Lagrangian perturbations at order 1/m${}_{\mathbf{Q}}$ and the non-forward amplitude in Heavy Quark Effective Theory

Abstract

We pursue the program of the study of the non-forward amplitude in HQET. We obtain new sum rules involving the elastic subleading form factors ${\chi }_i(w)$ $(i=1,2,3)$ at order $1/m_Q$ that originate from the ${\mathcal{L}}_{kin}$ and ${\mathcal{L}}_{mag}$ perturbations of the Lagrangian. To obtain these sum rules we use two methods. On the one hand we start simply from the definition of these subleading form factors and, on the other hand, we use the Operator Product Expansion. To the sum rules contribute only the same intermediate states $(j^P,J^P)=({\frac{1}{2}}^{-},1^{-}),({\frac{3}{2}}^{-},1^{-})$ that enter in the $1/m_Q^2$ corrections of the axial form factor $h_{A_1}(w)$ at zero recoil. This allows to obtain a lower bound on $-{\delta }_{1/m^2}^{(A_1)}$ in terms of the ${\chi }_i(w)$ and the shape of the elastic IW function $\xi (w)$. We find also lower bounds on the $1/m_Q^2$ correction to the form factors $h_{+}(w)$ and $h_1(w)$ at zero recoil. An important theoretical implication is that ${\chi }_1^{\prime }(1)$, ${\chi }_2(1)$ and ${\chi }_3^{\prime }(1)$ (${\chi }_1(1)={\chi }_3(1)=0$ from Luke theorem) must vanish when the slope and the curvature attain their lowest values ${\rho }^2\to \frac{3}{4}$, ${\sigma }^2\to \frac{15}{16}$. We discuss possible implications on the precise determination of $|V_{cb}|$.

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Cited by in corpus (3)

• Explicit form of the Isgur-Wise function in the BPS limit
• New results on the baryon decay Lambda_b -> Lambda_c ell nu in Heavy Quark Effective Theory
• On the form factors of semileptonic baryon decays in Heavy Quark Effective Theory