  The exact nature of unconventional superconductivity in Sr$_2$RuO$_4$ remains
a mystery. At the phenomenological level, no superconducting order parameter
proposed thus far seems able to coherently account for all essential
experimental signatures. Among the latter is the prominent polar Kerr effect,
which implies a nonzero ac anomalous Hall conductivity. Assuming the Kerr
effect is intrinsic, it can be accounted for by a bulk chiral Cooper pairing
with nonzero orbital angular momentum, such as $p+ip$ or $d+id$, which,
however, has difficulties in being reconciled with other experimental results.
Given the situation, in this paper, we propose alternative possibilities with
complex mixtures of distinct helical p-wave order parameters, namely,
$A_{1u}+iA_{2u}$ and $B_{1u}+iB_{2u}$ in the group theory nomenclature. These
states essentially consist of two copies of chiral p-wave pairings with
opposite chirality and different pairing amplitudes, and therefore support
intrinsic Hall and Kerr effects. We further show that these states exhibit
salient features that may explain several other key observations in this
material, including the absence of spontaneous edge current, a substantial
Knight shift drop, and possibly signatures in uniaxial strain and ultrasound
measurements.
