By Thomas Becher, Alessandro Broggio, Andrea Ferroglia
Among resummation concepts for perturbative QCD within the context of collider and style physics, soft-collinear powerful conception (SCET) has emerged as either a robust and flexible software, having been utilized to a wide number of approaches, from B-meson decays to jet creation on the LHC.
This booklet presents a concise, pedagogical advent to this method. It discusses the growth of Feynman diagrams round the high-energy restrict, by way of the specific building of the powerful Lagrangian - first for a scalar conception, then for QCD. The underlying suggestions are illustrated with the quark vector shape issue at huge momentum move, and the formalism is utilized to compute soft-gluon resummation and to accomplish transverse-momentum resummation for the Drell-Yan procedure using renormalization team evolution in SCET. eventually, the infrared constitution of n-point gauge-theory amplitudes is analyzed by means of touching on them to effective-theory operators.
This textual content is appropriate for graduate scholars and non-specialist researchers alike because it calls for basically uncomplicated wisdom of perturbative QCD.
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Additional info for Introduction to Soft-Collinear Effective Theory
1/ one requires that the corrections of order g 2 to the interaction of three scalar fields are the same in the full theory and in the effective theory. 1/ . 14) where all the external legs have momenta collinear to p, blue lines indicate collinear fields in the effective theory, while red lines indicates the soft field in the effective theory. The dots in Eq. 14) indicate two additional diagrams which can be obtained from the second diagram by moving the internal soft line in the other two possible positions.
This argument also applies if one considers higher loops; we can conclude that C D 1 to all orders in perturbation theory. The same kind of reasoning can be applied to all of the interaction terms appearing in Eq. 11). 26 3 Scalar SCET While the terms appearing in the Lagrangian in Eq. 11) do not receive matching corrections, the terms originating from the current operator J do. 15) where the subscript in Ji and Ci indicates the number of fields involved in the corresponding operator. In addition to operators with multiple fields, one should also consider operators involving derivatives on the fields.
This formulation is motivated by HQET, where the momentum of a heavy quark inside a meson is written as pQ D mQ v C r , where v is the meson velocity. The small residual momentum arises from interactions of the heavy quark with the light constituents of the meson and is of order ƒQCD 1 GeV, much smaller than the heavy-quark mass mQ .
Introduction to Soft-Collinear Effective Theory by Thomas Becher, Alessandro Broggio, Andrea Ferroglia