Sum Rules for Leading and Subleading Form Factors in Heavy Quark Effective Theory using the Non‐forward Amplitude

Within the OPE, we formulate new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/mQ, using the non‐forward amplitude. In the heavy quark limit, these sum rules imply that the elastic Isgur‐Wise function ξ(w) is an alternate series in powers of (w − 1). Moreover, one gets that the n‐th derivative of ξ(w) at w = 1 can be bounded by the (n − 1)‐th one, and the absolute lower bound for the n‐th derivative (−1)nξ(n)(1) ⩾ (2n+1)!!22n. Moreover, for the curvature we find ξ″(1) ⩾ 15[4ρ2 + 3(ρ2)2] where ρ2 = −ξ′(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for ξ(w). The method is extended to the subleading quantities in 1/mQ. Concerning the perturbations of the Current, we derive new simple relations between the functions ξ3(w) and Λξ(w) and the sums ∑ n ΔEj(n)τj(n)(1)τj(n)(w) (j = 12, 32), that involve leading quantities, Isgur‐Wise functions τj(n)(w) and level spacings ΔEj(n). Our results follow because t...