  Pairing symmetry in recently discovered Fe-based metallic superconductors
AFe$_2$Se$_2$ (A = K, Rb, Cs) with high transition temperature $T_c \sim 40$ K
is currently a subject of intensive debates. These systems contain only
electron pockets, according to photoemission, and differ from the majority of
Fe-based superconductors in which both electron and hole pockets are present.
Both d-wave and s-wave pairing symmetries have been proposed for AFe$_2$Se$_2$,
but a d-wave gap generally has nodes, while experiments clearly point to
no-nodal behavior, and a conventional s-wave gap is inconsistent with the
observation of the neutron resonance below $T_c$. We argue that current
theories of pairing in such systems are incomplete and must include not only
intra-pocket pairing condensate but also inter-pocket condensate made of
fermions belonging to different electron pockets. We analyze the interplay
between intra-pocket and inter-pocket pairing depending on the ellipticity of
electron pockets and the strength of their hybridization and show that
hybridization brings the system into a new $s^{+-}$ state, in which the gap
changes sign between hybridized pockets. This state has the full gap and at the
same time supports spin resonance, in agreement with the data. Near the
boundary of $s^{+-}$ state we found a long-thought $s+id$ state which breaks
time-reversal symmetry.
