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

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

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

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 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

Rare Kaon Decays - Overview

The theory of rare $K$ decays is reviewed, emphasizing short-distance processes and the prospects to probe the physics of flavour. A brief overview of the subject is presented, along with a more detailed discussion of the theory of $K\to\pi\nu\bar\nu$ decays.Comment: 10 pages, 3 figures, Invited Talk at KAON 2001, Pis

A Systematic Approach to the SILH Lagrangian

We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small $\xi=v^2/f^2$. Here $v$ is the electroweak scale and $f$ is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in $\xi$, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in $\xi$ has to be performed. We point out that terms of order $\xi^2$, which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order $\xi/16\pi^2$ that are retained, as long as $\xi > 1/16\pi^2$. Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset $SO(5)/SO(4)$ is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on $SU(2)_L\otimes SU(2)_R/SU(2)_V$.Comment: 22 pages, 1 figure; improved presentation of the results in section

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