M. Neubert: Theory of CP Violation in the B-Meson System (LP01) THEORY OF CP VIOLATION IN THE B-MESON SYSTEM

The phenomenon of CP violation is one of the most intriguing aspects of modern physics, with far-reaching implications for the microscopic world as well as for the macrocosmos. CP violation means that there is a fundamental difference between the interactions of matter and anti-matter, which in conjunction with the CPT theorem implies a microscopic violation of time-reversal invariance. CP violation is also responsible for the observed asymmetry in the abundance of matter and anti-matter in the Universe, which is a prerequisite for our existence. The Standard Model (SM) of particle physics provides us with a parameterization of CP violation but does not explain its origin in a satisfactory way. In fact, CP violation may occur in three sectors of the SM: in the quark sector via the phase of the Cabibbo– Kobayashi–Maskawa (CKM) matrix, in the lepton sector via the phases of the neutrino mixing matrix, and in the strong interactions via the parameter θQCD. CP violation in the quark sector has been studied in some detail and is the subject of this talk. The nonobservation of CP violation in the strong interactions is a mystery (the “strong CP puzzle”), whose explanation requires physics beyond the SM (such as a Peccei–Quinn symmetry, axions, etc.). CP violation in the neutrino sector has not yet been explored experimentally. The discovery of CP violation in the B system, as reported this summer by the BaBar and Belle Collaborations, is a triumph for the Standard Model. There is now compelling evidence that the phase of the CKM matrix correctly explains the pattern of CP-violating effects in mixing and weak decays of kaons, charm and beauty hadrons. Specifically, the CKM mechanism explains why CP violation is a small effect in K–K̄ mixing (ǫK) and K → ππ decays (ǫ/ǫ), why CP-violating effects in charm physics are below the sensitivity of present experiments, and why CP violation is small in B–B̄ mixing (ǫB) but large in the interference of mixing and decay in B → J/ψK (sin 2βψK). The significance of the sin 2βψK measurement is that for the first time a large CP asymmetry has been observed, proving that CP is not an approximate symmetry of Nature. Rather, the smallness of CP violation outside the B system simply reflects the hierarchy of CKM matrix elements. Besides CP violation, the CKM mechanism explains a vast variety of flavorchanging processes, including leptonic decays, semileptonic decays (from which the magnitudes of most CKM elements are determined), nonleptonic decays, rare loop processes, and mixing amplitudes. The CKM matrix is a unitary matrix in flavor space, which relates the mass eigenstates of the down-type quarks with the interaction eigenstates that are involved in flavor-changing weak transitions. It has a hierarchical structure, and (with the standard phase conventions) the CP-violating phase appears in the smallest matrix elements, Vub and Vtd. The