1. Measurement of  David Hutchcroft, University of Liverpool BEACH’06      

2. David Hutchcroft, BEACH’062 CKM angles  CKM matrix is a unitary matrix that connects the mass eigenstates and weak eigenstates  Elements appear in weak current interactions V ud V us V ub V cd V cs V cb V td V ts V tb 1 - c 2 c A c 3 (  - i  ) = - c 1 - c 2 /2 A c 2 A c 3 ( 1 -  - i  ) - A c 2 1 V CKM = + O( c 4 ) [ c = sin  c ] CP violation | V td | e -i  | V ub | e -i  A unitarity triangle : V * ub V ud + V * cb V cd + V * tb V td = 0 Wolfenstein parameterisation

3. David Hutchcroft, BEACH’063 B Factories KEKII Both are asymmetric e + e − colliders and 4  detectors Use e + e − annihilation at  (4s) resonance to make BB pairs Beam asymmetry means BB system has a relativisticly extended lifetime BaBar has collected 352 fb -1 and Belle has collected 610fb -1 1fb -1 ~ 1.1 million BB pairs

4. David Hutchcroft, BEACH’064 CP violation  Direct CP violation : Br(B 0 →f) ≠ Br(B 0 →f) Time integrated effect, event counting  Indirect CP violation from mixing and decay interference Time dependant effect Relevant for CKM angle measurements  Use coherence between B 0 and B 0 to decide what meson actually decayed Tag other side B decay Also measure  t between decays t  0 tag B + e e 0 CP B t=0  K e +          (4S) -    

5. David Hutchcroft, BEACH’065 Where B 0 is the physical state when it decays Indirect CP violationS ≠ 0 Direct CP violation C ≠ 0 Need to tag flavour of B using other B meson Must understand tag resolution and dilution [BaBar C = −A cp Belle]

6. David Hutchcroft, BEACH’066 Tree decay  B 0 B 0 mixing  Penguin decay  Decays depending on   Tree decays of B 0 and B 0 to two charmless mesons depend on   Trees onlyTrees + Penguins strong phase

7. David Hutchcroft, BEACH’067 Separating trees and penguins Use an isospin relation between similar decays to measure the amount of each type of decay Used to set a limit on  eff  eff                      Gronau-London: PRL65, 3381 (1990) etc Need to measure all of the related decays of  Penguin contribution depends on Br(     ) Charged B decay is tree only

8. David Hutchcroft, BEACH’068 Selecting B decays  Backgrounds are predominantly non resonant annihilation so reconstruct B mesons Variables  Other backgrounds are similar B decays Need to model all backgrounds in the fit  Use unbinned maximum likelihood fit where E B * is the CM energy of the B meson The mass of the B system using the initial beam energy constraint, p * B is the CM frame B momentum BaBar m ES ≡ M bc Belle

9. David Hutchcroft, BEACH’069 B0→B0→ 275×10 6 B pairs 666  43 signal events 227×10 6 B pairs 467  33 signal  events Phys.Rev.Lett. 95 (2005) 101801 Phys.Rev.Lett. 95 (2005) 151803

10. David Hutchcroft, BEACH’0610 B0→B0→ S = −0.67±0.16±0.06 C = −0.56±0.12±0.06 S = −0.30±0.17±0.03 C = −0.09±0.15±0.04 So two comparable measurements of S = sin(2  eff ) Measurements of direct CP asymmetry less compatible

11. David Hutchcroft, BEACH’0611 Using isospin in  system using 253fb -1 using 227 x 10 6 BB PRL 94, 181803(2005) PRL 94, 181802 (2005) Precision measurement of  not possible with current stats.

12. David Hutchcroft, BEACH’0612 B → ρρ  Vector/Vector meson final state: both CP odd and even final states  S, P, D wave components Need angular analysis to determine CP content of decay  ρρ is almost 100% longitudinally polarised (CP even) Polarisation

13. David Hutchcroft, BEACH’0613 B0→B0→  In  system the amount of neutral decays is small  Measure B 0 →     events in 227 x 10 6 BB events  Br < 1.1 x 10 -6 at 90% CL.  Isospin triangle for  is flattened compared to  Phys.Rev.Lett. 94 (2005) 131801  eff                    

14. David Hutchcroft, BEACH’0614 B±→±B±→± New result with 231 x 10 6 BB events Previous BaBar/Belle HFAG average hep−ex/0603003 Better match to isospin model Smaller uncertainty on |  eff −  compared  mode

15. David Hutchcroft, BEACH’0615 B 0 →     BaBar (227 x 10 6 BB)Belle (275 x 10 6 BB) PRL 95, 041805 (2005) PRL 96, 171801 (2006)

16. David Hutchcroft, BEACH’0616 B 0 →   analysis  B 0 →   →    −   is not a CP eigenstate 6 decays to disentangle: Tried by BaBar and Belle for just  ±  phase space Did not set limits on  Can use a Dalitz plot analysis to get  from decays Snyder & Quinn: Phys. Rev. D48, 2139 (1993)    Convert to a square Dalitz plot Mostly resonant decays Move signal away from edges Simplifies analysis MC events

17. David Hutchcroft, BEACH’0617 B 0 →   Dalitz plot analysis  Dalitz plot analysis yields CP asymmetries and strong phases of decays  Using 213 x 10 6 BB events hep-ex/0408099 m’ and  ’ are variables in a square Daltiz plot 1184 ± 58 B →       Signal events Blue bands are different types of backgrounds

18. David Hutchcroft, BEACH’0618 Conclusion Combined constraints on   gives single best measurement  resolves 2-fold ambiguity from  World Average: Global CKM Fit (w/o  ): msms