Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering

By T. Becher, M. Neubert, B. Pecjak. 2006

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Renormalization-group methods in soft-collinear effective theory are used to perform the resummation of large perturbative logarithms for deep-inelastic scattering in the threshold region x {yields} 1. The factorization theorem for the structure function F{sub 2}(x,Q{sup 2}) for x {yields} 1 is rederived in the effective theory, whereby contributions from the hard scale Q{sup 2} and the jet scale Q{sup 2}(1 - x) are encoded in Wilson coefficients of effective-theory operators. Resummation is achieved by solving the evolution equations for these operators. Simple analytic results for the resummed expressions are obtained directly in momentum space, and are free of the Landau-pole singularities inherent to the traditional moment-space results. We show analytically that the two methods are nonetheless equivalent order by order in the perturbative expansion, and perform a numerical comparison up to next-to-next-to-leading order in renormalization-group improved perturbation theory.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7fb0b4e70e147019f5fce597a7110fd873e942ea

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Citations in the corpus

Resummation of heavy jet mass and comparison to LEP data (2010, methodology): “The hard function was calculated in [ 26 ] and the jet functions in [7].”
Factorization for groomed jet substructure beyond the next-to-leading logarithm (2016, methodology): “The inclusive jet function has been calculated to two loops [75–78] and the non-cusp anomalous dimension of the inclusive jet function is known to three loops [79, 80].”
Erratum: On the structure of infrared singularities of gauge-theory amplitudes (2009, background): “The result was extracted in [97].”
Calculation of the quark and gluon form factors to three loops in QCD (2010, background): “While the cusp anomalous dimensions were first obtained to three loops from the asymptotic behaviour of splitting functions [29, 30], it is the calculation [31, 32] of the pole terms of the three-loop form factors (and finite plus subleading terms in the two-loop and one-loop form factors [33–37]), ”
Jet shapes and jet algorithms in SCET (2010, unknown): “) d d Z F(˝0;); (7.11) and taking the general form F(˝ a;) = F[ s] 2 j F ( ˝ a) ˝ a + ln 2 !2 (˝ a) + F[ s](˝ a): (7.12) The solution of an RGE of the form Eq. (7.10) has the solution [84, 87, 88, 89, 44] F(˝ a;) = Z d˝0U F(˝ a ˝ 0 a;; 0)F(˝ a 0; 0); (7.13) where the evolution kernel U F is give”
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Factorization properties of soft graviton amplitudes (2011, methodology): “A number of approaches exist, such as Feynman diagram methods [16, 17], Wilson line techniques [18, 19], effective field theories [20, 21, 22, 23, 24, 25], and the recently developed path integral approach of [26].”
Introduction to Soft-Collinear Effective Theory (2014, methodology): “In particular, the effective theory framework has been used to resum large logarithmic terms in Deep Inelastic Scattering (DIS) [38], Drell-Yan [10, 11], Higgs production [39–42], direct photon production [43], top-quark pair production at hadron colliders [44–46], electroweak boson production [47,4”
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