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CP, T and CPT analyses in EPR-correlated ¯ B 0B 0 decays

arXiv:hep-ph/0603102v1 14 Mar 2006

PhD Thesis

author ´ Ezequiel Alvarez director Jos´ Bernab´u Alberola e e

A Carla, mi raison d’ˆtre e

´ ´ JOSE BERNABEU ALBEROLA, Catedr´tico de F´ a ısica Te´rica de la o Universidad de Valencia,

CERTIFICA:

Que la presente memoria ”CP, T AND CPT ¯ ANALYSES IN EPR-CORRELATED B 0 B0 DECAYS” ha sido realizada bajo su direcci´n en el Departamento de F´ o ısica Te´rica o de la Universidad de Valencia por el Licen´ ciado D. EZEQUIEL ALVAREZ y constituye su Tesis Doctoral. Y para que as´ conste, presenta la referida ı memoria en Burjassot, a 1 de marzo de 2006

Firmado: Jos´ Bernab´u Alberola e e

Contents
Abstract Resumen [espa˜ol] n 1 Introduction 1.1 GeneralIntroduction . . . . . 1.2 Intoducci´n General [espa˜ ol] o n 1.3 Let the games begin . . . . . 1.3.1 General considerations 1.3.2 Structure of this work 2 CP 2.1 2.2 2.3 2.4 2.5 2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 5 5 8 10 10 12 15 15 16 19 22 24 25 25 27 29 31 32 32 35

violation in the Standard Model Introduction . . . . . . . . . . . . . . . . . . . . Transformation of fields and currents . . . . . . . CP operation in the Standard Model Lagrangian The CP invariance condition . . . . . . . . . . . The CP operators . . . .. . . . . . . . . . . . . The CKM matrix: hierarchy of flavour mixing . . 2.6.1 Parametrization of the CKM matrix . . . 2.6.2 Requirements for CP Violation . . . . . . 2.6.3 The Unitarity Triangles . . . . . . . . . .

3 The neutral meson system 3.1 The formalism for the decays in the neutral meson system . . 3.1.1 Time evolution in the Weisskopf-Wigner approximation . . . . . . . . . . . . . .. . . . . . . . . . . . . . 3.1.2 T, CP and CPT analysis in the time evolution (mixing) ix

3.2 3.3

The correlated neutral meson system . . . . . . . . . . . . Appendix: On the definition of probability using non-orthogonal basis 3.3.1 The Dirac definition, possible generalizations, and their problems . . . . . . . . . . . . . . . . . . 3.3.2 Conclusions . . . . . . . . . . . . . . . . . . . .. . state-of-the-art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . 41 . . 43 . . 44 . . 49 51 51 53 56 59 59 60 64 66 67 74 75 75 76 77 78 79 82 82 85 89

4 T, CP and CPT violation, 4.1 Time reversal violation 4.2 CP violation . . . . . . 4.3 CPT violation . . . . .

review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 T, CP and CPT violation incorrelated B meson mixing and decays through the CP-tag 5.1 The B meson system: the Golden Plate decay . . . . . . . . . 5.2 The determination of the CPΘΘ′ operator and the CP-tag . . 5.3 Time evolution with the rephasing-invariant ǫ and δ . . . . . . 5.4 The Intensity and its reduction to B-transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 The Intensity for correlated neutralB-meson decays . . . . . 5.6 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 CPT violation through distinguishability of particle and antiparticle 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Modification of the initial state due to distinguishability of particle-antiparticle . . . . . . . . . . . . . . . . 6.2 The demise of flavour tagging andthe equal-time decay observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Time evolution and conceptual changes due to the appearance of ’forbidden’ states . . . . . . . . . . . . . . 6.2.2 The experimental observables . . . . . . . . . . . . . . 6.3 Linear in ω time-dependent observables . . . . . . . . . . . . 6.3.1 Corrections to the equal-sign dilepton intensity . . . ....
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