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Precise measurements of the branching ratios for the $K\to\pi\nu\bar{\nu}$decays can provide unique constraints on CKM unitarity and, potentially,evidence for new physics. It is important to measure both decay modes,$K^+\to\pi^+\nu\bar{\nu}$ and $K_L\to\pi^0\nu\bar{\nu}$, since different newphysics models affect the rates for each channel differently. We areinvestigating the feasibility of performing a measurement ofBR($K_L\to\pi^0\nu\bar{\nu}$) using a high-energy secondary neutral beam at theCERN SPS in a successor experiment to NA62. The planned experiment would reusesome of the NA62 infrastructure, including possibly the NA48 liquid-kryptoncalorimeter. The mean momentum of $K_L$ mesons decaying in the fiducial volumeis 70 GeV; the decay products are boosted forward, so that less demandingperformance is required from the large-angle photon veto detectors. On theother hand, the layout poses particular challenges for the design of thesmall-angle vetoes, which must reject photons from $K_L$ decays escapingthrough the beam pipe amidst an intense background from soft photons andneutrons in the beam. We present some preliminary conclusions from ourfeasibility studies, summarizing the design challenges faced and thesensitivity obtainable for the measurement of BR($K_L\to\pi^0\nu\bar{\nu}$).

Prospects for an experiment to measure BR($K_L\to\pi^0\nu\bar{\nu}$) at the CERN SPS