Daily modulation due to channeling in direct dark matter crystalline detectors

The channeling of the ion recoiling after a collision with a WIMP in direct dark matter crystalline detectors produces a larger scintillation or ionization signal than otherwise expected. Channeling is a directional effect which depends on the velocity distribution of WIMPs in the dark halo of our Galaxy and could lead to a daily modulation of the signal. Here we compute upper bounds to the expected amplitude of daily modulation due to channeling using channeling fractions that we obtained with analytic models in prior work. After developing the general formalism, we examine the possibility of finding a daily modulation due to channeling in the data already collected by the DAMA/NaI and DAMA/LIBRA experiments. We find that even the largest daily modulation amplitudes (of the order of 10% in some instances) would not be observable for WIMPs in the standard halo in the 13 years of data taken by the DAMA collaboration. For these to be observable the DAMA total rate should be 1/40 of what it is or the total DAMA exposure should be 40 times larger. The daily modulation due to channeling will be difficult to measure in future experiments. We find it could be observed for light WIMPs in solid Ne, assuming no background.