Low Energy Probes of CP Violation in a Flavor Blind MSSM

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1 Low Energy Proe of CP Violation in a Flavor Blin MSSM Wolfgang Altmannhofer Phyik Department Techniche Univerität München Euroflavour 08 Septemer 22-26, 2008 Durham Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 1 / 16

2 Outline ae on: WA, Anrzej Bura an Parie Paraii arxiv: v1 [hep-ph] WA, Anrzej Bura an Parie Paraii in preparation 1 Introuction 2 The Flavor Blin MSSM 3 Phenomenology of CP Violation in the FBMSSM 4 Summary Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 2 / 16

3 CP violation in the SM Apart from the QCD θ term, the only ource for CP violation in the SM i the phae in the CKM matrix. CP violation from the CKM matrix can e viualize y Unitarity Triangle e.g. V u V u + V cv c + V tv t = 0 ( ρ, η) R α R t β Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 3 / 16

4 CP violation in the SM Apart from the QCD θ term, the only ource for CP violation in the SM i the phae in the CKM matrix η β m m m CP violation from the CKM matrix can e viualize y Unitarity Triangle e.g ε K V u V c in(2β+) α V u V u + V cv c + V tv t = 0 R ( ρ, η) α R t exclue area ha CL > in2β exclue at CL > 0.95 m & m ρ β η 0.5 ε K 0 α β α m V u -0.5 α Impreive confirmation of the CKM picture for CP violation -1 ol. w/ co2β < 0 (excl. at CL > 0.95) Summer 2007 CKM f i t t e r ρ ε K Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 3 / 16

5 Hint for new ource of CP violation? 1 CP Aymmetry in B ψk S an in 2β B Vt t W ± W ± t Vt B Tree level ecay enitivity to the phae of the mixing amplitue without NP in the ecay amplitue in SM: Arg(M 12 ) = Arg(V 2 t ) = 2β B W ± K c c ψ BaBar PRL 99 (2007) Belle J/ψ K 0 PRL 98 (2007) Belle ψ(2s) K S arxiv: Average HFAG in(2β) in(2φ 1 ) ± ± ± ± ± ± H F A G LP 2007 PRELIMINARY ± in 2β SM = S exp. ψk S = ± Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 4 / 16

6 Hint for new ource of CP violation? 1 CP Aymmetry in B ψk S an in 2β B Vt t W ± W ± t Vt B Tree level ecay enitivity to the phae of the mixing amplitue without NP in the ecay amplitue in SM: Arg(M 12 ) = Arg(V 2 t ) = 2β B W ± K c c ψ BaBar PRL 99 (2007) Belle J/ψ K 0 PRL 98 (2007) Belle ψ(2s) K S arxiv: Average HFAG in(2β) in(2φ 1 ) ± ± ± ± H F A G LP 2007 PRELIMINARY ± ± ± in 2β SM = S exp. ψk S = ± In the SM alo loop inuce moe like B φk S an B η K S give the ame value S SM φk S = S SM η K S = S SM ψk S = in 2β Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 4 / 16

7 Hint for new ource of CP violation? 1 CP Aymmetry in B ψk S an in 2β B Vt t W ± W ± t Vt B Tree level ecay enitivity to the phae of the mixing amplitue without NP in the ecay amplitue in SM: Arg(M 12 ) = Arg(V 2 t ) = 2β B W ± in 2β SM = S exp. ψk S = ± In the SM alo loop inuce moe like B φk S an B η K S give the ame value S exp. φk S = 0.39 ± 0.17 S SM φk S = S SM η K S = S SM ψk S = in 2β New Phae in ecay? S exp. η K S = 0.61 ± 0.07 K c c ψ BaBar PRL 99 (2007) Belle J/ψ K 0 PRL 98 (2007) Belle ψ(2s) K S arxiv: Average HFAG in(2β) in(2φ 1 ) ± ± ± ± ± ± cc η K 0 π 0 K S ω K S K + K - K 0 φ K 0 K S K S K S ρ 0 K S f 0 K 0 in(2β eff ) in(2φ e 1 ff ) HFAG HFAG HFAG LP 2007 HFAG HFAGLP 2007 LP HFAG 2007 HFAG LP 2007 LP 2007 LP 2007 LP 2007 HFAG LP 2007 HFAG LP 2007 H F A G LP 2007 PRELIMINARY ± H F A G LP 2007 PRELIMINARY Worl Average 0.68 ± 0.03 BaBar 0.21 ± 0.26 ± 0.11 Belle 0.50 ± 0.21 ± 0.06 Average 0.39 ± 0.17 BaBar 0.58 ± 0.10 ± 0.03 Belle 0.64 ± 0.10 ± 0.04 Average 0.61 ± 0.07 BaBar 0.71 ± 0.24 ± 0.04 Belle 0.30 ± 0.32 ± 0.08 Average 0.58 ± 0.20 BaBar 0.40 ± 0.23 ± 0.03 Belle 0.33 ± 0.35 ± 0.08 Average 0.38 ± 0.19 BaBar ± 0.09 ± 0.08 Average BaBar ± 0.02 Belle 0.11 ± 0.46 ± 0.07 Average 0.48 ± 0.24 BaBar 0.90 ± 0.07 Belle 0.18 ± 0.23 ± 0.11 Average 0.85 ± 0.07 BaBar 0.76 ± Belle 0.68 ± 0.15 ± Average 0.73 ± Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 4 / 16

8 Hint for new ource of CP violation? Lunghi, Soni 08 2 Tenion in the Unitarity Triangle perform UT fit incluing only ǫ K an M / M uing non perturative parameter B K = 0.72 ± ± (Antonio et al. 07) aitional effective uppreion factor in ǫ K : κ ǫ = 0.92 (Bura, Guaagnoli 08) Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 5 / 16

9 Hint for new ource of CP violation? Lunghi, Soni 08 2 Tenion in the Unitarity Triangle perform UT fit incluing only ǫ K an M / M uing non perturative parameter B K = 0.72 ± ± (Antonio et al. 07) aitional effective uppreion factor in ǫ K : κ ǫ = 0.92 (Bura, Guaagnoli 08) NP phae in B mixing? Aitional CP violation in K mixing? Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 5 / 16

10 Hint for new ource of CP violation? 3 B ψφ an in 2β t Vt c B W ± W ± B B W ± ψ Vt t φ c S ψφ = in 2(β + Φ NP ), β 1 B Lunghi, Soni 08 2 Tenion in the Unitarity Triangle perform UT fit incluing only ǫ K an M / M uing non perturative parameter B K = 0.72 ± ± (Antonio et al. 07) aitional effective uppreion factor in ǫ K : κ ǫ = 0.92 (Bura, Guaagnoli 08) NP phae in B mixing? Aitional CP violation in K mixing? Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 5 / 16

Hint for new ource of CP violation? 3 B ψφ an in 2β t Vt c B W ± W ± B B W ± ψ Vt t φ c S ψφ = in 2(β + Φ NP ), β 1 B Lunghi, Soni 08 2 Tenion in the Unitarity Triangle Φ NP B = (19.9 ± 5.6 ) (68.

11 Hint for new ource of CP violation? 3 B ψφ an in 2β t Vt c B W ± W ± B B W ± ψ Vt t φ c S ψφ = in 2(β + Φ NP ), β 1 B Lunghi, Soni 08 2 Tenion in the Unitarity Triangle Φ NP B = (19.9 ± 5.6 ) (68.2 ± 4.9 ) Large B mixing phae? perform UT fit incluing only ǫ K an M / M uing non perturative parameter B K = 0.72 ± ± (Antonio et al. 07) aitional effective uppreion factor in ǫ K : κ ǫ = 0.92 (Bura, Guaagnoli 08) NP phae in B mixing? Proaility enity Aitional CP violation in K mixing? o φ [ ] B Bona et al. 08 Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 5 / 16

12 A Flavor Blin MSSM with CP Violating Phae In a flavor lin MSSM (FBMSSM) there are no aitional flavor tructure apart from the CKM matrix. In particular, we aume univeral quark mae an iagonal trilinear coupling. no gluino contriution to FCNC Parameter of a flavor lin MSSM Higg ector: tan β, M H ± Higgino ma: µ Gaugino mae: M 1, M 2, M 3 quark mae: m 2 Q, m 2 U, m 2 D trilinear coupling: A, A, A, A u, A c, A t The Higgino an Gaugino mae a well a the trilinear coupling can in general e complex. Oervale only epen on particular comination of complex parameter. Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 6 / 16

13 A Flavor Blin MSSM with CP Violating Phae Main role i playe y one complex parameter comination µa t Intereting correlate effect in CP violating oervale WA, Bura, Paraii 08 Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 7 / 16

14 Mot important contraint: EDM an BR[B X ] exp. = (3.52 ± 0.25) 10 4 HFAG 08 BR[B X ] SM = (3.15 ± 0.23) 10 4 Miiak et al. 06 amplitue i helicity uppree typically large NP effect, even in a FBMSSM with low tan β Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 8 / 16

15 Mot important contraint: EDM an BR[B X ] exp. = (3.52 ± 0.25) 10 4 HFAG 08 BR[B X ] SM = (3.15 ± 0.23) 10 4 Miiak et al. 06 amplitue i helicity uppree typically large NP effect, even in a FBMSSM with low tan β ( C χ± 7,8 (µ SUSY) m2 t µ 2 m 4 t A t µ tan β f 7,8 m 2 t H Hu µ ) R L t L m ta t t R, g Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 8 / 16

16 Mot important contraint: EDM an BR[B X ] exp. = (3.52 ± 0.25) 10 4 HFAG 08 BR[B X ] SM = (3.15 ± 0.23) 10 4 Miiak et al. 06 amplitue i helicity uppree typically large NP effect, even in a FBMSSM with low tan β ( C χ± 7,8 (µ SUSY) m2 t µ 2 m 4 t A t µ tan β f 7,8 m 2 t H Hu µ ) R L t L m ta t t R BR[B X ] C SM 7 (m ) + C NP 7 (m ) 2 C SM 7 (m ) 2 + 2Re(C SM 7 (m )C NP 7 (m )) Contraint on Re(µA t ), g Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 8 / 16

17 Mot important contraint: EDM an exp. e ecm exp. n ecm SM e ecm SM n ecm In the MSSM, EDM can e inuce alreay at the 1loop level typically tight contraint on CP violating phae Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 9 / 16

18 Mot important contraint: EDM an exp. e ecm exp. n ecm SM e ecm SM n ecm In the MSSM, EDM can e inuce alreay at the 1loop level typically tight contraint on CP violating phae Example: Gluino contriution to the up-quark EDM g g g g ur ũr M g mua u ũl ul ul ũl M g muau ũr ur u eg2 Im(M g A u) 16π 2 mu m ũ 4 F! M g 2 m 2 ũ Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 9 / 16

19 Mot important contraint: EDM an exp. e ecm exp. n ecm SM e ecm SM n ecm In the MSSM, EDM can e inuce alreay at the 1loop level typically tight contraint on CP violating phae Example: Gluino contriution to the up-quark EDM g g g g ur ũr M g mua u ũl ul ul ũl M g muau ũr ur u eg2 Im(M g A u) 16π 2 mu m ũ 4 F! M g 2 m 2 ũ Contraint can e avoie y e.g. hierarchical trilinear coupling A u,c A t, A, A heavy 1 t an 2 n generation of quark But: izeale effect in flavor oervale till poile, a 3 r generation quark enter Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 9 / 16

20 Mot important contraint: EDM an Chang, Keung, Pilafti 98 2-loop Barr-Zee type iagram generating oth lepton an quark EDM enitive to 3 r generation of quark ecouple with 1/max(M 2 A 0, m 2 t ) e, q e, q e, q e, q e, q e, q A 0 µ t R + A 0 µ t L f Im(µA t ) t L m ta t t R t R m ta t t L Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

21 Mot important contraint: EDM an Chang, Keung, Pilafti 98 2-loop Barr-Zee type iagram generating oth lepton an quark EDM enitive to 3 r generation of quark ecouple with 1/max(M 2 A 0, m 2 t ) e, q e, q e, q e, q e, q e, q A 0 µ t R + A 0 µ t L f Im(µA t ) t L m ta t t R t R m ta t t L Contraint on Im(µA t ) Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

22 CP Aymmetrie in B φk S an B η K S B C 7,8, g K φ Time epenent CP Aymmetrie in ecay of neutral B meon to final CP Eigentate A CP (t, φk S ) = Γ(B(t) φk S) Γ( B(t) φk S ) Γ(B(t) φk S ) + Γ( B(t) φk S ) = C φks co( M t) S φks in( M t) S φks = 2Im(ξ φk S ) 1 + ξ φks 2, ξ φk S = e iarg(m 12 ) A( B φk S ) A(B φk S ) Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

23 CP Aymmetrie in B φk S an B η K S B C 7,8, g K φ Time epenent CP Aymmetrie in ecay of neutral B meon to final CP Eigentate A CP (t, φk S ) = Γ(B(t) φk S) Γ( B(t) φk S ) Γ(B(t) φk S ) + Γ( B(t) φk S ) = C φks co( M t) S φks in( M t) S φks = 2Im(ξ φk S ) 1 + ξ φks 2, ξ φk S = e iarg(m 12 ) A( B φk S ) A(B φk S ) ABP 08 izeale, correlate effect in S φks an S η K S larger effect in S φks a inicate y the ata Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

CP Aymmetrie in B φk S an B η K S B C 7,8, g K φ Time epenent CP Aymmetrie in ecay of neutral B meon to final CP Eigentate A CP (t, φk S ) = Γ(B(t) φk S) Γ( B(t) φk S ) Γ(B(t) φk S ) + Γ( B(t) φk S )

24 CP Aymmetrie in B φk S an B η K S B C 7,8, g K φ Time epenent CP Aymmetrie in ecay of neutral B meon to final CP Eigentate A CP (t, φk S ) = Γ(B(t) φk S) Γ( B(t) φk S ) Γ(B(t) φk S ) + Γ( B(t) φk S ) = C φks co( M t) S φks in( M t) S φks = 2Im(ξ φk S ) 1 + ξ φks 2, ξ φk S = e iarg(m 12 ) A( B φk S ) A(B φk S ) ABP 08 izeale, correlate effect in S φks an S η K S larger effect in S φks a inicate y the ata for S φks 0.4, lower oun on the electron an neutron EDM: e ecm, n ecm Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

25 Direct CP Aymmetry in Soare 91; Kagan, Neuert 98 A CP = Γ( B X ) Γ(B X ) Γ( B X ) + Γ(B X ) C2 u, c g + C 8 g + arie firt at orer α ouly Caio an GIM uppree in the SM izeale value woul e clear ignal for New Phyic A CP (SM) ( )% Hurth, Lunghi, Poro 03 A (exp.) (0.4 ± 3.6)% CP HFAG A CP α C 7 2 `27 Im(C 2 C 7 ) + 87Im(C 8 C 7 ) + 28Im(C 2 C 8 ) Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

Direct CP Aymmetry in Soare 91; Kagan, Neuert 98 A CP = Γ( B X ) Γ(B X ) Γ( B X ) + Γ(B X ) C2 u, c g + C 8 g + arie firt at orer α ouly Caio an GIM uppree in the SM izeale value woul e clear ignal

26 Direct CP Aymmetry in Soare 91; Kagan, Neuert 98 A CP = Γ( B X ) Γ(B X ) Γ( B X ) + Γ(B X ) C2 u, c g + C 8 g + arie firt at orer α ouly Caio an GIM uppree in the SM izeale value woul e clear ignal for New Phyic A CP (SM) ( )% Hurth, Lunghi, Poro 03 A (exp.) (0.4 ± 3.6)% CP HFAG A CP α C 7 2 `27 Im(C 2 C 7 ) + 87Im(C 8 C 7 ) + 28Im(C 2 C 8 ) Sign of A CP i correlate with ign of S φk S For S φks < S SM φk, A i unamiguouly poitive S CP value typically in the range 1% 6% ABP 08 Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

27 CP Violation in F = 2 tranition 1 Phae in the B an B mixing amplitue Leaing NP contriution to M 12 an M 12 turn out to e inenitive to the new phae of a flavor lin MSSM. Arg(M, 12 ) Arg(M, 12 (SM)) S ψks an S ψφ are SM like ABP 08 Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

28 CP Violation in F = 2 tranition 1 Phae in the B an B mixing amplitue Leaing NP contriution to M 12 an M 12 turn out to e inenitive to the new phae of a flavor lin MSSM. Arg(M, 12 ) Arg(M, 12 (SM)) S ψks an S ψφ are SM like ABP 08 2 CP violation in K mixing Alo M K 12 ha no enitivity to the new phae Still, ǫ K Im(M K 12) can get a poitive NP contriution up to 15% But only for a very light SUSY pectrum: µ, m t 1 200GeV Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

29 Implication for the Unitarity Triangle S ψks an M / M aically NP free UT can e contructe from the angle β an the ie R t in 2β = S ψks = ± R t = ξ 1 λ q mb q M m B M = ± Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

30 Implication for the Unitarity Triangle S ψks an M / M aically NP free UT can e contructe from the angle β an the ie R t in 2β = S ψks = ± R t = ξ 1 λ q mb q M m B M = ± Preiction for V u an the angle V u = (3.5 ± 0.2) 10 3 = 63.5 ± 4.7 Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

31 Implication for the Unitarity Triangle S ψks an M / M aically NP free UT can e contructe from the angle β an the ie R t in 2β = S ψks = ± R t = ξ 1 λ q mb q M m B M = ± Preiction for V u an the angle V u = (3.5 ± 0.2) 10 3 = 63.5 ± 4.7 ǫ K contraint (B K = 0.75 ± 0.07) Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

Implication for the Unitarity Triangle S ψks an M / M aically NP free UT can e contructe from the angle β an the ie R t in 2β = S ψks = 0.680 ± 0.025 R t = ξ 1 λ q mb q M m B M = 0.913 ± 0.

32 Implication for the Unitarity Triangle S ψks an M / M aically NP free UT can e contructe from the angle β an the ie R t in 2β = S ψks = ± R t = ξ 1 λ q mb q M m B M = ± Preiction for V u an the angle V u = (3.5 ± 0.2) 10 3 = 63.5 ± 4.7 ǫ K contraint (B K = 0.75 ± 0.07) an with +10% NP correction Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

effect in A CP 2% imply µ 600GeV an m t 1 800GeV Wolfgang

33 Implication for irect earche of SUSY particle ABP 08 S φks 0.4 implie µ 600GeV an m t 1 700GeV imilarly, large non tanar effect in A CP 2% imply µ 600GeV an m t 1 800GeV Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

34 Summary In the flavor lin MSSM izeale, correlate effect in S φks an S η K S are poile. Such effect imply: lower oun on the electron an neutron EDM at the level of e,n ecm a poitive, izeale irect CP aymmetry A CP 1% 6% Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

35 Summary In the flavor lin MSSM izeale, correlate effect in S φks an S η K S are poile. Such effect imply: lower oun on the electron an neutron EDM at the level of e,n ecm a poitive, izeale irect CP aymmetry A CP 1% 6% In aition, within the framework of the FBMSSM, there are mall effect in S ψφ mall effect in S ψks an in M / M The Unitarity Triangle can e contructe from the ie R t an the angle β. Preiction: V u = (3.5 ± 0.2) 10 3 an = 63.5 ± 4.7. poitive NP effect in ǫ K up to 15% Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour / 16

36 Back Up Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 / ack-up

37 The Anomalou Magnetic Moment of the Muon a exp. µ = (63) 10 9 Muon (g-2) collaoration a SM µ = (61) 10 9 Miller et al. 07 a µ = a exp. µ a SM µ (3 ± 1) σ icrepancy A very rough formula for SUSY contriution to a µ ««2 aµ SUSY tan β 300GeV 1.5 ign(re(µ)) m l with common SUSY ma m l S φks 0.4 naturally lea to a SUSY µ few 10 9 Wolfgang Altmannhofer (TUM) CP Violation in a Flavor Blin MSSM Euroflavour 08 1 / ack-up

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