Theory predictions for the muon (g 2): Status and Perspectives

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1 Theory predictions for the muon (g 2): Status and Perspectives Matthias Steinhauser Mass 2018, Odense, May 29 June 1, 2018 TTP KARLSRUHE KIT University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association

2 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Outline Introduction Contributions to (g 2) µ Future improvements New Physics

3 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, g 2 µ = g µ e 2m µc S a µ = (g 2)µ 2 Dirac: a µ = 0, g µ = 2 QED: a µ = α 2π +... Photon-muon vertex γ µ F 1 (q 2 ) + i σµν 2m q νf 2 (q 2 ) F 1 (0) = 1 F 2 (0) = a µ aµ SM = aµ QED + aµ weak + aµ HVP + aµ Hlbl

4 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, g 2 µ = g µ e 2m µc S a µ = (g 2)µ 2 Dirac: a µ = 0, g µ = 2 QED: a µ = α 2π +... Photon-muon vertex γ µ F 1 (q 2 ) + i σµν 2m q νf 2 (q 2 ) F 1 (0) = 1 F 2 (0) = a µ a µ = a QED µ + a weak µ + a HVP µ + a Hlbl µ + a NP µ (?)

5 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Theory and experiment electron a exp e = (28) [Hanneke,Hoogerheide,Gabrielse 11] ae th = (23)(16)(763) [Laporta 17] extract α muon aµ exp = (6.3) [BNL] aµ th = (3.56) [Keshavarzi,Nomura,Teubner 18] long-standing 3-4 σ discrepancy theory prediction wrong? measurement wrong? uncertainties underestimated? New Physics?... note: (g 2) µ is among the most precisely measured quantities! new experiments: Fermilab, J-PARC: 4 better precision up to 10 σ discrepancy!?

6 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Contributions to (g 2) µ (SM) numbers from: [Keshavarzi,Nomura,Teubner 18] QED ±0.007 electroweak corrections ±0.10 hadronic vacuum polarization ±2.42 hadronic light-by-light 9.8 ±2.6

7 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, QED muon g 2 [Schwinger 48] [Petermann 57; Sommerfield 58] [Laporta,Remiddi 96;... ; Passera 06] [Laporta 93;Kinoshita,Nio 06; Aoyama,Hayakawa,Kinoshita,Nio 07 08; Kurz,Marquard,Liu,Steinhauser 14; Kurz,Marquard,Liu,Smirnov,Smirnov,Steinhauser 15 16; Volkov 17; Laporta 17; vac.pol.: Baikov,Broadhurst 95] [Aoyama,Hayakawa,Kinoshita,Nio 12; vac.pol.: Baikov,Maier,Marquard 13]

8 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, QED muon g α π ( e ) α2 π 2 ( e ) α3 π 3 ( e ) α4 π 4 (9.168(571) (87) e ) α5 π 5

9 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, QED muon g α π ( e ) α2 π 2 ( e ) α3 π 3 a µ (exp) a µ (SM) a HVP µ a Hlbl µ ( e ) α4 π 4 (9.168(571) (87) e ) α5 π

10 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, e loops I(a) I(b) I(c) I(d) II(a) II(b) II(c) III IV(d) large logarithms log(m µ /m e ) approaches: 1. purely numerical calculation [Kinoshita et al. 04; Aoyama et al. 12] 2. (semi-)analytic expressions; asymptotic expansion in m e /m µ [Laporta 93;... ; Kurz,Marquard,Liu,Smirnov,Smirnov,Steinhauser 15 16] all contributions checked IV(a) IV(b) IV(c)

11 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, (g 2) µ : results A (8) 2 (e) [Kurz,Marquard,Liu,Smirnov, [Kinoshita et al.] Smirnov,Steinhauser 15 16] I(a0) ± I(a1) ± I(a2) ± I(a) ± I(bc0) ± ± I(bc1) ± ± I(bc2) ± ± I(bc) ± ± I(d) ± ± II(a) ± II(bc0) ± II(bc1) ± ± II(bc) ± ± III ± ± IV(a0) ± ± IV(a1) 2.69 ± ± IV(a2) 4.33 ± ± IV(a) ± ± IV(b) 0.38 ± ± IV(c) 2.94 ± ± IV(d) 4.32 ± ±

12 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, (g 2) µ : results A (8) 2 (e) [Kurz,Marquard,Liu,Smirnov, [Kinoshita et al.] Smirnov,Steinhauser 15 16] I(a0) ± I(a1) ± I(a) I(b) I(c) I(a2) ± I(d) II(a) II(b) II(c) I(a) ± I(bc0) ± ± I(bc1) ± ± I(bc2) ± ± I(bc) ± III IV(a) ± IV(b) IV(c) IV(d) V I(d) ± ± II(a) ± II(bc0) ± II(bc1) ± ± II(bc) ± ± III ± ± IV(a0) ± ± IV(a1) 2.69 ± ± IV(a2) 4.33 ± ± IV(a) ± ± IV(b) 0.38 ± ± IV(c) 2.94 ± ± IV(d) 4.32 ± ±

13 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, τ loops: ( α π ) 4 m 2 µ m 2 τ ( ) α 5 π 1. purely numerical calculation [Kinoshita et al. 04; Aoyama et al. 12] 2. asymptotic expansion in m µ /m τ fast convergence [Laporta,Remiddi 92;... ; Kurz,Marquard,Liu,Smirnov,Smirnov,Steinhauser 14]

14 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Highlight of the year 2017: [Laporta 17] Semi-analytic calculation of 4-loop coefficient a µ = α ( α ) 4 2π + + c π c 4 = T 0 + T 2 + T 3 + T 4 + T 5 + T 6 + T (V 4a + V 6a ) + V 6b + V 7b + W 6b + W 7b + 3 (E 4a + E 5a + E 6a + E 7a ) + E 6b + E 7b + U finalizing a 20-year effort high-precision (O(1000) digits) numerical result fit to analytic expressions (PSLQ)

15 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, (g 2) µ : photonic contr. and µ loops [Marquard,Smirnov,Smirnov, Steinhauser,Wellmann 17] [Aoyama,Hayakawa, Kinoshita,Nio 12] ± ± ± ± ± ± ± ± ± ±

16 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, (g 2) µ : photonic contr. and µ loops [Marquard,Smirnov,Smirnov, [Laporta 17] [Aoyama,Hayakawa, Steinhauser,Wellmann 17] Kinoshita,Nio 12] ± ± ± ± ± ± ± ± ± ±

17 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, (g 2) µ : photonic contr. and µ loops [Marquard,Smirnov,Smirnov, [Laporta 17] [Aoyama,Hayakawa, Steinhauser,Wellmann 17] Kinoshita,Nio 12] ± ± ± ± ± ± ± ± ± ± ± ±

18 III IV(a) IV(b) IV(c) IV(d) V Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, loop QED contribution a (8) µ = (α/π) (60)(e ) (12)(τ) (4)(e + τ) [Calmet et al. 75; Chlouber et al 77; Aoyama et al. 12; Kurz et al ; Laporta 17] group µ and e µ and τ µ, e and τ I(a) (42) (0) (0) I(b) (71) (0) (0) I(c) (40) (0) (0) I(d) (37) (0) 0 II(a) (38) (1) 0 II(b) (30) (0) (1) II(c) (83) (1) (2) III (27) (14) 0 IV(a) (44) (11) (36) IV(b) (37) (31) 0 IV(c) (44) (11) 0 IV(d) (58) (37) 0 cross-check completed I(a) I(b) I(c) I(d) II(a) II(b) II(c)

19 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Electroweak corrections a weak 1l µ = ± loops: [Fujikawa et al. 72; Jackiw et al. 72; Altarelli et al. 72; Bars et al. 72; Bardeen et al. 72] a weak µ = ± estimate 3 loops: a weak 3l µ = ± [Czarnecki,Krause,Marciano 95; Peris,Perrottet,de Rafael 95; Degrassi,Giudice 98; Knecht,Peris,Perrottet,de Rafael 02; Czarnecki,Marciano,Vainshtein 03; Gnendiger,Stöckinger,Stöckinger-Kim 13] γ γ γ γ H W µ µ f H γ, Z µ µ f Z γ µ µ µ µ µ Z f γ µ

20 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Hadronic vacuum polarization: LO a HVP LO µ = 1 3 ( α π ) 2 m 2 π ds R(s) s K (1) (s) R(s) = σ(e+ e hadrons) σ pt σ pt = 4πα 2 /(3s) K (1) (s) = 1 0 x 2 (1 x) dx x 2 + (1 x) s mµ 2

21 [Keshavarzi,Nomura,Teubner 18] Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1,

22 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, R data [Jegerlehner 18]

23 R data BESIII (15) KLOE combination CMD-2 (06) SND (04) [Keshavarzi,Nomura,Teubner 18] π a + π - µ (0.6 s 0.9 GeV) = ( ± 1.32) x χ 2 min /d.o.f. = CMD-2 (03) (σ 0 - σ 0 Fit )/σ0 Fit Fit of all π + π - data BaBar (09) σ 0 (e + e - π + π - ) σ 0 (e + e - π + π - ) [nb] s [GeV] 200 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1,

24 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, scan and radiative return 1. e + e hadrons, vary s CMD-2, SND, e + e annihilation with fixed s but: ISR photon dσ(e + e hadr. + γ(isr)) = H(Q 2, θ γ ) dσ(e + e hadr.)(s = Q 2 ) R(s) over wide range of s KLOE, BaBar, BES III,... (more) theory input needed [Czyz,Kühn,Rodrigo,... ]

25 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, R data π + π : several experiments; precise results: O(1%) systematic uncertainty; some tensions

26 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, R data π + π : several experiments; precise results: O(1%) systematic uncertainty; some tensions Fit of all π + π data: ± 1.32 Direct scan only: ± 2.61 KLOE combination: ± 2.15 BaBar (09): ± 2.72 BESIII (15): ± a µ π + π (0.6 s 0.9 GeV) x 10 10

27 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, R data π + π : several experiments; precise results: O(1%) systematic uncertainty; some tensions there are O(20) channels: e + e π + π π + π, π + π π 0 π 0, K + K, KK π,... inclusive data for s > 2 GeV challenge: proper combination of data from different experiments including statistic and systematic uncertainties

28 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a HVP LO µ comparison plot from:[knt:keshavarzi,nomura,teubner 18] [DEHZ:Davier,Eidelman,Höcker,Zhang; HMNT:Hagiwara,Martin,NomuraTeubner; FJ:Jegerlehner; DHMZ:Davier,Höcker,Malaescu,Zhang; JS:Jegerlehner,Szafron; HLMNT:Hagiwara,Liao,Martin,Nomura,Teubner] DEHZ03: ± 7.2 HMNT03: ± 6.4 DEHZ06: ± 4.4 HMNT06: ± 4.6 FJ06: ± 5.6 DHMZ10: ± 4.2 JS11: ± 4.7 HLMNT11: ± 4.3 FJ17: ± 4.1 DHMZ17: ± 3.4 KNT18: ± a µ had, LO VP x 10 10

29 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a HVP LO µ comparison plot from:[knt:keshavarzi,nomura,teubner 18] [DEHZ:Davier,Eidelman,Höcker,Zhang; HMNT:Hagiwara,Martin,NomuraTeubner; FJ:Jegerlehner; DHMZ:Davier,Höcker,Malaescu,Zhang; JS:Jegerlehner,Szafron; HLMNT:Hagiwara,Liao,Martin,Nomura,Teubner] δa HVP LO DEHZ03: ± 7.2 HMNT03: ± 6.4 DEHZ06: ± 4.4 µ HMNT06: ± 4.6 FJ06: ± 5.6 DHMZ10: ± 4.2 JS11: ± 4.7 HLMNT11: ± 4.3 FJ17: ± 4.1 DHMZ17: ± 3.4 KNT18: ± a µ had, LO VP x 10 10

30 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a HVP LO µ comparison plot from:[knt:keshavarzi,nomura,teubner 18] [DEHZ:Davier,Eidelman,Höcker,Zhang; HMNT:Hagiwara,Martin,NomuraTeubner; FJ:Jegerlehner; DHMZ:Davier,Höcker,Malaescu,Zhang; JS:Jegerlehner,Szafron; HLMNT:Hagiwara,Liao,Martin,Nomura,Teubner] DEHZ03: ± 7.2 HMNT03: ± 6.4 channel KNT18 DHMZ17 DEHZ06: ± 4.4 difference π + π δa HVP LO ± HMNT06: ± 4.6 µ ± ± 3.24 π + π π ± ± ± 1.70 FJ06: ± 5.6 [...] 1.8 s 3.7 GeV ± 0.56 (data) DHMZ10: ± (pqcd) ± 4.2 JS11: ± 4.7 HLMNT11: ± 4.3 FJ17: ± 4.1 DHMZ17: ± 3.4 KNT18: ± ± a µ had, LO VP x 10 10

31 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Hadronic vacuum polarization: lattice N f = [Jegerlehner 18] RBC/UKQCD ± 2.67 RBC/UKQCD ± BMW ± 19 HPQCD ± 13 ETM ± 29 N f = RBC/UKQCD ± 46 Aubin+Blum ± 21 Aubin+Blum ± 15 N f = 2 Mainz/CLS ± 38 Mainz/CLS ± 64 ETM ± 16 FJ17 e + e &τ ± 3.4 HLMNT11 e + e ± 3.7 BDDJ15 HLS fit ± 3.2 DHMZ16 e + e ± 4.2 DHMZ16 e + e &τ ± 4.6 HPV adjusted a NP µ = ± a HVP µ 10 10

32 Hadronic vacuum polarization: NLO and NNLO Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, compute higher order corrections to kernel K use same data [R(s)] as at LO

33 Hadronic vacuum polarization: NLO and NNLO Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1,

34 Hadronic vacuum polarization: NLO and NNLO Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a had NLO µ = 9.82 ± a had NNLO µ = 1.24 ± NLO: [Krause 97;... ; Keshavarzi,Nomura,Teubner 18] NNLO: [Kurz,Liu,Marquard,Steinhauser 14]

35 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Hadronic light-by-light I. model-dependent approaches exchanges and loops of π 0, K,... constraints from ChPT and experimental data (hadron-photon proceses, decays, from factors,... ) problem: 4-point function! separation of high and low energies problematic

36 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Hadronic light-by-light I. model-dependent approaches exchanges and loops of π 0, K,... constraints from ChPT and experimental data (hadron-photon proceses, decays, from factors,... ) problem: 4-point function! separation of high and low energies problematic k = p p = π π 0, η, η Exchanges of other resonances (a 1, f 0,...) + Q from:[nyfeller 17] +... µ (p) µ (p ) Contribution HKS BPP KN02 MV04 PdeRV09 N09, JN09 π 0, η, η 8.27 ± ± ± ± ± ± 1.6 axial vectors 0.17 ± ± ± ± ± 0.5 scalars 0.68 ± ± ± 0.2 π, K loops 0.45 ± ± ± ± 1.3 π,k loops +subl. N C 0 ± 1.0 quark loops 0.97 ± ± (c-quark) 2.1 ± 0.3 total 8.96 ± ± ± ± ± ± 3.9 [HKS: Hayakawa,Kinoshita,Sanda 95; Hayakawa,Kinoshita 98; BPP: Bijnens,Pallante,Prades ; KN02: Knecht,Nyffeler 02; MV04: Melnikov,Vainshtein 04; PdeRV09: Prades,de Rafael,Vainshtein 09; N09: Nyffeler 09; JN09: Jegerlehner,Nyffeler 09]

37 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Hadronic light-by-light I. model-dependent approaches a Hlbl µ = 9.8 ± no systematic uncertainty estimate a Hlbl NLO µ = 0.3 ± [Colangelo,Hoferichter,Nyffeler,Passera,Stoffer 14]

38 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Hadronic light-by-light I. model-dependent approaches a Hlbl µ = 9.8 ± no systematic uncertainty estimate a Hlbl NLO µ = 0.3 ± [Colangelo,Hoferichter,Nyffeler,Passera,Stoffer 14] II. model-independent calculations 1. dispersive approach [Colangelo,Hoferichter,Procura,Stoffer ; Pauk,Vanderhaeghen 14] use gauge invariance, crossing symmetry, unitarity, analyticity relate to experimentally accessible quantities example: pion pole: relate to pion transition form factors F γ γ ( ) π 0 [Hoferichter,Hoid,Kubis,Leupold,Schneider 18] 2. lattice [talk by Ruth van de Water]

39 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Contributions to (g 2) µ numbers from: [Keshavarzi,Nomura,Teubner 18] QED ±0.007 electroweak corrections ±0.10 hadronic vacuum polarization ±2.42 hadronic light-by-light 9.8 ±2.6 theory ±3.56 experiment ±6.3 experiment theory: ± σ

40 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, (g 2) µ comparisons DHMZ10 JS11 HLMNT11 FJ17 DHMZ17 KNT18 BNL 3.7σ BNL (x4 accuracy) 7.0σ (a µ SM x )

41 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Perspectives crucial contributions: δa HVP LO µ δa Hlbl µ a HVP LO µ? combination of many data sets true uncertainty of R(s)? data (in)compatibility among different experiments? use of perturbative QCD? radiative corrections for radiative return method new e + e hadrons measurements: π + π from BaBar, CMD-3, BELLE II (?) a HVP LO µ from e µ scattering?

42 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a HVP LO µ from e µ scattering aµ HVP LO ( = 1 α ) 2 3 π mπ 2 [Carloni Calame,Passera,Trentadue,Venanzoni 15; Abbiendi et al. 16] R(s) ds K (1) (s) s aµ HVP LO = α 1 π 0 dx(1 x) α had(t(x)) with t(x) = x 2 m 2 µ/(x 1) < 0 measure effective electromagnetic coupling in the space-like region CERN muon beam M2 with E µ = 150 GeV on a fixed e target δ stat a HVP LO µ 0.3% after 2 years (complicated) radiative corrections needed [Mastrolia,Passera,Primo,Schubert 17]

43 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a HVP LO e µ from e µ scattering µ aµ HVP LO = 1 T 1 3 e e µ e e µ ( α ) 2 π mπ 2 e e R(s) ds T 2 s µ µ µ [Carloni Calame,Passera,Trentadue,Venanzoni 15; Abbiendi et al. 16] e K (1) (s) e e T 3 e e aµ HVP LO = α 1 µ µ π 0 dx(1 x) α µ µ had(t(x)) µ µ with t(x) = x 2 m 2 µ/(x 1) < 0 T 4 T 5 T 6 measure e effectivee e electromagnetic e e coupling e in ethe space-likee region CERN muon beam M2 with E µ = 150 GeV on a fixed e target µ µ µ e µ µ µ µ µ µ δ stat aµ HVP LO T 7 0.3% T 8 after 2 years (complicated) radiative corrections needed T 9 T 10 [Mastrolia,Passera,Primo,Schubert 17]

44 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Perspectives δaµ HVP LO crucial contributions: δaµ Hlbl a HVP LO 10 µ aµ HVP LO from e µ scattering? aµ Hlbl dispersive approach lattice more information from γγ hadrons needed constraints on models 2 complementary future experiments: hot muons at Fermilab vs. ultra cold muons at J-PARK

45 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Perspectives a HVP LO µ a HVP LO µ from e µ scattering? a Hlbl µ dispersive approach lattice more information from γγ hadrons needed constraints on models 2 complementary future experiments: hot muons at Fermilab vs. ultra cold muons at J-PARK?? New Physics??

46 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a µ and SUSY Can SUSY explain a exp µ a SM µ O(25) 10 10? in general one has: a NP µ = C NP m 2 µ M 2 NP tan β ( ) 2 aµ SUSY GeV M SUSY wrong sign! But: all masses equal! [Czarnecki,Marciano 01] see, e.g., [Marchetti,Mertens,Nierste,Stöckinger 09]

47 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a µ and SUSY Can SUSY explain aµ exp aµ SM O(30) 10 10? tan β ( ) 2 aµ SUSY GeV M SUSY wrong sign! But: all masses equal! tan β, general case: [Back,Park,Stöckinger,Stöckinger-Kim 15] C M SUSY,min [TeV] see, e.g., [Marchetti,Mertens,Nierste,Stöckinger 09] M 1 = m R, M 2 = µ, M 2 < a NP µ = C m 2 µ M 2 SUSY,min log 10 [ m L / m R ] log 10 [ µ / m R ]

48 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a µ and MSSM Dark Matter [Cox,Han,Yanagida 18;... ] Xenon1T LZ tanβ=50 LHC(3000 fb -1 ) bino-like LSP bino-wino co-annhilation coloured sparticles decoupled additional Higgs heavy degenerate slepton masses LHC(300 fb -1 ) (g-2)μ LHC(36 fb -1 )

49 a µ and dark photons dark photon A µ coupling to SM: L mix = ε 2 F µν F µν dark photon aµ ε 2 f (m µ /m γ ) [Pospelov 09] discrepancy could be explained for ε and m γ MeV ε KLOE 2015 WASA KLOE 2013 KLOE 2014 BABAR (g-2) ± µ (g-2) e 2σ favored NA48/2 HADES PHENIX A1 APEX BABAR 2014 KLOE 2016 BESIII E E dark [GeV/c ] l+ l m γ' [BES III 17] Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1,

50 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, a µ and BR(µ eγ) [Isidori,Mescia,Paradisi,Temes 07;... ; Kersten,Park,Stöckinger,Velasco-Sevilla 14; Lindner,Platscher,Queiroz 16] 8 a µ and µ eγ have very similar Feynman diagrams MSSM correlation for 2 scenarios BR(µ eγ) BR (μ e γ) [10-13 ] Current Limit Large μ Sweet spot Similar SUSY masses a μ [10-9 ]

51 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, Conclusions QED: OK all 4-loop corrections computed by at least 2 groups weak: OK crucial: hadronic contribution vacuum pol. & light-by-light But: O(3σ) shifts unlikely a SM µ stable for many ( 10) years Many small effects which all push in the same direction? Do we see New Physics? Experimental issue? Wait for the FERMILAB (g 2) µ