Heavy-to-light correlators beyond the light cone
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ELEMENTARY PARTICLES AND FIELDS Theory
Heavy-to-Light Correlators Beyond the Light Cone W. Lucha1), D. I. Melikhov1), 2) , and S. Simula3) Received May 4, 2007; in final form, August 10, 2007
Abstract—We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe–Salpeter amplitude of the light meson near the light cone x2 = 0 and (ii) by adopting the known solution for the Bethe–Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x2 = 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x2 = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%. PACS numbers: 12.38.Lg DOI: 10.1134/S1063778808030150
1. INTRODUCTION QCD sum rules on the light cone (LC) [1] have been extensively applied to various exclusive form factors, in particular, to weak heavy-to-light transition form factors (see, e.g., [2]). Within this method, the relevant correlators are obtained as power expansions in x2 near the LC x2 = 0 in terms of the distribution amplitudes of increasing twist. In practice, however, only the few lowest twist distribution amplitudes are known with a reasonable accuracy. Thus, one has to rely on calculations which take into account only the lowest powers of x2 , at most up to terms linear in x2 , without a systematic study of the effects related to higher powers of x2 ([2–4] and references therein). However, the off-LC (x2 = 0) contributions to the correlator are not parametrically suppressed compared to the contribution evaluated at x2 = 0: for instance, Braun and Halperin [5] studied the pion elastic form factor with LC sum rules and found that contributions to the correlator from terms corresponding to higher powers of x2 in the pion Bethe–Salpeter (BS) amplitude 0|T u ¯(x)γµ γ5 d(0)|π(p) have in gen4 eral the same ∼1/q behavior. As we show here, a similar situation occurs for the heavy-to-light form factor: the contributions to the correlator coming from ∗
The text was submitted by the authors in English. Institute for High Energy Physics, Austrian Academy of Sciences, Vienna, Austria. 2) Nuclear Physics Institute, Moscow State University, Moscow, Russia. 3) INFN, Sezione di Roma III, Roma, Italy. 1)
the LC and the off-LC terms in the BS amplitude of the light meson have the same dependence in 1/mQ , mQ being the heavy-quark mass. Therefore, relying on calculations performed at x2 = 0 does not seem to be safe and the effects of all powers of x2 should be summed and taken into account in the sum rule. In this paper, we study the correlator relevant for the e
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