  Making use of an identity transformation independent of a nuclear model, we
represent the {\bb}-amplitude as a sum of two terms. One term accounts for most
of the sensitivity of the original {\bb}-amplitude to $g'_{pp}$ for realistic
$g'_{pp}\simeq 1$ (with $g'_{pp}$ being the ratio of the triplet and singlet
p-p interaction strengths) and is determined by a specific energy-weighted sum
rule. The sum rule depends only on the particle-particle residual interaction
(being linear function of $g'_{pp}$ in the QRPA) and passes through zero at the
point $g'_{pp}=1$ where the Wigner SU(4) symmetry is restored in the p-p sector
of the Hamiltonian. The second term in the decomposition of the {\bb}-amplitude
is demonstrated within the QRPA to be a much smoother function for the
realistic values of $g'_{pp}$ than the original {\bb}-amplitude. This term is
mainly determined by the intensity of the spin-orbit interaction of the nuclear
mean field. Thus, the analysis of the present work reveals the reasons for the
sensitivity of the {\bb}-amplitude to different components of the nuclear
Hamiltonian and thereby can help in constraining nuclear model uncertainties in
calculations of the amplitude.
