The DAMA/LIBRA signal: an induced modulation effect?

The persistence of the DAMA/LIBRA (DAMA) modulation over the past two decades has been a source of great contention within the dark matter community. The DAMA collaboration reports a persistent, modulating event rate within their setup of NaI(Tl) scintillating crystals at the INFN Laboratori Nazionali del Gran Sasso (LNGS) underground laboratory. A recent work alluded that this signal could have arisen due to an analysis artefact, caused by DAMA not accounting for time variation of decaying background radioisotopes in their analysis procedure. In this work, we examine in detail this 'induced modulation' effect, arguing that a number of aspects of the DAMA signal are incompatible with an induced modulation arising from decays of background isotopes over the lifetime of the experiment. Using a toy model of the DAMA/LIBRA experiment, we explore the induced modulation effect under different variations of the activities of the relevant isotopes - namely, $^3$H and $^{210}$Pb - highlighting the various inconsistencies between the resultant toy datasets and the DAMA signal. We stress the importance of the SABRE experiment, whose goal is to unambiguously test for the presence of such a modulating signal in an experiment using the same target material and comparable levels of background.