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The Black Book of Quantum ChromodynamicsA Primer for the LHC Era$
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John Campbell, Joey Huston, and Frank Krauss

Print publication date: 2017

Print ISBN-13: 9780199652747

Published to Oxford Scholarship Online: March 2018

DOI: 10.1093/oso/9780199652747.001.0001

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Hard Scattering Formalism

Hard Scattering Formalism

(p.12) 2 Hard Scattering Formalism
The Black Book of Quantum Chromodynamics

John Campbell

Joey Huston

Frank Krauss

Oxford University Press

The hard scattering formalism is introduced, starting from a physical picture based on the idea of equivalent quanta borrowed from QED, and the notion of characteristic times. Contact to the standard QCD treatment is made after discussing the running coupling and the Altarelli–Parisi equations for the evolution of parton distribution functions, both for QED and QCD. This allows a development of a space-time picture for hard interactions in hadron collisions, integrating hard production cross sections, initial and final state radiation, hadronization, and multiple parton scattering. The production of a W boson at leading and next-to leading order in QCD is used to exemplify characteristic features of fixed-order perturbation theory, and the results are used for some first phenomenological considerations. After that, the analytic resummation of the W boson transverse momentum is introduced, giving rise to the notion of a Sudakov form factor. The probabilistic interpretation of the Sudakov form factor is used to discuss patterns in jet production in electron-positron annihilation.

Keywords:   QCD, particle scattering, factorization theorem, initial state radiation, final state radiation, jets, fixed-order calculations, resummation, parton distribution functions, Altarelli–Parisi equation

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