Constraining Sommerfeld enhanced annihilation cross-sections of dark matter via direct searches

In a large class of models we show that the light scalar field responsible for the Sommerfeld enhancement in the annihilation of dark matter leads to observable direct detection rates, due to its mixing with the standard model Higgs. As a result the large annihilation cross-section of dark matter at present epoch, required to explain the observed cosmic ray anomalies, can be strongly constrained by direct searches. In particular Sommerfeld boost factors of order of a few hundred are already out of the CDMS-II upper bound at 90% confidence level for reasonable values of the model parameters.