  The region 1273-1290 cm$^{-1}$ of the $\nu$4 fundamental of the simplest
Criegee intermediate, CH$_2$OO, has been measured using a quantum cascade laser
transient absorption spectrometer, which offers greater sensitivity and
spectral resolution (< 0.004 cm$^{-1}$) than previous works based on thermal
light sources. Gas phase CH$_2$OO was generated from the reaction of CH$_2$I +
O2 at 298 K and 4 Torr. Analysis of the absorption spectrum has provided
precise values for the vibrational frequency and the rotational constants, with
fitting errors of a few MHz. The determined ratios of the rotational constants,
A'/A" = 0.9986, B'/B" = 0.9974 and C'/C" = 1.0010, and the relative intensities
of the a- and b-type transitions, 90:10, are in good agreement with literature
values from a theoretical calculation using the MULTIMODE approach, based on a
high-level ab initio potential energy surface. The low-K (= Ka) lines can be
fitted extremely well, but rotational perturbations by other vibrational modes
disrupt the structure for K = 4 and K $\geq$ 6. Not only the spectral
resolution but also the detection sensitivity of CH$_2$OO IR transitions has
been greatly improved in this work, allowing for unambiguous monitoring of
CH$_2$OO in kinetic studies at low concentrations.
