A definite prediction for 
coupling constants (both strong and weak
ones) can be obtained by using the framework of chiral perturbation theory
in the leading 
expansion (
) and leading order
, 
being the number of quark colors, combined with
factorization. Basically, noting that the quark effective nonleptonic
Hamiltonian (18) is of the 
form, in this
approach a `bosonization' prescription is separately applied to each of
the quark currents. For example, the left-handed currents, considered as
Noether currents of the chiral symmetry of the QCD effective action, can
be expanded in 
plus 
terms as:
where 
has been defined previously, and 
is a scale
characterizing chiral symmetry breaking (of the order of 
).
An analogous bosonization could be written for right-handed current
operators. Replacing Eq. (36) into the large 
effective nonleptonic quark Hamiltonian [34], the chiral weak
Lagrangian 
assumes the factorized, 
structure [35,36]
and an analogous expression can be obtained for the 27-plet component.
The advantage of factorization, which is expected to hold in the large 
approximation, is
that the strong Lagrangian, via the bosonization prescription
(36) of the chiral quark currents, uniquely determines the structure
of 
. In particular, the unknown weak counterterms can be
related to (known) strong counterterms. The additional advantage of
the large 
approximation is that, in this limit, the strong coupling
constants can be predicted [37], so that the number of free parameters
is reduced to a minimum. Numerical results in the 
approach,
from Refs. [35] and [36], are
reported in Tab. 6. The comparison with the data seems encouraging, although,
concerning the test in the 
sector and the needed accuracies,
the same comments hold as previously made with regard to
Eqs. (33) and (34).
Although being quite predictive, the leading 
scheme has also some
conceptual difficulties. For example, the results of Tab. 6 are obtained by
employing the values of 
in Eq. (37), and of the corresponding
27-plet coupling constant 
, measured from the experimental 
data, instead of taking the (rather different) leading 
values of these
coefficients. This opens the question of the quantitative role of
next-to-leading 
corrections and nonfactorizable contributions
[38], and of the convergence of the
expansion for 
. Another point is that chiral loops are negligible
at the leading order in 
, hence strong rescattering phases vanish
and must be included by hand. In the absence of meson loops, the counterterm
coupling constants become mass-scale independent, so that the problem of the
-dependence is not well-addressed and, at this order,
the comparison with the results obtained in the full chiral Lagrangian theory
is not unambiguous.
