Magnetic moment (g − 2)µ and new physics
Dominik Stöckinger
Dresden
Lepton Moments, July 2010
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction
exp SM A3σ deviation for aµ − aµ has been established!
Currently: exp SM −11 aµ − aµ = (255 ± 63 ± 49) × 10 Expected with new Fermilab exp. (and th. progress):
exp SM −11 aµ − aµ = (?? ± 16 ± 30) × 10
Which types of physics beyond the SM could explain this?
What is the impact of aµ on physics beyond the SM?
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Outline
1 Introduction
2 Different types of new physics
3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation
4 Conclusions
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Outline
1 Introduction
2 Different types of new physics
3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation
4 Conclusions
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Muon magnetic moment
Quantum field theory: Operator:
aµ µ¯ σ qνµ mµ L µν R
CP-, Flavour-conserving, chirality-flipping, loop-induced
2 Heavy particles contribute ∝ mµ Mheavy Sensitive to all SM interactions Sensitive to TeV-scale new physics in a unique way
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Why new physics? Big questions EWSB, Higgs, mass generation?
hierarchy MPl/MW ? Naturalness?
Unification of the Coupling Constants in the SM and the minimal MSSM i i α 60 α 60 1/α 1/ 1/ 1 MSSM 50 50
40 40 α 1/ 2 30 30
20 20
10 10 α 1/ 3 0 0 0 5 10 15 0 5 10 15 10log Q 10log Q dark matter? Grand Unification?
. . . point to the TeV scale. . . and to new physics
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Why new physics? Big questions EWSB, Higgs, mass generation?
hierarchy MPl/MW ? Naturalness?
Unification of the Coupling Constants in the SM and the minimal MSSM i i α 60 α 60 1/α 1/ 1/ 1 MSSM 50 50
40 40 α 1/ 2 30 30
20 20
10 10 α 1/ 3 0 0 0 5 10 15 0 5 10 15 10log Q 10log Q dark matter? Grand Unification?
Tevatron, LHC = era of TeV-scale physics Quest: discover new physics, solve big questions, understand EWSB
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Why new physics?
Big questions motivate radically new ideas —
How can EWSB, light Higgs, MPl/MW be natural? Supersymmetry? Fermi-Bose symmetry
≈10 TeV strong dyn.
≈1 TeV Little Higgs? states WH , lH . . .
≈250 GeV Higgs=Pseudo SM, Higgs Goldstone Boson Randall-Sundrum? Warped extra dim.
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Introduction Why new physics?
Big questions motivate radically new ideas —
How can EWSB, light Higgs, MPl/MW be natural? Supersymmetry? Fermi-Bose symmetry
≈10 TeV strong dyn.
≈1 TeV Little Higgs? states WH , lH . . .
≈250 GeV Higgs=Pseudo SM, Higgs Goldstone Boson Randall-Sundrum? Warped extra dim.
all these models predict aµ and are constrained by it
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Outline
1 Introduction
2 Different types of new physics
3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation
4 Conclusions
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Theory: g − 2 and chirality flips
g − 2 = chirality-flipping interaction µR µL
mµ = chirality-flipping interaction as well µR µL
are the two related?
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Theory: g − 2 and chirality flips
g − 2 = chirality-flipping interaction µR µL
mµ = chirality-flipping interaction as well µR µL
are the two related?
New physics loop contributions to aµ, mµ related by chiral symmetry! [Czarnecki, Marciano ’01]
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
α C = O( ), Z ′, W ′, UED, Littlest Higgs (LHT). . . 4π (UED, LHT can mimic SUSY at the LHC) −11 δaµ ∼ 255 × 10 for M < 100GeV → very small!
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
α C = O( ), Z ′, W ′, UED, Littlest Higgs (LHT). . . 4π (UED, LHT can mimic SUSY at the LHC) −11 δaµ ∼ 255 × 10 for M < 100GeV → very small!
such models already disfavoured by aµ, ruled out if deviation persists in new exp.
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
C = O(1), radiative muon mass generation technicolor, . . . [Czarnecki,Marciano ’01] −11 δaµ ∼ 255 × 10 for M > 1TeV → can be large!
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
C = O(1), radiative muon mass generation technicolor, . . . [Czarnecki,Marciano ’01] −11 δaµ ∼ 255 × 10 for M > 1TeV → can be large!
lower mass bounds from aµ
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
α C = O(tan β ), supersymmetry 4π 1 C = O(nc 2 ), extra dimensions (Randall/Sundrum) 16π [Davoudiasl, Hewett, Rizzo ’00] large ED, unparticles,. . . [Park et al ’01] [Kim et al ’01] [Graesser,’00] [Cheung, Keung, Yuan ’07] −11 δaµ >, <, ∼ 255 × 10 possible → can fit well!
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics Classification of new physics
2 mµ δmµ(N.P.) generally: δaµ(N.P.)= O(C) , C = M mµ α Allows to classify new physics: C = O( 4π ), O(1), O(intermediate)
α C = O(tan β ), supersymmetry 4π 1 C = O(nc 2 ), extra dimensions (Randall/Sundrum) 16π [Davoudiasl, Hewett, Rizzo ’00] large ED, unparticles,. . . [Park et al ’01] [Kim et al ’01] [Graesser,’00] [Cheung, Keung, Yuan ’07] −11 δaµ >, <, ∼ 255 × 10 possible → can fit well! strong constraints on model parameters and model building
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics g − 2 and new physics
Different types of new physics can lead to very different contributions to aµ SUSY, RS, ADD, . . . : constrain parameters Z ′, UED, LHT, . . . : ruled out if deviation confirmed
aµ can sharply distinguish between different types of new physics
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics g − 2 and new physics
Different types of new physics can lead to very different contributions to aµ SUSY, RS, ADD, . . . : constrain parameters Z ′, UED, LHT, . . . : ruled out if deviation confirmed
aµ can sharply distinguish between different types of new physics
This will be even more the case with a new, improved measurement!
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Different types of new physics g − 2 and new physics
Different types of new physics can lead to very different contributions to aµ SUSY, RS, ADD, . . . : constrain parameters Z ′, UED, LHT, . . . : ruled out if deviation confirmed
aµ can sharply distinguish between different types of new physics
And even for models we haven’t yet thought of!
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Outline
1 Introduction
2 Different types of new physics
3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation
4 Conclusions
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation SUSY and the MSSM
Big question: Why is there a Higgs scalar, why is it light? Answer: SUSY needs scalars, protects their masses, can even generate Higgs potential
free parameters: p˜ masses and mixings, hH i tan β = 2 → structure of EWSB hH1i µ = H2 − H1 transition → SUSY parameter, much discussed
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation g − 2 and SUSY
g − 2 = chirality-flipping interaction
aµ ν µ¯Lσµνq µR mµ
How is this generated in SUSY?
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation g − 2 and SUSY
g − 2 = chirality-flipping interaction
aµ ν µ¯Lσµνq µR mµ
How is this generated in SUSY?
chiral symmetry broken by λµ and mµ = λµhH1i
hH2i two Higgs doublets: tan β = , µ = H2 − H1 transition hH1i
⇒ all terms ∝ λµ but two options:
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation g − 2 and SUSY
∝ λµhH1i = mµ
∝ λµ µhH2i = mµ µ tan β
potential enhancement ∝ λµ ∝ tan β = 1 . . . 50 (and ∝sign(µ)) sensitive to muon mass generation mechanism structure of Higgs sector
2 aSUSY ≈ 130 × 10−11 tan β sign(µ) 100GeV µ MSUSY
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation g − 2 and SUSY
∝ hH1i, ⇐ SUSY ↓
∝ λµhH1i = mµ ˜ + + H1 W˜
∝ λµ µhH2i = mµ µ tan β µR ν˜µ µL
potential enhancement ∝ λµ ∝ tan β = 1 . . . 50 (and ∝sign(µ)) sensitive to muon mass generation mechanism structure of Higgs sector
2 aSUSY ≈ 130 × 10−11 tan β sign(µ) 100GeV µ MSUSY
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation g − 2 and SUSY
∝ hH2i, ⇐ SUSY ˜ + ↓ H2 W˜ +
∝ λµhH1i = mµ ˜ + + H1 W˜
∝ λµ µhH2i = mµ µ tan β µR ν˜µ µL
potential enhancement ∝ λµ ∝ tan β = 1 . . . 50 (and ∝sign(µ)) sensitive to muon mass generation mechanism structure of Higgs sector
2 aSUSY ≈ 130 × 10−11 tan β sign(µ) 100GeV µ MSUSY
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation Numerical results
tan β = 10 , µ > 0 800
700 mh = 114 GeV
600 mχ± = 104 GeV
500 (GeV) 0
m 400
300
200
100
0 100 200 300 400 500 600 700 800 900 1000
SPS benchmark points m1/2 (GeV) cf. SUSY without prejudice [Berger, Hewett, Gainer, Rizzo ’08] Constrained MSSM [Ellis, Olive, et al, update K. Olive] SUSY could be the origin of the observed deviation
aµ distinguishes SUSY models central, complementary in global analyses of SUSY parameters
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation Numerical results
tan β = 10 , µ > 0 800
700 mh = 114 GeV
600 mχ± = 104 GeV
500 (GeV) 0
m 400 new exp.
300
200
100
0 100 200 300 400 500 600 700 800 900 1000
SPS benchmark points m1/2 (GeV) cf. SUSY without prejudice [Berger, Hewett, Gainer, Rizzo ’08] Constrained MSSM [Ellis, Olive, et al, update K. Olive] SUSY could be the origin of the observed deviation
aµ distinguishes SUSY models central, complementary in global analyses of SUSY parameters
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation SUSY parameter measurements in the LHC era
aµ will remain central, complementary in SUSY parameter analyses a -predictions differ! Sfitter-analysis for µ global fit to LHC-data: degenerate χ2 minima for
[Sfitter: Adam, Kneur, Lafaye, Plehn, Rauch, Zerwas ’10] (µ, M1, M2) ≈ (+400, 200, 100) (−400, 200, 100) (+100, 400, 200) . . . aµ breaks degeneracies
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation SUSY parameter measurements in the LHC era
aµ will remain central, complementary in SUSY parameter analyses Measure tan β (case SPS1a) Sfitter-analysis for global fit to LHC-data: bad precision for tan β!
[Sfitter: Lafaye, Plehn, Rauch, Zerwas ’08] (tan β)LHC,masses = 10 ± 4.5 aµ improves precision: 2-fold (current g − 2) 4-fold (future g − 2) [Hertzog, Miller, de Rafael, Roberts, DS ’07]
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination SUSY could explain the deviation SUSY parameter measurements in the LHC era
aµ will remain central, complementary in SUSY parameter analyses Measure tan β (case SPS1a) Why important? tan β = v2 central for v1 understanding EWSB, mass generation we will want many measurements!
[Hertzog, Miller, de Rafael, Roberts, DS ’07]
MW vision: test universality of tan β, like for cos θW = in the SM: MZ aµ LHC,masses H b (tβ) = (tβ) = (tβ) = (tβ) ?
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Littlest Higgs (T-parity) cannot explain the deviation Littlest Higgs (with T-parity)
Big question: Why is the Higgs light? ≈10 TeV strong dyn. Answer: it’s a Pseudo Goldstone Boson! [Georgi; Arkani-Hamed,Cohen,Georgi] Concrete LHT model: [Cheng, Low ’03] [Hubisz, Meade, Noble, Perelstein ’06] ≈1 TeV
Bosonic SUSY! states WH , lH . . . partner states, same spin cancel quadratic div.s T-parity⇒lightest partner ≈250 GeV stable SM, Higgs
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Littlest Higgs (T-parity) cannot explain the deviation g − 2 in LHT
2 a ∝ α mµ µ 4π f
MWH = (f /v)MW
no enhancement factor exists ⇒ prediction [Blanke, Buras, et al ’07]
LHT −11 aµ < 12 × 10
Clear-cut prediction, sharp distinction from SUSY possible
[Blanke, Buras, et al ’07]
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation Randall-Sundrum models
17 Big question: Where does the hierarchy MPl : MW ∼ 10 come from? Answer: beautifully explained by warp factor e−kL
TeV-scale determined by:
coupling k/MPl −kL scale Λπ = e MPl
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation Randall-Sundrum models
17 Big question: Where does the hierarchy MPl : MW ∼ 10 come from? Answer: beautifully explained by warp factor e−kL
TeV-scale determined by:
coupling k/MPl −kL scale Λπ = e MPl
Gravity propagates in extra dimension
→ KK-Gravitons mn ∼ 0.76(1 + 4n) × (coupling) × (scaleΛπ)
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation g − 2 and Randall-Sundrum models
Gravity propagates in extra dimension
µR KK-Graviton µL
each KK-Graviton contributes equally, weakly, no decoupling!
theory breaks down at scale ∼ Λπ, nc KK-gravitons up to that scale 2 RS 5nc mµ → aµ ∼ 2 2 16π Λπ
potential enhancement ∝ nc = O(1 . . . 100 ∼ 1/coupling) feels all KK-gravitons very sensitive to UV-completion of theory
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics aµ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation g − 2 and Randall-Sundrum models
Complementarity: LHC lowest KK-gravitons determines model parameters
aµ tells us what the cutoff is hint to full 5-dim dynamics guides model building of [Kim, Kim, Song’01] full theory
potential enhancement ∝ nc = O(1 . . . 100 ∼ 1/coupling) feels all KK-gravitons very sensitive to UV-completion of theory
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Conclusions Outline
1 Introduction
2 Different types of new physics
3 aµ, parameter measurements and model discrimination SUSY could explain the deviation Littlest Higgs (T-parity) cannot explain the deviation Randall-Sundrum models could explain the deviation
4 Conclusions
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics Conclusions Conclusions
Big questions of TeV-scale (EWSB) motivate radically new ideas
N.P. −11 aµ very model-dependent, typically O(10 . . . 500) × 10 Today: e.g. SUSY fits well, aµ is central in global analyses
−11 Measurement of aµ, in particular if improved to ±16 × 10 , can sharply distinguish models exclude some models, pin down important details of others
Understanding TeV-scale phenomena discovered at the LHC/Tevatron requires input from complementary experiments. aµ will provide critical input and sharp constraints and will help in establishing a New Standard Model.
Dominik Stöckinger Magnetic moment (g − 2)µ and new physics