In this work we present the first non-perturbative determination of the hadronic susceptibilities that constrain the form factors entering the semileptonic $B to D^{(*)} ell u_ell $ transitions due to unitarity and analyticity. The susceptibilities are obtained by evaluating moments of suitable two-point correlation functions obtained on the lattice. Making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a simeq 0.062, 0.082, 0.089$ fm) and with pion masses in the range $simeq 210 - 450$ MeV, we evaluate the longitudinal and transverse susceptibilities of the vector and axial-vector polarization functions at the physical pion point and in the continuum and infinite volume limits. The ETMC ratio method is adopted to reach the physical $b$-quark mass $m_b^{phys}$. At zero momentum transfer for the $b to c$ transition we get $chi_{0^+}(m_b^{phys}) = 7.58,(59) cdot 10^{-3}$, $chi_{1^-}(m_b^{phys}) = 6.72,(41) cdot 10^{-4}$ GeV$^{-2}$, $chi_{0^-}(m_b^{phys}) = 2.58,(17) cdot 10^{-2}$ and $chi_{1^+}(m_b^{phys}) = 4.69,(30) cdot 10^{-4}$ GeV$^{-2}$ for the scalar, vector, pseudoscalar and axial susceptibilities, respectively. In the case of the vector and pseudoscalar channels the one-particle contributions due to $B_c^*$- and $B_c$-mesons are evaluated and subtracted to improve the bounds, obtaining: $chi_{1^-}^{sub}(m_b^{phys}) = 5.84,(44) cdot 10^{-4}$ GeV$^{-2}$ and $chi_{0^-}^{sub}(m_b^{phys}) = 2.19,(19) cdot 10^{-2}$.
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