Bootstrapping One-Loop QCD Amplitudes

We review the recently developed bootstrap method for the computation of high-multiplicity QCD amplitudes at one loop. We illustrate the general algorithm step by step with a six-point example. The method combines (generalized) unitarity with on-shell recursion relations to determine the not cut-constructible, rational terms of these amplitudes. Our bootstrap approach works for arbitrary configurations of gluon helicities and arbitrary numbers of external legs.Comment: 18 pages, 9 figures; extended version of talks given at the 7th Workshop On Continuous Advances In QCD, 11-14 May 2006, Minneapolis, Minnesota; at SUSY06: 14th International Conference On Supersymmetry And The Unification Of Fundamental Interactions, 12-17 Jun 2006, Irvine, California; at the LoopFest V: Radiative Corrections For The International Linear Collider: Multi-Loops And Multi-Legs, 19-21 Jun 2006, SLAC, Menlo Park, California; and at the Vancouver Linear Colliders Workshop (ALCPG 2006), 19-22 Jul 2006, Vancouver, British Columbi

Power Corrections to e+e- Dijet Event Shapes

We discuss a class of event shapes for e+e- dijet events that include the thrust as a special case. Large logarithmic corrections to the corresponding cross sections can be resummed to all logarithmic orders at leading power. However, irrespective of the order up to which the perturbative expansion is calculated, it has to be supplemented by nonperturbative corrections due to its at best asymptotic nature. We find that the leading power corrections are universal for the class of event shapes discussed here. Based on these findings, we provide sample numerical predictions for the distributions of the new event shapes.Comment: 3 pages, 1 figure; presented by C.F. Berger at the International Europhysics Conference on High-Energy Physics (HEP 2003), Aachen, Germany, 17-23 July 200

Scaling of Power Corrections for Angularities from Dressed Gluon Exponentiation

We study power corrections to a recently introduced family of event shapes, the class of angularities, within the formalism of dressed gluon exponentiation (DGE). We find that the universal scaling rule for the leading power corrections deduced from resummation also holds when taking renormalon enhancements into account. The scaling is due to boost invariance of eikonal dynamics in the two-jet limit, which we recover in the context of DGE. Furthermore, dressed gluon exponentiation provides an ansatz for non-leading power corrections that violate the scaling. These non-leading corrections are further suppressed by non-integer powers of the hard scale.Comment: 24 page

Multi-Parton Scattering Amplitudes via On-Shell Methods

We present an overview of recent developments, based on on-shell techniques, in the calculation of multi-parton scattering amplitudes at one loop that are relevant for phenomenological studies at hadron colliders. These new on-shell methods make efficient use of the physical properties of the hard scattering, such as unitarity and factorization.Comment: Invited review, Annual Review of Nuclear and Particle Science; v2: references adde

Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes

We consider a scalar field, such as the Higgs boson H, coupled to gluons via the effective operator H tr G_{mu nu} G^{mu nu} induced by a heavy-quark loop. We treat H as the real part of a complex field phi which couples to the self-dual part of the gluon field-strength, via the operator phi tr G_{SD mu nu} G_{SD}^{mu nu}, whereas the conjugate field phi^dagger couples to the anti-self-dual part. There are three infinite sequences of amplitudes coupling phi to quarks and gluons that vanish at tree level, and hence are finite at one loop, in the QCD coupling. Using on-shell recursion relations, we find compact expressions for these three sequences of amplitudes and discuss their analytic properties.Comment: 63 pages, 7 figures; v2 references added; v3 minor typos corrected and note added; v4 fixed error in eq. (7.11) (lower limit of sum should be l=2, not l=3), also affecting eqs. (7.14), (8.20), (8.21), (8.27) and (8.28

Interjet Energy Flow/Event Shape Correlations

We identify a class of perturbatively computable measures of interjet energy flow, which can be associated with well-defined color flow at short distances. As an illustration, we calculate correlations between event shapes and the flow of energy, Q_Omega, into an interjet angular region, Omega, in high-energy two-jet e^+e^- -annihilation events. Laplace transforms with respect to the event shapes suppress states with radiation at intermediate energy scales, so that we may compute systematically logarithms of interjet energy flow. This method provides a set of predictions on energy radiated between jets, as a function of event shape and of the choice of the region Omega in which the energy is measured. Non-global logarithms appear as corrections. We apply our method to a continuous class of event shapes.Comment: 9 pages, 5 figures. Based on talk given by C.F. Berger at TH-2002, International Conference on Theoretical Physics, Theme 2: "QCD, Hadron dynamics, etc.", Paris, France, 2002. Slight changes to text, reference adde

Tvrda ekskluzivna tvorba bariona-antibariona u sudarima 2-γ

We present a perturbative calculation of baryon pair production in two-photon collisions, γγ → BB, in which baryons are treated as quark-diquark systems. Our approach accounts for constituent mass effects in a systematic way. Taking the diquark-model parameters from foregoing studies of other electron- and photon-induced baryonic reactions, our results agree well with the most recent large momentum-transfer data for the p¯p, ΛΛ, and Σ0Σ¯0 channels.Izlažemo perturbativan račun tvorbe barionskog para, γγ → BB, u kojemu se barioni predstavljaju kao sustav kvark-dikvark. Ovaj pristup na sustavan način objašnjava učinke sastavnica (konstituenata) masa. Uzimajući parametre ranijih istraživanja drugih barionskih reakcija izazvanih elektronima i fotonima, postigli smo slaganje ishoda naših računa s najnovijim podacima za kanale p¯p, ΛΛ i Σ0 Σ¯0 na velikim prijenosima impulsa

Tvrda ekskluzivna tvorba bariona-antibariona u sudarima 2-γ

We present a perturbative calculation of baryon pair production in two-photon collisions, γγ → BB, in which baryons are treated as quark-diquark systems. Our approach accounts for constituent mass effects in a systematic way. Taking the diquark-model parameters from foregoing studies of other electron- and photon-induced baryonic reactions, our results agree well with the most recent large momentum-transfer data for the p¯p, ΛΛ, and Σ0Σ¯0 channels.Izlažemo perturbativan račun tvorbe barionskog para, γγ → BB, u kojemu se barioni predstavljaju kao sustav kvark-dikvark. Ovaj pristup na sustavan način objašnjava učinke sastavnica (konstituenata) masa. Uzimajući parametre ranijih istraživanja drugih barionskih reakcija izazvanih elektronima i fotonima, postigli smo slaganje ishoda naših računa s najnovijim podacima za kanale p¯p, ΛΛ i Σ0 Σ¯0 na velikim prijenosima impulsa

Bootstrapping One-Loop QCD Amplitudes with General Helicities

The recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD combines the unitarity method with loop-level on-shell recursion. For generic helicity configurations, the recursion relations may involve undetermined contributions from non-standard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through use of pairs of recursion relations. To illustrate the strategy, we present sets of recursion relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive solution for the one-loop n-gluon QCD amplitudes with three or four color-adjacent gluons of negative helicity and the remaining ones of positive helicity. We provide an explicit analytic formula for the QCD amplitude A_{6;1}(1^-,2^-,3^-,4^+,5^+,6^+), as well as numerical results for A_{7;1}(1^-,2^-,3^-,4^+,5^+,6^+,7^+), A_{8;1}(1^-,2^-,3^-,4^+,5^+,6^+,7^+,8^+), and A_{8;1}(1^-,2^-,3^-,4^-,5^+,6^+,7^+,8^+). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.Comment: 77 pages, 17 figures; v2, corrected minor typos in text and small equation