10$~GeV on the scattered lepton, and pseudo-rapidities $|\eta|<3.5$ %$\eta=-\ln\tan(\theta/2)$ for the scattered lepton and jets. Also, jets must have transverse momenta of at least 2~GeV in the lab and the Breit frame. Within these general cuts four different jet definition schemes are considered. i) A cone algorithm with a jet separation cut of $\Delta R<1$ and a minimum jet transverse momentum of $p_{Tj}>5$~GeV in the lab frame. ii) The $k_T$ algorithm (in the Breit frame) as defined in Ref.~\cite{kt} with a hard scattering scale $E_T^2=40$~GeV$^2$ and a resolution parameter $y_{cut}=1$ for resolving the macro-jets. In addition, jets are required to have a minimal transverse momentum of 5 GeV in the Breit frame. iii) The $W$-scheme where parton/cluster pairs (including the proton remnant) with invariant mass squared, $M_{ij}^2=(p_i+p_j)^2 < y_{cut}W^2$ are recombined~\cite{previous}. iv) The ``JADE'' algorithm \cite{jade} which is obtained from the $W$-scheme by replacing the invariant definition $M_{ij}^2$ by $2E_iE_j(1-\cos\theta_{ij})$. In the $W$ and JADE schemes we set $y_{cut}=0.02$. %\begin{table}[t] \begin{tabular}{l|ccccc} & \mbox{\phantom{spac}2-jet\phantom{sp} } & \mbox{\phantom{sp}2-jet excl.\phantom{sp}} & \mbox{\phantom{sp}2-jet incl.\phantom{sp}} & \mbox{\phantom{sp}2-jet incl.\phantom{sp}} & \mbox{\phantom{sp}2-jet incl.\phantom{sp}} \\ & \mbox{LO} & \mbox{NLO} ($E$) & \mbox{NLO} ($E$) & \mbox{NLO} ($E0$) & \mbox{NLO} ($P$)\\ \hline\\ \mbox{cone} & 1107~pb & 1047~pb & 1203~pb & 1232 pb & 1208 pb \\ $k_T$ & 1067 pb & 946 pb & 1038 pb & 1014 pb & 944 pb \\ $W$ & 1020 pb & 2061 pb & 2082 pb & 1438 pb & 1315 pb \\ \mbox{JADE} & 1020 pb & 1473 pb & 1507 pb & 1387 pb & 1265 pb \\ \hline \end{tabular} \caption{Two-jet cross sections in DIS at HERA. Results are given at LO and NLO for the four jet definition schemes and acceptance cuts described in the text. The 2-jet inclusive cross section at NLO is given for three different recombination schemes. }\label{table_dijet} %\end{table} The resulting cross sections (see Table~\ref{table_dijet}) show large NLO corrections for the JADE and $W$-schemes while $K$-factors close to unity are found for the $k_T$ and cone algorithms. Another disadvantage of the $W$ and JADE schemes is their strong recombination scheme dependence. Since even in a NLO calculation the internal structure of a jet is only calculated at tree level, these strong variations point to large uncertainties from two-loop effects in the $W$ and JADE schemes. In both schemes widely separated but relatively soft partons tend to be clustered to what is then defined as a jet, even though these clusters can be very massive and quite distinct from the pencil-like and low-mass objects which one starts out with in the parton model or at LO~\cite{mepjet}. These differences then result in the large higher order corrections to jet cross sections shown in Table~\ref{table_dijet}. These effects are much smaller in the cone and the $k_T$ schemes which are hence favored for precision QCD studies in DIS. \vspace*{-0.1in} \section*{Probing BFKL in Forward Jet Production} \vspace*{-0.1in} Recently much interest has been focused on the small Bjorken-$x$ region, where one would like to distinguish BFKL evolution~\cite{bfkl}, which resums the leading $\alpha_s \ln 1/x$ terms, from the more traditional DGLAP evolution equation~\cite{dglap}, which resums leading $\alpha_s \ln Q^2$ terms. BFKL evolution can be enhanced and DGLAP evolution suppressed by studying DIS events which contain an identified jet of longitudinal momentum fraction $x_{jet}=p_z(jet)/E_{proton}$ (in the proton direction) which is large compared to Bjorken $x$~\cite{mueller}. When tagging a forward jet with $p_{Tj}\approx Q$ this leaves little room for DGLAP evolution while the condition $x_{jet}\gg x$ leaves BFKL evolution active. This leads to an enhancement of the forward jet production cross section proportional to $(x_{jet}/x)^{\alpha_P -1}$ over the DGLAP expectation. % \begin{figure}[t] \epsfxsize=4.0in \epsfysize=3.0in \begin{center} \hspace*{0in} \epsffile{h1new.ps} \vspace*{0.5cm} \caption{ Forward jet cross section at HERA as a function of Bjorken $x$ within the H1 acceptance cuts~\protect\cite{H1-forward}. The solid histogram gives the NLO MEPJET result for the scale choice $\mu_R^2=\mu_F^2=\xi(0.5\sum k_T)^2$ with $\xi=1$. The two dotted histograms show the uncertainty of the NLO prediction, corresponding to a variation of $\xi$ between 0.1 and 10. The BFKL result of Bartels et al.~\protect\cite{bartelsH1} is shown as the dashed histogram. The data points are the new, preliminary H1 measurements~\protect\cite{H1-forward}. \label{fig:h1comp} } \vspace*{-0.1in} \end{center} \end{figure} % A conventional fixed order QCD calculation up to ${\cal O}(\alpha_s^2)$ does not yet contain any BFKL resummation and must be considered a background for its detection; one must search for an enhancement in the forward jet production cross section above the expectation for two- and three-parton final states. The full calculation of the forward jet inclusive cross section in DIS, at ${\cal O}(\alpha_s^2)$, has been performed in Ref.~\cite{MZ-prl}. Ordinarily, such a calculation would contain 3-parton final states at tree level, 1-loop corrections to 2-parton final states and 2-loop corrections to 1-parton final states. However, these 2-loop contributions vanish identically, once the condition $x\ll x_{jet}$ is imposed. The remaining 2-parton and 3-parton differential cross sections, and the cancellation of divergences between them, are the same as those entering a calculation of 2-jet inclusive rates. These elements are already implemented in the MEPJET program, which, therefore, can be used to determine the inclusive forward jet cross section at ${\cal O}(\alpha_s^2)$. In Fig.~\ref{fig:h1comp} numerical results are compared with recent data from H1~\cite{H1-forward}. Here the conditions $p_{Tj}\approx Q$ and $x_{jet}\gg x$ are satisfied by selecting events with forward jets (in the angular region $7^o < \theta_j < 20^o$) with \begin{eqnarray} 0.5 & < & p_{Tj}^2/Q^2\; < \; 2\;, \label{eq:fjb} \\ x_{jet} & \approx & E_j/E_{proton} > 0.035\;. \label{eq:fja} \end{eqnarray} Clearly H1 observes substantially more forward jet events than expected from NLO QCD. However, since H1 accepted jets of rather low transverse momentum, $p_{Tj}>3.5$~GeV, the comparison of our parton level calculation to the data may be subject to sizable hadronization corrections. A recent BFKL calculation~\cite{bartelsH1} (dashed histogram) agrees better with the data, but here the overall normalization is uncertain and the agreement may be fortuitous. 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 renormalization and factorization scales $\mu_R^2$ and $\mu_F^2$. Very similar results are found by ZEUS~\cite{woelfle}. We conclude that the HERA data show evidence for BFKL dynamics in forward jet events via an enhancement in the observed forward jet cross section above NLO expectations. However, additional data, with harder forward jets, are needed to make the comparison of QCD calculations with data more reliable. \vspace*{-0.1in} \section*{Acknowledgments} \vspace*{-0.1in} We thank M.~Seymour for his help comparing MEPJET and DISENT. This research was supported by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation and by the U.~S.~Department of Energy under Grant No.~DE-FG02-95ER40896. The work of E.~M. was supported in part by DFG Contract Ku 502/5-1. \vspace*{-0.1in} \begin{references} \vspace*{-0.1in} \bibitem{alphas} See contribution by M. Weber, these proceedings. \bibitem{mikunas} See contribution by D. Mikunas, these proceedings. \bibitem{H1-forward} M.~Wobisch for the H1 Collaboration, these proceedings. \bibitem{woelfle} See contribution by S. W\"olfle, these proceedings. \bibitem{rabbertz} See contribution by K. 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