0.0992(16) A 0,c (35) jet charge asymmetry: sin 2 θ lept

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4 data SM without A j LEP 1 est fit pull est fit pull line-shape & FB asym.: Γ Z (GeV) (23) σ 0 h (n) (37) R l (25) A 0,l FB (95) τ polarization: A τ (P τ ) (32) and c quark results: R (66) R c (30) A 0, FB (16) A 0,c FB (35) jet charge asymmetry: sin 2 θ lept eff (12) SLC A 0 LR (A e) (21) A 0.923(20) A c 0.670(27) Tevatron + LEP 2 m W (GeV) (23) Γ W (GeV) 2.085(42) Numerical inputs m Z (GeV) (21) G F (10 5 GeV 2 ) (1) Parameters α (5) had (m2 Z ) (15) ˆα s (m Z ) 5q (7) m t (GeV) 172.0(1.6) m HSM (GeV) χ 2 min d.o.f

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7 e f Z 0 e + s = E e+ e = m Z f

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9 Hagiwara, Haidt, Kim, Matsumoto Z.Phys.C64:559,1994, (E) C68:352,1995

10 s 2 (0) s 2 (m 2 Z ) (m 2 Z ) ḡ 2 Z(0) ḡ 2 Z(m 2 Z)

11 Peskin, Takeuchi, PRL65,964,1990

12 5 4 3 LEP/SLC 2 T lq APV (Cs + Tl) ν µ q (FH + CCFR) ν µ e All L.E.N.C S

13 4π ḡ 2 Z(m 2 Z) 4π ḡ 2 Z(0) 1 4 R S Z S + R 0.064x T Z T +1.49R G GCC, Hagiwara (2000) m W = S T U +

14 gl ν = ḡ2 Z s2 + gl ν, gl e = ḡ2 Z s2 + gl e, gr e = ḡz s 2 + gr, e gl u = ḡ2 Z s2 + gl u, gr u = ḡ2 Z s2 + gr u, gl d = ḡz s 2 + gl, d gr d = ḡ2 Z s2 + gr d, gl = ḡ2 Z s2 + gl, gr = ḡ2 Z s2 + gr, (g L = I 3f Q f sin 2 W =0.5 at tree)

15 gl ν = ḡ2 Z s2 + gl ν, gl e = ḡ2 Z s2 + gl e, gr e = ḡz s 2 + gr, e gl u = ḡ2 Z s2 + gl u, gr u = ḡ2 Z s2 + gr u, gl d = ḡz s 2 + gl, d gr d = ḡ2 Z s2 + gr d, gl = ḡ2 Z s2 + gl, gr = ḡ2 Z s2 + gr,

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17 S Z 33.7 gl = ± T Z 60.3 gl = ± m W (GeV)= ± 0.046, ( g χ 2 ) min =15.4+ L , }, ρ =0.89, ΔT Z 60.3Δg L % SM (m t ) % (m H ) ΔS Z 33.7Δg L

18 % % ΔT Z 0.47 Δg L m t (5) Δα had (m Z 2 ) ΔS Z Δg L

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21 S = 1 πm 2 Z f C f I 3f Y fl F 5 (m 2 Z : m fl,m fl ), I 3f Y f ( S) q 1 12π ( S) l π m 2 ũ L m 2 dl m 2 ũ L + m 2 dl m 2 ν l m 2 ll m 2 ν l + m 2 ll [ 1+O( m 2 ũ L m 2 dl m 2 ũ L + m 2 dl [ 1+O( m 2 ν l m 2 ll m 2 ν l + m 2 ll )], )],

22 T = G [ F π 2 α C f 2 (m2 t + m2 L L )+ m2 t m 2 L ] L ln m2 L m 2 t m 2 L m 2 t L L G F 24 2π 2 α C f (m 2 t L m 2 L ) 2 m 2 t L + m 2 L [ 1+O( m 2 t m 2 L )] L. m 2 t + m 2 L L G F 1 2 4π 2 α C q U t 11 4 F 5 (0 : m t 1 ),m L G F 1 2 4π 2 α C q U t 11 4[ 1 2 (m2 t + m2 L 1 )+ m2 t m 2 L 1 ln m2 L m 2 t m 2 L m 2 t 1 1 ].

23 tanβ = 2 tanβ = 50 0 (A eff ) squarks ΔT Z 60.3Δg L % sleptons (m L ) (m Q ) SM 175 (m t ) % (m H ) ΔS Z 33.7Δg L

24 tanβ = 2 tanβ = 50 µ = +300 GeV S Z S + R 0.064x T Z T +1.49R G ΔT Z 60.3Δg L % 39% inos (M 2 ) (m t ) (m H ) SM ΔS Z 33.7Δg L for m 2 m Z /2, ( 1 R ĉ 4 β 16 3π = 1 ), 4m 2 m 2 Z

25 20 19 LEP2 m 2 /µ = 10 m 2 /µ = 1 m 2 /µ = 0.1 SM with m H = 106 GeV χ 2 tot 18 SM (m H = 117GeV) 17 tanβ = m (χ ~ ) [GeV] 1

26 m Q % squarks A eff = ΔT Z 0.50 Δg L sleptons m τ1 = m L % 150 m χ 1 m L m t inos M 2 /µ= (5) Δα had (m Z 2 ) ΔS Z Δg L Figure 5: The squark, slepton and ino contriutions to ( S, T ) for tanβ = 10. The

27 EW precision data and muon g-2 oughout the past decade, there has een a hint of new physics from the muon g-2 asurement. The most recent update shows:..! B! H! W!0 H! B m2lr µl JN (09) µl µ L (d) + Davier et al, e e (10) 500 JS (11) 450 m~e (GeV) HLMNT (11)! B!0 H µr µr µ L (c) µl µr µ R (e) (a) tanβ= µ=200 GeV Aµ1=0! 400 " G1 (x) = (x 1)(x2 5x 2) + 6x ln x, 4 12(x m~l =1)m~ E 350 "! 1 where (5a) (x 1)(2x2 + 5x 1) 6x2 ln x, 12(x 1) G3 (x) = [(x 1)(x 3) + 2 ln x], 2(x 1) [(x 1)(x + 1) 2x ln x]. G4 (x) = 3 3 2(x 1) G2 (x) = experiment µl Figure 1: The SUSY contriutions to the muon g 2 which give the leading terms of the 500 expansion in mz /msusy. The photon (wavy line) is attached to all the charged particles. 400 HLMNT (10) µr µ R ()!0 H!0 W Davier et al, τ (10) µr ν µ (a) µ L m~e (GeV) HMNT (06) µl () tanβ=10 µ=800 GeV Aµ=0 m~l = m~e (5) (5c) (5d) 200 Even though these expressions are useful for numerical calculations, they are not particularly 4 150on the SUSY parameters. illuminating for the purpose of understanding their dependences 2 The main disadvantage of the aove expressions is that they are written in terms of the 100 mass eigenstates, in terms of which the dependences on the SUSY 100 reaking parameters are 100hidden 200y symmetry that causes complex the electroweak reaking mixings. In the weak M eigenstates, the structure of the one-loop contriutions ecomes muchmmore (GeV) (GeV) transparent. This2simplification occurs since the expressions in the weak eigenstates 2are equivalent to the mz /msusy expansion, where msusy is the typical SUSY reaking mass scale. The price we have to pay is that the leading terms in the expansion are not useful 1000 when msusy mz. However, we will find elow that this expansion 1000 is very useful when (c) tanβ=50 (d) tanβ=50 analyzing the SUSY parameter dependence µ=800 GeV The leading terms in the mzµ=200 /msusygev expansion are given y the five diagrams (a) to (e) 150 BNL (new from shift in λ) Aµ=0 m~l = m~e 800 m~e (GeV) aµ Hagiwara, Liao, Martin, Nomura, Teuner (2011), R.Liao, A.D.Martin, D.Nomura, T.Teuner, J.Phys.G(2011) [arxiv: ] M2 (GeV) Aµ=0 m~l = m~e 800 m~e (GeV) BNL M2 (GeV) GCC, Hagiwara, Matsumoto, Nomura (2011) 2000 Figure 3: The muon g 2, plotted against M2 (the SU(2)L gaugino mass) and me (the righthanded smuon soft SUSY reaking mass) for tan β = 10 (top two panels) and tan β 27 = 50 (ottom two panels), and for µ = 200 GeV (left two panels) and µ = 800 GeV (right two panels). The curves are, from the lower left corner, +3σ, +2σ, +1σ, 1σ and 2σ contour

28 scenarios from SUSY r...! B! H! W scenarios from some SUSY reaking scenarios (m2τ )LR (88)2 (261)2 (194)2 (90)2 (92)2 (103)2 (102)2 Aµ M1 M mu L mu R md R mt L mt R (m2t )LR SG (322)2 S G (435)2 GM (215)2 GM (241)2 MM (336)2 MM (397)2 MM (353)2 M ma (m2 )LR (153)2 (435)2 (316)2 (153)2 (159)2 (184)2 (183)2 µl 450 SG 1 SG 2 GM 1 GM 2 MM1 MM2 MM3 (a) () (c) (d) (e) (a)-(e) total pull µl! B!0 H µr µr µ L (c) µl µr µ R (e) Figure 1: The SUSY contriutions to the muon g 2 which give the leading terms of the 500 expansion in mz /msusy. The photon (wavy line) is attached to all the charged particles. (a) tanβ= µ=200 GeV Aµ1=0! 400 " G1 (x) = (x 1)(x2 5x 2) + 6x ln x, 4 12(x m~l =1)m~ E 350 "! 1 where (5a) (x 1)(2x2 + 5x 1) 6x2 ln x, 12(x 1) G3 (x) = [(x 1)(x 3) + 2 ln x], 2(x 1) [(x 1)(x + 1) 2x ln x]. G4 (x) = 3 3 2(x 1) G2 (x) = () tanβ=10 µ=800 GeV Aµ=0 m~l = m~e (5) (5c) (5d) 200 Even though these expressions are useful for numerical calculations, they are not particularly 4 150on the SUSY parameters. illuminating for the purpose of understanding their dependences 2 The main disadvantage of the aove expressions is that they are written in terms of the 100 mass eigenstates, in terms of which the dependences on the SUSY 100 reaking parameters are 100hidden 200y symmetry that causes complex the electroweak reaking mixings. In the weak M eigenstates, the structure of the one-loop contriutions ecomes muchmmore (GeV) (GeV) transparent. This2simplification occurs since the expressions in the weak eigenstates 2are equivalent to the mz /msusy expansion, where msusy is the typical SUSY reaking mass scale. The price we have to pay is that the leading terms in the expansion are not useful 1000 when msusy mz. However, we will find elow that this expansion 1000 is very useful when (c) tanβ=50 (d) tanβ=50 analyzing the SUSY parameter dependence µ=800 GeV The leading terms in the mzµ=200 /msusygev expansion are given y the five diagrams (a) to (e) 150 Tale 2: The values of the relevant SUSY parameters for the selected scenarios. The parameters SG: with the mass dimension are given in GeV units. (m2f )LR (f = τ, t, ) are the left-right minimal SUGRA mixing element in the mass-squared matrices of the sfermion f. As for the notation of the minimalwegauge othergm: SUSY parameters, use that ofmediation Ref. [1]. Aµ=0 m~l = m~e 800 m~e (GeV) MM: mixed moduli-anomaly mediation µ L (d) µr µ R ()!0 H!0 W 500 µr ν µ (a) µ L m~e (GeV) mµ R µl µl M2 (GeV) Aµ=0 m~l = m~e 800 m~e (GeV) µ mµ L m2lr m~e (GeV) SG 1 SG 2 GM 1 GM 2 MM1 MM2 MM3 tan β !0 H! B M2 (GeV) GCC, Hagiwara, Matsumoto, Nomura (2011) 2000 Figure 3: The muon g 2, plotted against M2 (the SU(2)L gaugino mass) and me (the righthanded smuon soft SUSY reaking mass) for tan β = 10 (top two panels) and tan β 28 = 50 (ottom two panels), and for µ = 200 GeV (left two panels) and µ = 800 GeV (right two panels). The curves are, from the lower left corner, +3σ, +2σ, +1σ, 1σ and 2σ contour

29 0.1 tan β µ m µl m µr (m 2 τ) LR A µ M 1 M 2 M 3 m A SG (88) SG (261) GM (194) GM (90) MM (92) MM (103) MM (102) mũl mũr m dr m t L m t R (m 2 t ) LR (m 2 ) LR SG (322) 2 (153) 2 SG (435) 2 (435) 2 GM (215) 2 (316) 2 GM (241) 2 (153) 2 MM (336) 2 (159) 2 MM (397) 2 (184) 2 MM (353) 2 (183) 2 ΔT Z 0.50 Δg L % 2 39% GM2 SG1 MM1 4 MM2 MM3 SG2 1 GM m t (5) 2 Δα had (m Z ) ΔS Z Δg L

30 80.41 tan β µ m µl m µr (m 2 τ) LR A µ M 1 M 2 M 3 m A SG (88) SG (261) GM (194) GM (90) MM (92) MM (103) MM (102) mũl mũr m dr m t L m t R (m 2 t ) LR (m 2 ) LR SG (322) 2 (153) 2 SG (435) 2 (435) 2 GM (215) 2 (316) 2 GM (241) 2 (153) 2 MM (336) 2 (159) 2 MM (397) 2 (184) 2 MM (353) 2 (183) 2 m W (GeV) GM SG1 SG2 MM1 MM3 3 GM2 4 m 175 t MM (5) Δα had (m Z 2 ) ΔS Z ΔT Z Δg L 2 39% 90%

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33 leptonic data only hadronic data only average s 2

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35 from lept. asym. data only from jet asym. data only average Δ s 2

36 % ΔT Z 1.24 Δg L GM2 SG1 MM1 4 MM2 MM3 SG2 1 GM m t 172 ΔT Z 0.50 Δg L % GM2 SG1 MM1 4 MM2 MM3 SG2 1 GM m t % % ΔS Z 1.50 Δg L (5) 2 Δα had (m Z ) (5) 2 Δα had (m Z ) ΔS Z Δg L

37 ΔT Z 1.24 Δg L % 2 GM2 SG1 MM1 4 MM2 MM3 5 3 SG2 1 GM m t m W (GeV) MM2 GM SG1 SG2 MM1 MM3 4 GM2 175 m t 2 Δα had (m Z) ΔS Z ΔT Z Δg L (5) 2 39% 90% % ΔS Z 1.50 Δg L (5) 2 Δα had (m Z )

38 A FB(exp.) = ± A FB(SM) = σ deviation

39 A FB = 3 4 A ea

40 Z Z Z

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43 ds 2 = e 2k y µ dx µ dx dy 2 v O(100GeV) = e kr c v 0 = e kr c GeV kr c = 11 12

44 A µ (x, )= L,R(x, )= n=0 n=0 A ( ) A (n) µ (x) (n) r c (n) ( ) L,R (x)e2 r c ˆf (n) L,R ( )

45 = gffa 001 g SM d e ˆf (m) L ˆf (n) L (q) A g ffa 001 /g SM 0.2 ( < 0.5) ( > 0.5) f

46 (a) : ( L, R) = (6, 0.2) () : ( L, R) = (0.2, 6) A FB = A FB(SM) + A FB = A FB(SM) g L g R g I 3 Q sin 2 W g L < 0, g R > 0 small R small m g (1)

47 Exp. SM est fit Pull A FB ± R ± A ± A FB(NP) = [A FB] SM g L g R R (NP) = [R ] SM 0.78 g L g R A (NP) = [A ] SM 0.30 g L 1.63 g R

48 Exp. SM est fit Pull A FB ± R ± A ± A FB(NP) = [A FB] SM gl gr R (NP) = [R ] SM 0.78 g L g R A (NP) = [A ] SM 0.30 g L 1.63 g R A FB R A 2 pull(sm) pull m g (1) 250GeV for R =6

49 g (1) 0 (p p g (1) + X) Br(g (1) ) ( L, R) = (0.2, 6) (CDF) arxiv: ,

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