arXiv subjects

Z. Bern

Publications and source records attributed to Z. Bern.

At least 91 records · Page 5Linked to original sources

arXiv1996

One-Loop Self-Dual and N=4 Super Yang-Mills

We conjecture a simple relationship between the one-loop maximally helicity violating gluon amplitudes of ordinary QCD (all helicities identical) and those of N=4 supersymmetric Yang-Mills (all but two helicities identical). Because the amplitudes in self-dual Yang Mills have been shown to be the same as the maximally helicity violating ones in QCD, this conjecture implies that they are also related to the maximally helicity violating ones of N=4 supersymmetric Yang-Mills. We have an explicit proof of the relation up to the six-point amplitude; for amplitudes with more external legs, it remains a conjecture. A similar conjecture relates amplitudes in self-dual gravity to maximally helicity violating N=8 supergravity amplitudes.

hep-th↗

arXiv1996

One-Loop Amplitudes for e^+ e^- to q-bar q Q-bar Q

We present the one-loop helicity amplitudes for processes involving a vector boson V (V=W,Z, or gamma^*) and four massless quarks, 0 to V q-bar q Q-bar Q, where V couples to a massless lepton pair. These amplitudes are required for next-to-leading order O(alpha_s^3) numerical programs for four-jet production at e^+ e^- colliders, for W, Z or Drell-Yan production in association with two jets at hadron colliders, and for three-jet production in deeply inelastic scattering experiments. We obtained the amplitudes presented here by using their analytic properties to constrain their form.

hep-ph↗

arXiv1996

Unitarity-based Techniques for One-Loop Calculations in QCD

We discuss new techniques developed in recent years for performing one-loop calculations in QCD, and present an example of results from the process 0 -> V q q-bar g g. Talk presented at the 1996 Zeuthen Workshop on Elementary Particle Theory, "QCD and QED in Higher Order", Rheinsberg, Brandenburg, April 21-26, 1996.

hep-ph↗

arXiv1996

Progress in One-Loop QCD Computations

We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the spinor helicity formalism, color decompositions, supersymmetry, string theory, factorization and unitarity. We provide explicit examples illustrating these techniques.

hep-ph↗

arXiv1996

Massive Loop Amplitudes from Unitarity

We show, for previously uncalculated examples containing a uniform mass in the loop, that it is possible to obtain complete massive one-loop gauge theory amplitudes solely from unitarity and known ultraviolet or infrared mass singularities. In particular, we calculate four-gluon scattering via massive quark loops in QCD. The contribution of a heavy quark to five-gluon scattering with identical helicities is also presented.

hep-ph↗

arXiv1995

Factorization in One-Loop Gauge Theory

Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared divergences complicate factorization. Here we prove that factorization in such theories is described by a set of universal functions. In particular, a proof of the universality of one-loop splitting functions as the momenta of two particles become collinear is presented. Factorization in multi-particle channels is also given. The discontinuity functions that appear in the splitting functions may also be used to obtain infrared divergent box integral functions from finite ones.

hep-ph↗

arXiv1995

One-Loop Corrections to Two-Quark Three-Gluon Amplitudes

We present the one-loop QCD amplitudes for two external massless quarks and three external gluons ($\bar{q}qggg$). This completes the set of one-loop amplitudes needed for the next-to-leading-order corrections to three-jet production at hadron colliders. We also discuss how to use group theory and supersymmetry to minimize the amount of calculation required for the more general case of one-loop two-quark $n$-gluon amplitudes. We use collinear limits to provide a stringent check on the amplitudes.

hep-ph↗

arXiv1995

EFFICIENT ANALYTIC COMPUTATION OF HIGHER-ORDER QCD AMPLITUDES

We review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints.

hep-ph↗

arXiv1994

Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes

We identify a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities. One-loop amplitudes for massless supersymmetric gauge theories fall into this class; in addition, many non-supersymmetric amplitudes can be rearranged to take advantage of the result. As applications, we construct the one-loop amplitudes for $n$-gluon scattering in $N=1$ supersymmetric theories with the helicity configuration of the Parke-Taylor tree amplitudes, and for six-gluon scattering in $N=4$ super-Yang-Mills theory for all helicity configurations.

hep-ph↗

arXiv1994

Recent Progress in One-Loop Multi-Parton Calculations

We describe techniques that simplify the calculation of one-loop QCD amplitudes with many external legs, which are needed for next-to-leading-order (NLO) corrections to multi-jet processes. The constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes are particularly useful. Certain sequences of one-loop helicity amplitudes may be obtained for an arbitrary number of external gluons using these techniques. We also report on progress in completing the set of one-loop helicity amplitudes required for NLO three-jet production at hadron colliders, namely the amplitudes with two external quarks and three gluons. (Contribution presented by L. Dixon at the workshop ``QCD'94'', Montpellier, France, July 7-13, 1994. To appear in those proceedings.)

hep-ph↗

arXiv1994

One-Loop Gauge Theory Amplitudes with an Arbitrary Number of External Legs

We review recent progress in calculations of one-loop QCD amplitudes. By imposing the consistency requirements of unitarity and correct behavior as the momenta of two legs become collinear, we construct ansatze for one-loop amplitudes with an arbitrary number of external legs. For supersymmetric amplitudes, which can be thought of as components of QCD amplitudes, the cuts uniquely specify the amplitude.

hep-ph↗

arXiv1994

One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits

We present a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contribution to amplitudes for $n$ gluon scattering in $N=4$ supersymmetric Yang-Mills theory with the helicity configuration of the Parke-Taylor tree amplitudes. We prove that our $N=4$ ansatz is correct using general properties of the relevant one-loop $n$-point integrals. We also give the ``splitting amplitudes'' which govern the collinear behavior of one-loop helicity amplitudes in gauge theories.

hep-ph↗

arXiv1994

One-Loop N Gluon Amplitudes with Maximal Helicity Violation via Collinear Limits

We present a conjecture for the $n$-gluon one-loop amplitudes with maximal helicity violation. The conjecture emerges from the powerful requirement that the amplitudes have the correct behavior in the collinear limits of external momenta. One implication is that the corresponding amplitudes where three or more gluon legs are replaced by photons vanish for $n>4$.

hep-ph↗

arXiv1993

Supersymmetry Relations Between Contributions To One-Loop Gauge Boson Amplitudes

We apply ideas motivated by string theory to improve the calculational efficiency of one-loop weak interaction processes with massive external gauge bosons. In certain cases ``supersymmetry'' relations between diagrams with a fermion loop and with a gauge boson loop hold. This is explicitly illustrated for a particular one-loop standard model process with four-external gauge bosons. The supersymmetry relations can be used to provide further significant improvements in calculational efficiency.

hep-ph↗

arXiv1993

New QCD Results from String Theory

We discuss new results in QCD obtained with string-based methods. These methods were originally derived from superstring theory and are significantly more efficient than conventional Feynman rules. This technology was a key ingredient in the first calculation of the one-loop five-gluon amplitude. We also present a conjecture for a particular one-loop helicity amplitude with an arbitrary number of external gluons.

hep-th↗

arXiv1993

String-Based Methods in Perturbative Gravity

String theory implies a relatively modest growth in computational complexity for perturbative gravity calculations as compared to gauge theory calculations, contrary to field theory expectations. An explicit string-based calculation, which would be extremely difficult using conventional techniques, is presented to illustrate this.

hep-th↗

arXiv1993

One-Loop Corrections to Five-Gluon Amplitudes

We present the one-loop helicity amplitudes with five external gluons. The computation employs string-based methods, new techniques for performing tensor integrals, and improvements in the spinor helicity method.

hep-ph↗

arXiv1992

Dimensionally Regulated One-Loop Integrals

We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such integrals thus reduces to the calculation of box diagrams ($n=4$). The tensor integrals required in gauge theory may be obtained by differentiating the scalar integral with respect to certain combinations of the kinematic variables. Such relations also lead to differential equations for scalar integrals. For box integrals with massless internal lines these differential equations are easy to solve.

hep-ph↗