Search for the decay K⁺ → π⁺νν̄ in the momentum region P_π < 195 MeV/c

We have searched for the decay K⁺ → π⁺νν̄ in the kinematic region with pion momentum below the K⁺ → π⁺π⁰ peak. One event was observed, consistent with the background estimate of 0.73 ± 0.18. This implies an upper limit on B(K⁺ → π⁺ νν̄ < 4.2 × 10^-9 (90% C.L.), consistent with the recently measured branching ratio of (1.57+_-0.82^+1.75) × 10^-10, obtained using the standard model spectrum and the kinematic region above the K⁺ → π⁺π⁰ peak. The same data were used to search for K⁺ → π⁺X⁰, where X⁰ is a weakly interacting neutral particle or system of particles with 150 < M_X0 < 250 MeV/c².