Aims: We report the discovery that Mira variables with and without absorption lines of the element technetium (Tc) occupy two different regions in a diagram of near- to mid-infrared colour versus pulsation period. Tc is an indicator of a recent or ongoing mixing event called the third dredge-up (3DUP), and the near- to mid-IR colour, such as the (K-[22]) colour where [22] is the the 22 micron band of the WISE space observatory, is an indicator of the dust mass-loss rate of a star. Methods: We collected data from the literature about the Tc content, pulsation period, and near- and mid-infrared magnitudes of more than 190 variable stars on the asymptotic giant branch (AGB) to which Miras belong. The sample is naturally biased towards optical AGB stars, which have low to intermediate (dust) mass-loss rates. Results: We show that a clear relation between dust mass-loss rate and pulsation period exists if a distinction is made between Tc-poor and Tc-rich Miras. Surprisingly, at a given period, Tc-poor Miras are redder in (K-[22]) than are Tc-rich Miras; i.e. they have higher mass-loss rates than the Tc-rich Miras. A few stars deviate from this trend; physical explanations are given for these exceptions, such as binarity or high mass. Conclusions: We put forward two hypotheses to explain this dichotomy and conclude that the two sequences formed by Tc-poor and Tc-rich Miras are probably due to the different masses of the two groups. The pulsation period has a strong correlation with the dust-mass loss rate, indicating that the pulsations are indeed triggering a dust-driven wind. The location in the (K-[22]) vs. period diagram can be used to distinguish between pre- and post-3DUP Miras, which we apply to a sample of Galactic bulge AGB stars. We find that 3DUP is probably not common in AGB stars in the inner bulge.
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