QCD Amplitudes in the High - Energy Limit

Dijet production with a rapidity gap between the jets is considered as a test ground for the production of a heavy Higgs boson via weak-boson fusion at hadron supercolliders. It is argued that in order to perform a detailed analysis of dijet production with a rapidity gap we need an O(αs) calculation including the relevant collinear enhancements which give structure to the jets. Such a calculation needs not be exact, but must include the full leading power in ŝ/t̂ of the rate of dijet production in the high-energy limit. The QCD amplitudes must be determined to the corresponding accuracy. Accordingly, the scattering amplitudes necessary to compute the full leading power in ŝ/t̂ of dijet production to O(αs) are analysed. 1 Rapidity gaps between jets In recent years strong-interaction processes characterised by two large and disparate energy scales, which are tipically the squared center-of-mass energy s and the squared momentum transfer t, with s ≫ t, have been extensively analysed. The interest stems from the presumption that their description in terms of perturbative-QCD calculations at a ∗On leave of absence from I.N.F.N., Sezione di Torino, Italy. 1 fixed order in the coupling constant αs might not be adequate, and that a resummation at all orders of αs of large contributions of the type of ln(s/t), performed through the BFKL equation [1], might be needed. These processes can be divided in two categories: a) inclusive processes, like deeply inelastic scattering (DIS) at small xbj , dijet production in pp̄ collisions at large rapidity intervals, forward jet production in DIS; b) diffractive processes, like diffractive DIS, diffractive vector meson production, or dijet production in hadron collisions with a rapidity gap between the tagging jets. The last of these processes, dijet production with a rapidity gap, is an example of double hard diffraction and is characterised by two large and disparate energy scales, the squared parton center-of-mass energy ŝ and a momentum-transfer scale of the order of the squared transverse energy of the jets E ⊥, and by a soft scale, μs, the threshold energy for the detection of secondary hadrons within the rapidity gap. This process has been studied both at the Tevatron Collider [2] and in photoproduction at HERA [3]. Since the formation of a rapidity gap can happen only through the exchange of a colour singlet, which could be modeled by the BFKL resummation [4, 5], it is obvious in that respect the interest for dijet production with a rapidity gap. However, the main motivation for the analysis of dijet production with a rapidity gap is to use it as a test ground for the production of a heavy Higgs boson at hadron supercolliders [6]. A Higgs boson is mainly produced via gluon fusion, g g → H , mediated by a top-quark loop. The Higgs boson then decays mainly into a pair of W or Z bosons. Such a signal, though, is going to be swamped by the W W QCD and the t t̄ backgrounds. A heavy Higgs boson is also produced via weak-boson fusion, W W, Z Z → H , though at a smaller rate [7], however such a production mechanism would have a distinctive radiation pattern with a gap in parton production in the central-rapidity region, because no color is exchanged between the quarks that emit the weak bosons [6, 8]. Producing a rapidity gap at the parton level is not sufficient though, since the gap is usually filled by soft hadrons produced in the rescattering between the spectators partons in the underlying event. Accordingly, Bjorken [6] introduced the gap survival probability, < |S2| >, i.e. the probability for a gap formed at the parton level to survive the rescattering between the spectators partons. The gap survival probability deals with the soft, i.e. low transverse-momentum, physics of the scattering between the two hadrons; therefore it can only be estimated using non-perturbative models [6, 9] (within perturbative QCD, the necessity of fulfilling the factorization theorems [10] would always allow for the emission of soft hadrons in the rescattering between the spectators partons [5]).