The muon g-2: what does it tell us?

Transcription

1 The muon g-2: what does it tell us? Fred Jegerlehner Institute of Physics, University of Silesia, Katowice KWW LHC 2009, Warsaw University, May 20, 2010 Abstract On status and prospects of physics of the muon anomalous magnetic moment and its role it may play in the LHC era. Keyword: New Physics Supported by the Foundation for Polish Science On leave from DESY Zeuthen/Humboldt University Berlin F. Jegerlehner KWW LHC 2009, Warsaw, May 2010

2 The muon anomalous magnetic moment 1. a µ what is it? µ = g µ e 2m µ c s ; g µ = 2 (1 + a µ ) Dirac: g µ = 2, a µ muon anomaly Stern, Gerlach 22: g e = 2; Kusch, Foley 48: g e = 2 ( ± ) γ(q) µ(p ) µ(p) = ( ie) ū(p ) [ ] γ µ F 1 (q 2 ) + i σµν q ν 2m µ F 2 (q 2 ) u(p) F 1 (0) = 1 ; F 2 (0) = a µ F. Jegerlehner KWW LHC 2009, Warsaw, May

3 a µ responsible for the Larmor precession ω a = e m [ a µ B ( ) E 3.1GeV a µ 1 β E] γ 2 1 at magic γ directly proportional at magic energy 3.1 GeV e m [ aµ B ] Basic principle of experiment: measure Larmor precession of highly polarized muons circulating in a ring µ CERN, BNL g-2 experiments Storage Ring Note: a µ = 0 would mean no rotation of spin relative to muon momentum! spin momentum ω a = a µ eb mc actual precession 2 Spin precession in the g 2 ring: 12 /circle F. Jegerlehner KWW LHC 2009, Warsaw, May

4 BNL muon storage ring: r= meters, aperture of the beam pipe 90 mm, field 1.45 Tesla, momentum of the muon p µ = GeV/c (see F. Jegerlehner KWW LHC 2009, Warsaw, May

5 F. Jegerlehner KWW LHC 2009, Warsaw, May

6 The role of a µ in precision physics Precision measurement of a µ provides most sensitive test of magnetic helicity flip transition ψ L σ µν F µν ψ R ( dim 5 operator ) such a term must be absent for any fermion in any renormalizable theory at tree level a µ is a pure quantum correction effect: a finite model-specific prediction in any renormalizable quantum field theory (QFT) test of quantum structure monitor for new physics F. Jegerlehner KWW LHC 2009, Warsaw, May

7 Theory vs experiment: do we see New Physics? Contribution Value Error Reference QED incl. 4-loops+LO 5-loops Remiddi, Kinoshita... Leading hadronic vac. pol update Subleading hadronic vac. pol update Hadronic light by light new evaluation (J&N) Weak incl. 2-loops CMV06 Theory Experiment BNL Exp.- The. 3.2 standard deviations Standard model theory and experiment comparison [in units ] F. Jegerlehner KWW LHC 2009, Warsaw, May

8 Hadronic stuff: the limitation to theory (a) µ µ + γ γ(z) (b) γ γ µ (c) u,d, u,d, γ Z + µ γ + (a) Hadronic vacuum polarization O(α 2 ), O(α 3 ) (b) Hadronic light-by-light scattering O(α 3 ) (c) Hadronic effects in 2-loop EWRC O(αG F m 2 µ) Light quark loops Hadronic blob Hadronic vacuum polarization based on e + e annihilation data: (689.4 ± 4.0) [Teubner et al.] (690.3 ± 5.3) [FJ, FJ&Nyffeler] (695.5 ± 4.1) [Davier et al.] F. Jegerlehner KWW LHC 2009, Warsaw, May

9 Differences between experiments [in common range] (examples): 4.8 between KLOE 08 and SND between KLOE 08 and BABAR 09 Recent results for hadronic LbL: (10.5 ± 2.6) PdeRV (11.6 ± 3.9) JN 83(12) (13) (3) π 0, η, η π ±, K ± q = (u, d, s,...) L.D. L.D. S.D. Hadronic light by light scattering is dominated by π 0 exchange in the odd parity F. Jegerlehner KWW LHC 2009, Warsaw, May

10 channel, pion loops etc. at long distances (L.D.) and quark loops incl. hard gluonic corrections at short distances (S.D.) The spectrum of invariant γγ masses obtained with the Crystal Ball detector. The three rather pronounced spikes seen are the γγ pseudoscalar (PS) γγ excitations: PS=π 0, η, η F. Jegerlehner KWW LHC 2009, Warsaw, May

11 Present: a Exp. µ = (63) 10 3 a The. µ = (65) 10 3 δa NP? µ = a Exp. µ a The. µ = (290 ± 90) 10 11, 3.2 σ Uncertainties: experiment 0.54ppm = theory 0.57ppm = What is it? statistical fluctuation of experimental result underestimated systematic error missing higher-order SM contributions underestimated theory error (incl. possible computational) physics beyond SM F. Jegerlehner KWW LHC 2009, Warsaw, May

12 New Physics coniributing to a µ F. Jegerlehner KWW LHC 2009, Warsaw, May

13 New physics typically: a NP µ = C m2 µ M 2 NP where naturally C = O(α/π) ( lowest order a SM µ ); Typical New Physics scales required to satisfy a NP µ = δa µ : C 1 α/π (α/π) 2 M NP TeV GeV GeV Different extensions of the SM yield very different effects in a µ a µ very good monitor to hint and/or constrain possible SM extensions F. Jegerlehner KWW LHC 2009, Warsaw, May

14 ( General: δa NP m 2 ) µ = C µ M 2 C F. Jegerlehner KWW LHC 2009, Warsaw, May

15 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... F. Jegerlehner KWW LHC 2009, Warsaw, May

16 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... very small contributions! δa µ for M < 100 GeV F. Jegerlehner KWW LHC 2009, Warsaw, May

17 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... very small contributions! δa µ for M < 100 GeV new strong interaction C = O(1) technicolor,... Czarnecki, Marciano 01 F. Jegerlehner KWW LHC 2009, Warsaw, May

18 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... very small contributions! δa µ for M < 100 GeV C = O(1) new strong interaction technicolor,... Czarnecki, Marciano 01 large contributions! δa µ for M > 1 TeV F. Jegerlehner KWW LHC 2009, Warsaw, May

19 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... very small contributions! δa µ for M < 100 GeV C = O(1) new strong interaction technicolor,... Czarnecki, Marciano 01 large contributions! δa µ for M > 1 TeV C = O(tan β α 4π ) Supersymmetry, 2HDMs F. Jegerlehner KWW LHC 2009, Warsaw, May

20 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... very small contributions! δa µ for M < 100 GeV new strong interaction C = O(1) technicolor,... Czarnecki, Marciano 01 large contributions! δa µ for M > 1 TeV C = O(tan β α 4π ) Supersymmetry, 2HDMs fits precisely! δa µ for M 300 GeV, tan β 10 F. Jegerlehner KWW LHC 2009, Warsaw, May

21 ( General: δa NP m 2 ) µ = C µ M 2 C a µ very usefull monitor Classification: C = O( α 4π ) Extra Dim.,Z, W,... very small contributions! δa µ for M < 100 GeV new strong interaction C = O(1) technicolor,... Czarnecki, Marciano 01 large contributions! δa µ for M > 1 TeV C = O(tan β α 4π ) Supersymmetry, 2HDMs fits precisely! δa µ for M 300 GeV, tan β 10 Most promising New Physics scenario: SUSY F. Jegerlehner KWW LHC 2009, Warsaw, May

22 Super Symmetric extension of SM: in particular MSSM Need two Higgs doublets! and R party (Z 2 invariance), dark matter candidate. Doubling spectrum of SM plus second Higgs doublet free parameters x masses and mixings, µ and tan β MSSM has particular type of 2HDM Higgs sector: Type II 2HDM share relevant properties for (g µ 2) [Maria Krawczyk] F. Jegerlehner KWW LHC 2009, Warsaw, May

23 a) b) χ χ µ µ ν χ 0 Leading SUSY contributions to g 2 in supersymmetric extension of the SM. m lightest SUSY particle; SUSY requires two Higgs doublets tan β = 1 2, i =< H i > ; i = 1, 2 a SUSY µ sign(µm 2) α(m Z ) 8π sin 2 Θ W ( ) 5 + tan 2 Θ W 6 m 2 µ M 2 SUSY tan β ( 1 4α π ln M ) SUSY m µ F. Jegerlehner KWW LHC 2009, Warsaw, May

24 with M SUSY a typical SUSY loop mass and the sign is determined by the Higgsino mass term µ, RG improved. tan β m t /m b 40 [4 40] There are a lot of SUSY s General MSSM has > 100 free parameters CMSSM constrained and, related but even more constrained MSUGRA, and others These models assume many degeneracies of masses and couplings in order to restrict the number of parameters Typically, m o, m 1/2, sign(µ), tan β, A (or even more) Then there is R parity is sparticle number conserved (dark matter candidate!) F. Jegerlehner KWW LHC 2009, Warsaw, May

25 And, many ways to describe EW symmetry breaking Role for LHC searches: 3 σ deviation in muon g-2 (if real) requires sign(µ) positive and tan β preferable large Note: sign(µ) cannot be obtained from LHC (hadron collider) tan β can t be pinned down by LHC (hadron collider) so muon g-2 important hint for constraining SUSY parameter space (is SUSY) More scenarios: two Higgs doublet models Maria Krawzcyk s field F. Jegerlehner KWW LHC 2009, Warsaw, May

26 tan β enhanced contributions: (2) 2HDM a µ (h) (2) 2HDM a µ (A) 2Gµ m 2 µ tan 2 β m2 µ 4π 2 m 2 h 2Gµ m 2 µ tan 2 β m2 µ 4π 2 m 2 A ln m2 h 7 > 0, m 2 µ 6 ln m2 A m 2 µ < 0. Potentially large 2 loop contributions: Barr-Zee type diagrams: a bos,2l µ (MSSM SM) < , parameter range m A > 50 GeV, tan β < 50. sequential fermions (4th family?) Present bounds m L > 100 GeV heavy lepton, m b > 200 GeV heavy quark. Note a µ (τ) only! Grand Unified Theories: Z, W, leptoquarks etc F. Jegerlehner KWW LHC 2009, Warsaw, May

27 Present bounds M Z,W > GeV depending on the GUT scenario. Essentially rescaling weak SM contribution with (M W /M W ) , i.e., 1% of only, too small to be of relevance. extra dimensions, graviton excitations etc Integrating out the extra coordinates under the hypothesis of factorization one obtains M Pl = M Pl / 8π = ( 8π G N ) 1 = GeV (G N Newton s gravitational constant) from the relation M 2 Pl = M 2+ D V = M 2+ D (2π R) = M 2+ D R. Phenomenology: 1/R is about 300 GeV or larger, contributions to g 2 small, model dependent, towers of Kaluza-Klein excitations: Barbieri, Hall and Nomura (2) KK a µ = g s 2 12c 2 (m µ R) 2 F. Jegerlehner KWW LHC 2009, Warsaw, May

28 numerically, for 1/R = 370 ± 70 GeV, it is given by (2) KK a µ = a(2) EW µ = ( ) Appelquist, Chang and Dobrescu model (universal extra dimension), (2) KK a (2) EW µ = a µ = 53.7[ 24.8] which again for any sensible value of R yields a result well inside the uncertainties of the SM prediction. Little Higgs Models of EW symmetry breaking Contributions at most a LH µ Littlest Higgs model with T-parity a LHT µ < F. Jegerlehner KWW LHC 2009, Warsaw, May

29 Future improvements feasible! Experimental: new proposal for muon g 2 at FNAL The New (g 2) Experiment: A proposal to Measure the Muon Anomalous Magnetic Moment to ±0.14 ppm Precision Present Status: Experimental uncertainty: (0.54 ppm) 0.46 ppm statistical 0.28 ppm systematics Theory uncertainty: (0.44 ppm) Present: δa µ (Exp. The.) = (295 ± 81) F. Jegerlehner KWW LHC 2009, Warsaw, May

30 Experimental situation after new experiment: Experimental uncertainty: (0.14 ppm) 0.10 ppm statistical 0.10 ppm systematics Theory uncertainty: (0.26 ppm) Future: δa µ (Exp. The.) = (xx ± 34) If central values remain as now: present deviation 9σ! If SUSY or 2HDM most sensitive tan β monitor! F. Jegerlehner KWW LHC 2009, Warsaw, May

31 Constrain SUSY/2HDMs constrains general MSSM [Stöckinger 06] F. Jegerlehner KWW LHC 2009, Warsaw, May

32 orthogonal constraints on CMSSM parameters [Olive 09] F. Jegerlehner KWW LHC 2009, Warsaw, May

33 Superconservative bounds regions under the curves excluded by a µ and nothing else [Martin Wells 02] F. Jegerlehner KWW LHC 2009, Warsaw, May

34 Scanning SUSY parameter space selection of Supersymmetric Parameter Spaces [Hertzog, Stöckinger 08] F. Jegerlehner KWW LHC 2009, Warsaw, May

36 tan β measurement [Hertzog, Miller, de Rafael, Roberts, Stöckinger 07; Rauch 08 (Sfitter)] important input for pinning down SUSY parametr space for LHC searches! In conjunction with other SM precision tests: F. Jegerlehner KWW LHC 2009, Warsaw, May

38 Example: SUSY parameter test point SPS1a a µ (SUSY, SPS1a ) = 34.7(3.1) [Stöckinger 06] F. Jegerlehner KWW LHC 2009, Warsaw, May

39 Example: SUSY parameter test point SPS1a a µ (SUSY, SPS1a ) = 34.7(3.1) [Stöckinger 06] a µ (Exp SM) = 29.5(8.8) [Roberts et al. 07] F. Jegerlehner KWW LHC 2009, Warsaw, May

40 Example: SUSY parameter test point SPS1a a µ (SUSY, SPS1a ) = 34.7(3.1) [Stöckinger 06] a µ (Exp SM) = 29.5(8.8) [Roberts et al. 07] M W (SPS1a ) = (18) GeV [Hollik et al. 06] F. Jegerlehner KWW LHC 2009, Warsaw, May

41 Example: SUSY parameter test point SPS1a a µ (SUSY, SPS1a ) = 34.7(3.1) [Stöckinger 06] a µ (Exp SM) = 29.5(8.8) [Roberts et al. 07] M W (SPS1a ) = (18) GeV [Hollik et al. 06] M W (Exp.) = (25) GeV [CDF,LEPEWWG 08] F. Jegerlehner KWW LHC 2009, Warsaw, May

42 SUSY improves agreement with experiment or both observables! Dark Matter: SM 0.00 F. Jegerlehner KWW LHC 2009, Warsaw, May

43 SUSY improves agreement with experiment or both observables! Dark Matter: SM 0.00 SPS1a 0.10 [SPA Report 05] F. Jegerlehner KWW LHC 2009, Warsaw, May

44 SUSY improves agreement with experiment or both observables! Dark Matter: SM 0.00 SPS1a 0.10 [SPA Report 05] Exp. 0.11(1) [WMAP 08] F. Jegerlehner KWW LHC 2009, Warsaw, May

45 The Muon g 2 the closer you look the more there is to see BNL CERN III CERN II CERN I th QED 6th 8th hadronic VP hadronic LBL weak New Physics??? SM precision a µ uncertainty [ppm] History of sensitivity to various contributions The anomalous magnetic moment of the muon by itself a tiny % effect now measured at ! F. Jegerlehner KWW LHC 2009, Warsaw, May

46 Outlook LHC the big challenge ahead! its running! Precision experiments remain an important complement of LHC: a µ maybe the best! this we hope will be realised! Time horizon for next step in imporvement: 10 years Will provide important information on Physics Beyond the SM scenarios! F. Jegerlehner KWW LHC 2009, Warsaw, May

47 Provided deviation is real 3σ 9σ possible? If SUSY: δa µ sign(µ) and tan β If not SUSY or 2HDM may be even more interesting! In any case establishing a new theory replacing SM likely is a long way to go and requires efforts on very different levels So we hope muon (g 2) has a bight future, as we hope for the LHC! All challenging physics for our young colleagues in experiment and theory. F. Jegerlehner KWW LHC 2009, Warsaw, May