  The effects of spin independent hybridization potential and spin orbit
coupling on two band superconductor with equal time s-wave inter band pairing
order parameter is investigated theoretically. To study symmetry classes in two
band superconductors the Gorkov equations are solved analytically. By defining
spin singlet and spin triplet s wave order parameter due to two band degree of
freedom the symmetry classes of Cooper pair are studied. For spin singlet case
it is shown that spin independent hybridization generates Cooper pair belongs
to even frequency spin singlet even momentum even band parity (ESEE) symmetry
class for both intraband and interband pairing correlations. For spin triplet
order parameter, intraband pairing correlation generates odd frequency spin
triplet even momentum even band parity (OTEE) symmetry class whereas, interband
pairing correlation generates even frequency spin triplet even momentum odd
band parity ETEO) class. For the spin singlet, spin orbit coupling generates
pairing correlation that belongs to odd frequency spin singlet odd momentum
even band parity (OSOE) symmetry class and even frequency spin singlet even
momentum even band parity (ESEE) for intraband and interband pairing
correlation respectively. In the spin triplet case for itraband and interband
correlation, spin orbit coupling generates even-frequency spin triplet odd
momentum even band parity (ETOE) and even frequency spin triplet even momentum
odd band parity (ETEO) respectively.
