Systematic Errors of Transition Form Factors Extracted by Means of Light-cone Sum Rules

This talk presents results of our study of heavy-to-light transition form factors extracted with the help of light-cone sum rules. We employ a model with scalar particles interacting via massless-boson exchange and study the heavy-to-light correlator, relevant for the extraction of the transition form factor. We calculate this correlator in two different ways: by making use of the Bethe–Salpeter wave function of the light bound state and by making use of the light-cone expansion. This allows us to calculate the full correlator and separately the light-cone contribution to it. In this way we show that the off-light cone contributions are not suppressed compared to the light-cone one by any large parameter. Numerically, the difference between the value of the form factor extracted from the full correlator and from the light-cone contribution to this correlator is found to be about 20–30% in a wide range of masses of the particles involved in the decay process. In a previous talk 1) (see also Ref. [2] for details) we have shown that the hadron parameters can be extracted from sum rules only with some accuracy, which lies beyond the control of the standard procedure adopted in the method of sum rules, even if the correlator in a limited range of the Borel parameter is known precisely. In the light-cone sum-rule analysis of hadron form factors, the relevant correlator is not known precisely and is obtained as an expansion near the light cone (LC) 3). This entails additional uncertainties in the extraction of hadron parameters, in this case, of the form factors. This talk reports the results of our recent systematic analysis of off-light-cone effects in sum rules for heavy-to-light form factors 4). The effects are investigated in a model involving scalar constituents. We consider two types of scalar “quarks”, viz., heavy quarks Q of mass mQ and light quarks φ of mass m, and study the weak transition of the heavy scalar “meson” MQ(Qφ) to the light “meson” M(φφ) induced by the weak heavy-tolight Q → φ quark transition. The analysis of this model is technically simpler but allows one to study some essential features of the corresponding QCD case. For calculating the correlator of interest, we need the Bethe–Salpeter (BS) amplitude of the light meson, defined by ΨBS(x, p ′) = 〈0|Tφ(x)φ(0)|M(p′)〉 = Ψ(x, xp′, p = M). (1) As a function of xp, this amplitude may be represented by the Fourier integral