  Partial conservation of the nine axial currents $A^\beta_\mu$ for
$\beta=0,1,...,8$ applied to the vacuum expectation values of the equal-time
commutators of the nine axial charges $Q_A^\alpha(x_0)$ for $\alpha=0,1,...,8$
with the corresponding axial current divergences $\partial^\mu A_\mu^\beta $
implies that the non-vanishing current quark masses $m_u, m_d, m_s$ of the
light quarks $u, d, s$ have the same sign. Under the more realistic assumption
of partial conservation of only the eight axial currents of $SU(3)\otimes
SU(3)$, i.e. $\alpha=1,...,8$ and $\beta=1,...,8$ in the above, inequalities
for the quark masses follow. They are trivially fulfilled if the three light
quark masses have the same sign and imply, for non-vanishing quark masses $m_u,
m_d, m_s$, that at least two of these masses have the same sign as their sum
$m_u + m_d + m_s$. If one of the three quark masses vanishes, one of the other
two might also. If both do not, they have the same sign (the same, of course,
as their sum). Our assumptions include the standard vector SU(3) symmetry of
the vacuum.
