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 Poincar´e — 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 • M = 80.423 0.039GeV M = 91.1876 0.0021GeV W Z W couples only to left–handed fermions • Fermions have non-zero masses •
Theory: We would like to describe electroweak physics by an SU(2) U(1) gauge theory. 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 mass:
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: Gauge boson masses • 1 1 2 2 MW = gv MZ = g + g0 v 2 2q Fermion 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 Hadron Collider (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+X) [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 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 particles with different spins
Coleman-Mandula theorem: Most general symmetries 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¯)
quarks, leptons squarks, sleptons gauge bosons ←→ gauginos neutralinos & charginos Higgs bosons ←→ higgsinos ←→ } “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 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 E Visible Sector 6
Exact Supersymmetry
Gravitational interactions with hidden Gauge theory becomes gravity - 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 Supergravity ♦ An essential ingredient of String Theory ♦ Both of the above very exciting but only imply SuSy at some (high?) scale They are no motivation for low (TeV) scale SuSy
Gauge coupling unification ♦ 60 If we want to unify the 3 forces 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 Matter ♦ Supersymmetry allows lepton and baryon number violating interactions
d e-
~ b λ λ Proton 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-parity:
P = ( 1)3B 3L+2S R − −
SM particle: P = 1 SuSy partner: P = 1 R R −
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)
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 quantum 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 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 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