Beyond the Standard Model Markus Luty UC Davis Big Picture Three - - PowerPoint PPT Presentation
Beyond the Standard Model Markus Luty UC Davis Big Picture Three major paradigms for particle physics beyond the standard model Supersymmetry Logos From the Greek: reason, word Strong dynamics, extra dimensions Stratus
Markus Luty UC Davis
“Logos”
From the Greek: reason, word
“Stratus”
From the Latin: a cover or spread; low-lying clouds
“Chaos”
From the Greek: formlessness, confusion
“It is better to uncover a little, than to cover a lot.”
An old idea: approximate theory using only degrees of freedom that can be excited at low energy E.g. QED valid for E ≪ mµ Standard model breaks down at high energies ⇒ must be effective theory
Also lots of concrete motivation for physics beyond standard model
(Hambye, Riesselmann 1997) Neutrinos, dark matter, baryogenesis, strong CP problem, gauge coupling unification, origin of flavor,...
What effective theory describes our present understanding of strong/electroweak physics? Not the standard model! We haven’t found the Higgs... Leff = LSM(h0, Aµ, W ±
µ , Zµ, Gµ, q, ℓ)
(unitary gauge)
Expansion in powers of E 4πv ∼ E TeV Example: WW scattering
∼ E4 + E2 + · · · ∼ E4 + E2 + · · ·
∼ E2 + · · · ∼ E0 ∼ E4 + E2 + · · · ∼ E4 + E2 + · · · ∼ E2
Equivalent to nonlinearly realized SU(2)W × U(1)Y → U(1)EM
Effective standard model breaks down at TeV scale ⇒ new physics below TeV! Higgs boson is only one possibility... Maybe the only appearance of Higgs at LHC
Not a question of “canceling UV divergences...” Dependence of effective parameters on (more) fundamental ones LSM = −m2
HH†H + · · ·
invariant under all symmetries* H†H
*Except supersymmetry
⇒ scale of new physics mH ∼ E.g. grand unification:
H X H
⇒ ∆m2
H ∼ g2 GUT
16π2 M 2
X ∼ (1015 GeV)2
Higgs quartic coupling: λ ∼ g2 + 3y4
t
16π2 ln m˜
t
mt
t
t
+ ˜ t
⇒ ∆m2
H ∼ 3y2 t
16π2m2
˜ t ∼ (1 TeV)2
m2
h0 > 114 GeV requires m˜ t >
∼ 1 TeV ⇒ 1% tuning in MSSM Exactly the problem SUSY was meant to solve... ⇒ m2
h0 ∼ λv2 ∼ m2 Z + 3y4 t v2
16π2 ln m˜
t
mt
Naturalness breaks down at TeV scale ⇒ new physics at TeV scale?
All have problems...
Another hint for new physics at the TeV scale Ω ∼ 0.1
σannv
pb
−1
Thermal weak-scale relic ⇒ Standard collider signature: missing energy Many models, wide range of predictions (including no collider signatures)
Expect new physics at TeV colliders Anything else is a welcome surprise...
Required Highly recommended Suggested
ΨL =
UL
DL
UR
DR
SU(2)W singlet SU(2)W
New gauge force strong at TeV scale SU(N) Copy QCD...
Y (UR) = Y (ΨL) + 1
2
Y (DR) = Y (ΨL) − 1
2
¯ ΨLaΨb
R = Λ3 TCδab
ΛTC ∼ TeV ¯ ΨLUR ∼ H ¯ ΨLDR ∼ H∗ ⇒ same symmetry breaking pattern as SM
Weinberg 1976; Susskind 1976
LTC = −1
4HµνAHµνA
+¯ Ψi / DΨ No singlet operator with dimension < 4 (c.f. ) LSM = −m2
HH†H + · · ·
Technifermion mass forbidden by gauge invariance
¯ ΨΨ
Higgs sector = strong TeV resonances E.g. WW scattering + + · · · +
m ∼ TeV
QCD suggests vector resonances most prominent Spin 0 “composite Higgs” may be absent or obscure
f0(600)
IG (JPC ) = 0+(0 + +)
A REVIEW GOES HERE – Check our WWW List of Reviews
f0(600) T-MATRIX POLE √s f0(600) T-MATRIX POLE √s f0(600) T-MATRIX POLE √s f0(600) T-MATRIX POLE √s
Note that Γ ≈ 2 Im(spole).
VALUE (MeV) DOCUMENT ID TECN COMMENT
(400–1200)−i(250–500) OUR ESTIMATE (400–1200)−i(250–500) OUR ESTIMATE (400–1200)−i(250–500) OUR ESTIMATE (400–1200)−i(250–500) OUR ESTIMATE
PDG 2010
Cut Value for keeping events Leptonic W PT PT > 320 GeV Hadronic W PT PT > 320 GeV Hadronic W mass 66.09 < M < 101.89 GeV Y-scale 1.55 < Y − scale < 2.0 Top veto 130 < MW+jet < 240 GeV Tag Jets PT > 20 GeV, E > 300 GeV, 2.0 < |η| < 4.5 Hard Scatter PT PT < 50 GeV Number of mini-jets (PT > 15 GeV with |η| < 2.0)
Enhanced forward emission of W, Z
A model-independent signal for strong Higgs sector
(Chanowitz, Gaillard 1984)
5σ discovery with 30 fb-1 for models with resonances
Standard model → technicolor ( solves naturalness problem) H → ¯ ΨΨ dim(¯ ΨΨ) = 3 LSM = yt ¯ QLHtR + · · · → 1 Λ2
t
( ¯ QLtR)(¯ ΨΨ)
dim = 6 Effective 4-fermion interaction can arise from heavy particle exchange (c.f. Fermi theory) scale where effective flavor theory breaks down Λt = ∼ few TeV ⇒ must address flavor near TeV scale
Topcolor Walking/conformal technicolor
Hill 1991
H = operator in Higgs sector Consider general values of (unitarity)
(naturalness) ⇒ want as small as possible
Possible in conformal (scale invariant) theories d = dim(H) d ≥ 1 dim( ¯ QLHtR) = 3 + d d
⇒ d ≤ 2 ?
β function in QCD with colors and flavors: Nc Nf Nf ∼ 1 Nf ≃ 11
2 Nc
⇒ confining ⇒ conformal
g µ µ
g g∗
Under active study by lattice community
perturbative expansion parameter a = Ncg2 16π2 = x = Nf Nc = 11 2 − ǫ continuous for large Nc, Nf β(a) ≃ −3ǫa2 + 3 4(75 − 26ǫ)a3 + · · · Expect “conformal window” for xc ≤ x < 11 2 ⇒ perturbative fixed point at for a∗ = 4ǫ 75 ǫ ≪ 1 Lattice studies suggest xc ≃ 4 a β(a) a∗
Plausible at x = xc
g µ
∆L = −m¯ χχ χ = sterile technifermion
Soft breaking of spacetime symmetry triggers electroweak symmetry breaking (c.f. SUSY)
(Holdom 1985; Appelquist, Karabali, Wijewardhana 1986; Yamawaki, Bando, Matumoto 1986)
It “just does it”
(ML, Okui 2004)
Λt ∼ TeV
TeV
mt
1/(d−1)
∼
3 TeV dim(H) = 3 10 TeV dim(H) = 2 50 TeV dim(H) = 1.5 Still wanted: a complete theory of flavor without large flavor-changing neutral currents Complete theory still lacking (Something I’m working on...)
Leff = 1 Λd−1
t
¯ QLHtR + · · · ⇒ production of strong resonances: J = 0, CP = ±, I = 0, 1
Resonance Mass (GeV) 1000 1500 2000 2500 3000 LHC Production Cross Section (fb) 1 10
210
310
Pseudoscalar Scalar Charged
g g t
ϕ0
g b t t ϕ± ϕ → WW suppressed for ⇒ can be narrow I = 1 ϕ+ → ¯ bt, W +W +W −, W +ZZ, . . . ϕ0 → ¯ tt, W +W −Z, ZZZ, . . .
(Evans, ML 2009)
Many interesting signals:
Effective theory below TeV contains gauge-violating terms ∆Leff = 1
2∆M 2W µ 3 W3µ − 1 2ǫW µν 3 Bµν + · · ·
⇒ leading corrections to
γ, W, Z
ρ, T ∝ ∆M 2 S ∝ ǫ
0.1 0.2 0.3 0.4 0.5 0.6
S
0.1 0.2 0.3 0.4 0.5
T
a l l : M
H= 1 1 7 G e V a l l : M
H= 3 4 G e V a l l : M
H= 1 G e V M
H= 1 1 7 G e V l
e n e r g y :
Z lineshape asymmetries W mass scattering e scattering APV
Erler, Langacker 2010
NDA QCD
0.6 0.4 0.2 0.2 0.4 0.6 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5
S T
mh,ref = 1 TeV 90% CL
NDA: all interactions → strong at TeV QCD: assume scaled-up QCD dynamics, use QCD data No reliable prediction for walking/conformal theories Not ruled out!
dim(H†H) ≥ 4 Topcolor?
Mandarin: crisis = danger + opportunity
dim(H) < 3 ?