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

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

Non-perturbative Effects in B→Xsl+l−B\to X_sl^+l^-

The rare decay $B\to X_sl^+l^-$ provides excellent prospects for precision tests of Standard Model flavour dynamics. The process can be computed in perturbation theory with small uncertainty. However, in order to ensure a reliable theoretical prediction, also potentially important effects from non-perturbative QCD have to be controlled with sufficient accuracy. The present article summarizes recent developments related to this topic.Comment: Invited Talk presented at the QCD Euroconference 98, Montpellier, 2-8 July 1998, 7 pages, 1 figur

K+→π+ννˉK^+\to \pi^+\nu\bar\nu: a rising star on the stage of flavour physics

Motivated by the new experimental information reported by the BNL--E787 Collaboration, we analyse the present impact and the future prospects opened by the measurement of \br(K^+\to\pi^+\nu\bar\nu). Although still affected by a large error, the BNL--E787 result favours values of \br(K^+\to \pi^+\nu\bar\nu) substantially larger than what expected within the Standard Model. As a result, this data already provide non-trivial constraints on the unitarity triangle, when interpreted within the Standard Model framework. We stress the importance of the clean relation between \br(K^+\to \pi^+\nu\bar\nu), $\sin2\beta$ and $\Delta M_{B_d}/\Delta M_{B_s}$ that in the next few years could provide one of the deepest probes of the Standard Model in the sector of quark-flavour dynamics. A speculative discussion about possible non-standard interpretations of a large \br(K^+\to \pi^+\nu\bar\nu) is also presented. Two main scenarios naturally emerge: those with direct new-physics contributions to the $s \to d \nu\bar\nu$ amplitude and those with direct new-physics effects only in $B_d$--$\bar B_d$ mixing. Realistic models originating these two scenarios and possible future strategies to clearly identify them are briefly discussed.Comment: 13 pages, 3 figures; minor modifications, version to appear in Phys.Lett.

sin⁡2β\sin 2\beta from K→πννˉK\to\pi\nu\bar\nu

We point out that the measurement of just the two branching fractions \linebreak $B(K^+\to\pi^+\nu\bar\nu)$ and $B(K_L\to\pi^0\nu\bar\nu)$ can in a theoretically clean manner determine $\sin 2\beta$ almost independently of $m_t$ and $V_{cb}$. This allows to obtain an interesting relation between the CP asymmetry $A_{CP}(\psi K_S)$ in B physics and the branching ratios for these two rare K decays. The recently calculated next-to-leading order QCD corrections improve the accuracy of this analysis. We find typically $\Delta\sin 2\beta=\pm 0.11$ provided B(\kpn) and B(\klpn) are measured within $\pm 10\%$ accuracy. With decreasing uncertainty in $\Lambda_{\overline{MS}}$ and $m_c$ this error could be reduced to $\Delta\sin 2\beta < \pm 0.10$. The determination of $\sin 2\alpha$ and $\sin 2\gamma$ on the other hand is rather poor. However respectable determinations of the Wolfenstein parameter $\eta$ and of $\mid V_{td}\mid$ can be obtained.Comment: 9 pages, MPI-PhT/94-1