The Rare Decays K→πννˉK\to\pi\nu\bar\nu, B→XννˉB\to X\nu\bar\nu and B→l+l−B\to l^+l^- -- An Update

We update the Standard Model predictions for the rare decays $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$. In view of improved limits on $B_s$--$\bar B_s$ mixing we derive a stringent and theoretically clean Standard Model upper limit on $B(K^+\to\pi^+\nu\bar\nu)$, which is based on the ratio of $B_d$--$\bar B_d$ to $B_s$--$\bar B_s$ mixing, $\Delta M_d/\Delta M_s$, alone. This method avoids the large hadronic uncertainties present in the usual analysis of the CKM matrix. We find $B(K^+\to\pi^+\nu\bar\nu)< 1.67\cdot 10^{-10}$, which can be further improved in the future. In addition we consider the extraction of $|V_{td}|$ from a future measurement of $B(K^+\to\pi^+\nu\bar\nu)$, discussing the various sources of uncertainties involved. We also investigate theoretically clean constraints on $B(K_L\to\pi^0\nu\bar\nu)$. We take the opportunity to review the next-to-leading order (NLO) QCD corrections to $K\to\pi\nu\bar\nu$, $K_L\to\mu^+\mu^-$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$, including a small additional term that had been missed in the original publications. The phenomenological impact of this change is negligible, the corresponding numerical shift being essentially within the small perturbative uncertainties at the NLO level.Comment: 19 pages, no figure

Effects from the charm scale in K+ -> pi+ nu nubar

We consider contributions to the rare decay K+ -> pi+ nu nubar which become nonlocal at the charm scale. Compared to the leading term, such amplitudes are suppressed by two powers of mK/mc and could potentially give corrections at the level of 15%. We compute the leading coefficients of the subleading dimension eight operators in the effective theory below the charm mass. The matrix elements of these operators cannot all be calculated from first principles and some must be modeled. We find that these contributions are likely to be small, but the estimate is sufficiently uncertain that the result may be as large as the existing theoretical uncertainty from other sources.Comment: 9 pages, 3 figures; Eq. (15) fixed, all results and conclusions unaltere

Heavy Quark Theory

These lectures describe the most important theoretical methods in b-physics. We discuss the formalism of effective weak Hamiltonians, heavy quark effective theory, the heavy quark expansion for inclusive decays of b-hadrons and, finally, the more recent ideas of QCD factorization for exclusive nonleptonic B decays. While the main emphasis is put on introducing the basic theoretical concepts, some key applications in phenomenology are also presented for illustration.Comment: 50 pages, Lectures given at the 55th Scottish Universities Summer School in Physics, 7-23 August 2001, St. Andrews, Scotlan

Theoretical Update on Rare K Decays

We review the status of rare kaon decays, concentrating on modes with sensitivity to short-distance flavour physics.Comment: Invited talk presented at Daphne 99, Frascati, Nov. 1999, 13 pages, 3 figure

CP Violation in K Decays and Rare Decays

The present status of CP violation in decays of neutral kaons is reviewed. In addition selected rare decays of both K and B mesons are discussed. The emphasis is in particular on observables that can be reliably calculated and thus offer the possibility of clean tests of standard model flavor physics.Comment: LaTeX, 21 pages, 4 figure

QCD and Heavy Hadron Decays

We review recent developments in QCD pertaining to its application to weak decays of heavy hadrons. We concentrate on exclusive rare and nonleptonic B-meson decays, discussing both the theoretical framework and phenomenological issues of current interest.Comment: 13 pages, 8 figures, talk at Lepton Photon 03, 11-16 August 2003, Fermila

CP Violation and Rare Kaon Decays

We summarize both the study of CP violation with $K$ and $B$ mesons, as well as rare decays of kaons, emphasizing recent developments. The topics discussed include the unitarity triangle, $\epsilon'/\epsilon$, $K\to\pi\nu\bar\nu$ and other rare $K$ decays, T-odd asymmetries in kaon physics, theoretical aspects of CP violation in B decays, $B\to J/\Psi K_S$, $B\to\pi\pi$, $B\to\pi K$ and inclusive CP asymmetries.Comment: Plenary talk at EPS-HEP99, Tampere, Finland, 21 pages, 6 figure