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The count rate of Weakly Interacting Massive Particle (WIMP) dark mattercandidates in direct detection experiments experiences an annual modulation dueto the Earth's motion around the Sun. In the standard isothermal halo model,the signal peaks near June 2nd at high recoil energies; however, the signalexperiences a phase reversal and peaks in December at low energy recoils. Weshow that this phase reversal may be used to determine the WIMP mass. If anannual modulation were observed with the usual phase ({\it i.e.}, peaking onJune 2nd) in the lowest accessible energy recoil bins of the DAMA, CDMS-II,CRESST-II, EDELWEISS-II, GENIUS-TF, ZEPLIN-II, XENON, or ZEPLIN-IV detectors,one could immediately place upper bounds on the WIMP mass of [103, 48, 6, 97,10, 52, 29, 29] GeV, respectively. In addition, detectors with adequate energyresolution and sufficiently low recoil energy thresholds may determine thecrossover recoil energy at which the phase reverses, thereby obtaining anindependent measurement of the WIMP mass. We study the capabilities of variousdetectors, and find that CRESST-II, ZEPLIN-II, and GENIUS-TF should be able toobserve the phase reversal in a few years of runtime, and can thus determinethe mass of the WIMP if it is $\mathcal{O}(100$ GeV). Xenon based detectorswith 1000 kg (XENON and ZEPLIN-IV) and with energy recoil thresholds of a fewkeV require 25 kg-yr exposure, which will be readily attained in upcomingexperiments.Comment: 15 pages. Four Figures. Accepted for publication in Phys. Rev.

Phase of the annual modulation as a tool for determining the mass of the weakly interacting massive particle