SCET sum rules for heavy-to-light form factors

We consider a sum rule for heavy-to-light form factors in soft-collinear effective theory (SCET). Using the correlation function given by the time-ordered product of a heavy-to-light current and its hermitian conjugate, the heavy-to-light soft form factor ζP can be related to the leading-order B meson shape function. Using the scaling behavior of the heavy-to-light form factor in ΛQCD/mb, we put a constraint on the behavior of the B meson shape function near the endpoint. We employ the sum rule to estimate the size of ζP with the model for the shape function and find that it ranges from 0.01 to 0.07.