CP Violation Beyond the Standard Model
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1 CP Violation Beyond the Standard Model 5th Recontres du Vietnam Hanoi August 7, 2004 Yossi Nir (Weizmann Institute of Science) Thanks to: Sandrine Laplace, Zoltan Ligeti CPV BSM 1/21
2 Motivation Why do theorists like CP violation? 1. The study of CPV is experiment-driven. 2. CP is a symmetry of the strong interactions = Various CP asymmetries can be cleanly interpreted. 3. Almost any model of NP gives new sources of CPV; In particular, CPV probes the mechanism of supersymmetry breaking. 4. Baryogenesis implies that there must exist sources of CPV beyond the KM phase. θ QCD is irrelevant in meson decays CPV BSM 2/21
3 Plan of Talk Plan of Talk 1. CP asymmetries 2. s uūd: K ππ (ε and ε ) 3. b c cs: B ψk 4. b s ss: B φk, η K, KKK 5. Supersymmetry CPV BSM 3/21
4 CP Asymmetries P 0 A 1 A 2 f CP M 12 Ā 1 Γ 12 Ā 2 P 0 CPV BSM 4/21
5 CP Asymmetries P 0 A 1 1 f CP A 2 2 M 12 3 Ā 1 1 Γ 12 Ā 2 P 0 1 Decay Ā/A 1 Ā A = Ā1+Ā2 A 1 +A 2 Re ε P ± f ± 2 Mixing q/p 1 3 Interference Imλ 0 λ = M 12 M 12 q p = 2M 12 iγ 12 M i Γ Re ε P 0, P 0 l ± X Ā A S ψks P 0, P 0 f CP CPV BSM 4/21
6 CP asymmetries Direct vs. Indirect CPV Indirect CPV Can be accounted for by a phase in M 12 only q/p 1 and/or a single S f Imλ f 0 Superweak models: only indirect CPV Direct CPV cannot be accounted for by a phase in M 12 only Ā/A 1 and/or S f 1 S f2 SM: possibly large direct CPV CPV BSM 5/21
7 Results and Implications: s uūd K ππ K 0 Im ε Re ε ππ Re ε K 0 ) ε = (2.284 ± 0.014) 10 (ε 3 = 1 λ 0 1+λ 0 Christenson, Cronin, Fitch, Turlay (64) Re ε /ε = (1.67 ± 0.26) 10 3 ( ε = 1 6 (λ 00 λ + ) ) NA31 (88), KTeV (01), NA48 (02) CPV BSM 6/21
8 Results and Implications: s uūd Lessons from ε CP violation has been observed. Old new physics: a third generation is required. A useful CKM constraint: the KM phase is large. The NP CP/flavor problem. CPV BSM 7/21
9 CP/Flavor problems The NP CP/Flavor Problem m 2 H (m2 H ) tree π 2 Λ 2 NP To avoid fine-tuning of the Higgs mass, Λ NP < 4πm W 1 T ev. L NP 1 Λ 2 NP s ds d To avoid too large contributions to ε K and to m K,D,B, Λ NP > T ev. New Physics at the TeV scale must have a very non-generic flavor and CP structure CPV BSM 8/21
10 Results and Implications: s uūd Lessons from ε /ε Direct CP violation has been observed. The result is consistent with the SM predictions. Large hadronic uncertainties = no useful CKM constraint. The superweak scenario is excluded. Wolfenstein (64) New physics (e.g. Supersymmetry) may contribute significantly. e.g. Masiero and Murayama (99) CPV BSM 9/21
11 Results and Implications: b c cs B 0 ψk S Carter and Sanda (80) Bigi and Sanda (81) B 0 Within SM, dominated by a single phase = C ψks = 0 (Subleading phase CKM- and loop-suppressed) Within SM, M 12 (V tb V td) 2, A V cb V cd = S ψks = sin 2β With NP, still S ψks sin[arg(m12) 2 arg(vcb V cd)] and C ψks 0, but S ψks sin 2β is possible. BABAR and BELLE measure mode CP S ψks C ψks ψk S ± ± 0.04 CPV BSM 10/21
12 Results and Implications Unitarity Triangles 1 m d m s & m d η 0 V ub /V cb -1 C K M f i t t e r p a c k a g e Tree level + CPC observables m B, m Bs ρ Using CKMFitter package (Höcker et al., Eur. Phys. J. C21, 225 (01)) CPV BSM 11/21
13 Results and Implications Unitarity Triangles 1 m d 1 m s & m d ε K η 0 V ub /V cb η 0 V ub /V cb sin 2β WA ε K -1-1 C K M f i t t e r p a c k a g e Tree level + CPC observables m B, m Bs ρ C K M f i t t e r p a c k a g e Tree level + CPV observables ε, S ψks ρ Using CKMFitter package (Höcker et al., Eur. Phys. J. C21, 225 (01)) CPV BSM 11/21
14 Results and Implications: b c cs Lessons from S ψk CPV in B decays has been observed. The Kobayashi-Maskawa mechanism of CPV has successfully passed its first precision test. A significant constraint on the CKM parameters ( ρ, η): Imλ ψks = sin 2β = 2 η(1 ρ) η 2 +(1 ρ) 2 = 0.74 ± 0.05 Approximate CP (in the sense that all CPV phases are small) is excluded. New, CPV physics that contributes > 20% to B 0 B 0 mixing is disfavored. CPV BSM 12/21
15 Results and Implications: b c cs The KM mechanism The KM mechanism successfully passed its first precision test Very likely, the KM mechanism is the dominant source of CP violation in flavor changing processes CPV BSM 13/21
16 Results and Implications: b c cs The KM mechanism The KM mechanism successfully passed its first precision test Very likely, the KM mechanism is the dominant source of CP violation in flavor changing processes Very likely : The consistency could be accidental = More measurements of CPV are crucial. Dominant : There is still room for NP at the O(20%) level = A challenge for theorists. FC processes : FD CPV can still be dominated by NP = Search for EDMs. CPV BSM 13/21
17 Results and Implications B 0 C f CP S B 0 f CP b q qq SM η CP S = ± 2Imλ 1+ λ 2 C = 1 λ 2 1+ λ 2 ψk S b c cs sin 2β ± ± 0.04 φk S b s ss sin 2β ± ± 0.23 η K S b s ss sin 2β ± ± 0.13 K + K K S b s ss sin 2β ± ± 0.13 π 0 K S b uūs sin 2β eff ± ± 0.30 D + D b c cd sin 2β eff 0.05 ± ± 0.19 ψπ 0 b c cd sin 2β eff ± ± 0.24 π + π b uūd sin 2α eff ± ± 0.20 ρ + ρ b uūd sin 2α eff ± ± 0.30 CPV BSM 14/21
18 b s ss B 0 C φk S, η K S, KKK S B 0 Within SM, dominated by a single phase = C 0 (Subleading phase CKM-suppressed) Within SM, A V cb V cd = S S ψks ( +0.74) With NP, S S ψks, S f1 S f2 and C 0 are possible. mode CP η CP S C φk S ± 0.29(0.67) ± 0.23 η K S ± ± 0.13 K + K K S ± ± 0.13 Babar: ± 0.34 ± 0.07; Belle: 0.96 ± 0.50 ± 0.10 Isospin analysis is used to argue CP = + dominance. CPV BSM 15/21
19 CP/Flavor problems A SM CP/Flavor Problem? CP asymmetries in b s ss: S η K S, S φks Polarization in B φk : f σ A σ 2 A A 2 + A 2 Theoretically (HQE), (f + f )/f 0 = O(1/m 2 B ), f /f = 1 + O(1/m B ). Experimentally, f 0 (ρ 0 K + ) = 0.96 ± 0.16, f 0 (ρ 0 ρ + ) = 0.96 ± 0.07, f 0 (ρ + ρ ) = 0.99 ± 0.08 but f 0 (φk 0 ) = 0.58 ± 0.10, f (φk 0 ) = 0.41 ± 0.11, f 0 (φk + ) = 0.46 ± The lipkin sum rule: R L 2 Γ(B+ K + π 0 )+Γ(B 0 K 0 π 0 ) Γ(B + K 0 π + )+Γ(B 0 K + π ) Theoretically (isospin), R L = 1 + O ( ) P EW +T 2 P = 1 + O(10 2 ) Experimentally, R L = 1.24 ± CPV BSM 16/21
20 CP/Flavor problems A SM CP/Flavor Problem Not Yet... S η K S = 0.27 ± 0.21: 2σ. S φks = ± 0.67: Experimental situation needs to be resolved. f 0 (φk 0 ) = 0.58 ± 0.10, f (φk 0 ) = 0.41 ± 0.11: Charming penguins (SCET) / Annihilation diagrams (QCDF) can account for the data. R L = 1.24 ± 0.10: 2.4σ More theoretical effort is needed to determine T/P CPV BSM 17/21
21 Supersymmetry Supersymmetry for Phenomenologists FV CPV Y + + µ + A + + m g + m 2 f + + B + 80 real + 44 imaginary parameters CPV BSM 18/21
22 Supersymmetry CP Violation in Supersymmetry K physics: ImM SUSY 12 ImM exp ( 1 T ev m Heavy squarks: m > 1 T ev ; Universality: m 2 21 m 2 ; Alignment: K d 12 1; (Approximate CP: sin φ 1) ) 2 ( m 2 12 m 2 ) 2 Im [ (K d 12 ) 2] B physics: S exp ψk SSM ψk consistent with exact universality, constrains U(2) and U(1) models, disfavors heavy squarks. D physics: x, y < 0.05 probes alignment. d EDMs: SUSY N 300 ( ) 100 GeV e cm m sin φa,b can distinguish MFV ( < ) from SUSY CPV ( > ). CPV BSM 19/21
23 Supersymmetry SUSY contributions to B φk S b s (δ 23 d ) RR s R s br s R s Could there be large effects in B φk S and not in B ψk S? CPV BSM 20/21
24 Supersymmetry SUSY contributions to B φk S b s (δ 23 d ) RR s R s br s R s Could there be large effects in B φk S and not in B ψk S? Yes: δ d 23 δ d 13 Could there be large effects in B φk S and not in B X s γ? CPV BSM 20/21
25 Supersymmetry SUSY contributions to B φk S b s (δ 23 d ) RR s R s br s R s Could there be large effects in B φk S and not in B ψk S? Yes: δ d 23 δ d 13 Could there be large effects in B φk S and not in B X s γ? Yes: δ d RR δd LR Are there well-motivated models with (δ d 23) RR = O(1)? CPV BSM 20/21
26 Supersymmetry SUSY contributions to B φk S b s (δ 23 d ) RR s R s br s R s Could there be large effects in B φk S and not in B ψk S? Yes: δ d 23 δ d 13 Could there be large effects in B φk S and not in B X s γ? Yes: δ d RR δd LR Are there well-motivated models with (δ d 23) RR = O(1)? U(1) flavor symmetry: (δ d 23) RR (m s /m b )/ V cb SO(10) GUTs: (δ d 23) RR θ l 23 CPV BSM 20/21
27 Conclusions Conclusions The KM mechanism is, very likely, the dominant source of the CP violation observed in meson decays CPV observed ( 3σ from Babar+Belle) in three modes: S ψks = 0.74 ± 0.05, S K+ K K S = 0.54 ± 0.18, A K π ± = ± (direct CPV!) No evidence for new flavor/cp physics 2σ effect in S η K S 2.5σ effect in S D + D We left the era of hoping for NP altenratives to KM; We are in the era of seeking for NP corrections to KM The field is experiment-driven Waiting for new results from Belle/Babar/TeVatron CPV BSM 21/21
28 Conclusions Unitarity Triangles excluded area has CL < 0.05 excluded area has CL < 0.05 excluded area has CL < K + π + νν 1 sin 2β m d 1 sin 2β m s & m d 0.5 α 0.5 α B ρρ 0.5 α η 0 ε K γ β η 0 γ β η 0 γ β V ub /V cb V ub /V cb V ub /V cb ε K -1 C K M f i t t e r s d ε, B(K + π + ν ν) ρ -1 C K M f i t t e r B ρρ ρ b d m Bd, S ψk, S ρρ -1 C K M f i t t e r ρ b s m Bs, S φk,η K,KKK There is still a lot to be learnt from future measurements Laplace (04) CPV BSM 22/21
29 Conclusions Unitarity Triangles K + π + νν 1 m d 1 m s & m d ε K η 0 V ub /V cb η 0 V ub /V cb sin 2β J/ΨKs η 0 V ub /V cb sin 2β ΦKs -1 ε K -1-1 C K M f i t t e r p a c k a g e C K M f i t t e r p a c k a g e C K M f i t t e r p a c k a g e s d ε, B(K + π + ν ν) ρ ρ b d b s m Bd, S ψks m Bs, ρ S φks There is still a lot to be learnt from future measurements Laplace (02) CPV BSM 23/21
30 CP asymmetries The case theorists love B 0 A f CP S fcp M 12 B 0 Ā 1. Decay dominated by a single CPV phase: Ā/A = 1 2. CPV in mixing negligible: q/p = 1 3. The only remaining effect is A fcp (t)=s fcp sin( m B t) S fcp = Imλ fcp = ± sin[arg(m 12) + arg(āf CP ) arg(a fcp )] CPV BSM 24/21
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