Sum Rules for Leading and Subleading Form Factors in Heavy Quark Effective Theory using the Non-forward Amplitude
- Instituto de Fisica Corpuscular, Valencia (Spain)
- Laboratoire de Physique Theorique (UMR 8627 CNRS), Universite de Paris Sud-XI, Batiment 210, 91405 Orsay cedex (France)
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 {xi}(w) is an alternate series in powers of (w - 1). Moreover, one gets that the n-th derivative of {xi}(w) at w = 1 can be bounded by the (n - 1)-th one, and the absolute lower bound for the n-th derivative (-1){sup n}{xi}{sup (n)}(1) {>=} ((2n+1){exclamation_point}{exclamation_point}/2{sup 2n}). Moreover, for the curvature we find {xi}''(1) {>=} (1/5)[4{rho}{sup 2} + 3({rho}{sup 2}){sup 2}] where {rho}2 = -{xi}'(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for {xi}(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 {xi}3(w) and {lambda}-bar{xi}(w) and the sums n {delta}E{sub j}{sup (n)}{tau}{sub j}{sup (n)}(1){tau}{sub j}{sup (n)}(w) (j = (1/2), (3/2)), that involve leading quantities, Isgur-Wise functions {tau}{sub j}{sup (n)}(w) and level spacings {delta}E{sub j}{sup (n)}. Our results follow because the non-forward amplitude depends on three variables (wi, wf, wif) = (vi {center_dot} v', vf {center_dot} v', vi {center_dot} vf), and we consider the zero recoil frontier (w, 1, w) where only a finite number of jP states contribute ((1/2){sup +}, (3/2){sup +}). We also obtain new sum rules involving the elastic subleading form factors {chi}i(w) (i = 1, 2, 3) at order 1/mQ that originate from the Lkin and Lmag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (j{sup P}, J{sup P}) = ((1/2){sup -}, 1{sup -}),((3/2){sup -}, 1{sup -}) that enter in the 1/m{sub Q}{sup 2} corrections of the axial form factor hA1(w) at zero recoil. This allows to obtain a lower bound on -{delta}{sub 1/m{sup 2}}{sup (A{sub 1})} in terms of the {chi}i(w) and the shape of the elastic IW function {xi}(w). An important theoretical implication is that {chi}{sub 1}{sup '}(1), {chi}2(1) and {chi}{sub 3}{sup '}(1) ({chi}{sub 1}(1) = {chi}{sub 3}(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values {rho}{sup 2} {yields} (3/4), {sigma}{sup 2} {yields} (15/16). These constraints should be taken into account in the exclusive determination of Vcb.
- OSTI ID:
- 20787633
- Journal Information:
- AIP Conference Proceedings, Vol. 806, Issue 1; Conference: International workshop on quantum chromodynamics: Theory and experiment, Conversano, Bari (Italy), 16-20 Jun 2005; Other Information: DOI: 10.1063/1.2163760; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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