  Since the launch of the Fermi Gamma-ray Space Telescope on 11 June 2008,
significant detections of high energy emission have been reported only in six
Gamma-ray Bursts (GRBs) until now. In this work we show that the lack of
detection of a GeV spectrum excess in almost all GRBs, though somewhat
surprisingly, can be well understood within the standard internal shock model
and several alternatives like the photosphere-internal shock (gradual magnetic
dissipation) model and the magnetized internal shock model. The delay of the
arrival of the >100 MeV photons from some Fermi bursts can be interpreted too.
We then show that with the polarimetry of prompt emission these models may be
distinguishable. In the magnetized internal shock model, high linear
polarization level should be typical. In the standard internal shock model,
high linear polarization level is still possible but much less frequent. In the
photosphere-internal shock model, the linear polarization degree is expected to
be roughly anti-correlated with the weight of the photosphere/thermal
component, which may be a unique signature of this kind of model. We also
briefly discuss the implication of the current Fermi GRB data on the detection
prospect of the prompt PeV neutrinos. The influences of the intrinsic proton
spectrum and the enhancement of the neutrino number at some specific energies,
due to the cooling of pions (muons), are outlined.
