B Physics Theory Overview

Transcription

1 B Phyic Theory Overview Standard LHC Copenhagen April 13, 2012 Martin Gorahn TU München-IAS & Excellence Cluter `Univere 1

2 Flavour Phyic Flavour Phyic: Effect of highly virtual particle at lower energie Meaure the tandard model W ± coupling in B and K decay Tet the tandard model in proce i) where CP i violated ii) which are uppreed through (accidental) ymmetrie, and iii) which can e calculated with high preciion Symmetrie: CP and Flavour 2

3 Flavour Symmetry The tandard model gauge ector conerve CP L g = f + 1 ψ 4 g i F i µνf iµν f /Dψ f i f {u, d, e, Q, L} large gloal flavour ymmetry Yukawa coupling reak ymmetry Ma flavour eigentate G flavour = f SU(3) f x U(1) x [Chivukula, Georgi `87] L q Y = ū RY u ϕ Q L + d R Y u ϕ Q L diagonal Yd: Y u = 1 v m u m c m t V ud V u V u V cd V c V c V td V t V t CKM matrix: CP and flavour violation in the SM B tree and loop decay: determine CKM matrix 3

4 Flavour Changing Interaction Ma flavour eigentate L V u W + u L f i δ ij Z 0 f j Loopuppreion tet TeV-cale SM: Only charged current change the flavour ( V u ) V CKM = SM: Neutral current do not change the flavour (i=j) at tree-level V ud V u V u V cd V c V c V td V t V t CKM matrix: CP and flavour violation in the SM B tree and loop decay: determine CKM matrix 4

5 Unitarity Triangle 3 CKM angle Vu, Vc & Vu from emileptonic B & K decay CP violation in the tandard model area of unitarity triangle Unitarity of V V u V ud + V c V cd + V t V td = 0 Aλ 3 (ρ + iη) Aλ 3 + Aλ 3 (1 ρ iη) = 0 Graphically, ( ρ, η) t d!u l!!u q q (tree-level Weak int.) α V u V td λv c λv c require top loop V u = V u e iγ V td = V td e iβ γ β (0, 0) 1 (1, 0) d d W W t u, c, t W g 5

6 Minimal Flavour Violation unitarity triangle implicitly depend on new phyic 0.7 ρ 0.6 γ M M d Minimal Flavour Violation Univeral Unitarity Triangle [Bura, Gamino, MG, Jäger, Silvetrini `00] Independent of detail of new phyic Retrictive cenario can e relaxed [d Amroio et al `02;...] in 2β (B d J/ΨK ) V u V c η Yet, model of dynamical flavour reaking do not follow thee cenario 6

7 CKM input for tet of SM CKM parameter: input for new phyic enitive oervale ρ γ(b DK) γ ɛ K Tree level determination of UT Precie new phyic independent determination of γ important (talk: γ from B DK) V u V c η 7

8 CKM input for tet of SM CKM parameter: input for new phyic enitive oervale ρ γ(b DK) γ ɛ K Tree level determination of UT Precie new phyic independent determination of γ important (talk: γ from B DK) V u V c η Important for CP violation in Kaon: εk at NNLO [Brod, MG `11] 7

9 CKM input for tet of SM CKM parameter: input for new phyic enitive oervale ρ γ(b DK) γ ɛ K Tree level determination of UT Precie new phyic independent determination of γ important (talk: γ from B DK) V u V c η Important for CP violation in Kaon: εk at NNLO [Brod, MG `11] CP violation in Bd mixing tranition almot independent of ρ and η: Domain of LHC 7

10 B Mixing B 0 (t) M11 M 12 Γ11 Γ 12 B 0 (t) i d dt B 0 (t) = M 12 M 11 i 2 Γ 12 Γ 11 B 0 (t) CP ± eigentate of time evolution: B L/H = p B 0 q B 0 diperive part: M12 t W ± W Re( ) ± ``off-hell top-quark; one-loop enitive to new phyic mall complex phae in SM: ( φ = arg M ) 12 = 2β Γ 12 t 8

11 B Mixing B 0 (t) M11 M 12 Γ11 Γ 12 B 0 (t) i d dt B 0 (t) = M 12 M 11 i 2 Γ 12 Γ 11 B 0 (t) CP ± eigentate of time evolution: B L/H = p B 0 q B 0 diperive part: M12 t W ± W Re( ) ± ``off-hell top-quark; one-loop enitive to new phyic mall complex phae in SM: ( φ = arg M ) 12 = 2β Γ 12 t aorptive part: Γ12 c, u W ± W Im( ) ± c, u tree decay into light up-quark new phyic ha to compete with tree-level ΔF=1 operator trong contraint from experiment 8

12 Oervale in B Mixing Ma difference MH - ML = 2 M Decay rate difference ΓL - ΓH = 2 Γ Mixing induced CP violation e.g. A mix CP(B J/Ψ Φ) = in(φ) = in(- 2 β) Flavour Specific CP aymmetrie B (t = 0) f and B (t = 0) f a l = Γ( B (t) f) Γ(B (t) f) Γ = Γ( B (t) f)+γ(b (t) f) M tan φ 9

13 SM Prediction v Data Oervale Theory [Lenz, Nierte ] Experiment ΔM[p^-1] 17.3 ± ± 0.05 [CDF&LHC] ΔΓ [p^-1] ± ± [LHC] Φ(J/Ψ Φ) [ ] -2.1± ± 5.0 [LHC] (talk: Φ LHC) 10

14 Like-ign dimuon aymmetry Like-ign dimuon charge aymmetry diagree with SM If there i only NP in M12: Φ and ASL would e correlated: A SL = N++ N ++ N + N 2 = C d a d f + C a f 1 M Φ JΨΦ a l 0.02 RM in ΦM 0 a f 0 SM 1 Standard Model 2 [Boeth, Haich `11] B Factory W.A. DØ B µd X DØ A l DØ Al 95% C.L. DØ, 9.0 f a d l R M co Φ M How large can NP modify Γ12? 11

15 New Phyic in Γ12? New Phyic contriuting to Γ12 i tightly contrained (They mut couple light SM particle to the B) One poile exception: ( )(τ τ) operator [Dighe, Kundu, Nandi `07...] Recent analyi for calar, vector and tenor operator: Contraint from rare decay do not allow for large effect [Boeth, Haich `11] plu τ τ l l + 12

16 Rare decay Many intereting rare decay two highlight at LHC: # theory accuracy B µ + µ B K ( ) + # of oervale 13

17 B µ + µ l t Z t W + l B i peudocalar no photon penguin Q A =( L γ µ q L )( lγ µ γ 5 l) Dominant operator (SM) Wilon helicity uppreion m2 l M 2 B Effective Hamiltonian in the SM (NP + chirality flipped): L eff = G F 2 αv t V t π in 2 θ W (C S Q S + C P Q P + C A Q A ) + h.c. Q S = m ( R q L )( ll) Q P = m ( R q L )( lγ 5 l) B(B (t = 0) µ + µ )=3.2(2) 10 9 [De Bruyn, Fleicher et. al. `12] meaurement i time integrated B(B µ + µ )=3.5(2)

18 MSSM: MFV and Large tan β Lagrangian of 2HDM of type 2 H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. 15

19 MSSM: MFV and Large tan β m Lagrangian of 2HDM of type 2 H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. 15

20 MSSM: MFV and Large tan β m Y d v d Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. 15

21 MSSM: MFV and Large tan β m Y d v d Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. H u ũ R A QL Q L H u µ H d D R One loop: 2HDM of type 3 L Y eff = Y d R Y d Y u Y u H u Q L 15

22 MSSM: MFV and Large tan β δyv u m Y d v d Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. H u ũ R A QL Q L H u µ H d D R One loop: 2HDM of type 3 L Y eff = Y d R Y d Y u Y u H u Q L 15

23 MSSM: MFV and Large tan β δyv u m Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. H u ũ R A QL Q L H u µ H d D R One loop: 2HDM of type 3 L Y eff = Y d R Y d Y u Y u H u Q L 15

24 MSSM: MFV and Large tan β δyv u m Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. H u ũ R A QL Q L H u µ H d D R One loop: 2HDM of type 3 L Y eff = Y d R Y d Y u Y u H u Q L 15

25 MSSM: MFV and Large tan β δyv u m Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. Y d v d H u ũ R A QL Q L H u µ H d D R One loop: 2HDM of type 3 L Y eff = Y d R Y d Y u Y u H u Q L 15

26 MSSM: MFV and Large tan β δyv u m Lagrangian of 2HDM of type 2 Hd dr H u u R L = Y d ijh d di R q j + Y u ijh u ū i Rq j + h.c. Y d v d H u ũ R A QL Redefinition m & V CKM Q L H u µ H d D R Mae and Yukawa not aligned One loop: 2HDM of type 3 L Y eff = Y d R Y d Y u Y u H u Q L 15

27 Flavour Violation at large tan β Large tan β: O(1) flavour violation [Bau, Kolda 02] and O(1) coupling to quark and lepton B(B µ + µ ) tan β 300GeV 50 M A can e mall for large MA, medium tan β, or different A term to fulfil the experimental upper ound from LHC: (ATLAS &CMS) 4 h d B(B µ + µ ) < µ µ B μ μ (o far) not relevant for Q 9 =( L γ µ L )( lγ µ γ 5 l) Q 10 =( L γ µ L )( lγ µ γ 5 l) Q 9 =( R γ µ R )( lγ µ γ 5 l) Q 10 =( R γ µ R )( lγ µ γ 5 l) 16

28 B K ( ) [ Kπ]+ + K Many angular oervale for B K ( ) [ Kπ]+ + B + K* K* + z 32π 9 d 4 Γ dq 2 dcoθ dcoθ K dφ = J 1 in 2 θ K + J 1c co 2 θ K +(J 2 in 2 θ K + J 2c co 2 θ K ) co 2θ +J 3 in 2 θ K in 2 θ co 2φ + J 4 in 2θ K in 2θ coφ + J 5 in 2θ K inθ coφ +(J 6 in 2 θ K + J 6c co 2 θ K ) coθ + J 7 in 2θ K inθ inφ +J 8 in 2θ K in 2θ inφ + J 9 in 2 θ K in 2 θ in 2φ From thee one can contruct oervale a e.g. forward ackward aymmetry 17

29 L eff for l + l - (q q ) SM Wilon coefficient: Matching at μ MW u,c C 2 C 9,10 u,c + l l Renormaliation Group Equation μ MW u,c u,c q l q q l + q C L NNLL in QCD and NLL EW [Boeth, Gamino, MG `04, Haich; MG, Haich `05] q l l q 18

30 Excluive B K ( ) + decay Sytematic theoretical decription aed on heavy-quark expanion (Λ/m) for q 2 << m 2 (J/ψ) (SCET) [Benke, Feldmann, Seidel `01] OPE for q 2 >> m 2 (J/ψ) [Grintein et.al. ; Beylich et. al. `11] Uncertaintie: Form factor & power correction Form factor inenitive / enitive quantitie [Krüger, Matia;... Boeth et. al.] 19

31 Contraint on New Phyic A new phyic contriution to the Z-penguin correlate C9 and C10 a well a hadronic and leptonic decay. Senitivity to the chirality of the coupling Im(Z^L) [Boeth, MG, Vicker] Z-penguin l + l - Im(Z^R) chirality flipped Z-penguin Re(Z^L) Re(Z^R) 20

32 Contraint on New Phyic A new phyic contriution to the Z-penguin correlate C9 and C10 a well a hadronic and leptonic decay. Senitivity to the chirality of the coupling Im(Z^L) [Boeth, MG, Vicker] l + l - Z-penguin Im(Z^R) & hadronic decay chirality flipped Z-penguin Re(Z^L) Re(Z^R) 21

33 Concluion Overall: tandard model agree well with current LHC data Still: there i plenty of room to improve i) the tet of the tandard model ii) earch for new phyic (alo at NA62, Belle II) Many more intereting thing (B X γ, B τ υ, B hh,...) 22