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Neutral Kaon system

Neutral Kaon system. :. K o K o system. Kaon mesons in two isospin doublets. Part of pseudo-scalar J P =0 - meson octet with ,. K + = us K o = ds. K - = us K o = ds. I 3 =+1/2 I 3 =-1/2. S=+1. S=-1. Kaon production. K o :  - + p  o + K o

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Neutral Kaon system

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  1. Neutral Kaon system :

  2. Ko Ko system • Kaon mesons in two isospin doublets Part of pseudo-scalar JP=0- meson octet with , K+ = us Ko = ds K- = us Ko = ds I3=+1/2 I3=-1/2 S=+1 S=-1 • Kaon production Ko : - + p o + Ko But from baryon number conservation: Ko : + + p K+ + Ko + p Or Ko : - + p o + Ko + n +n S 0 0 -1 +1 Requires higher energy S 0 0 +1 -1 0 Muchhigher S 0 0 +1 -1 0 0

  3. Kaon oscillations d s • So say at t=0, pure Ko, • later a superposition of states W- u, c, t u, c, t _ _ W+ - d s K0 K0 u, c, t _ d s W+ W- _ _ _ _ u, c, t d s

  4. Assume CP Ko Decay KS show mass eigenstates CP=+1 CP=-1 KL • In that case KS branching fractions: p+p- 69%, p0p0 31% KL branching fractions: p0p0p0 21%, p+p-p0 13%, pn 66% Ksoo Ks+- KL+-o KLooo CP=+1 CP=-1

  5. Time dependent probabilities for the neutral kaon case. t (1/G+)

  6. Ko Regeneration • Start with Pure Ko beam • After time all Ks component decayed • Introduce slab of material in beam • reactions 1) Elastic scatttering 2) Charge exchange 3) Hyperon production • Hence Ko absorbed more strongly i.e. Ks regenerated

  7. Discovery of CP Violation K1oo K1+- K2+-o K2ooo So if KL =K1 CP eigenstate, Observe no two pion component BUT Can one find KL decaying into +-? CP=+1 CP=-1 But if broken get: Where  quantifies degree of CP violation

  8. J.H. Christenson et al., PRL 13,138 (1964) Discovery of CP violation • Mass and angular spectrum KL p+p-+X m(p+p-) < mK p+- = pp+ + pp- q = angle between pKL and p+- If X = 0, p+- = pKL: cos q = 1 If X 0, p+-pKL: cos q 1 q m(p+p-) = mK KL m(p+p-) > mK KL  cos q

  9. So CP symmetry is violated in the neutral kaon system. Mass eigenstates (KS and KL)  CP eigenstates Both KS and KL could decay into +--. • Experimentally well known: • The majority of KS decays intop+-p-and KL intop+-p--p0. In KL Small but with profound implications

  10. CPLEAR revisited S = 0 Decay final state at time t Spin(p) = 0 Lp-p = 0 p+-p- CP(p+-p-) = +1 i.e. CP eigenstate K0 at t = 0 decays into p+ p- vs K0 at t = 0 decays into p+ p- any difference = CP violation Initial state at t = 0 S = 0 • Tag Ko/Ko from charged pion/kaon

  11. CPLEAR R+-(t) and R+-(t) K0 _ _ K0 CP violation

  12. CPLEAR CP asymmetry _ R+-(t) -R+-(t) R+-(t) +R+-(t) _ A+-(t) = large difference! • CP violation in mixing • The two mass eigenstates are not CP eigenstates

  13. Kaons: CP violation in Decay CP violation first through existence of certain decay modes ~2.3x10-3 If CP violation is only in mixing, i.e. independent of decay So, put channel independent term  and channel dependent ’ Hence, by measuring only rates: get

  14. So, two expts in the 80’s did it: • NA31 (CERN) • E731 (Fermilab) • Ambiguous result! So, two expts did it again…….

  15. NA48

  16. KTeV

  17. p+p-andp0p0at the same time: NA31, NA48 KSis regenerated from KL: E731, KTeV Measure Normalisation constants No normalization is required, but efficiencies, acceptances etc. have to be corrected…

  18. e e e e Effort over 30 years! Not easy to compare with SM theory 0.0050  0.0005  0  |h+-||h00| Note; 3 Re = |h+-/h00 |- 1, i.e.Re  0

  19. CKM parameters with CP conserving parameters • |Vud| : nuclear Beta decay 0.97340.0008 • |Vus| : semileptonic Kaon and hyperon decay (CCFR) 0.21960.0026 • |Vcd| : Neutrino and anti-neutrino production of charm off valence d quarks 0.2240.016 • |Vcs| : W decays (LEP/me!) 0.9960.013 • |Vcb| : semileptonic inclusive and exclusive B decays (LEP/CLEO) 0.04120.0020 • |Vub| end point spectrum in semileptonic B decays(LEP/CLEO) 0.0036 0.0007 • Bo mixing xd, + lattice gauge inputs |Vtb*Vtd| 0.0079 0.0015 • Can use Unitarity constraints

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