Benchmark parameters for CMB polarization experiments

The recently detected polarization of the cosmic microwave background (CMB) holds the potential for revealing the physics of inflation and gravitationally mapping the large-scale structure of the universe, if so called B-mode signals below 10^-7, or tenths of a, can be reliably detected. We provide a language for describing systematic effects which distort the observed CMB temperature and polarization fields and so contaminate the B modes. We identify 7 types of effects, described by 11 distortion fields, and show their association with known instrumental systematics such as common mode and differential gain fluctuations, line cross-coupling, pointing errors, and differential polarized beam effects. Because of aliasing from the small-scale structure in the CMB, even uncorrelated fluctuations in these effects can affect the large-scale B modes relevant to gravitational waves. Many of these problems are greatly reduced by having an instrumental beam that resolves the primary anisotropies (full width at half maximum 10^'). To reach the ultimate goal of an inflationary energy scale of 310^15GeV, polarization distortion fluctuations must be controlled at the 10^-2--10^-3 level and temperature leakage to the 10^-4--10^-3 level depending on the effect. For example, pointing errors must be controlled to 1. 5^''rms for arcminute scale beams or a percent of the Gaussian beam width for larger beams; low spatial frequency differential gain fluctuations or line cross-coupling must be eliminated at the level of 10^-4rms.