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Azimuthal correlations from transverse momentum conservation and possible local parity violation

We analytically calculate the contribution of transverse momentum conservation to the azimuthal correlations that have been proposed as signals for possible local strong parity violation and recently measured in heavy ion collisions. These corrections are of the order of the inverse of the total final state particle multiplicity and thus are of the same order as the observed signal. The corrections contribute with the same sign to both like-sign and opposite-sign pair correlations. Their dependence on the momentum is in qualitative agreement with the measurements by the STAR collaboration, while the pseudorapidity dependence differs from the data.