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

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 new physics models affect the rates for each channel differently. We are investigating the feasibility of performing a measurement of BR($K_L\to\pi^0\nu\bar{\nu}$) using a high-energy secondary neutral beam at the CERN SPS in a successor experiment to NA62. The planned experiment would reuse some of the NA62 infrastructure, including possibly the NA48 liquid-krypton calorimeter. The mean momentum of $K_L$ mesons decaying in the fiducial volume is 70 GeV; the decay products are boosted forward, so that less demanding performance is required from the large-angle photon veto detectors. On the other hand, the layout poses particular challenges for the design of the small-angle vetoes, which must reject photons from $K_L$ decays escaping through the beam pipe amidst an intense background from soft photons and neutrons in the beam. We present some preliminary conclusions from our feasibility studies, summarizing the design challenges faced and the sensitivity obtainable for the measurement of BR($K_L\to\pi^0\nu\bar{\nu}$).