Two-loop g→gg splitting amplitudes in QCD
By Z. Bern, L. Dixon, David A. Kosower. 2004
187 citations recorded by the source corpus.
Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g?gg splitting amplitudes in QCD, = 1, and = 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 -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/ pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/22eb39203708876b1455427f9f64cd483a4c5f7f
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In Nuclear and High Energy Physics
Citations in the corpus
- One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices (2004, methodology): “Much of this progress was achieved thanks to powerful unitarity-based methods [30,31,33,34, 38 ], whereby properties of loop amplitudes are derived from cutting rules and tree amplitudes.”
- Sharpening The Leading Singularity (2008, methodology): “These techniques came to be known as the unitarity based method [7, 8, 9, 10, 11, 12, 13].”
- A brief introduction to modern amplitude methods (2013, unknown): “For the simplest 2 → 2 processes, the principles of generalized unitarity were applied a while ago [58, 59, 60], but not in a way that could be automatically extended to more complicated processes.”
- Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, methodology): “A detailed, general algorithm for assembling the amplitude was described in [77].”
- The Lagrangian origin of MHV rules. (2005, unknown): “(The loop level results build on earlier work that exploited unitarity to construct complete expressions for amplitudes at any number of loops from simpler on-shell amplitudes both in supersymmetric theories and non-supersymmetric ones, see [6] for a general discussion and references).”
- The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, methodology): “At one-loop, very efficient on-shell methods now exist [9, 10] and at higher-loop level generalizations of the unitarity-based method [11–14] have made a five-loop computation possible [15], which should soon determine the five-loop cusp anomalous dimension [16].”
- Loop amplitudes in gauge theories: modern analytic approaches (2010, methodology): “nitarity methods have been applied to compute the 4-gluon amplitude to two-loop order [117], as well as the two-loop splitting amplitudes (universal functions governing collinear behavior) for g → gg [130] and q → qg and g → q¯q [131]. Seven master integrals were needed, of which four vanished throu”
- Analytic boosted boson discrimination (2015, background): “While one-loop, and even two-loop, splitting helicity amplitudes exist in the literature [185, 187, 188], to our knowledge, the one-loop unpolarized splitting functions have not not been explicitly written down before.”