The Rare Decays $K\toπν\barν$, $B\to Xν\barν$ and $B\to l^+l^-$ -- An Update

Details The Rare Decays $K\toπν\barν$, $B\to Xν\barν$ and $B\to l^+l^-$ -- An Update The Rare Decays $K\toπν\barν$, $B\to Xν\barν$ and $B\to l^+l^-$ -- An Update

1999-01-13

arxiv.org/abs/hep-ph/9901288v1

Nucl.Phys.B548:309-327,1999

Physics

High Energy Physics

High Energy Physics - Phenomenology

19 pages, no figures

Scientific paper

10.1016/S0550-3213(99)00149-2

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.

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