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This paper characterizes the effective beams,the effective beam windowfunctions and the associated errors for the Planck HFI detectors. The effectivebeam is the angular response including the effect of the optics,detectors,dataprocessing and the scan strategy. The window function is the representation ofthis beam in the harmonic domain which is required to recover an unbiasedmeasurement of the CMB angular power spectrum. The HFI is a scanning instrumentand its effective beams are the convolution of: (a) the optical response of thetelescope and feeds;(b)the processing of the time-ordered data anddeconvolution of the bolometric and electronic time response; and (c) themerging of several surveys to produce maps. The time response functions aremeasured using observations of Jupiter and Saturn and by minimizing surveydifference residuals. The scanning beam is the post-deconvolution angularresponse of the instrument, and is characterized with observations of Mars. Themain beam solid angles are determined to better than 0.5% at each HFI frequencyband. Observations of Jupiter and Saturn limit near sidelobes (within 5deg) toabout 0.1% of the total solid angle. Time response residuals remain as longtails in the scanning beams, but contribute less than 0.1% of the total. Thebias and uncertainty in the beam products are estimated using ensembles ofsimulated planet observations that include the impact of instrumental noise andknown systematic effects.The correlation structure of these ensembles iswell-described by five error eigenmodes that are sub-dominant to samplevariance and instrumental noise in the harmonic domain. A suite of consistencytests provide confidence that the error model represents a sufficientdescription of the data. The total error in the effective beam window functionsis below 1% at 100GHz up to ell~1500$,and below 0.5% at 143 and 217GHz up to~2000.

Planck 2013 results. VII. HFI time response and beams