rpp2010-rev-cp-viol-kl-decays

rpp2010-rev-cp-viol-kl-decays - 1 CP VIOLATION IN KL DECAYS...

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–1– CP VIOLATION IN K L DECAYS Updated May 2010 by L. Wolfenstein (Carnegie-Mellon Univer- sity), T.G. Trippe (LBNL), and C.-J. Lin (LBNL). The symmetries C (particle-antiparticle interchange) and P (space inversion) hold for strong and electromagnetic inter- actions. After the discovery of large C and P violation in the weak interactions, it appeared that the product was a good symmetry. In 1964 violation was observed in K 0 decays at a level given by the parameter ± 2 . 3 × 10 3 . A uniFed treatment of violation in K , D , B ,a n d B s mesons is given in “ Violation in Meson Decays” by D. Kirkby and Y. Nir in this Review . A more detailed review including a thorough discussion of the experimental techniques used to determine violation parameters is given in a book by K. Kleinknecht [1]. Here we give a concise summary of the formalism needed to deFne the parameters of violation in K L decays, and a description of our Fts for the best values of these parameters. 1. Formalism for violation in Kaon decay: violation has been observed in the semi-leptonic decays K 0 L π ² ± ν , and in the nonleptonic decay K 0 L 2 π .The experimental numbers that have been measured are A L = Γ( K 0 L π ² + ν ) Γ( K 0 L π + ² ν ) Γ( K 0 L π ² + ν )+Γ( K 0 L π + ² ν ) (1 a ) η + = A ( K 0 L π + π ) /A ( K 0 S π + π ) = | η + | e + (1 b ) η 00 = A ( K 0 L π 0 π 0 ) ( K 0 S π 0 π 0 ) = | η 00 | e 00 . (1 c ) violation can occur either in the K 0 K 0 mixing or in the decay amplitudes. Assuming CPT invariance, the mass eigenstates of the K 0 K 0 system can be written | K S ± = p | K 0 ± + q | K 0 ± , | K L ± = p | K 0 ±− q | K 0 ± . (2) If invariance held, we would have q = p so that K S would be -even and K L -odd. (We deFne | K 0 ± as | K 0 ± ). CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34
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–2– CP violation in K 0 K 0 mixing is then given by the parameter e ± where p q = (1 + e ± ) (1 e ± ) . (3) violation can also occur in the decay amplitudes A ( K 0 ππ ( I )) = A I e I ,A ( K 0 ( I )) = A I e I , (4) where I is the isospin of , δ I is the Fnal-state phase shift, and A I would be real if invariance held. The -violating observables are usually expressed in terms of ± and ± ± deFned by η + = ± + ± ± 00 = ± 2 ± ± . (5 a ) One can then show [2] ± = e ± + i (Im A 0 / Re A 0 ) , (5 b ) 2 ± ± = ie i ( δ 2 δ 0 ) (Re A 2 / Re A 0 )( Im A 2 / Re A 2 Im A 0 / Re A 0 ) , (5 c ) A L =2Re ±/ (1 + | ± | 2 ) 2Re ±. (5 d ) In Eqs. (5a), small corrections [3] of order ± ± × Re ( A 2 /A 0 )are neglected, and Eq. (5 d ) assumes the Δ S Q rule. The quantities Im A 0 ,Im A 2 ,andIm e ± depend on the choice of phase convention, since one can change the phases of K 0 and K 0 by a transformation of the strange quark state | s ±→| s ± e ; of course, observables are unchanged. It is possible by a choice of phase convention to set Im A 0 or Im A 2 or Im e ± to zero, but none of these is zero with the usual phase conventions in the Standard Model. The choice Im A 0 = 0 is called the Wu-Yang phase convention [4], in which case ± = e ± .Theva lue of ± ±
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This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.

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rpp2010-rev-cp-viol-kl-decays - 1 CP VIOLATION IN KL DECAYS...

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