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Z. Bern

Publications and source records attributed to Z. Bern.

At least 73 records · Page 4Linked to original sources
arXiv2001

Perturbative Quantization of Gravity Theories

We discuss string theory relations between gravity and gauge theory tree amplitudes. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for calculating complete gravity $S$-matrices to any loop orders. This leads to a practical method for computing non-trivial gravity $S$-matrix elements by relating them to much simpler gauge theory ones. We also describe arguments that N=8 D=4 supergravity is less divergent in the ultraviolet than previously thought.

hep-th↗
arXiv2000

Counterterms in Supergravity

We examine the ultraviolet behaviour of supergravity theories as a function of dimension and number of supercharges. We do so by the computation of one and two-loop physical on-shell four point amplitudes. For maximal supergravity, our computations prove the non-renomalisability of supergravity for $D \geq 6$ (including the maximal D=11 case) and give strong evidence for the existance of a five-loop counterterm in D=4. For type I supergravity our results indicate similar patterns. e shall also explore a remarkable relationship between gravity amplitudes and those of Yang-Mills theories. In many ways gravity calculations discover features which relate to the equivalent Yang-Mills features by a squaring proceedure.

hep-th↗
arXiv2000

Two-Loop Correction to Bhabha Scattering

We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at e^+ e^- colliders. The calculation also tests methods that may be applied to analogous QCD processes.

hep-ph↗
arXiv2000

On Perturbative Gravity and Gauge Theory

We review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for obtaining loop contributions. We also review recent applications of these ideas showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4 supergravity is less divergent than previously thought, though it does appear to diverge at five loops. Finally, we describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relationship between gravity and gauge theory.

hep-th↗
arXiv1999

The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order

We present universal factorization formulas describing the behavior of one-loop QCD amplitudes as external momenta become either soft or collinear. Our results are valid to all orders in the dimensional regularization parameter, $\eps$. Terms through $\Ord(\eps^2)$ can contribute in infrared divergent phase space integrals associated with next-to-next-to-leading order jet cross-sections.

hep-ph↗
arXiv1999

On the Coupling of Gravitons to Matter

Using relationships between open and closed strings, we present a construction of tree-level scattering amplitudes for gravitons minimally coupled to matter in terms of gauge theory partial amplitudes. In particular, we present examples of amplitudes with gravitons coupled to vectors or to a single fermion pair. We also present two examples with massive graviton exchange, as would arise in the presence of large compact dimensions. The gauge charges are represented by flavors of dynamical scalars or fermions. This also leads to an unconventional decomposition of color and kinematics in gauge theories.

hep-th↗
arXiv1999

Perturbative Gravity from QCD Amplitudes

We demonstrate that QCD gluon amplitudes can be used to construct a Lagrangian for gravity. This procedure makes use of perturbative `squaring' relations between gravity and gauge theory that follow from string theory. We explicitly carry out the construction for up to five-point interactions and discuss a set of field variables in the Einstein-Hilbert Lagrangian for interpreting the Lagrangian obtained from QCD. A spin-off from our analysis is that it can be used to provide simpler tree-level gravity Feynman rules than for conventional gauges.

hep-th↗
arXiv1999

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the `maximally helicity-violating' amplitudes in N=8 supergravity, and the `all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n < 7, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found `dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N=4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n < 7 N=8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations.

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arXiv1998

One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity

We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are rational functions of the momenta, also arise in the quantization of self-dual gravity in four-dimensional Minkowski space. Our ansatz agrees with explicit computations via D-dimensional unitarity cuts for n less than or equal to 6. It also has the expected analytic behavior, for all n, as a graviton becomes soft, and as two momenta become collinear. The gravity results are closely related to analogous amplitudes in (self-dual) Yang-Mills theory.

hep-th↗
arXiv1998

Perturbative Relationships Between QCD and Gravity and Some Implications

We discuss nontrivial examples illustrating that perturbative gravity is in some sense the `square' of gauge theory. This statement can be made precise at tree-level using the Kawai, Lewellen and Tye relations between open and closed string tree amplitudes. These relations, when combined with modern methods for computing amplitudes, allow us to obtain loop-level relations, and thereby new supergravity loop amplitudes. The amplitudes show that N=8 supergravity is less ultraviolet divergent than previously thought. As a different application, we show that the collinear splitting amplitudes of gravity are essentially squares of the corresponding ones in QCD.

hep-th↗
arXiv1998

On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences

String theory implies that field theories containing gravity are in a certain sense `products' of gauge theories. We make this product structure explicit up to two loops for the relatively simple case of N=8 supergravity four-point amplitudes, demonstrating that they are `squares' of N=4 super-Yang-Mills amplitudes. This is accomplished by obtaining an explicit expression for the $D$-dimensional two-loop contribution to the four-particle S-matrix for N=8 supergravity, which we compare to the corresponding N=4 Yang-Mills result. From these expressions we also obtain the two-loop ultraviolet divergences in dimensions D=7 through D=11. The analysis relies on the unitarity cuts of the two theories, many of which can be recycled from a one-loop computation. The two-particle cuts, which may be iterated to all loop orders, suggest that squaring relations between the two theories exist at any loop order. The loop-momentum power-counting implied by our two-particle cut analysis indicates that in four dimensions the first four-point divergence in N=8 supergravity should appear at five loops, contrary to the earlier expectation, based on superspace arguments, of a three-loop counterterm.

hep-th↗
arXiv1998

Dimensionally Regulated Pentagon Integrals

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O(epsilon) corrections, a result which is the dimensionally-regulated version of a D=4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O(epsilon^0).

hep-ph↗
arXiv1998

Multi-Parton Loop Amplitudes and Next-to-Leading Order Jet Cross-Sections

We review recent developments in the calculation of QCD loop amplitudes with several external legs, and their application to next-to-leading order jet production cross-sections. When a number of calculational tools are combined together --- helicity, color and supersymmetry decompositions, plus unitarity and factorization properties --- it becomes possible to compute multi-parton one-loop QCD amplitudes without ever evaluating analytically standard one-loop Feynman diagrams. One-loop helicity amplitudes are now available for processes with five external partons (ggggg, q\bar{q}ggg and q\bar{q}q'\bar{q}'g), and for an intermediate vector boson V \equiv γ^*,Z,W plus four external partons (Vq\bar{q}gg and Vq\bar{q}q'\bar{q}'). Using these amplitudes, numerical programs have been constructed for the next-to-leading order corrections to the processes p\bar{p} to 3 jets (ignoring quark contributions so far) and e^+e^- to 4 jets.

hep-ph↗
arXiv1997

Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills

Using cutting techniques we obtain the two-loop N=4 super-Yang-Mills helicity amplitudes for four-gluon scattering in terms of scalar integral functions. The N=4 amplitudes are considerably simpler than corresponding QCD amplitudes and therefore provide a testing ground for exploring two-loop amplitudes. The amplitudes are constructed directly in terms of gauge invariant quantities and therefore remain relatively compact throughout the calculation. We also present a conjecture for the leading color four-gluon amplitudes to all orders in the perturbative expansion.

hep-ph↗
arXiv1997

One-Loop Amplitudes for e^+ e^- to Four Partons

We present the first explicit formulae for the complete set of one-loop helicity amplitudes necessary for computing next-to-leading order corrections for e^+ e^- annihilation into four jets, 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 include a simpler form of the previously published amplitudes for e^+ e^- to four quarks. We obtain the amplitudes using their analytic properties to constrain their form. Systematically eliminating spurious poles from the amplitudes leads to relatively compact results.

hep-ph↗
arXiv1997

Neutralino Annihilation into Two Photons

We compute the annihilation cross-section of two neutralinos at rest into two photons, which is of importance for the indirect detection of neutralino dark matter in the galactic halo through a quasi-monochromatic gamma-ray line. We include all diagrams to one-loop level in the minimal supersymmetric extension of the standard model. We use the helicity formalism, the background-field gauge, and an efficient loop-integral reduction method. We confirm the result recently obtained by Bergstrom and Ullio in a different gauge, which disagrees with other published calculations.

hep-ph↗
arXiv1997

Two-Loop N=4 Supersymmetric Amplitudes and QCD

Two-loop four-gluon N=4 susy amplitudes are evaluated via cutting techniques as a testing ground for QCD. A conjecture for four-point amplitudes to all loop orders is described. We also present a new conjecture for the leading-color part of the two-loop five-gluon amplitudes.

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