Amplitudes - Explore the Science & Experts | ideXlab

Scan Science and Technology

Contact Leading Edge Experts & Companies

Amplitudes

The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform

Zvi Bern – 1st expert on this subject based on the ideXlab platform

  • iteration of planar Amplitudes in maximally supersymmetric yang mills theory at three loops and beyond
    Physical Review D, 2005
    Co-Authors: Zvi Bern, Lance J Dixon, V Smirnov

    Abstract:

    We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 – 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop Amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 Amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point Amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.

  • planar Amplitudes in maximally supersymmetric yang mills theory
    Physical Review Letters, 2003
    Co-Authors: Charalampos Anastasiou, Zvi Bern, Lance J Dixon, D A Kosower

    Abstract:

    The collinear factorization properties of two-loop scattering Amplitudes in dimensionally-regulated N = 4 super-Yang-Mills theory suggest that, in the planar (‘t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop Amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point Amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N{sub c} L-loop Amplitudes should be simple enough to allow a resummation to all orders.

V Smirnov – 2nd expert on this subject based on the ideXlab platform

  • iteration of planar Amplitudes in maximally supersymmetric yang mills theory at three loops and beyond
    Physical Review D, 2005
    Co-Authors: Zvi Bern, Lance J Dixon, V Smirnov

    Abstract:

    We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 – 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop Amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 Amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point Amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.

Lance J Dixon – 3rd expert on this subject based on the ideXlab platform

  • iteration of planar Amplitudes in maximally supersymmetric yang mills theory at three loops and beyond
    Physical Review D, 2005
    Co-Authors: Zvi Bern, Lance J Dixon, V Smirnov

    Abstract:

    We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 – 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop Amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 Amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point Amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.

  • planar Amplitudes in maximally supersymmetric yang mills theory
    Physical Review Letters, 2003
    Co-Authors: Charalampos Anastasiou, Zvi Bern, Lance J Dixon, D A Kosower

    Abstract:

    The collinear factorization properties of two-loop scattering Amplitudes in dimensionally-regulated N = 4 super-Yang-Mills theory suggest that, in the planar (‘t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop Amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point Amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N{sub c} L-loop Amplitudes should be simple enough to allow a resummation to all orders.