  Let $E$ be an elliptic curve over $\mathbb{Q}$ and $A$ be another elliptic
curve over a real quadratic number field. We construct a $\mathbb{Q}$-motive of
rank $8$, together with a distinguished class in the associated Bloch-Kato
Selmer group, using Hirzebruch-Zagier cycles, that is, graphs of
Hirzebruch-Zagier morphisms. We show that, under certain assumptions on $E$ and
$A$, the non-vanishing of the central critical value of the (twisted) triple
product $L$-function attached to $(E,A)$ implies that the dimension of the
associated Bloch-Kato Selmer group of the motive is $0$; and the non-vanishing
of the distinguished class implies that the dimension of the associated
Bloch-Kato Selmer group of the motive is $1$. This can be viewed as the triple
product version of Kolyvagin's work on bounding Selmer groups of a single
elliptic curve using Heegner points.
