Precision Observables M W, (g 2) µ

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1 Precision Observables M W, (g 2) µ Dominik Stöckinger Edinburgh SUSY 2006 main refs: [Heinemeyer, Hollik, DS, Weber, Weiglein, 06] (M W ) [DS 06 (soon... )] (review on (g 2) µ and SUSY)

2 Outline 1 Motivation 2 M W 3 (g 2) µ

3 Outline Motivation 1 Motivation 2 M W 3 (g 2) µ

4 Precision Observables Motivation Quantum effects from SUSY particles can have an influence on precision observables M W t H t H t, (g 2) b µ

5 Precision Observables Motivation Quantum effects from SUSY particles can have an influence on precision observables M W t H H t, (g 2) b µ t M W [GeV] experimental errors 68% CL: M W = GeV M W = GeV M W = GeV M H = 114 GeV SM LEP2/Tevatron (today) Tevatron/LHC ILC/GigaZ M H = 400 GeV m m t = GeV t = 172.9GeV m t = GeV light SUSY MSSM heavy SUSY SM MSSM both models Heinemeyer, Hollik, Stockinger, Weber, Weiglein m t [GeV]

6 Motivation Precision Observables Quantum effects from SUSY particles can have an influence on precision observables M W t H H t, (g 2) b µ t a µ (exp SM) = 25(9) a µ (SUSY) tan β = 50 tan β = σ 1σ

7 Precision Observables Motivation Quantum effects from SUSY particles can have an influence on precision observables M W t H t H t, (g 2) b µ MSSM tends to agree better with experimental data than SM

8 Outline M W 1 Motivation 2 M W 3 (g 2) µ

9 M W Muon-decay, M W, and ρ Muon lifetime ( G µ ) related to M W : ( ) M 2 W 1 M2 W M 2 Z = πα 2Gµ (1 + r) Prediction for M W in terms of M Z, α, G µ, r(m t, M H, m t,...) Loop calculation: r = c2 W sw 2 ρ + rest ρ: breaking of isospin invariance t b-mass splitting...

10 Muon-decay: Status M W SM: ρ: 3-loop, 4-loop rest: complete 2-loop MSSM: ρ: 2-loop [Haestier,Heinemeyer,DS,Weiglein 05] rest: 1-loop complete [Heinemeyer,Hollik,DS,Weber,Weiglein 06] new results

11 ρ at 2-loop order M W New result on Yukawa-enhanced corrections of O(α 2 t,b ) t,b t, b t, b t,b H (already known) H (new) induced shift in M W as function of stop mixing: up to M W 8 MeV, SUSY loops can be as large as SM quark loops H (new) M W [MeV] (q ~ ~, H) (q ~ ~, H), Mh = 0 (q): MSSM - SM -(q): SM [Haestier,Heinemeyer,DS,Weiglein 05] M SUSY = 300 GeV, M A = 300 GeV, tanβ = 50, µ = 500 GeV X t [GeV] sin 2 θ eff [10-5 ]

12 M W New result for M W in the MSSM [Heinemeyer,Hollik,DS,Weber,Weiglein 06] Complete 1-loop calculation of r with complex parameters Incorporation of 2-loop calculation of ρ [Haestier,Heinemeyer,DS,Weiglein 05] Incorporation of higher-order SM contributions r MSSM = r SM + r MSSM SM 1 loop c2 W sw 2 ρ MSSM SM 2 loop Best available prediction of M W in the MSSM implemented in computer program

13 M W Compare MSSM prediction for M W with experimental result M W [GeV] m t = GeV m t = ( ) GeV m t = ( ) GeV M Wexp = ± 0.032GeV M~ f [GeV] [Heinemeyer,Hollik,DS,Weber,Weiglein 06] tan β = 10 A t,b = 2M f µ = 300 GeV m g = 300 GeV M A = 300 GeV M 2 = 300 GeV Preference for light SUSY scale M f = M t, b

14 M W Compare MSSM prediction for M W with experimental result experimental errors 68% CL: LEP2/Tevatron (today) Tevatron/LHC ILC/GigaZ m~ t2,b2 ~ / m~ t1,b1 ~ > 2.5 light SUSY M W [GeV] M H = 114 GeV SM M H = 400 GeV MSSM heavy SUSY SM MSSM both models Heinemeyer, Hollik, Stöckinger, Weber, Weiglein 05 [Heinemeyer,Hollik,DS,Weber,Weiglein 06] Scan of all SUSY parameters m t [GeV] Preference for MSSM over SM

15 Outline (g 2) µ 1 Motivation 2 M W 3 (g 2) µ

16 (g 2) µ (g 2) µ : Status BNL experiment: finalized, very stable development SM-theory: several errors fixed, e + e data preferred a µ (exp SM) = (23.9 ± 9.9) 10 10

17 (g 2) µ (g 2) µ : Status BNL experiment: finalized, very stable development SM-theory: several errors fixed, e + e data preferred a µ (exp SM) = (23.9 ± 9.9) Historical comparison: 1978, CERN experiment: a µ (CERN SM, without had) = (720 ± 85) a µ (SM, had) = (667 ± 81) Established had contributions, agreement with SM

18 (g 2) µ (g 2) µ : Status BNL experiment: finalized, very stable development SM-theory: several errors fixed, e + e data preferred a µ (exp SM) = (23.9 ± 9.9) Now: compare with weak contributions only: a µ (BNL SM, without weak) = (39.3 ± 9.9) a µ (SM, weak) = (15.4 ± 2.2) existence of weak contributions, but disagreement with SM! SUSY?

19 (g 2) µ Status of SUSY prediction 1-Loop 2-Loop logs 2-Loop non-log tan β log M SUSY m µ tan β µ m t χ 0,± γ χ + H t γ µ µ µ, ν [Fayet 80],... [Kosower et al 83],[Yuan et al 84],... [Lopez et al 94],[Moroi 96] µ µ ν µ [Degrassi,Giudice 98] µ µ, ν µ µ [Chen,Geng 01][Arhib,Baek 02] [Heinemeyer,DS,Weiglein 03] [Heinemeyer,DS,Weiglein 04] complete complete half (no internal µ, ν)

20 SUSY prediction (g 2) µ Implementation of 1-Loop and leading 2-Loop straightforward: 1-Loop: { aµ χ0 = mµ 16π i,m mµ ( n L 2 12m 2 µm im 2 + nim R 2 )F1 N(xim) + m } χ 0 i Re[n L 3m 2 µm im nr im ]F 2 N(xim), a χ± µ = mµ 16π 2 k { mµ 12m 2 νµ n L im = 1 2 (g1ni1 + g2ni2)u µ m1 yµni3u µ m2, ( ck L 2 + ck R 2 )F1 C(xk ) + 2m χ ± k Re[c L 3m 2 νµ k cr k ]F 2 }, C(xk ) n R im = 2g1Ni1U µ m2 + yµni3u µ m1, c L k = g2vk1, c R k = yµuk2. F N 1 (x) = 2 (1 x) 4 [ 1 6x + 3x 2 + 2x 3 6x 2 log x ], F N 2 (x) = 3 (1 x) 3 [ 1 x 2 + 2x log x ], F C 1 (x) = 2 (1 x) 4 [ 2 + 3x 6x 2 + x 3 + 6x log x ], F C 2 (x) = 3 (1 x) 3 [ 3 + 4x x 2 2 log x ],

21 SUSY prediction (g 2) µ Implementation of 1-Loop and leading 2-Loop straightforward: 2-Loop: a logs µ = 4α π log M SUSY a (χγh) µ = α2 m 2 µ 8π 2 M 2 W s2 W a ( f γh) µ = α2 m 2 µ 8π 2 M 2 W s2 W { λ {h0,h 0,A 0 } µ = λ {h0,h 0,A 0 } = χ + k a 1 Loop µ m µ [ k=1,2 Re[λ A0 µ λ A0 ] f χ + PS (m 2 /M 2 ) + χ + A k k 0 S=h 0,H 0 Re[λS µλ S ] f χ + S (m 2 /M χ + S ], 2) k k [ f = t, b, τ i=1,2 S=h 0,H 0(NcQ2 ) f Re[λ S µλ S f ] i f f (m 2 fi /MS ]. 2) sα, cα cβ 2MW ( Uk1Vk2 m χ + k },, cβ tβ { } { }) cα, sα, cβ + Uk2Vk1 sα, cα, sβ. λ {h0,h 0 } ( = 2mt t i m + µ { { sα, cα} + At cα, 2 t sα sβ i λ {h0,h 0 } = 2m ( b b i m µ { { cα, sα} + Ab sα, 2 bi cα cβ λ {h0,h 0 } ( τ i = 2mτ m µ { { cα, sα} + Aτ sα, 2 τ cα cβ i [ ( ) ( )] f PS (z) = 2z y Li2 1 1 y 2z Li2 1 1+y 2z f S (z) = (2z [ 1)f PS (z) 2z(2 ] + log z), (z) = f f z log z f PS (z). }) (U t i1 ) U t i2, }) (U bi1 ) U b i2, }) (U τ i1 ) U τ i2.

22 Numerical result (g 2) µ tan β = 50, all parameters < 3 TeV m µ, ν arbitrary typically: tan β ( ) GeV M SUSY sign(µ) SUSY a Μ m µ, ν > 1 TeV M LOSP GeV SUSY contributions in the observed range for low M SUSY!

23 Numerical result (g 2) µ tan β = 50, all parameters < 3 TeV m µ, ν arbitrary typically: tan β ( ) GeV M SUSY sign(µ) SUSY a Μ possible enhancement for large µ 10 m µ, ν > 1 TeV M LOSP GeV SUSY contributions in the observed range for low M SUSY!

24 Numerical result (g 2) µ tan β = 50, all parameters < 3 TeV m µ, ν arbitrary typically: tan β ( ) GeV M SUSY sign(µ) SUSY a Μ m µ, ν > 1 TeV M LOSP GeV possible enhancement for large µ suppression for large m µ, ν 2-Loop important SUSY contributions in the observed range for low M SUSY!

25 (g 2) µ Conclusions Two precision observables: M W and (g 2) µ current measurements sensitive to 2-Loop SM and SUSY effects 2-Loop SUSY contributions: M W : Computer code for M MSSM W [Haestier,Heinemeyer, DS, Weiglein 05] [Heinemeyer, DS, Weiglein 03, 04] [Heinemeyer,Hollik, DS, Weber,Weiglein 06] (g 2) µ : 1-,2-Loop contributions easy to implement SUSY with low mass scale GeV fits very well SM cannot be excluded at the moment Future, more precise measurements very important and promising!