1. Weak interactions I. Radulescu Sub-atomic physics seminar October 2005 _____________________________________________ Nuclear Geophysics Division Kernfysisch Versneller Instituut Zernikelaan 25 9747 AA Groningen The Netherlands

2. Outline ___________________________________ Introduction The Cabibbo Model – Kobayashi-Maskawa matrix CP violation in kaon decay Conclusion

3. Nuclear  decay is the best known example of weak interaction n  p + e - +(semi-leptonic) d  u + e - +  -  e - + +(leptonic) (non-leptonic) (semi-leptonic) Introduction ___________________________________

4. The Cabibbo Model ___________________________________ In  decay of  0 the s quark transforms into a u quark (strangeness-changing,  S=1) The weak interaction eigenstates are linear superpositions of the strong interaction eigenstates

5. The Cabibbo Model ___________________________________ Relationship between the strong and the weak quark eigenstates is by a rotation matrix, Y = B + S

6. Kobayashi – Maskawa mixing matrix ___________________________________ Kobayashi – Maskawa include a third generation of quarks – t (top) and b (bottom) Is a 3  3 unitary matrix V operating on the charge -1/3 quarks (d, s, b) The matrix between weak eigenstates (d’, s’, b’) and mass eigenstates (d, s, b) The element V ud specifies the coupling of the u and d quarks:

7. Kobayashi – Maskawa mixing matrix ___________________________________ Where c ij = cos  ij and s ij = sin  ij (  12,  13,  23, and a phase  13 =0-2  ) In the limit  13 =  23 =0 the third generation decouples and if  12 =  c  original Cabibbo mixing for non-zero values of  13  CP violation in weak interaction

8. The particles K S and K L ___________________________________, (pair particle-antiparticle) :,, S = +1, :,, S = -1 I3I3

9. Decay channels of mesons ___________________________________ MesonsLifetime (s)Most common decay channels Comments 00 2.6  10 -8 8.4  10 -17 2  99% Electromagnetic KK 1.2  10 -8 64% 3  7% 8.9  10 -11 2   100% K 0 decay 5.2  10 -8 3  34%  27%  e 39% 2  2.9  10 -3 CP violating  5.5  10 -19 3  56% 2  39% Electromagnetic ’’ 3.3  10 -21    65% Pseudoscalar mesons

10. parity eigenstate neither nor are CP eigenstates CP = +1 CP = -1 These are CP eigenstates CP violation in kaon decay ___________________________________

11. (  0  0,  +  - ) B=L=S=Q=0 2  (  0  0  0,  +  -  0 ) conservation of angular momentum  0 has C=+1, P=-1 CP=-1 for 3  3 

12. Strangeness oscillations ___________________________________ (extremely small mass difference)

13. K 0 regeneration ___________________________________ (BR=3  10 -3 )  CP violation

14. K 0 regeneration ___________________________________ K S component regenerated from K L beam

15. |  00 | = (2.253  0.024)·10 -3 and  +- =  00 = (43.68  0.14)   46.6  (1.2;2) |  +- | = (2.268  0.023)·10 -3 CP violation, mixing ___________________________________

16. CP violation (direct), CPT invariance ___________________________________ =  -2  ’ =  +  ’

17. Experiment NA48 ___________________________________ 450 GeV proton beam two targets – K L target is placed 126 m up-stream K S target (beryllium) - 6 m up-stream 70-170 GeV

18. Experiment NA48 ___________________________________ correction for background, acceptance and uncorrelated activity in detectors R = 0.9889  0.0027(stat)  0.0035(syst) Re(  `/  ) = (18.5  4.5  5.8)  10 -4 Direct CP violation measured!

19. Conclusions ___________________________________ Summary of  ’ /  measurement and prediction