  The nuclear symmetry energy (E_sym(\roh)) is a vital ingredient of our
understanding of many processes, from heavy-ion collisions to neutron stars
structure. While the total nuclear symmetry energy at nuclear saturation
density (\rho_0) is relatively well determined, its value at supranuclear
densities is not. The latter can be better constrained by separately examining
its kinetic and potential terms and their density dependencies. The kinetic
term of the symmetry energy, E_sym^kin(\rho_0), equals the difference in the
per-nucleon kinetic energy between pure neutron matter (PNM) and symmetric
nuclear matter (SNM), often calculated using a simple Fermi gas model. However,
experiments show that tensor force induced short-range correlations (SRC)
between proton-neutron pairs shift nucleons to high-momentum in SNM, but have
almost no effect in PNM. We present an approximate analytical expression for
E_sym^kin(\rho) of correlated nucleonic matter. In our model, E_sym^kin(\rho_0)
= -10 MeV, which differs significantly from +12.5 MeV for the widely-used free
Fermi gas model. This result is consistent with our analysis of recent data on
the free proton-to-neutron ratios measured in intermediate energy
nucleus-nucleus collisions as well as with microscopic many-body calculations,
and previous phenomenological extractions. We then use our calculated
E_sym^kin(\rho) in combination with the known total symmetry energy and its
density dependence at saturation density to constrain the value and density
dependence of the potential part and to extrapolate the total symmetry energy
to supranuclear densities.
