Possible GeV counterpart at the ground level associated with Fermi LAT gamma-ray bursts

From June 2014 to February 2017, the Fermi LAT detected 46 gamma-ray bursts (GRBs) with photon energies above 20 MeV, and the trigger coordinates of seven of them were within the FoV of New-Tupi detector located in the central region of the South Atlantic Anomaly (SAA). We show in this paper that two of these seven GRBs have a probable GeV counterpart observed at ground level by New-Tupi detector. The first is GRB 160609A, a short duration GRB with a bright emission of photons over a broad energy range extending up to GeV energies. The second is GRB 160625B, a very long duration GRB, for which the Fermi LAT detected more than 300 photons with energies above 100 MeV in the $\sim$ 1 ks interval after the GBM trigger. In the first case, the signal at New-Tupi has a nominal significance of $3.5\sigma$ in the counting rate time profiles, within the T90($=5.6$ s) duration on Fermi GBM. However, the effective significance is only $3.0\sigma$. In the second case, New-Tupi detector registered at least two excess (peaks) with a nominal statistical significance of $4.8\sigma$ and $5.0\sigma$ at 438 s and 558 s after the trigger. The first is within the $T90(=460$ s) on Fermi GBM. Even so, the effective significance is only $\sim 2.0\sigma$. In addition, from a Monte Carlo analysis, we show that the expected signal-to-noise ratio is compatible with the observation of GRB 160709A, only if the differential index of the GRB energy spectrum be equal or higher than -2.2 (a non-steep spectrum).