  The cosmological constraints from the kinetic Sunyaev-Zeldovich experiments
are degenerate with the optical depth measurement, which is commonly known as
the optical-depth degeneracy. In this work, we introduce a new statistic based
on the first moment of relative velocity between pairs in a triplet, which is
capable of constraining cosmological parameters independent of the optical
depth, and $\sigma_8$. Using 22,000 $N$-body simulations from the Quijote
suite, we quantify the information content in the new statistic using Fisher
matrix forecast. We find that it is able to obtain strong constraints on the
cosmological parameters, particularly on the summed neutrino mass. The
constraints have a factor of 6.2-12.9, and 2.3-5.7 improvement on all
cosmological model parameters when compared to those obtained from the mean
pairwise velocity, and the redshift-space halo power spectrum, respectively.
Thus the new statistic paves a way forward to constrain cosmological parameters
independent of the optical depth and $\sigma_8$ using data from future kinetic
Sunyaev-Zeldovich experiments alone.
