Examining the time dependence of DAMA's modulation amplitude

If dark matter is composed of weakly interacting particles, Earth's orbital motion may induce a small annual variation in the rate at which these particles interact in a terrestrial detector. The DAMA collaboration has identified at a 9.3$\sigma$ confidence level such an annual modulation in their event rate over two detector iterations, DAMA/NaI and DAMA/LIBRA, each with $\sim7$ years of observations. We statistically examine the time dependence of the modulation amplitudes, which "by eye" appear to be decreasing with time in certain energy ranges. We perform a chi-squared goodness of fit test of the average modulation amplitudes measured\ by the two detector iterations which rejects the hypothesis of a consistent modulation amplitude at greater than 80\%, 96\%, and 99.6\% for the 2--4~keVee, 2--5~keVee and 2--6~keVee energy ranges, respectively. We also find that among the 14 annual cycles there are three $\gtrsim 3\sigma$ departures from the average in the 5-6~keVee energy range. In addition, we examined several phenomenological models for the time dependence of the modulation amplitude. Using a maximum likelihood test, we find that descriptions of the modulation amplitude as decreasing with time are preferred over a constant modulation amplitude at anywhere between 1$\sigma$ and 3$\sigma$, depending on the phenomenological model for the time dependence and the signal energy range considered. A time dependent modulation amplitude is not expected for a dark matter signal, at least for dark matter halo morphologies consistent with the DAMA signal. New data from DAMA/LIBRA--phase2 will certainly aid in determining whether any apparent time dependence is a real effect or a statistical fluctuation.