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Two-loop gluon to gluon gluon Splitting Amplitudes in QCD.

DE2004826914

Publication Date	2004
Personal Author	Bern, Z.; Dixon, L. J.; Kosower, D. A.
Page Count	104
Abstract	Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g (yields) gg splitting amplitudes in QCD, N = 1, and N = 4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The (epsilon)-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/(epsilon) pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.
Keywords	Amplitudes Quantum chromodynamics Gluons Lorentz invariance Light cone Scattering amplitudes
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Stanford Linear Accelerator Center, CA.; California Univ., Los Angeles. Dept. of Physics.; Department of Energy, Washington, DC.; CEA Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette (France).
Supplemental Notes	Prepared in cooperation with California Univ., Los Angeles. Dept. of Physics. and CEA Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette (France). Service de Physique Theorique. Sponsored by Department of Energy, Washington, DC.
Document Type	Technical Report
NTIS Issue Number	200509

Two-loop gluon to gluon gluon Splitting Amplitudes in QCD.

Two-loop gluon to gluon gluon Splitting Amplitudes in QCD.
DE2004826914

Publication Date	2004
Personal Author	Bern, Z.; Dixon, L. J.; Kosower, D. A.
Page Count	104
Abstract	Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g (yields) gg splitting amplitudes in QCD, N = 1, and N = 4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The (epsilon)-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/(epsilon) pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.
Keywords	Amplitudes Quantum chromodynamics Gluons Lorentz invariance Light cone Scattering amplitudes
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Stanford Linear Accelerator Center, CA.; California Univ., Los Angeles. Dept. of Physics.; Department of Energy, Washington, DC.; CEA Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette (France).
Supplemental Notes	Prepared in cooperation with California Univ., Los Angeles. Dept. of Physics. and CEA Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette (France). Service de Physique Theorique. Sponsored by Department of Energy, Washington, DC.
Document Type	Technical Report
NTIS Issue Number	200509