Azimuthal decorrelation of forward and backward jets at the Tevatron

We analyse the azimuthal decorrelation of ‘Mueller-Navelet’ dijets produced in the pp̄ collisions at Tevatron energies using a BFKL framework which incorporates dominant subleading effects. We show that these effects significantly reduce the decorrelation yet they are still insufficient to give satisfactory description of experimental data. However a good description of the data is obtained after incorporating within formalism the effective rapidity defined by Del Duca and Schmidt. An ideal test of log(1/x) dynamics is the “Mueller-Navelet” process [1, 2, 3] in hadron-hadron collisions with one backward jet separated from a forward jet by a large rapidity interval. The test has been under study for several years, but has recently been sharpened by the considerable improvement in the precision of the data [4]. The relevant hard scale is specified by the transverse momenta of the jets (k1,k2). An advantage of this process is that these momenta can be of comparable magnitude so the intervening DGLAP evolution is suppressed. The behaviour of the cross-section is therefore sensitive to the diffusion of transverse momenta of the intermediate gluons, which is a property of leading log(1/x) dynamics [5, 6]. The characteristic features of this process are (i) a rapid increase of the 2-jet production cross section with increasing incident energy and (ii) a weakening of the azimuthal back-to-back correlation between the jets as the rapidity interval is increased. The analyses have so far been within the leading order log(1/x) BFKL framework, and indicate much more decorrelation than shown by the data. The improvement of the 2-jet data has been accompanied by progress in understanding and quantifying the effect of sub-leading log(1/x) corrections. The full NLO BFKL (log(1/x)) contributions have been obtained and found to be large [7, 8, 9]. However the major contribution can be resummed to all orders in a straightforward way [10, 11]. To be precise the resummation is effected by requiring that the virtuality of the intermediate gluons is dominated by their transverse momenta squared, which although formally sub-leading, is implicit in the derivation of the BFKL equation. We call this the consistency condition (CC). The resummation is found to stabilise the solution of the NLO BFKL equation. The purpose of this paper is to incorporate those subleading effects generated by the consistency constraint in the theoretical description of the dijet production in hadronic collisions. The cross-section describing the production of a forward jet (x1, k 2 1) and a backward jet (x2, k 2 2), with relative azimuthal angle φ− π, may be written dσ dx1dx2dk 1dk 2 2dφ = 1 x1x2 [ x1feff(x1, k 2 1) x2feff(x2, k 2 2) ] dσ̂ dk 1dk 2 2dφ , (1) where feff = g+ 4 9 (q+ q̄) is the effective parton distribution of the incoming proton (antiproton). Note, that with this convention the back-to-back configuration of the jets in the transverse plain corresponds to φ = 0. The hard partonic cross section (defined here for the gluon-gluon scattering) is of the form dσ̂ dk 1dk 2 2dφ = ᾱ sπ 4(k1k2) ∞