cp ckm - CP violation and the CKM matrix 1 CP violation and...

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arXiv:hep-ph/0605217v2 22 Jun 2006 CP violation and the CKM matrix 1 CP violation and the CKM matrix Andreas H¨ocker CERN, CH–1211 Geneva 23, Switzerland Zoltan Ligeti Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 Abstract Our knowledge of quark-flavor physics and CP violation increased tremendously over the past five years. It is confirmed that the Standard Model correctly describes the dominant parts of the observed CP -violating and flavor- changing phenomena. Not only does CP violation provide some of the most precise constraints on the flavor sector, but several measurements performed at the B -factories achieved much better precision than had been expected. We review the present status of the Cabibbo-Kobayashi-Maskawa matrix and CP violation, recollect the relevant experimental and theoretical inputs, display the results from the global CKM fit, and discuss their implications for the Standard Model and some of its extensions. CERN-PH-EP/2006-007, LBNL-59882, MIT-CTP 3729 CONTENTS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Quark Mixing and CP Violation in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The CKM Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Unitarity Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 CP Violation and Neutral-Meson Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Physics Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Theoretical Framework and Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Effective Hamiltonians for Weak Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Chiral Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Heavy-Quark Symmetry and Heavy-Quark Effective Theory . . . . . . . . . . . . . . . . . . . . . . . . . 13 Factorization and Soft-Collinear Effective Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 The Operator Product Expansion for Inclusive Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Lattice QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Determining Magnitudes of CKM Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 | V ud | from β -Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 CKM Elements from (Semi)Leptonic Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
ARNPS 2006 56 CKM Elements from Rare Loop-Mediated B Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Neutral B -Meson Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 CKM Matrix Constraints from Kaon Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Indirect CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Direct CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 K + π + ν ν and K 0 L π 0 ν ν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Unitarity Triangle Angle Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 β from B Decays to Charmonium Final States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 α from Charmless B Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 γ from B Decays to Open Charm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2 β + γ from B Decays to Open Charm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Weak-Phase Information from Direct CP Violation in B Decays . . . . . . . . . . . . . . . . . . . . . . 38 The Global CKM Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Fit Inputs and Initial Tests of Unitarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Fit Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 The CKM Matrix and the Search for New Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 New Physics Extensions of the Standard Model and their Relation to CKM . . . . . . . . . . . . . . . . 45 CP Asymmetries in Loop-Dominated Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 The D System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 The B s System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Model-Independent Constraints on New Physics in B Oscillation . . . . . . . . . . . . . . . . . . . . . . 50 Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1 Introduction 1.1 Quark Mixing and CP Violation in the Standard Model In the Standard Model (SM), quark masses and their mixing and CP violation have a common origin. Local gauge invariance forbids bare mass terms for fermions, just as it forbids gauge boson masses. Masses are generated after spontaneous electroweak symmetry breaking, owing to the Yukawa couplings of the fermions to the Higgs condensate. Therefore CP violation and

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