinburgh, July 2, 2004 page 19 of 25

2. Supersymmetry

Introduce R-parity:

PR = (−1)3B−3L+2S

SM particle: PR = 1 SuSy partner: PR = −1

R-parity conservation ⇒

• Both B & L conserved ⇒ No proton decay

• The Lightest Supersymmetric Particle (LSP) is stable

Could the LSP be dark matter?

D.J. Miller, Edinburgh, July 2, 2004 page 20 of 25

2. Supersymmetry

Minimal Supersymmetric Standard Model (MSSM)

has minimum particle content for a supersymmetric model

Now have two Higgs doublets (analyticity and cancellation of anomalies)

Hd =

(

H0d

H−d

)

, Hu =

(

H+u

H0u

)

neutral components gain (real) vacuum expectation values

〈Hd〉 = 1√2

(

vd0

)

, 〈Hu〉 = 1√2

(

0vu

)

v2u + v2

d = v2 vu/vd ≡ tanβ

8 degrees of freedom: 3 eaten by W±, Z −→ 5 Higgs bosons left

2 scalar Higgs fields h, H1 pseudoscalar Higgs field A2 charged Higgs fields H±

D.J. Miller, Edinburgh, July 2, 2004 page 21 of 25

2. Supersymmetry

An example of MSSM Higgs boson masses

0 50 100 150 200 250 300 350 400 450 500MA

0

50

100

150

200

250

300

350

400

450

500

Hig

gs M

ass

[GeV

]

ScalarPseudoscalarCharged

MSUSY = 1 TeV

µ = 500 GeV

tanβ = 3

lightest Higgs mass . 135 GeV

D.J. Miller, Edinburgh, July 2, 2004 page 22 of 25

2. Supersymmetry

LHC Higgs coverage at ATLAS

ATLAS

LEP 2000

ATLAS

mA (GeV)

tan

β

1

2

3

4

56789

10

20

30

40

50

50 100 150 200 250 300 350 400 450 500

0h 0H A

0 +-H

0h 0H A

0 +-H

0h 0H A

00h H

+-

0h H+-

0h only

0 0Hh

ATLAS - 300 fbmaximal mixing

-1

LEP excluded

D.J. Miller, Edinburgh, July 2, 2004 page 23 of 25

2. Supersymmetry

Neutralinos & charginos

Supersymmetric partners to gauge bosons and Higgs bosons arefermions with the same quantum numbers ⇒ they mix

2 gauginos + 2 higgsinos −→ 4 neutralinos (χ0i , i = 1,4)

2 charged gauginos + 2 charged higgsinos −→ 4 charginos (χ±i , i = 1,2)

For many parameter choices, a neutralino is the “lightest supersymmetric particle”

R partity ⇒ LSP stable

Supersymmetry has very distinctive missing energy signatures

D.J. Miller, Edinburgh, July 2, 2004 page 24 of 25

3. Conclusions & Summary

3. Conclusions & Summary

♦ The Higgs mechanism breaks electroweak symmetry, providing massesfor the W & Z bosons and fermions

— it(or some altenative) will be discovered at the LHC

— Unlikely to be valid up to the GUT scale

— The SM Higgs mechanism needs extreme fine tuning(the hierarchy problem)

♦ Supersymmetry:

— extends space-time adding new fermionic coordinates

— cures the hierarchy problem in a very natural way

— explains the mexican hat

— provides a dark matter candidate – the neutralino

— contains multiple Higgs bosons

We should have some answers soon... (by 2010)

D.J. Miller, Edinburgh, July 2, 2004 page 25 of 25