  We investigate the Glauber-gluon effect on the $B \to \pi \pi$ and $\rho
\rho$ decays, which is introduced via a convolution of a universal Glauber
phase factor with transverse-momentum-dependent(TMD) meson wave functions in
the $k_T$ factorization theorem. For an appropriate parametrization of the
Glauber phase, it is observed that a TMD wave function for the pion ($\rho$
meson) with a weak (strong) falloff in parton transverse momentum $k_T$ leads
to significant (moderate) modification of the $B^0 \to \pi^0 \pi^0$ ($B^0 \to
\rho^0 \rho^0$) branching ratio: the former (latter) is enhanced (reduced) by
about a factor of 2 (15\%). This observation is consistent with the dual role
of the pion as a massless Nambu-Goldstone boson and as a $q \bar q$ bound
state, which requires a tighter spatial distribution of its leading Fock state
relative to higher Fock states. The agreement between the theoretical
predictions and the data for all the $B \to \pi \pi$ and $\rho^0 \rho^0$
branching ratios is then improved simultaneously, and it is possible to resolve
the $B \to \pi \pi$ puzzle.
