  We propose that the origin of ultra-high energy cosmic rays beyond the GZK
cutoff and the origin of small cosmological constant can both be explained by
vacuum tunneling effects in a theory with degenerate vacua and fermionic
doublets. By considering the possibility of tunneling from a particular winding
number state, accompanied by violation of some global quantum number of
fermions, the small value of the vacuum dark energy and the production of high
energy cosmic rays are shown to be related. We predict that the energy of such
cosmic rays should be at least $5\times 10^{14}$ GeV.
