Magnetic moment (g 2) µ and new physics

Transcription

1 Dresden Lepton Moments, July 2010

2 Introduction A 3σ deviation for a exp µ a SM µ has been established! Currently: a exp µ a SM µ = (255 ± 63 ± 49) Expected with new Fermilab exp. (and th. progress): a exp µ a SM µ = (?? ± 16 ± 30) Which types of physics beyond the SM could explain this? What is the impact of a µ on physics beyond the SM?

3 Outline 1 Introduction 2 Different types of new physics 3 a µ, 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

4 Outline Introduction 1 Introduction 2 Different types of new physics 3 a µ, 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

5 Introduction Muon magnetic moment Quantum field theory: Operator: a µ m µ µ L σ µν q ν µ R CP-, Flavour-conserving, chirality-flipping, loop-induced Heavy particles contribute Sensitive to all SM interactions ( mµ M heavy ) 2 Sensitive to TeV-scale new physics in a unique way

6 Why new physics? Big questions Introduction EWSB, Higgs, mass generation? hierarchy M Pl /M W? Naturalness? Unification of the Coupling Constants in the SM and the minimal MSSM 1/α i /α i /α 1 MSSM /α dark matter? /α log Q Grand Unification? log Q... point to the TeV scale... and to new physics

7 Why new physics? Big questions Introduction EWSB, Higgs, mass generation? hierarchy M Pl /M W? Naturalness? Unification of the Coupling Constants in the SM and the minimal MSSM 1/α i /α i /α 1 MSSM /α dark matter? /α log Q Grand Unification? log Q Tevatron, LHC = era of TeV-scale physics Quest: discover new physics, solve big questions, understand EWSB

8 Introduction Why new physics? Big questions motivate radically new ideas How can EWSB, light Higgs, M Pl /M W be natural? Supersymmetry? Fermi-Bose symmetry 10 TeV strong dyn. 1 TeV states WH, lh GeV SM, Higgs Little Higgs? Higgs=Pseudo Goldstone Boson Randall-Sundrum? Warped extra dim.

9 Why new physics? Introduction Big questions motivate radically new ideas How can EWSB, light Higgs, M Pl /M W be natural? Supersymmetry? Fermi-Bose symmetry 10 TeV strong dyn. 1 TeV states WH, lh GeV SM, Higgs Little Higgs? Higgs=Pseudo Goldstone Boson Randall-Sundrum? Warped extra dim. all these models predict a µ and are constrained by it

10 Outline Different types of new physics 1 Introduction 2 Different types of new physics 3 a µ, 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

11 Different types of new physics Theory: g 2 and chirality flips g 2 = chirality-flipping interaction µ R µ L m µ = chirality-flipping interaction as well µ R µ L are the two related?

12 Different types of new physics Theory: g 2 and chirality flips g 2 = chirality-flipping interaction µ R µ L m µ = chirality-flipping interaction as well µ R µ L are the two related? New physics loop contributions to a µ, m µ related by chiral symmetry! [Czarnecki, Marciano 01] generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ

13 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate)

14 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate) C = O( α 4π ), Z, W, UED, Littlest Higgs (LHT)... (UED, LHT can mimic SUSY at the LHC) δa µ for M < 100GeV very small!

15 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate) C = O( α 4π ), Z, W, UED, Littlest Higgs (LHT)... (UED, LHT can mimic SUSY at the LHC) δa µ for M < 100GeV very small! such models already disfavoured by a µ, ruled out if deviation persists in new exp.

16 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate) C = O(1), radiative muon mass generation technicolor,... [Czarnecki,Marciano 01] δa µ for M > 1TeV can be large!

17 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate) C = O(1), radiative muon mass generation technicolor,... [Czarnecki,Marciano 01] δa µ for M > 1TeV can be large! lower mass bounds from a µ

18 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate) C = O(tan β α ), supersymmetry 4π C = O(n c 1 16π 2), extra dimensions (Randall/Sundrum) [Davoudiasl, Hewett, Rizzo 00] large ED, unparticles,... [Park et al 01] [Kim et al 01] [Graesser, 00] [Cheung, Keung, Yuan 07] δa µ >, <, possible can fit well!

19 Different types of new physics Classification of new physics generally: δa µ (N.P.) = O(C) ( mµ ) 2 δm µ (N.P.), C = M m µ Allows to classify new physics: C = O( α 4π ), O(1), O(intermediate) C = O(tan β α ), supersymmetry 4π C = O(n c 1 16π 2), extra dimensions (Randall/Sundrum) [Davoudiasl, Hewett, Rizzo 00] large ED, unparticles,... [Park et al 01] [Kim et al 01] [Graesser, 00] [Cheung, Keung, Yuan 07] δa µ >, <, possible can fit well! strong constraints on model parameters and model building

20 Different types of new physics g 2 and new physics Different types of new physics can lead to very different contributions to a µ SUSY, RS, ADD,... : constrain parameters Z, UED, LHT,... : ruled out if deviation confirmed a µ can sharply distinguish between different types of new physics

21 Different types of new physics g 2 and new physics Different types of new physics can lead to very different contributions to a µ SUSY, RS, ADD,... : constrain parameters Z, UED, LHT,... : ruled out if deviation confirmed a µ can sharply distinguish between different types of new physics This will be even more the case with a new, improved measurement!

22 Different types of new physics g 2 and new physics Different types of new physics can lead to very different contributions to a µ SUSY, RS, ADD,... : constrain parameters Z, UED, LHT,... : ruled out if deviation confirmed a µ can sharply distinguish between different types of new physics And even for models we haven t yet thought of!

23 a µ, parameter measurements and model discrimination Outline 1 Introduction 2 Different types of new physics 3 a µ, 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

24 a µ, parameter measurements and model discrimination SUSY and the MSSM SUSY could explain the deviation 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, tan β = H 2 H 1 structure of EWSB µ = H 2 H 1 transition SUSY parameter, much discussed

25 a µ, parameter measurements and model discrimination g 2 and SUSY SUSY could explain the deviation g 2 = chirality-flipping interaction How is this generated in SUSY? a µ m µ µ L σ µν q ν µ R

26 a µ, parameter measurements and model discrimination g 2 and SUSY SUSY could explain the deviation g 2 = chirality-flipping interaction How is this generated in SUSY? a µ m µ µ L σ µν q ν µ R chiral symmetry broken by λ µ and m µ = λ µ H 1 two Higgs doublets: tan β = H 2 H 1, µ = H 2 H 1 transition all terms λ µ but two options:

27 a µ, parameter measurements and model discrimination SUSY could explain the deviation g 2 and SUSY λ µ H 1 = m µ λ µ µ H 2 = m µ µ tanβ potential enhancement λ µ tanβ = (and sign(µ)) sensitive to muon mass generation mechanism structure of Higgs sector ( ) 2 a SUSY µ tan β sign(µ) 100GeV M SUSY

28 a µ, parameter measurements and model discrimination SUSY could explain the deviation g 2 and SUSY H 1, SUSY λ µ H 1 = m µ H + 1 W + λ µ µ H 2 = m µ µ tanβ µ R ν µ µ L potential enhancement λ µ tanβ = (and sign(µ)) sensitive to muon mass generation mechanism structure of Higgs sector ( ) 2 a SUSY µ tan β sign(µ) 100GeV M SUSY

29 a µ, parameter measurements and model discrimination g 2 and SUSY SUSY could explain the deviation H 2, SUSY H + 2 W + λ µ H 1 = m µ λ µ µ H 2 = m µ µ tanβ H + 1 W + µ R ν µ µ L potential enhancement λ µ tanβ = (and sign(µ)) sensitive to muon mass generation mechanism structure of Higgs sector ( ) 2 a SUSY µ tan β sign(µ) 100GeV M SUSY

30 a µ, parameter measurements and model discrimination Numerical results SUSY could explain the deviation m h = 114 GeV tan β = 10, µ > 0 m 0 (GeV) mχ± = 104 GeV SPS benchmark points m 1/2 (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 a µ distinguishes SUSY models central, complementary in global analyses of SUSY parameters

31 a µ, parameter measurements and model discrimination Numerical results SUSY could explain the deviation 800 tan β = 10, µ > 0 m 0 (GeV) mχ± = 104 GeV m h = 114 GeV new exp SPS benchmark points m 1/2 (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 a µ distinguishes SUSY models central, complementary in global analyses of SUSY parameters

32 a µ, parameter measurements and model discrimination SUSY could explain the deviation SUSY parameter measurements in the LHC era a µ will remain central, complementary in SUSY parameter analyses Sfitter-analysis for global fit to LHC-data: degenerate χ 2 minima for [Sfitter: Adam, Kneur, Lafaye, Plehn, Rauch, Zerwas 10] (µ, M 1, M 2 ) (+400, 200, 100) ( 400, 200, 100) (+100, 400, 200)... a µ breaks degeneracies a µ -predictions differ!

33 a µ, parameter measurements and model discrimination SUSY could explain the deviation SUSY parameter measurements in the LHC era a µ will remain central, complementary in SUSY parameter analyses 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 a µ improves precision: 2-fold (current g 2) 4-fold (future g 2) Measure tan β (case SPS1a) [Hertzog, Miller, de Rafael, Roberts, DS 07]

34 a µ, parameter measurements and model discrimination SUSY could explain the deviation SUSY parameter measurements in the LHC era a µ will remain central, complementary in SUSY parameter analyses Why important? tan β = v 2 v 1 central for understanding EWSB, mass generation we will want many measurements! Measure tan β (case SPS1a) [Hertzog, Miller, de Rafael, Roberts, DS 07] vision: test universality of tan β, like for cos θ W = M W MZ in the SM: (t β ) aµ = (t β ) LHC,masses = (t β ) H = (t β ) b?

35 a µ, 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? Answer: it s a Pseudo Goldstone Boson! [Georgi; Arkani-Hamed,Cohen,Georgi] Concrete LHT model: [Cheng, Low 03] [Hubisz, Meade, Noble, Perelstein 06] Bosonic SUSY! partner states, same spin cancel quadratic div.s T-parity lightest partner stable 10 TeV strong dyn. 1 TeV states W H, l H GeV SM, Higgs

36 a µ, parameter measurements and model discrimination g 2 in LHT Littlest Higgs (T-parity) cannot explain the deviation a µ α 4π ( mµ ) 2 f M WH = (f/v)m W no enhancement factor exists prediction [Blanke, Buras, et al 07] a LHT µ < Clear-cut prediction, sharp distinction from SUSY possible [Blanke, Buras, et al 07]

37 a µ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation Randall-Sundrum models Big question: Where does the hierarchy M Pl : M W come from? Answer: beautifully explained by warp factor e kl TeV-scale determined by: coupling k/m Pl scale Λ π = e kl M Pl

38 a µ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation Randall-Sundrum models Big question: Where does the hierarchy M Pl : M W come from? Answer: beautifully explained by warp factor e kl TeV-scale determined by: coupling k/m Pl scale Λ π = e kl M Pl Gravity propagates in extra dimension KK-Gravitons m n 0.76(1 + 4n) (coupling) (scaleλ π )

39 a µ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation g 2 and Randall-Sundrum models Gravity propagates in extra dimension µ R KK-Graviton µ L each KK-Graviton contributes equally, weakly, no decoupling! theory breaks down at scale Λ π, n c KK-gravitons up to that scale a RS µ 5nc 16π 2 m 2 µ Λ 2 π potential enhancement n c = O( /coupling) feels all KK-gravitons very sensitive to UV-completion of theory

40 a µ, parameter measurements and model discrimination Randall-Sundrum models could explain the deviation g 2 and Randall-Sundrum models [Kim, Kim, Song 01] Complementarity: LHC lowest KK-gravitons determines model parameters a µ tells us what the cutoff is hint to full 5-dim dynamics guides model building of full theory potential enhancement n c = O( /coupling) feels all KK-gravitons very sensitive to UV-completion of theory

41 Outline Conclusions 1 Introduction 2 Different types of new physics 3 a µ, 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

42 Conclusions Conclusions Big questions of TeV-scale (EWSB) motivate radically new ideas a N.P. µ very model-dependent, typically O( ) Today: e.g. SUSY fits well, a µ is central in global analyses Measurement of a µ, in particular if improved to ± , 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. a µ will provide critical input and sharp constraints and will help in establishing a New Standard Model.