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Mild, unavoidable deviations from circular-symmetry of instrumental beams incurrent Cosmic Microwave Background (CMB) experiments now pose a significantchallenge to deriving high precision inferences from the high sensitivity andresolution of CMB measurements. We present analytic results, verified bynumerical simulations, that CMB maps of cosmological signal that respectunderlying statistical isotropy (SI) symmetry, measured with an instrument thathas mildly non-circular (NC) beam would, nevertheless, exhibit SI violation.Further, we show that appropriate observable measures constructed within theBipolar spherical harmonic (BipoSH) representation of SI violation capturesubtle NC-beam effects coupled with the scan strategy of the instrument.  Accompanying their latest 7-year data release, the WMAP team published veryhigh significance measurements of non-zero BipoSH spectra, A^{20}_{l l} andA^{20}_{l-2 l}, in the "W" and "V" band of the experiment. We present a strongcase that the BipoSH measurement are primarily explained by the quadrupolar(m=2) component of the NC-beams, b_{l2}, of the respective channels. The factthat subtle levels of non-circularity, e.g., WMAP beams |b_{l2}|/b_{l0} < 0.01,lead to measurable BipoSH spectra points to the immense promise and potentialof the BipoSH representation. The key result of this work is that using BipoSHmeasurements it is possible to estimate an equivalent single hit,'paralleltransported' effective NC-beam that matches both the angular power spectrum andthe non-zero BipoSH measurements of the observed maps. Hence, BipoSH analysisprovides a very simple and effective characterization of CMB maps made withNC-beam. (Abridged)

Revealing Non-circular beam effect in WMAP-7 CMB maps with BipoSH measures of Statistical Isotropy