  CMB lensing from current and upcoming wide-field CMB experiments such as
AdvACT, SPT-3G and Simons Observatory relies heavily on temperature (vs.
polarization). In this regime, foreground contamination to the temperature map
produces significant lensing biases, which cannot be fully controlled by
multi-frequency component separation, masking or bias hardening. In this
letter, we split the standard CMB lensing quadratic estimator into a new set of
optimal "multipole" estimators. On large scales, these multipole estimators
reduce to the known magnification and shear estimators, and a new shear B-mode
estimator. We leverage the different symmetries of the lensed CMB and
extragalactic foregrounds to argue that the shear-only estimator should be
approximately immune to extragalactic foregrounds. We build a new method to
compute separately and without noise the primary, secondary and trispectrum
biases to CMB lensing from foreground simulations. Using this method, we
demonstrate that the shear estimator is indeed insensitive to extragalactic
foregrounds, even when applied to a single-frequency temperature map
contaminated with CIB, tSZ, kSZ and radio point sources. This dramatic
reduction in foreground biases allows us to include higher temperature
multipoles than with the standard quadratic estimator, thus increasing the
total lensing signal-to-noise beyond the quadratic estimator. In addition,
magnification-only and shear B-mode estimators provide useful diagnostics for
potential residuals. Our Python code LensQuEst to forecast the signal-to-noise
of the various estimators, generate mock maps, lense them, and apply the
various lensing estimators to them is publicly available at
https://github.com/EmmanuelSchaan/LensQuEst .
