  According to the Hugenholtz-Van Hove theorem, nuclear symmetry energy \esym
and its slope \lr at an arbitrary density $\rho$ are determined by the nucleon
isovector (symmetry) potential \usym and its momentum dependence
$\frac{\partial U_{sym}}{\partial k}$. The latter determines uniquely the
neutron-proton effective k-mass splitting $m^*_{n-p}(\rho,\delta)\equiv (m_{\rm
n}^*-m_{\rm p}^*)/m$ in neutron-rich nucleonic matter of isospin asymmetry
$\delta$. Using currently available constraints on the \es0 and \l0 at normal
density $\rho_0$ of nuclear matter from 28 recent analyses of various
terrestrial nuclear laboratory experiments and astrophysical observations, we
try to infer the corresponding neutron-proton effective k-mass splitting
$m^*_{n-p}(\rho_0,\delta)$. While the mean values of the
$m^*_{n-p}(\rho_0,\delta)$ obtained from most of the studies are remarkably
consistent with each other and scatter very closely around an empirical value
of \emass$=0.27\cdot\delta$, it is currently not possible to scientifically
state surely that the \emass is positive within the present knowledge of the
uncertainties. Quantifying, better understanding and then further reducing the
uncertainties using modern statistical and computational techniques in
extracting the \es0 and \l0 from analyzing the experimental data are much
needed.
