Azimuthal Dependence of Forward-Jet Production in DIS in the High-Energy Limit

As a signal for the BFKL Pomeron in small-x deep inelastic $ep$ scattering, we calculate the azimuthal dependence of the inclusive cross section of forward jets relative to the outgoing electron. For not very large differences in rapidity between the current jet and the forward jet the cross section peaks at $\pi/2$. For increasing rapidity BFKL dynamics predicts a decorrelation in the azimuthal dependence between the electron and the forward jet.Comment: 13 pages, Latex, 1 figur

Iterated amplitudes in the high-energy limit

We consider the high-energy limits of the colour ordered four-, five- and six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge kinematics where all the gluons are strongly ordered in rapidity. We show that various building blocks occurring in the Regge factorisation (the Regge trajectory, the coefficient functions and the Lipatov vertex) satisfy an iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This iterative structure, combined with the universality of the building blocks, enables us to show that in the Euclidean region any two- and three-loop amplitude in multi-Regge kinematics is guaranteed to satisfy the BDS ansatz. We also consider slightly more general kinematics where the strong rapidity ordering applies to all the gluons except the two with either the largest or smallest rapidities, and we derive the iterative formula for the associated coefficient function. We show that in this kinematic limit the BDS ansatz is also satisfied. Finally, we argue that only for more general kinematics - e.g. with three gluons having similar rapidities, or where the two central gluons have similar rapidities - can a disagreement with the BDS ansatz arise.Comment: Version corresponding to the Erratum sent to JHEP on October 16th 200

Kinematical Limits on Higgs Boson Production via Gluon Fusion in Association with Jets

In this paper, we analyze the high-energy limits for Higgs boson plus two jet production. We consider two high-energy limits, corresponding to two different kinematic regions: a) the Higgs boson is centrally located in rapidity between the two jets, and very far from either jet; b) the Higgs boson is close to one jet in rapidity, and both of these are very far from the other jet. In both cases the amplitudes factorize into impact factors or coefficient functions connected by gluons exchanged in the t channel. Accordingly, we compute the coefficient function for the production of a Higgs boson from two off-shell gluons, and the impact factors for the production of a Higgs boson in association with a gluon or a quark jet. We include the full top quark mass dependence and compare this with the result obtained in the large top-mass limit.Comment: 35 pages, 6 figure

Symbols of One-Loop Integrals From Mixed Tate Motives

We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization. The algorithm proceeds via recursion in m seeded by the well-known box integrals in four dimensions. As a simple application of this method we write down the symbol of a three-mass hexagon integral in six dimensions.Comment: 13 pages, v2: minor typos correcte

Dijet Production at Hadron--Hadron Colliders in the BFKL Approach

The production in high-energy hadron collisions of a pair of jets with large rapidity separation is studied in an improved BFKL formalism. By recasting the analytic solution of the BFKL equation as an explicit order-by-order sum over emitted gluons, the effects of phase space constraints and the running coupling are studied. Particular attention is paid to the azimuthal angle decorrelation of the jet pair. The inclusion of sub-leading effects significantly improves the agreement between the theoretical predictions and recent preliminary measurements from the Dzero collaboration.Comment: 19 pages LaTeX; one figure corrected; conclusions unchange

Next-to-Leading order Higgs + 2 jet production via gluon fusion

We present phenomenological results for the production of a Higgs boson in association with two jets at the LHC. The calculation is performed in the limit of large top mass and is accurate to next-to-leading order in the strong coupling, i.e. ${\cal O}(\alpha_s^6)$Comment: 13 pages, 6 figures; v2: references added, modified acknowledgments, final version as published in JHE

Forward jets and forward WW-boson production at hadron colliders

In this talk we give a short review of forward jets and forward $W$-boson production at hadron colliders, in view of the extraction of footprints of BFKL physics. We argue that at Tevatron energies, dijet production at large rapidity intervals is still subasymptotic with respect to the BFKL regime, thus the cross section is strongly dependent on the various cuts applied in the experimental setup. In addition, the choice of equal transverse momentum cuts on the tagging jets makes the cross section dependent on large logarithms of non-BFKL origin, and thus may spoil the BFKL analysis. For vector boson production in association with two jets, we argue that the configurations that are kinematically favoured tend to have the vector boson forward in rapidity. Thus $W + 2$ jet production lends itself naturally to extensions to the high-energy limit.Comment: LaTeX, JHEP style, 10 pages, 3 figures. Based on a talk at EPS2001, Budapest, Hungar

Rapidity-Separation Dependence and the Large Next-to-Leading Corrections to the BFKL Equation

Recent concerns about the very large next-to-leading logarithmic (NLL) corrections to the BFKL equation are addressed by the introduction of a physical rapidity-separation parameter $\Delta$. At the leading logarithm (LL) this parameter enforces the constraint that successive emitted gluons have a minimum separation in rapidity, $y_{i+1}-y_i>\Delta$. The most significant effect is to reduce the BFKL Pomeron intercept from the standard result as $\Delta$ is increased from 0 (standard BFKL). At NLL this $\Delta$-dependence is compensated by a modification of the BFKL kernel, such that the total dependence on $\Delta$ is formally next-to-next-to-leading logarithmic. In this formulation, as long as $\Delta\gtrsim2.2$ (for $\alpha_{s}=0.15$): (i) the NLL BFKL pomeron intercept is stable with respect to variations of $\Delta$, and (ii) the NLL correction is small compared to the LL result. Implications for the applicability of the BFKL resummation to phenomenology are considered.Comment: 16 pages, 3 figures, Late

Differential equations for multi-loop integrals and two-dimensional kinematics

In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop eight-point finite diagrams which relate them to massive hexagons. After the reduction to two-dimensional kinematics, we solve them using symbol technology. The terms invisible to the symbols are found through boundary conditions coming from double soft limits. These equations are valid at all-loop order for double pentaladders and allow to solve iteratively loop integrals given lower-loop information. Comments are made about multi-leg and multi-loop integrals which can appear in this special kinematics. The main motivation of this investigation is to get a deeper understanding of these tools in this configuration, as well as for their application in general four-dimensional kinematics and to less supersymmetric theories.Comment: 25 pages, 7 figure

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes

We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.Comment: 46 page