Light-cone expansion of heavy-to-light form factors

We present the results of our recent systematic study of the light-cone expansion of heavy-to-light transition form factors in a model with scalar constituents [1]. We show that the higher-twist contributions (represented in this model by off-light-cone effects) all have the same behaviour in the 1/mQ expansion. The suppression parameter of the higher-twist contributions compared to the lower-twist contributions is, in general, the inverse Borel parameter β. The only exception here is the case of the leading and the subleading twists: they are of the same order in 1/β because of an extra suppression of the leading-twist contribution to the form factor. Light-cone (LC) sum rules [2] belong to the most widely used approaches for calculating hadron form factors in QCD. The form factor of an individual bound state obtained from a LC sum rule depends on two ingredients: (i) the field-theoretic calculation of the relevant correlator by constructing its LC expansion in terms of hadron distribution amplitudes (DA) of increasing twist, and (ii) the technical “extraction procedure” (cutting the correlator and determining the effective continuum threshold), which introduces a systematic error into the extracted form factor (for a recent study of the serious issue of the systematic errors, see [3]). In QCD one can calculate only a few terms of the LC expansion of the correlator; it is impossible to study the full series and to estimate the typical size of the omitted higher-twist effects. Therefore, we have systematically analysed the LC expansion in a model with scalar constituents: a heavy “quark” field Q (of mass mQ) and a light “quark” field φ (of mass m) interacting by exchange of a massless boson in ladder approximation [1]. The basic object here is the heavy-to-light correlator Γ(p, q) = i ∫ dx exp(ipx)〈M(p′)|T (φ(x)Q(x)Q(0)φ(0)) |0〉. (1) One should (i) obtain the dispersion representation in p, Γ(p, q) = ∫ ds s− p2 − i0 ∆(s, q), (2) and (ii) perform the Borel transform 1/(s− p) → exp [−s/(2mQβ)] (β ≪ mQ) and relate the cut Borel image to the form factor of interest: fMQ FMQ→M(q ) = exp ( M Q 2mQβ )