5 Soft and Hard Jets in QCD

Multiplicity of sets of soft jets with energies ranging in some interval is determined. The possible role of collective effects is discussed. The phenomenon of jet emission is well known in QCD and firmly established in experiment. The two-jet events in e + e −-annihilation provide us with unique possibility to measure jets with fixed energy equal to that of colliding particles. In all other cases we have to deal with sets of jets with different energies. In three-jet events and in any high-p t process the produced jets are somehow distributed in their energies. E.g., energies of gluon jets in three-jet process change from some lower limit determined by the requirement to separate this process to any value defined by experimental choice. Therefore, one has to deal with sets of jets with energies ranging in some interval. Multiplicity of jets at a given energy has been calculated in QCD, and results agree quite well with experiment (see the reviews in [1, 2, 3]). This can be done for sets of jets as well [4]. The proper weights for jets with different energies in the set are provided by the QCD equations. The collective effects due to strings pulled apart during the separation of jets and color screening are somehow accounted in QCD. They lead, e.g., to different suppression of multiplicities between q ¯ q and qg pairs of jets. By measuring the multiplicity of sets of soft jets, this effect can become more pronounced. To simplify the presentation, I consider gluodynamics (see also [5]). If the probability to create n particles 2 in a jet is denoted as P n , the generating function G is defined as G(z, y) = ∞ n=0 P n (y)(1 + z) n , (1) where z is an auxiliary variable, y = ln(pΘ/Q 0) = ln(2Q/Q 0) is the evolution parameter, defining the energy scale, p is the initial momentum, Θ is the angle of the divergence of the jet (jet opening angle), assumed here to be fixed, Q is the jet virtuality, Q 0 = const. The gluodynamics equation for the generating function is written as dG/dy = 1 0 dxK(x)γ 2 0 [G(y + ln x)G(y + ln(1 − x)) − G(y)], (2) where γ 2 0 = 6α S π , (3) α S is the coupling strength and the kernel K(x) is K(x) = 1 x − (1 …