CP Violation: A New Era

Transcription

1 CP Violation: A New Era Ringberg Phenomenology Workshop on Heavy Flavors 2/5/23 Yossi Nir (Weizmann Institute of Science) Collaborations with: Yuval Grossman, Zoltan Ligeti, Helen Quinn Sandrine Laplace, Zoltan Ligeti, Gilad Perez CP Violation 1/2

2 Motivation B C φk S, η K S, KKK, DD, ψπ, ππ S B f CP b q qq η CP S = ± 2Imλ 1+ λ 2 C = 1 λ 2 1+ λ 2 ψk S b c cs +.73 ± ±.4 φk S b s ss.39 ± ±.67 η K S b s ss +.33 ±.34.8 ±.18 K + K K S b s ss +.52 ± ±.37 D + D b c cd.31 ± ±.27 ψπ b c cd +.46 ± ±.29 ππ b uūd +.48 ± ±.24 A lot of new data! CP Violation 2/2

3 Plan of Talk Plan of Talk 1. CP asymmetries in b c cs, b s ss hep-ph/ SU(3) relations and S η K S, S φks, S K+ K K S hep-ph/ The CP Asymmetry in semileptonic B decays hep-ph/221 CP Violation 3/2

4 CP Violation in b c cs B ψk S B Within SM, dominated by a single phase = C ψks = (Subleading phase is 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, but S ψks sin 2β is possible. BABAR and BELLE measure mode η ψk S ψk C ψk ψk S +.73 ±.6.5 ±.4 CP Violation 4/2

5 CP Violation in b c cs Lessons from A CP (B ψk S ) 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 =.734 ±.54 Approximate CP (in the sense that all CPV phases are small) is excluded. New, CPV physics that contributes > 2% to B B mixing is disfavored. CP Violation 5/2

6 CP Violation in b c cs 1 m d m s & m d η ε K V ub /V cb ε K -1 C K M f i t t e r p a c k a g e ρ Without S ψk m B, m Bs, ε Using CKMFitter package (Höcker et al., Eur. Phys. J. C21, 225 (1)) CP Violation 6/2

7 CP Violation in b c cs 1 m d m s & m d ε K η V ub /V cb sin 2β WA ε K -1 C K M f i t t e r p a c k a g e ρ Without S ψk m B, m Bs, ε Using CKMFitter package (Höcker et al., Eur. Phys. J. C21, 225 (1)) CP Violation 6/2

8 CP Violation in b c cs 1 m d 1 m d m s & m d m s & m d η ε K V ub /V cb sin 2β WA η ε K V ub /V cb sin 2β WA ε K 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 Without S ψk m B, m Bs, ε ρ With S ψk m B, m Bs, ε, S ψks ρ Using CKMFitter package (Höcker et al., Eur. Phys. J. C21, 225 (1)) CP Violation 6/2

9 CP Violation in b s ss B C φk S, η K S, KKK S B Within SM, dominated by a single phase = C (Subleading phase is CKM-suppressed) Within SM, A V cb V cd = S S ψks ( +.73) With NP, S S ψks, S f1 S f2 and C are possible. mode ηs C φk S.39 ± ±.67 η K S +.33 ±.34.8 ±.18 K + K K S +.52 ± ± Isospin analysis is used to argue CP = + dominance. CP Violation 7/2

10 CP Violation in b s ss 1 K + π + νν 1 m d 1 m s & m d ε K η V ub /V cb η V ub /V cb sin 2β J/ΨKs η 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 CP Violation 8/2

11 CP Violation in b s ss 1 K + π + νν 1 m d 1 m s & m d ε K η V ub /V cb η V ub /V cb sin 2β J/ΨKs η 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 It is still possible that corrections to SM are large in m Bs, in CP asymmetries in B s decays, and in Imλ ( ss)ks. CP Violation 8/2

12 SU(3) The Question Within SM, there is a second, CKM suppressed, phase: A η K S = Vcb V csa c η K S + Vub V usa u η K S = S η K S sin 2β = 2 cos 2β sin γ cos δ ξ η K S ξ η K S V ub V us a u η K S Vcb V cs a c η K S How large can ξ η K S be? O(λ 2 ) [CKM suppression] Quark model [London and Soni, hep-ph/974277:.2] BBNS [Beneke and Neubert, hep-ph/2185:.7] SU(3) relations [GLNQ, hep-ph/33171] CP Violation 9/2

13 SU(3) The Strategy For b q qs transitions: A f = V cb V cs a c f + V ub V us a u f = V cb V cs a c f (1 + ξ f ) For b q qd transitions: A f = Vcb V cd b c f + V ub V ud b u f SU(3) gives relations among the a q f, bq f : a u f = f x f b u f = V ub V ud b u f (1 + λ 2 ξ 1 f ) The branching ratios B(f) constrain a c f, bu f : V ud V ub b u f V cs V cb a c f B(f ) B(f) Combining SU(3) and experimental data gives, conservatively, ξ f = V usv ub a u f V cs V cb a < V c us f V ud f x f B(f ) B(f) CP Violation 1/2

14 SU(3) SU(3) decomposition for P 8 P 8 ( bu)(ūq) B f ( ) A A 8 15 A 8 6 A 8 3 A 1 3 η 8 K 4 6/5 1/ 6 1/ 6 1/ 6 η 8 π 5/ 3 1/ 3 1/ 3 π π 13/5 1/2 1/2 1/6 1 η 8 η 8 3/5 1/2 1/2 1/6 1 π π + 14/ /3 2 K K + 2/5 2 2/3 2 K K 2/ /3 2 SM: 5 SU(3)-amplitudes describe 15 final states = Many relations among the matrix elements CP Violation 11/2

15 SU(3) The Answer For example, (s = sin θ ηη, c = cos θ ηη ) a u η K = s2 2c 2 2 b u η 2 π 3cs 3s 2 2 bu ηπ bu π π 3s(1 + c 2 ) 3sc 2 b u 2 3c 3 η 2 η bu ηη + b u ηη 2 = ξ η K S < V us V ud +.39 [.59 B(η π ) B(η K ) +.33 B(η η ) B(η K ) +.18 B(ηπ ) B(η K ) +.2 B(ηη) B(η K ) B(ηη ) B(η K ) B(π π ) B(η K ) ]. = ξ η K S <.3 CP Violation 12/2

16 SU(3) Another Strategy For φk: Grossman, Isidori, Worah, hep-ph/97835 Similar relations hold for the charged mode (x = free): (3 x)cs a η K + = b 2 ηπ + + (x 1)s2 + 2c 2 2 (x 3)s + 2 b π+ π 3 + xs b 6 K K + b η π + Using experimental data, we obtain ξ η K + <.1 We have a c η K = a c η K + but a u η K a u η K +. However, a u η K = color-suppressed, a u η K + = color-allowed Using the mild dynamical assumption, a u η K a u η K + = ξ η K S <.1 CP Violation 13/2

17 SU(3) Results ξ η K S <.3 SU(3) ξ η K S <.1 SU(3) + leading N c assumption ξ φks <.25 SU(3) + non-cancellation assumption ξ K+ K K S.1 U-spin CP Violation 14/2

18 SU(3) Comments The same bound applies to C f : C f 2 sin γ sin δ ξ f The bounds apply also to MFV models Our bounds are weaker than estimates based on explicit calculations, but have the advantage of being model independent With better data, the bounds will improve SU(3) breaking effects could be significant, but our bounds are probably still conservative If experiments find deviations larger than our bounds = A convincing case for new physics CP Violation 15/2

19 A SL M 12 B B l X Γ 12 SM.13 < A SL <.5 MFV.18 < A SL <.3 NP in loops.4 < A SL < +.4 Experiments.21 < A SL < +.25 An interesting constraint on the NP parameters r 2 d, θ d CP Violation 16/2

20 A SL New Physics 1. The 3 3 CKM matrix is unitary 2. Tree level processes are dominated by the SM CP Violation 17/2

21 A SL New Physics 1. The 3 3 CKM matrix is unitary 2. Tree level processes are dominated by the SM Γ 12 = Γ SM 12 M 12 = rd 2e2iθ d M12 SM m B = rd 2( m B) SM S ψk = sin(2β + 2θ d ) A SL = Re ( Γ12 M 12 ) SM sin 2θd r 2 d + Im ( Γ12 M 12 ) SM cos 2θd r 2 d CP Violation 17/2

22 A SL Constraining r 2 d, 2θ d C K M f i t t e r R&D a SL New Physics a SL Measurement θ d (rad) 2 2θ d (rad) a SL R&D CK M f i t t e r R&D CK M f i t t e r r d r d 2 Without A SL With A SL m Bd, S ψks CP Violation 18/2

23 A SL B ψk S B λ ψk = q p Ā ψk A ψk =.95 ±.4? CP Violation 19/2

24 A SL B ψk S B λ ψk = q p Ā ψk A ψk =.95 ±.4? A SL =.2 ±.14 = q/p =.999 ±.7 CPV in mixing can be safely neglected at present C Babar f CP A Belle f CP = CPV in decay A ψk =.8 ±.25 = ĀψK/A ψk = 1.8 ±.25 = λ ψk = 1.7 ±.26! CP Violation 19/2

25 Conclusions Conclusions One clean measurement can teach us a lot! S ψk = The KM mechanism is, very likely, the dominant source of the observed CPV We learn a lot from dirty measurements too! B(f) s + SU(3) relations = Model independent constraints on S ( ss)ks S ψks A SL = Constraints on r 2 d, 2θ d A SL = CPV in mixing ( q/p 1) can be safely neglected in λ fcp CP Violation 2/2

26 CP violation 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 CP Violation 21/2

27 CP violation 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(2%) level = A challenge for theorists. FC processes : FD CPV can still be dominated by NP = Search for EDMs. CP Violation 21/2