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Home , Gauge boson, Higgs boson

Higgs and

1. The in the — The story so far — The SM Higgs at the LHC — Problems with the SM

2. Supersymmetry — Surpassing Poincar´e — Supersymmetry motivations — The MSSM

3. Conclusions & Summary

D.J. Miller, , July 2, 2004 page 1 of 25 1. Electroweak Breaking in the Standard Model

1. Electroweak in the Standard Model

Observation: Weak nuclear mediated by •  M = 80.423 0.039GeV M = 91.1876 0.0021GeV W  Z  W couples only to left–handed • Fermions have non-zero •

Theory: We would like to describe electroweak by an SU(2) U(1) . L ⊗ Y Left–handed fermions are SU(2) doublets Chiral theory ⇒ {right–handed fermions are SU(2) singlets

There are two problems with this, both concerning :

gauge symmetry massless gauge bosons • SU(2) forbids m⇒(ψ¯ ψ + ψ¯ ψ ) terms massless fermions • L L R R L ⇒

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 2 | | − | | Minimum of the potential is not at zero

1 0 µ2 φ = with v = h i √2  v  r λ Electroweak symmetry is broken

Interactions with scalar field provide: masses • 1 1 2 2 MW = gv MZ = g + g0 v 2 2q masses • Y ψ¯ ψ φ m = Y v/√2 f R L −→ f f 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) M > 114.4 GeV at 95% C.L. − → ⇒ H

Electroweak Precision tests:

6 Theory uncertainty (5) ∆αhad = 5 0.02761±0.00036 0.02747±0.00012 4 incl. low Q2 data 2 3 ∆χ

2

1

Excluded Preliminary 0 20 100 400

mH [GeV]

+60 MH = 96 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

Summer 2003 2421 Winter 2004

ΓZ ΓZ [GeV] σ0 had σ0 [nb] R0 had l 0 0,l Rl Afb A0,l Al(Pτ) fb 0 Rb Al(Pτ) R0 0 c Rb 0,b A 0 fb R 0,c c Afb 0,b Afb Ab 0,c Afb Ac A Al(SLD) b 2 lept sin θeff (Qfb) Ac m W Al(SLD) 2 lept ΓW sin θeff (Qfb)

mW [GeV] QW(Cs) 2 − − ΓW [GeV] sin θMS−−(e e ) 2 sin θW(νN) 2 2 '$NuTeV gL(νN) sin θW(νN) g2 (νN) R QW(Cs) 0 0 1 2 3 4 5 2 &%3 theo meas 10 10 10 Sensitivity |∂O /∂logMH|/σ MH [GeV]

logarithmic sensitivity to MH [c.f. top mass] Not clear how to combine different measurements

D.J. Miller, Edinburgh, July 2, 2004 page 5 of 25 1. Electroweak Symmetry Breaking in the Standard Model

The Large (LHC) will switch on in 2007 • main goal: discover the mechanism of Electroweak Symmetry Breaking

Guaranteed to see something

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

W- W-

H

W+ W+

2 8π√2 2 MH . . (780 GeV) ⇒ 5GF

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+) [pb] 2 10 √s = 14 TeV M = 175 GeV Main production channel is gg H gg→H t  →  10 CTEQ4M      1  + ¥

-1 _ qq→Hqq 10 qq’→HW

¡ ¢¤£

-2 10 ¥ _ _ gg,qq→Htt -3 10 _ _ _ gg,qq→Hbb qq→HZ -4 10 0 200 400 600 800 1000

MH [GeV]

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

0 100 200 300 400 500 600 700 800 900 1000 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

H → γ γ + WH, ttH (H → γ γ ) ttH (H → bb) ATLAS H → ZZ(*) → 4 l H → WW(*) → lνlν (*) 2 WH → WWW 10 H → ZZ → llνν H → WW → lνjj Total significance Signal significance

10

5 σ

∫ L dt = 100 fb-1 (no K-factors)

1 2 3 10 10 mH (GeV)

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) M = 2λ(v2)v † − † H p

Coupling λ runs with energy, t log Q2/v2: ≡ dλ = 3 (4λ2 + λm2v2 m4v4/4) dt 16π2 t − t

Triviality upper bound on MH • 2 Large λ: λ(Q2) λ(v2)/(1 3λ(v ) log Q2/v2) < ≈ − 4π2 ∞ 2 M 2 8π2v2/3 log Q −→ H ≤ v2 [this triviality problem is endemic to scalar theories]

Vacuum stability lower bound on M • H 2 Small λ: large mt pulls λ(Q ) < 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 M 1016 GeV GUT ≈ M 130–170 GeV ⇒ H ≈ 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

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

f Quadratic divergence:

2 2 λf 2 δM = 2 | | Λ + ... H H H − 16π2

Λ Scale of new physics 1016 GeV (?) ∼ ∼ δM 2 1030 GeV ! ⇒ H ∼ 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 with different spins

Coleman-Mandula theorem: Most general of the S matrix are boosts, rotations and translations of the Poincar´e 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 Poincar´e group by introducing new fermionic coordinates of space-time, θ, θ¯ [anticommuting Weyl spinors]

promoted fields φ(x) 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 (D¯αΨ = 0) Ψ(x, θ, θ¯) = φ(x˜) + θψ(x˜) + θθF (x˜) [x˜µ = xµ + iθσµθ¯]  6 @I @ @ @ @ @ scalar fermion auxilliary field

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

, squarks, sleptons gauge bosons ←→ & Higgs bosons ←→ ←→ } “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

f ~f

H H

H H

2 2 λf 2 2 λf˜ 2 δM = +2 | | Λ + ... δM = 2 Λ + ... H 16π2 H − 16π2 2 Supersymmetry λ = λ ˜ ⇒ | f | f quadratic divergence cancels (to all orders in )

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

Hidden Sector E Visible Sector 6

Exact Supersymmetry

Gravitational with hidden Gauge theory becomes - sector produce soft supersymmetry strongly interacting 2 Condensates form F F MΛ h i breaking terms: φ†φ MPlanck

logarithmic running

? Low energy softly broken supersymmetry

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

More motivations for Supersymmetry

Local supersymmetry ♦ An essential ingredient of ♦ Both of the above very exciting but only imply SuSy at some (high?) scale They are no motivation for low (TeV) scale SuSy

Gauge unification ♦ 60 If we want to unify the 3 at −1 50 α 1 SM MGUT, need to unify their couplings 40 Supersymmetry more compatible −1 α 30 with gauge unification −1 α 2 3 20 SuSy Desert between MEW 10 GeV 16≈ and MGUT 10 GeV 10 −1 ≈ α3 0 2 4 6 8 10 12 14 16 18

Log10(Q/1 GeV)

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

“Natural” mechanism of electroweak symmetry breaking ♦

d 6 16π2 M 2 6h2(M 2 + M 2 + M 3 ) 6g2M 2 g2M 2 dt Hu ≈ t Hu Q3 u3 − 2 2 − 5 1 1

[t = log Q ] MGUT

~g ~q 600 ~ L qR ~ 2 t large top mass pulls M < 0, L Hu ~t breaking Electroweak Symmetry 400 R 2 2 µ + M0 Hd m ~ 1/2 Explains why we have a L 200 “mexican hat” potential ~W M0 ~ B

Running Mass (GeV) Mass Running 0 [Still doesn’t explain why Hu M (MGUT) MGUT] H  –200

2 4 6 8 10 12 14 16 5–97 Log10Q (GeV) 8303A15

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

Dark ♦ Supersymmetry allows and number violating interactions

d e-

~ b λ λ decay! B L ⇒ u u u u

Observation: life-time of the proton > 1032 years

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

Introduce R-:

P = ( 1)3B 3L+2S R − −

SM : P = 1 SuSy partner: P = 1 R R −

R-parity conservation ⇒ Both B & L conserved No • ⇒ The Lightest Supersymmetric Particle (LSP) is stable •

Could the LSP be ?

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)

ˆ 0 ˆ + ˆ Hd ˆ Hu Hd = ˆ , Hu = ˆ 0  Hd−   Hu  neutral components gain (real) vacuum expectation values

1 vd 1 0 Hˆd = , Hˆu = h i √2  0  h i √2  vu 

2 2 2 v + v = v vu/v tan β u d d ≡ 8 degrees of freedom: 3 eaten by W , Z 5 Higgs bosons left  −→ 2 scalar Higgs fields h, H 1 pseudoscalar Higgs field A 2 charged Higgs fields H

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

An example of MSSM Higgs boson masses

500

450 Scalar Pseudoscalar 400 Charged

350 MSUSY = 1 TeV µ = 500 GeV 300 tanβ = 3 250

200 Higgs Mass [GeV] 150

100

50

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

lightest Higgs mass . 135 GeV

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

LHC Higgs coverage at ATLAS

50 β ATLAS -1 40 ATLAS - 300 fb

tan maximal mixing 30

0 0 0 -+ 20 h H A H

0 -+ 0 0 0 h H h H A 10 9 8 7 6 h0 only 5 4 LEP 2000 3 0 0 h H LEP excluded

2 0 0 0 -+ 0 -+ h H A H h H

1 50 100 150 200 250 300 350 400 450 500

mA (GeV)

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

Neutralinos & charginos

Supersymmetric partners to gauge bosons and Higgs bosons are fermions with the same numbers they mix ⇒ 2 gauginos + 2 higgsinos 4 neutralinos (χ˜0, i = 1, 4) −→ i

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

For many parameter choices, a 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 masses ♦ for 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