BFKL versus DGLAP Evolution

In the DGLAP parton evolution scheme [9] the parton cascade follows a strong ordering in transverse momentum $k_{Tn}^2 \gg k_{Tn-1}^2 \gg... \gg k_{T1}^2$,while there is only a soft (kinematical) ordering for the fractional momentum x_n<x_n-1<...<x₁. However for low-x at HERA the BFKL scheme [10] could well be the dominant scheme. In this scheme the cascade follows a strong ordering in fractional momentum $x_n \ll x_{n-1} \ll... \ll x_1$,while there is no ordering in transverse momentum.

BFKL evolution can be enhanced by studying DIS events which contain an identified jet of longitudinal momentum fraction x_jet=p_z(j)/E_proton (in the proton direction) which is large compared to Bjorken x [42]. By tagging a forward jet with $p_T(j)\simeq Q$ this allows minimal phase space for DGLAP evolution while the condition $x_{jet}\gg x$ leaves BFKL evolution active. This leads to the forward jet production cross section in BFKL dynamics being larger than that of the ${\cal O}(\alpha_S^2)$ QCD calculation with DGLAP evolution [43].

In Fig. 8, recent data from H1 [44] and ZEUS [45] are compared with BFKL predictions [46] and fixed order QCD predictions as calculated with the MEPJET [17] program at NLO. The conditions $p_T(j)\simeq Q$ and $x_{jet}\gg x$ are satisfied in the two experiments by slightly different selection cuts. H1 selects events with a forward jet of p_T(j)>3.5 GeV (in the angular region $7^o < \theta(j) < 20^o$) with  

$$0.5 < p_T(j)^2/Q^2\; < \; 2\;, \qquad \qquad x_{jet} \simeq E_{jet}/E_{proton} \gt 0.035\;;$$ (5)

while ZEUS triggers on somewhat harder jets of p_T(j)>5 GeV and $\eta(j)<2.4$ with  

$$0.5 < p_T(j)^2/Q^2\; < \; 4\;, \qquad \qquad x_{jet} = p_z(j)/E_{proton} \gt 0.035\;.$$ (6)

 

Figure: Forward jet cross section at HERA as a function of Bjorken x within (a) the H1 [44] and (b) the ZEUS [45] acceptance cuts. The BFKL result of Bartels et al. [46] is shown as the dashed line. The solid and dotted line give the NLO MEPJET result and a measure for the uncertainity of NLO prediction through changes in the choice of scale.  

Fig. 8 shows that both experiments observe substantially more forward jet events than expected from NLO QCD. A very rough estimate of the uncertainty of the NLO calculation is provided by the two dotted lines, which correspond to variations by a factor 10 of the renormalisation and factorisation scales $\mu_R^2$ and $\mu_F^2$.A recent BFKL calculation (dashed lines) gives a better agreement with the data. The overall normalisation in this calculation is uncertain and the agreement may be fortuitous, indeed it should also be noted that both experiments observe more centrally produced dijet events than predicted by the NLO QCD calculations. Further careful investigation is necessary before claiming that BFKL is the mechanism for this enhanced forward jet production.