Planck 2015 results. IV. Low Frequency Instrument beams and window
  functions
  This paper presents the characterization of the in-flight beams, the beam
window functions, and the associated uncertainties for the Planck Low Frequency
Instrument (LFI). The structure of the paper is similar to that presented in
the 2013 Planck release; the main differences concern the beam normalization
and the delivery of the window functions to be used for polarization analysis.
The in-flight assessment of the LFI main beams relies on measurements performed
during observations of Jupiter. By stacking data from seven Jupiter transits,
the main beam profiles are measured down to -25 dB at 30 and 44 GHz, and down
to -30 dB at 70 GHz. It has been confirmed that the agreement between the
simulated beams and the measured beams is better than 1% at each LFI frequency
band (within the 20 dB contour from the peak, the rms values are 0.1% at 30 and
70 GHz; 0.2% at 44 GHz). Simulated polarized beams are used for the computation
of the effective beam window functions. The error budget for the window
functions is estimated from both main beam and sidelobe contributions, and
accounts for the radiometer band shapes. The total uncertainties in the
effective beam window functions are 0.7% and 1% at 30 and 44 GHz, respectively
(at $\ell \approx 600$); and 0.5% at 70 GHz (at $\ell \approx 1000$).
