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

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 www.kit.edu

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

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 3 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

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 3 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 (?)

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 4 Theory and experiment electron a exp e = 1 159 652 180.73(28) 10 12 [Hanneke,Hoogerheide,Gabrielse 11] ae th = 1 159 652 181.664(23)(16)(763) 10 12 [Laporta 17] extract α muon aµ exp = 11 659 209.1(6.3) 10 10 [BNL] aµ th = 11 659 182.05(3.56) 10 10 [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!?

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 5 Contributions to (g 2) µ (SM) numbers from: [Keshavarzi,Nomura,Teubner 18] 10 10 QED 11658471.8971 ±0.007 electroweak corrections 15.36 ±0.10 hadronic vacuum polarization 684.69 ±2.42 hadronic light-by-light 9.8 ±2.6

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 6 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]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 6 QED muon g 2 0.5 α π ( 0.328... + 1.094... e ) α2 π 2 (1.181... + 22.868... e ) α3 π 3 ( 1.910... + 132.682... e ) α4 π 4 (9.168(571) + 742.18(87) e ) α5 π 5

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 6 QED muon g 2 0.5 α π ( 0.328... + 1.094... e ) α2 π 2 (1.181... + 22.868... e ) α3 π 3 a µ (exp) a µ (SM) 25 10 10 a HVP µ 2.5 4 10 10 a Hlbl µ 2.5 10 10 ( 1.910... + 132.682... e ) α4 π 4 (9.168(571) + 742.18(87) e ) α5 π 5 40 10 10 0.5 10 10

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 7 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 ) 5.3 2 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)

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 8 (g 2) µ : results A (8) 2 (e) [Kurz,Marquard,Liu,Smirnov, [Kinoshita et al.] Smirnov,Steinhauser 15 16] I(a0) 7.223076 7.223077 ± 0.000029 I(a1) 0.494072 0.494075 ± 0.000006 I(a2) 0.027988 0.027988 ± 0.000001 I(a) 7.745136 7.74547 ± 0.00042 I(bc0) 8.56876 ± 0.00001 8.56874 ± 0.00005 I(bc1) 0.1411 ± 0.0060 0.141184 ± 0.000003 I(bc2) 0.4956 ± 0.0004 0.49565 ± 0.00001 I(bc) 9.2054 ± 0.0060 9.20632 ± 0.00071 I(d) 0.2303 ± 0.0024 0.22982 ± 0.00037 II(a) 2.77885 2.77888 ± 0.00038 II(bc0) 12.212631 12.21247 ± 0.00045 II(bc1) 1.683165 ± 0.000013 1.68319 ± 0.00014 II(bc) 13.895796 ± 0.000013 13.89457 ± 0.00088 III 10.800 ± 0.022 10.7934 ± 0.0027 IV(a0) 116.76 ± 0.02 116.759183 ± 0.000292 IV(a1) 2.69 ± 0.14 2.697443 ± 0.000142 IV(a2) 4.33 ± 0.17 4.328885 ± 0.000293 IV(a) 123.78 ± 0.22 123.78551 ± 0.00044 IV(b) 0.38 ± 0.08 0.4170 ± 0.0037 IV(c) 2.94 ± 0.30 2.9072 ± 0.0044 IV(d) 4.32 ± 0.30 4.43243 ± 0.00058

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 8 (g 2) µ : results A (8) 2 (e) [Kurz,Marquard,Liu,Smirnov, [Kinoshita et al.] Smirnov,Steinhauser 15 16] I(a0) 7.223076 7.223077 ± 0.000029 I(a1) 0.494072 0.494075 ± 0.000006 I(a) I(b) I(c) I(a2) 0.027988 0.027988 ± 0.000001 I(d) II(a) II(b) II(c) I(a) 7.745136 7.74547 ± 0.00042 I(bc0) 8.56876 ± 0.00001 8.56874 ± 0.00005 I(bc1) 0.1411 ± 0.0060 0.141184 ± 0.000003 I(bc2) 0.4956 ± 0.0004 0.49565 ± 0.00001 I(bc) 9.2054 ± 0.0060 III 9.20632 IV(a) ± 0.00071 IV(b) IV(c) IV(d) V I(d) 0.2303 ± 0.0024 0.22982 ± 0.00037 II(a) 2.77885 2.77888 ± 0.00038 II(bc0) 12.212631 12.21247 ± 0.00045 II(bc1) 1.683165 ± 0.000013 1.68319 ± 0.00014 II(bc) 13.895796 ± 0.000013 13.89457 ± 0.00088 III 10.800 ± 0.022 10.7934 ± 0.0027 IV(a0) 116.76 ± 0.02 116.759183 ± 0.000292 IV(a1) 2.69 ± 0.14 2.697443 ± 0.000142 IV(a2) 4.33 ± 0.17 4.328885 ± 0.000293 IV(a) 123.78 ± 0.22 123.78551 ± 0.00044 IV(b) 0.38 ± 0.08 0.4170 ± 0.0037 IV(c) 2.94 ± 0.30 2.9072 ± 0.0044 IV(d) 4.32 ± 0.30 4.43243 ± 0.00058

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 9 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]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 10 Highlight of the year 2017: [Laporta 17] Semi-analytic calculation of 4-loop coefficient a µ = α ( α ) 4 2π + + c 4 +... π c 4 = T 0 + T 2 + T 3 + T 4 + T 5 + T 6 + T 7 + 3 (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)

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 11 (g 2) µ : photonic contr. and µ loops [Marquard,Smirnov,Smirnov, Steinhauser,Wellmann 17] [Aoyama,Hayakawa, Kinoshita,Nio 12] 2.161 ± 0.065 2.1755 ± 0.0020 0.077 ± 0.031 0.05596 ± 0.0001 0.3048 ± 0.021 0.3162 ± 0.0002 0.07461 ± 0.00008 0.074665 ± 0.000005 0.597204 ± 0.0012 0.598838 ± 0.000019 0.000876865... 0.000876865...

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 11 (g 2) µ : photonic contr. and µ loops [Marquard,Smirnov,Smirnov, [Laporta 17] [Aoyama,Hayakawa, Steinhauser,Wellmann 17] Kinoshita,Nio 12] 2.161 ± 0.065 2.1755 ± 0.0020 2.176866027739540077443259355895893938670 0.077 ± 0.031 0.05596 ± 0.0001 0.05611089989782836483146927441890884223 0.3048 ± 0.021 0.3162 ± 0.0002 0.31653839064894015884326038238151328482 0.07461 ± 0.00008 0.074665 ± 0.000005 0.0746711843261055138601599657227931268 0.597204 ± 0.0012 0.598838 ± 0.000019 0.598842072031421820464649513201747727836 0.000876865... 0.000876865... 0.000876865858889990697913748939713726165

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 11 (g 2) µ : photonic contr. and µ loops [Marquard,Smirnov,Smirnov, [Laporta 17] [Aoyama,Hayakawa, Steinhauser,Wellmann 17] Kinoshita,Nio 12] 2.161 ± 0.065 2.1755 ± 0.0020 2.176866027739540077443259355895893938670 0.077 ± 0.031 0.05596 ± 0.0001 1.91298 ± 0.00084 0.05611089989782836483146927441890884223 0.556893 + 0.00245 10 10 1.87 ± 0.12 0.544 + 0.35 10 10 1.9122457649264 0.3048... ± 0.021 0.556679601365032 0.3162... ± 10 0.0002 10 0.31653839064894015884326038238151328482 0.07461 ± 0.00008 0.074665 ± 0.000005 0.0746711843261055138601599657227931268 0.597204 ± 0.0012 0.598838 ± 0.000019 0.598842072031421820464649513201747727836 0.000876865... 0.000876865... 0.000876865858889990697913748939713726165

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, 2018 12 4-loop QED contribution a (8) µ 10 10 = (α/π) 4 1.9122 + 132.6852(60)(e ) + 0.04234(12)(τ) + 0.06272(4)(e + τ) [Calmet et al. 75; Chlouber et al 77; Aoyama et al. 12; Kurz et al. 15 16; Laporta 17] group µ and e µ and τ µ, e and τ I(a) 7.74547 (42) 0.000032 (0) 0.003209 (0) I(b) 7.58201 (71) 0.000252 (0) 0.002611 (0) I(c) 1.624307 (40) 0.000737 (0) 0.001807 (0) I(d) -0.22982 (37) 0.000368 (0) 0 II(a) -2.77888 (38) -0.007329 (1) 0 II(b) -4.55277 (30) -0.002036 (0) -0.009008 (1) II(c) -9.34180 (83) -0.005246 (1) -0.019642 (2) III 10.7934 (27) 0.04504 (14) 0 IV(a) 123.78551 (44) 0.038513 (11) 0.083739 (36) IV(b) -0.4170 (37) 0.006106 (31) 0 IV(c) 2.9072 (44) -0.01823 (11) 0 IV(d) -4.43243 (58) -0.015868 (37) 0 cross-check completed I(a) I(b) I(c) I(d) II(a) II(b) II(c)

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 13 Electroweak corrections a weak 1l µ = 19.480 ± 0.001 10 10 1 + 2 loops: [Fujikawa et al. 72; Jackiw et al. 72; Altarelli et al. 72; Bars et al. 72; Bardeen et al. 72] a weak µ = 15.36 ± 0.10 10 10 estimate 3 loops: a weak 3l µ = ±0.02 10 10 [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

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 14 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

[Keshavarzi,Nomura,Teubner 18] Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 15

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 16 R data [Jegerlehner 18]

R data 0.4 0.3 BESIII (15) KLOE combination CMD-2 (06) SND (04) [Keshavarzi,Nomura,Teubner 18] π a + π - µ (0.6 s 0.9 GeV) = (369.41 ± 1.32) x 10-10 χ 2 min /d.o.f. = 1.30 1400 1200 CMD-2 (03) (σ 0 - σ 0 Fit )/σ0 Fit 0.2 0.1 0 Fit of all π + π - data BaBar (09) σ 0 (e + e - π + π - ) 1000 800 600 400 σ 0 (e + e - π + π - ) [nb] -0.1 0 0.6 0.65 0.7 0.75 0.8 0.85 0.9 s [GeV] 200 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 16

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 17 scan and radiative return 1. e + e hadrons, vary s CMD-2, SND,... 2. 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,... ]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 18 R data π + π : several experiments; precise results: O(1%) systematic uncertainty; some tensions

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 18 R data π + π : several experiments; precise results: O(1%) systematic uncertainty; some tensions Fit of all π + π data: 369.41 ± 1.32 Direct scan only: 370.77 ± 2.61 KLOE combination: 366.88 ± 2.15 BaBar (09): 376.71 ± 2.72 BESIII (15): 368.15 ± 4.22 360 365 370 375 380 385 390 395 a µ π + π (0.6 s 0.9 GeV) x 10 10

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 18 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

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 19 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: 696.3 ± 7.2 HMNT03: 692.4 ± 6.4 DEHZ06: 690.9 ± 4.4 HMNT06: 689.4 ± 4.6 FJ06: 692.1 ± 5.6 DHMZ10: 692.3 ± 4.2 JS11: 690.8 ± 4.7 HLMNT11: 694.9 ± 4.3 FJ17: 688.1 ± 4.1 DHMZ17: 693.1 ± 3.4 KNT18: 693.3 ± 2.5 685 690 695 700 705 710 715 a µ had, LO VP x 10 10

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 19 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: 696.3 ± 7.2 HMNT03: 692.4 ± 6.4 DEHZ06: 690.9 ± 4.4 µ 2.5 4 10 10 HMNT06: 689.4 ± 4.6 FJ06: 692.1 ± 5.6 DHMZ10: 692.3 ± 4.2 JS11: 690.8 ± 4.7 HLMNT11: 694.9 ± 4.3 FJ17: 688.1 ± 4.1 DHMZ17: 693.1 ± 3.4 KNT18: 693.3 ± 2.5 685 690 695 700 705 710 715 a µ had, LO VP x 10 10

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 19 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: 696.3 ± 7.2 HMNT03: 692.4 ± 6.4 channel KNT18 DHMZ17 DEHZ06: 690.9 ± 4.4 difference π + π 503.74 δa HVP LO ± 1.96 507.14 HMNT06: 689.4 ± 4.6 µ 2.5 4 10 ± 10 2.58 3.40 ± 3.24 π + π π 0 47.70 ± 0.89 46.20 ± 1.45 1.50 ± 1.70 FJ06: 692.1 ± 5.6 [...] 1.8 s 3.7 GeV 34.54 ± 0.56 (data) 33.45 DHMZ10: ± 0.65 692.3 (pqcd) ± 4.2 JS11: 690.8 ± 4.7 HLMNT11: 694.9 ± 4.3 FJ17: 688.1 ± 4.1 DHMZ17: 693.1 ± 3.4 KNT18: 693.3 ± 2.5 1.09 ± 0.86 685 690 695 700 705 710 715 a µ had, LO VP x 10 10

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 20 Hadronic vacuum polarization: lattice N f = 2 + 1 + 1 [Jegerlehner 18] RBC/UKQCD 18 692.5 ± 2.67 RBC/UKQCD 18 715.4 ± 18.72 BMW 17 711 ± 19 HPQCD 16 667 ± 13 ETM 15 678 ± 29 N f = 2 + 1 RBC/UKQCD 11 641 ± 46 Aubin+Blum 07 748 ± 21 Aubin+Blum 07 713 ± 15 N f = 2 Mainz/CLS 17 654 ± 38 Mainz/CLS 11 618 ± 64 ETM 11 572 ± 16 FJ17 e + e &τ 688.8 ± 3.4 HLMNT11 e + e 694.4 ± 3.7 BDDJ15 HLS fit 681.9 ± 3.2 DHMZ16 e + e 692.3 ± 4.2 DHMZ16 e + e &τ 701.5 ± 4.6 HPV adjusted a NP µ = 0 720.26 ± 7.01 600 650 700 750 800 a HVP µ 10 10

Hadronic vacuum polarization: NLO and NNLO Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 21 compute higher order corrections to kernel K use same data [R(s)] as at LO

Hadronic vacuum polarization: NLO and NNLO Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 21

Hadronic vacuum polarization: NLO and NNLO Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 21 a had NLO µ = 9.82 ± 0.04 10 10 a had NNLO µ = 1.24 ± 0.01 10 10 NLO: [Krause 97;... ; Keshavarzi,Nomura,Teubner 18] NNLO: [Kurz,Liu,Marquard,Steinhauser 14]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 22 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

01 000 111 00000 11111 00 11 0000 1111 000000 111111 0 1 00 11 0 1 000000 111111 0000 1111 00 11 00000 11111 000 111 0 1 00000 11111 0 1 00000 11111 0 1 00000 11111 00000 11111 01 00000 11111 00000 11111 Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 22 00000 11111 01 00000 11111 00000 11111 00000 11111 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 ± 0.64 8.5 ± 1.3 8.3 ± 1.2 11.4 ± 1.0 11.4 ± 1.3 9.9 ± 1.6 axial vectors 0.17 ± 0.17 0.25 ± 0.10 2.2 ± 0.5 1.5 ± 1.0 2.2 ± 0.5 scalars 0.68 ± 0.20 0.7 ± 0.7 0.7 ± 0.2 π, K loops 0.45 ± 0.81 1.9 ± 1.3 1.9 ± 1.9 1.9 ± 1.3 π,k loops +subl. N C 0 ± 1.0 quark loops 0.97 ± 1.11 2.1 ± 0.3 0.23 (c-quark) 2.1 ± 0.3 total 8.96 ± 1.54 8.3 ± 3.2 8.0 ± 4.0 13.6 ± 2.5 10.5 ± 2.6 11.6 ± 3.9 [HKS: Hayakawa,Kinoshita,Sanda 95; Hayakawa,Kinoshita 98; BPP: Bijnens,Pallante,Prades 95 96 02; KN02: Knecht,Nyffeler 02; MV04: Melnikov,Vainshtein 04; PdeRV09: Prades,de Rafael,Vainshtein 09; N09: Nyffeler 09; JN09: Jegerlehner,Nyffeler 09]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 22 Hadronic light-by-light I. model-dependent approaches a Hlbl µ = 9.8 ± 2.6 10 10 no systematic uncertainty estimate a Hlbl NLO µ = 0.3 ± 0.2 10 10 [Colangelo,Hoferichter,Nyffeler,Passera,Stoffer 14]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 22 Hadronic light-by-light I. model-dependent approaches a Hlbl µ = 9.8 ± 2.6 10 10 no systematic uncertainty estimate a Hlbl NLO µ = 0.3 ± 0.2 10 10 [Colangelo,Hoferichter,Nyffeler,Passera,Stoffer 14] II. model-independent calculations 1. dispersive approach [Colangelo,Hoferichter,Procura,Stoffer 14... ; 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]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 23 Contributions to (g 2) µ numbers from: [Keshavarzi,Nomura,Teubner 18] 10 10 QED 11658471.8971 ±0.007 electroweak corrections 15.36 ±0.10 hadronic vacuum polarization 684.69 ±2.42 hadronic light-by-light 9.8 ±2.6 theory 11 659 182.05 ±3.56 experiment 11 659 209.1 ±6.3 experiment theory: 27.05 ±7.26 3.7σ

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 24 (g 2) µ comparisons DHMZ10 JS11 HLMNT11 FJ17 DHMZ17 KNT18 BNL 3.7σ BNL (x4 accuracy) 7.0σ 160 170 180 190 200 210 220 (a µ SM x 10 10 ) 11659000

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 25 Perspectives crucial contributions: δa HVP LO µ 2.5... 4 10 10 δa Hlbl µ 2.5 10 10 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?

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 26 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]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 26 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]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 27 Perspectives δaµ HVP LO 2.5... 4 10 10 crucial contributions: δaµ Hlbl 2.5 10 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

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 27 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??

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 28 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 70 10 10 1000 GeV M SUSY wrong sign! But: all masses equal! [Czarnecki,Marciano 01] see, e.g., [Marchetti,Mertens,Nierste,Stöckinger 09]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 29 a µ and SUSY Can SUSY explain aµ exp aµ SM O(30) 10 10? tan β ( ) 2 aµ SUSY 70 10 10 1000 GeV M SUSY wrong sign! But: all masses equal! tan β, general case: [Back,Park,Stöckinger,Stöckinger-Kim 15] C M SUSY,min [TeV] 2 1.5 see, e.g., [Marchetti,Mertens,Nierste,Stöckinger 09] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.62 0.88 1.08 1.25 1.39 1.53 1.65 1.76 1.87 1.97 M 1 = m R, M 2 = µ, M 2 < 0-1.7-1.5-2.0 a NP µ = C m 2 µ M 2 SUSY,min log 10 [ m L / m R ] 1 0.5 0-0.5 1.0 2.0 0.3 0.1 0.05 0.01-1 -1-0.5 0 0.5 1 1.5 2 log 10 [ µ / m R ]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 30 a µ and MSSM Dark Matter [Cox,Han,Yanagida 18;... ] 1000 800 Xenon1T LZ tanβ=50 LHC(3000 fb -1 ) bino-like LSP bino-wino co-annhilation coloured sparticles decoupled additional Higgs heavy degenerate slepton masses 600 400 200 LHC(300 fb -1 ) (g-2)μ LHC(36 fb -1 ) 1000 2000 3000 4000 5000

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 1 2 10 3 and m γ 10 100 MeV ε -2 10 KLOE 2015 WASA KLOE 2013 KLOE 2014 BABAR 2009-3 10 (g-2) ± µ (g-2) e 2σ favored NA48/2 HADES PHENIX A1 APEX BABAR 2014 KLOE 2016 BESIII E774-4 10 E141-2 10-1 dark 10 1 10 2 [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, 2018 31

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 32 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) 4.2 10 13 BR (μ e γ) [10-13 ] 6 4 2 0 Current Limit Large μ Sweet spot Similar SUSY masses 0 2 4 6 8 a μ [10-9 ]

Matthias Steinhauser Theory predictions for the muon (g 2) Mass 2018, Odense, May 29 June 1, 2018 33 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