Principal Shapes and Squeezed Limits in the Effective Field Theory of
  Large Scale Structure
  We apply an orthogonalization procedure on the effective field theory of
large scale structure (EFT of LSS) shapes, relevant for the angle-averaged
bispectrum and non-Gaussian covariance of the matter power spectrum at one
loop. Assuming natural-sized EFT parameters, this identifies a linear
combination of EFT shapes - referred to as the principal shape - that gives the
dominant contribution for the whole kinematic plane, with subdominant
combinations suppressed by a few orders of magnitude. For the covariance, our
orthogonal transformation is in excellent agreement with a principal component
analysis applied to available data. Additionally we find that, for both
observables, the coefficients of the principal shapes are well approximated by
the EFT coefficients appearing in the squeezed limit, and are thus measurable
from power spectrum response functions. Employing data from N-body simulations
for the growth-only response, we measure the single EFT coefficient describing
the angle-averaged bispectrum with $\mathcal{O}(10\%)$ precision. These methods
of shape orthogonalization and measurement of coefficients from response
functions are valuable tools for developing the EFT of LSS framework, and can
be applied to more general observables.
