Dirac: g = 2 2 + muon anomaly Electromagnetic Lepton Vertex ( - PowerPoint PPT Presentation

The Muon g − 2 : present and future Fred Jegerlehner, DESY Zeuthen/Humboldt University Berlin ✬ ✩ “Strong Coupling Gauge Theories Beyond the Standard Model” (SCGT14mini) March 5 - March 7, 2014 Nagoya University, Nagoya, Japan ✫ ✪ F . Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014

Outline of Talk: ❖ Introduction ❖ Standard Model Prediction for a µ ❖ The hadronic effects and precision limitations ❖ Effective field theory: the Resonance Lagrangian Approach ❖ The hadronic LbL: setup and problems ❖ Theory vs experiment: do we see New Physics? ❖ Future F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 1

Introduction Particle with spin � s ⇒ magnetic moment � µ (internal current circulating) e � � µ = g µ 2 m µ c � g µ = 2 (1 + a µ ) s ; , a µ = α Dirac: g µ = 2 2 π + · · · muon anomaly Electromagnetic Lepton Vertex µ ( p ′ ) γ ( q ) � � γ µ F 1 ( q 2 ) + i σ µν q ν u ( p ′ ) 2 m µ F 2 ( q 2 ) = ( − i e ) ¯ u ( p ) µ ( p ) F 1 (0) = 1 ; F 2 (0) = a µ a µ responsible for the Larmor precession F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 2

ω of beam of spin particles in a homogeneous magnetic field � Larmor precession � B µ ⇒ ⇒ Million Events per 149.2ns ⇒ 10 ⇒ Storage 1 ⇒ Ring -1 ⇒ 10 eB ω a = a µ ⇒ mc -2 ⇒ 10 spin ⇒ momentum ⇒ -3 10 0 20 40 60 80 100 Time modulo 100 s [ s] µ µ ∼ 12 ′ /circle actual precession × 2 ω is directly proportional to � Magic Energy: � B at magic energy ∼ 3.1 GeV � E ∼ 3 . 1 GeV � � � � � a µ � � β × � a µ � ω a = e 1 at ”magic γ ” ≃ e � B − a µ − E B γ 2 − 1 m m CERN, BNL g-2 experiments Stern, Gerlach 22: g e = 2 ; Kusch, Foley 48: g e = 2 (1 . 00119 ± 0 . 00005) F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 3

In a uniform magnetic field, as in muon g − 2 experimental setup: ω a /ω p ω a R a µ = γ ω c = µ µ /µ p − ω a /ω p = λ −R ❒ ω p = ( e / m p c ) � B � free proton NMR frequency ❒ R = ω a /ω p = 0 . 003 707 2063(20) from E-821 ❒ λ = ω L /ω p = µ µ /µ p = from hyperfine splitting of muonium 3 . 18334539(10) value used by E-821 3 . 183345107(84) new value CODATA 2011: [raXiv:1203.5425v1] ⇒ change in a µ : + 1 . 10 × 10 − 10 ✤ ✜ = (11 659 209 . 1 ± 5 . 4 ± 3 . 3[6 . 3]) × 10 − 10 updated a exp µ ✣ ✢ F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 4

Standard Model Prediction for a µ What is new? ● new CODATA values for lepton mass ratios m µ / m e , m µ / m τ ● spectacular progress by Aoyama, Hayakawa, Kinoshita and Nio on 5–loop QED calculation (as well as improved 4–loop results) ❒ O ( α 5 ) electron g − 2 , substantially more precise α ( a e ) ❒ Complete O ( α 5 ) muon g − 2 , settles better the QED part ❒ QED Contribution The QED contribution to a µ has been computed through 5 loops m µ Growing coefficients in the α/π expansion reflect the presence of large ln m e ≃ 5 . 3 terms coming from electron loops. Input: F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 5

a exp = 0 . 001 159 652 180 73(28) Gabrielse et al. 2008 e α − 1 ( a e ) = 137 . 0359991657(331)(68)(46)(24)[0 . 25 ppb] Aoyama et al 2012 a QED [0 . 36] × 10 − 11 = 116 584 718 . 851 (0 . 029) (0 . 009) (0 . 018) (0 . 007) µ � �� �� �� � � �� �� �� � � �� �� �� � � �� �� �� � α inp m e / m µ α 4 α 5 The current uncertainty is well below the ± 60 × 10 − 11 experimental error from E821 a QED C i [ ( α/π ) n ] × 10 11 # n of loops µ 1 +0.5 116140973.289 (43) 2 +0.765 857 426(16) 413217.628 (9) 3 +24.050 509 88(32) 30141.9023 (4) 4 +130.8796(63) 381.008 (18) 5 +753.290(1.04) 5.094 (7) tot 116584718.851 (0.036) F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 6

1 diagram Schwinger 1948 ❶ 7 diagrams Peterman 1957, Sommerfield 1957 ❷ ❸ 72 diagrams Lautrup, Peterman, de Rafael 1974, Laporta, Remiddi 1996 ❹ 871 diagrams Kinoshita 1999, Kinoshita, Nio 2004, Ayoama et al. 2009/2012 ❺ estimates of leading terms Karshenboim 93, Czarnecki, Marciano 00, Kinoshita, Nio 05 ❏ all 12672 diagrams (fully automated numerical) Ayoama et al. 2012 F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 7

❒ Weak contributions Brodsky, Sullivan 67, ..., Bardeen, Gastmans, Lautrup 72 Higgs contribution tiny! W W a weak(1) = (194 . 82 ± 0 . 02) × 10 − 11 + + µ ν µ Z H Kukhto et al 92 π ln MZ α potentially large terms ∼ G F m 2 µ m µ e , u , d , · · · W W Peris, Perrottet, de Rafael 95 µ µ ν µ ν µ γ • • Z quark-lepton (triangle anomaly) cancellation + + + · · · γ µ Z W Czarnecki, Krause, Marciano 96 Heinemeyer, St¨ ockinger, Weiglein 04, Gribouk, Czarnecki 05 full 2–loop result Most recent evaluations: improved hadronic part (beyond QPM) a weak = (154 . 0 ± 1 . 0[had] ± 0 . 3[m H , m t , 3 − loop]) × 10 − 11 new: m H known! µ (Knecht, Peris, Perrottet, de Rafael 02, Czarnecki, Marciano, Vainshtein 02, FJ 12, Gnendiger, St¨ ockinger, St¨ ockinger-Kim 13) F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 8

❒ Hadronic stuff: the limitation to theory General problem in electroweak precision physics: contributions from hadrons (quark loops) at low energy scales Leptons Quarks g e, µ, τ < α : weak coupling u, d, s, · · · < pQED ✓ γ γ γ γ γ > > α s : strong coupling ✗ pQCD (a) (b) (c) u , d , · · · u , d , · · · µ µ γ γ γ γ Z • • + + + · · · γ γ ( Z ) µ µ (a) Hadronic vacuum polarization O ( α 2 ) , O ( α 3 ) Light quark loops (b) Hadronic light-by-light scattering O ( α 3 ) ↓ (c) Hadronic effects in 2-loop EWRC O ( α G F m 2 µ ) Hadronic “blobs” F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 9

� ❒ Evaluation of a had µ � � � � Leading non-perturbative hadronic contributions a had � � can be obtained in terms of µ R γ ( s ) ≡ σ (0) ( e + e − → γ ∗ → hadrons) / 4 πα 2 3 s data via dispersion integral: E 2 ∞ cut ds R pQCD ( s ) ˆ R data ( s ) ˆ � � K ( s ) � α m µ K ( s ) � 2 � � γ γ a had = ds + µ 3 π s 2 s 2 4 m 2 E 2 π cut ● Experimental error implies theoretical uncertainty! ● Low energy contributions enhanced: ∼ 75% come from region 4 m 2 π < m 2 ππ < M 2 Φ Data: CMD-2, SND, KLOE, BaBar a had(1) = (690 . 7 ± 4 . 7)[695 . 5 ± 4 . 1] 10 − 10 µ e + e − –data based [incl. BaBar MD09] 1.0 GeV ρ, ω ρ, ω 0.0 GeV, ∞ 0.0 GeV, ∞ Υ 3.1 GeV 9.5 GeV ψ 3.1 GeV 2.0 GeV 2.0 GeV φ, . . . φ, . . . 1.0 GeV F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 10

γ hard e + γ φ π + π − , ρ 0 hadrons e − φ ; s ′ = s (1 − k ) , k = E γ /E beam s = M 2 a) b) a) Radiative return, b) Standard energy scan. ❖ Good old idea: use isospin symmetry to include existing high quality τ –data (including isospin corrections) u, ¯ e + ¯ d γ γ π + π − , · · · [ I = 1] e − u, d ⇑ isospin rotation ⇓ u ¯ τ − W W π 0 π − , · · · ν µ ¯ d Corrected data: large discrepancy [ ∼ 10%] persists! τ vs. e + e − problem! [manifest since 2002] F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 11

Recent: τ (charged channel) vs. e + e − (neutral channel) puzzle resolved F.J.& R. Szafron, ρ − γ interference (absent in charged channel): − i Π µν ( π ) ( q ) = + . γρ ✛ ✘ � 0 ( s ) = r ργ ( s ) R IB ( s ) � − ( s ) ✚ ✙ ❒ τ require to be corrected for missing ρ − γ mixing! ❒ results obtained from e + e − data is what goes into a µ ❒ off-resonance tiny for ω, φ in ππ channel (scaled up Γ V / Γ ( V → ππ ) F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 12

τ decays ALEPH 1997 390 . 75 ± 2 . 65 ± 1 . 94 388 . 74 ± 4 . 00 ± 2 . 07 ALEPH 2005 380 . 25 ± 7 . 27 ± 5 . 06 OPAL 1999 391 . 59 ± 4 . 11 ± 6 . 27 CLEO 2000 394 . 67 ± 0 . 53 ± 3 . 66 Belle 2008 391 . 06 ± 1 . 42 ± 2 . 06 τ combined e + e − +CVC 386 . 58 ± 2 . 76 ± 2 . 59 CMD-2 2006 383 . 99 ± 1 . 40 ± 4 . 99 SND 2006 380 . 21 ± 0 . 34 ± 3 . 27 KLOE 2008 377 . 35 ± 0 . 71 ± 3 . 50 KLOE 2010 389 . 35 ± 0 . 37 ± 2 . 00 BABAR 2009 e + e − combined 385 . 12 ± 0 . 87 ± 2 . 18 a µ [ ππ ] , I = 1 , (0 . 592 − 0 . 975) GeV 380 390 400 × 10 − 10 I=1 part of a had µ [ ππ ] F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 13

τ decays ALEPH 1997 385 . 63 ± 2 . 65 ± 1 . 94 383 . 54 ± 4 . 00 ± 2 . 07 ALEPH 2005 375 . 39 ± 7 . 27 ± 5 . 06 OPAL 1999 386 . 61 ± 4 . 11 ± 6 . 27 CLEO 2000 389 . 62 ± 0 . 53 ± 3 . 66 Belle 2008 385 . 96 ± 1 . 40 ± 2 . 10 τ combined e + e − +CVC 386 . 58 ± 2 . 76 ± 2 . 59 CMD-2 2006 383 . 99 ± 1 . 40 ± 4 . 99 SND 2006 380 . 21 ± 0 . 34 ± 3 . 27 KLOE 2008 377 . 35 ± 0 . 71 ± 3 . 50 KLOE 2010 389 . 35 ± 0 . 37 ± 2 . 00 BABAR 2009 e + e − combined 385 . 12 ± 0 . 87 ± 2 . 18 a µ [ ππ ] , I = 1 , (0 . 592 − 0 . 975) GeV 380 390 400 × 10 − 10 I=1 part of a had µ [ ππ ] F. Jegerlehner SCGT14Mini, Nagoya, Japan , March 5 - March 7, 2014 14