Multi-loop amplitudes and resummation☆

By G. Sterman, M. Tejeda-Yeomans. 2002

382 citations recorded by the source corpus.

Abstract We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each order of perturbation theory. For these amplitudes, previously-observed relations between single and double poles in different 2→2 processes can now be interpreted in terms of universal functions associated with external partons and process-dependent anomalous dimensions that describe coherent soft radiation. Catani's proposal for multiple poles in dimensionally-continued amplitudes emerges naturally.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0fd7b0b8269befbcbae390d2d4b0b1b62dbafc68

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In Nuclear and High Energy Physics

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Citations in the corpus

• The quark form factor at higher orders (2005, background): “For the four-quark amplitude at N 3 LO, qq ! qq, for instance, an explicit prediction has been derived in Ref. [ 13 ], for which Eqs.”
• Integrability and transcendentality (2006, background): “rated in the ǫ→ 0 limit by the function f(g) = 4 X∞ ℓ=1 g2ℓ f(ℓ)(0). (3) This function is in fact related to the large spin anomalous dimension of so-called leadingtwist operators in the gauge theory [4]. Alternative names are “soft” anomalous dimension, or “cusp” anomalous dimension. The simplest r”
• When does the gluon reggeize? (2013, background): “are absorbed into the factor Z P i ; s(2); = exp 1 2 Z 2 0 d2 2 P i ;(2); ! : (4.21) For further discussion and for a detailed breakdown of the content of the exponent, we refer to [22,23,88] and references therein. The soft anomalous dimension is a matrix that acts on the set of all possible c”
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, background): “the “scaling function” or “cusp anomalous dimension” [3, 4, 5]) should be a function of λ that smoothly interpolates between the weak and strong coupling regimes ∆ = E = S + f(λ) lnS +O(S) .”
• MHV amplitudes in N=4 super Yang-Mills and Wilson loops (2007, background): “The form of the BDS conjecture is inspired by the soft and collinear behaviour of amplitudes in gauge theory [16–23], and is expressed by”
• Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, background): “t be renormalized away, but rather should cancel once gluon scattering amplitudes are combined to compute infraredsafe quantities. Their structure has been thoroughly studied and understood (see e.g. [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]). Here we briefly review some of the results spe”
• Infrared structure at NNLO using antenna subtraction (2013, methodology): “It is well known that the explicit poles of the virtual contributions are described by Catani’s one- and two-loop factorisation formulae [64, 65] and follow a colour-dipole structure, reflected by the IR singularity operators I (1) ij ( ) and I (2) ij ( ) which describe the IR singularities associat”
• Calculation of the quark and gluon form factors to three loops in QCD (2010, background): “Independently, Becher and Neubert [39] and Gardi and Magnea [44] have proposed a remarkable all-loops conjecture that describes the pole structure of massless on-shell multi-loop multi-leg QCD amplitudes (generalizing earlier results at two [45] and three loops [ 46 ]) in terms of the cusp anomalous”