B-Zerfälle aus QCD Summenregeln

Abstract

B -Zerfälle aus QCD Summenregeln In the Standard Model of elementary particle physics, the asymmetry between matter and antimatter, called CP -violation, is explained by a complex phase in the CKM -matrix which governs the coupling of the quarks to the W boson mediating the weak interaction. In order to test this theoretical framework and to determine its fundamental parameters, the CKM matrix elements, weak decays of hadrons have to be investigated. One interesting class of such decays are those of B mesons to two light pseudoscalars ( π , K ). They are sensitive to the weak CP -violating phases α and γ of the CKM matrix. The theoretical treatment required to extract them from the measured data is however very difficult, as the bound states of quarks cannot be described by perturbation theory. In the literature, the limits m b → ∞ (heavy beauty quark) and m s → 0 (light strange quark) are often used in the calculation of physical observables. With the help of QCD twopoint and light-cone sum rules, corrections to this limits can be calculated. In B → ππ decays, for example, one observes a discrepancy between the theoretical description in the m b → ∞ limit and the measured quantities. In this work, the contributions from the annihilation mechanism have been calculated using light-cone sum rules, in addition to several already known 1/ m b -corrections. They were found to be too small to reconcile theory and experiment, however. The same method was also applied to perturbative corrections to the dominant emission diagrams. The latter ones have already been calculated in other methods and the results are consistent with each other. At the same time, the new result includes a new 1/ m b -suppressed strong phase and does not depend on the poorly known distribution amplitude of the B meson. In B ( s ) → π K and KK -decays, the effects of the strange quark mass were calculated. To this end, nonperturbative, process-independent quantities related to the light-cone distribution amplitudes have been computed in two-point sum rules. Using this values, it was found that the m s → 0 limit is not a very good approximation for the decay amplitudes, and that QCD sum rules successfully describe the amplitudes without relying on this limit.