Conformal couplings and “azimuthal matching” of QCD Pomerons

نویسنده

  • N. Marchal
چکیده

Using the asymptotic conformal invariance of perturbative QCD we derive the expression of the coupling of external states to all conformal spin p components of the forward elastic amplitude. Using the wave-function formalism for structure functions at small x, we derive the perturbative coupling of the virtual photon for p = 1 , which is maximal for linear transverse polarization. The non-perturbative coupling to the proton is discussed in terms of “azimuthal matching” between the proton color dipoles and the qq̄ configurations of the photon. As an application, the recent conjecture of a second QCD Pomeron related to the conformal spin-1 component is shown to rely upon a strong azimuthal matching of the p = 1 component in γ∗-proton scattering. 1 Conformal invariance of the BFKL equation As well-known the Balitskii, Fadin, Kuraev, Lipatov (BFKL) equation [1] expresses the elastic amplitude of two off-shell gluons in the high energy limit corresponding to the perturbative QCD resummation of leading logarithms. In terms of transverse coordinates (Fourier transforms of the four external gluon transverse momenta), the equation can be schematically written ∂f ∂Y (k, k′, q;Y ) = K ⊗ f, where Y (in the case of structure functions Y = log 1/xbj ) is the whole rapidity range, k, k′, the two-dimensional initial gluon momenta and q, the 2momentum transfer. The BFKL integro-differential kernel K is known to possess a global conformal SL(2,C) invariance [2]. The BFKL derivation is made in the framework of the leading log approximation but it is interesting to investigate the more general consequences of the asymptotic conformal invariance, which could be maintained at higher order. Indeed, for instance, next leading BFKL calculations could preserve an approximate conformal invariance [3]. Deviations from asymptotic conformal invariance could also be studied by comparison with the results obtained with this assumption. ∗Stagiaire de Diplôme d’Etudes Approfondies de Physique Théorique (ENS,Paris)

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تاریخ انتشار 2008