Bπ form factors from QCD Sum Rules

The H * Hπ form factor for H = B and D mesons is evaluated in a QCD sum rule calculation. We study the Borel sum rule for the three point function of two pseudoscalar and one vector meson currents up to order four in the operator product expansion. The double Borel transform is performed with respect to the heavy meson momenta. We discuss the momentum dependence of the form factors and two different approaches to extract the H * Hπ coupling constant. The coupling of the pion to the heavy mesons (g B * Bπ and g D * Dπ) is related to the form factor at zero pionic momentum and its precise value has been often needed in phenomenol-ogy. In particular, the g D * Dπ coupling is needed in the context of quark gluon plasma (QGP) physics. Suppression of charmonium production in heavy ion collisions is one of the signatures of QGP formation [1]. Therefore a precise evaluation of the background, i.e., conventional J/ψ absorption by co-moving pions and ρ mesons [2], is of fundamental importance. Since pions are so abundant in a dense nuclear environment, the reactions π + J/ψ → D + D * (and consequently the coupling g D * Dπ) are of special relevance [3]. In the case of g D * Dπ , the D * + → D 0 π + decay is observed experimentally. However, present data provide only an upper bound: g D * Dπ ≤ 21 [4]. For g B * Bπ , there cannot be a direct experimental indication because there is no phase space for the B * → Bπ decay. Recently, a direct preliminary determination of g B * Bπ on the lattice has been attempted [5]. The D * Dπ and B * Bπ couplings have been studied by several authors using different approaches of the QCD sum rules (QCDSR): two point function combined with soft pion techniques [6], light cone sum rules [7,8], light cone sum rules including perturbative corrections [9], sum rules in a external field [10], double momentum sum rules [11]. Unfortunately, the numerical results from these calculations may differ by almost a factor two.