BFKL-motivated measurements

 

Figure 10: Gluon ladder diagram contributing to jet production in DIS. The position and kinematics of the parton which can give rise to the forward jet is indicated.  

Recently, much interest has been focused on the small Bjorken-x region, where one would like to distinguish BFKL [42] from the more traditional DGLAP evolution equation [43]. One of the dominant Feynman graphs responsible for parton evolution in DIS is shown in Fig. 10. The x_i denote the momentum fractions (relative to the incoming proton) of the incident virtual partons and p_Ti is the transverse momentum of emitted parton i. Such ``ladder-type'' diagrams with strong ordering in transverse momenta, $Q^2\simeq p_{Tn}^2 \gg \ldots \gg p_T(j)^2$, but only soft ordering for the longitudinal fraction $x_1 \gt x_2\gt\ldots\gt x_n\simeq x$ are the source of the leading log Q² contributions which are summed in the DGLAP evolution equation [43]. In the BFKL approximation, transverse momenta are no longer ordered along the ladder while there is a strong ordering in the fractional momentum $x_n \ll x_{n-1}\ll\ldots \ll x_1\simeq x_{jet}$.

BFKL evolution can be enhanced and DGLAP evolution suppressed 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 [44]. Furthermore, tagging a forward jet with $p_T(j)\simeq Q$ allows little room for DGLAP evolution while the condition $x_{jet}\gg x$ leaves BFKL evolution active. Assuming BFKL dynamics leads to an enhancement of the forward jet production cross section proportional to $(x_{jet}/x)^{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}-1}$,where $\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}$ is the BFKL pomeron intercept, compared to the ${\cal O}(\alpha_S^2)$ QCD calculation with DGLAP evolution [46].

 

Figure: Forward jet cross section at HERA as a function of Bjorken x within (a) the H1 [47] and (b) the ZEUS [48] acceptance cuts. The BFKL result of Bartels et al. [49] is shown as the dashed line. The solid and dotted lines give the NLO MEPJET result for the scale choice $\mu_R^2=\mu_F^2=\xi(0.5\sum k_T)^2$ with $\xi=0.1, 1$ and 10, which provides a measure for the uncertainty of the NLO prediction.  

In Fig. 11, recent data from H1 [47] and ZEUS [48] are compared with BFKL predictions [49] and fixed order QCD predictions as calculated with the MEPJET [32] 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  

$$0.5 < p_T(j)^2/Q^2\; < \; 2\;, \qquad \qquad x_{jet} \simeq E_{jet}/E_{proton} \gt 0.035\;;$$ (1)

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

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

Clearly, 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) agrees better with the data, but here the overall normalisation is uncertain and the agreement may be fortuitous. Also, we recall that both experiments observe more centrally produced dijet events than predicted by the NLO QCD calculations. Whatever mechanism is responsible for the enhancement in central jet production may also play a role in the enhanced forward jet cross section. Clearly these issues must be resolved before the evidence for BFKL dynamics can be elevated to the status of discovery.

The multiple gluon emission in ladder-type diagrams is also studied in jet-jet decorrelations at the Tevatron. D0 presented preliminary results as a function of the pseudorapidity separation of the two leading jets in an event [50]. The measurement is compared to HERWIG and PYTHIA [5] parton-shower Monte Carlo simulations, and to BFKL predictions. The soft gluon emissions are expected to decorrelate the transverse energy (E_T) and azimuthal angle ($\phi$) of the produced jets as the rapidity interval between them increases. HERWIG and PYTHIA simulations reproduce the observed decorrelation reasonably well. However, the leading-log BFKL resummation [51] predicts a larger decorrelation while a NLO QCD calculation underestimates the decorrelation effects. Therefore, no clear conclusion on the question of BFKL dynamics can be drawn from the present Tevatron data.