rpp2010-rev-cpt-invariance-tests

rpp2010-rev-cpt-invariance-tests - 1 CP T INVARIANCE TESTS...

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–1– CPT INVARIANCE TESTS IN NEUTRAL KAON DECAY Updated October 2009 by M. Antonelli (LNF-INFN, Frascati) and G. D’Ambrosio (INFN Sezione di Napoli). theorem is based on three assumptions: quantum feld theory, locality, and Lorentz invariance, and thus it is a ±undamental probe o± our basic understanding o± particle physics. Strangeness oscillation in K 0 K 0 system, described by the equation i d dt · K 0 K 0 ¸ =[ M i Γ / 2] · K 0 K 0 ¸ , where M and Γ are hermitian matrices (see PDG review [1], re±erences [2,3], and KLOE paper [4] ±or notations and previous literature), allows a very accurate test o± symmetry; indeed since requires M 11 = M 22 and Γ 11 22 ,themass and width eigenstates, K S,L ,havea -violating piece, δ ,in addition to the usual -conserving parameter ± : K S,L = 1 q 2 ( 1+ | ± S,L | 2 ) h ( ± S,L ) K 0 + ( 1 ± S,L ) K 0 i ± S,L = i ± ( M 12 ) 1 2 ± 12 ) 1 2 · M 11 M 22 i 2 11 Γ 22 ) ¸ m L m S + i S Γ L ) / 2 ± ² δ. (1) Using the phase convention ± 12 ) = 0, we determine the phase ± to be ϕ SW arctan 2( m L m S ) Γ S Γ L . Imposing unitarity to an arbitrary combination o± K 0 and K 0 wave ±unctions, we obtain the Bell-Steinberger relation [5] connecting CP and violation in the mass matrix to and violation in the decay; in ±act, neglecting O ( ± ) corrections to the coefficient o± the -violating parameter, δ , we can write [4] [ Γ S L Γ S Γ L + i tan φ SW ][ ³ ( ± ) | ± | 2 i ± ( δ )] = 1 Γ S Γ L X f A L ( f ) A S ( f ) , (2) 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– where A L,S ( f ) A ( K L,S f ). We stress that this relation is phase-convention-independent. The advantage of the neutral kaon system is that only a few decay modes give signiFcant contributions to the r.h.s. in Eq. (2); in fact, deFning for the hadronic modes α i 1 Γ S ±A L ( i ) A
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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-cpt-invariance-tests - 1 CP T INVARIANCE TESTS...

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