The Fully-Differential Quark Beam Function at NNLO

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Abstract

We present the first calculation of a fully-unintegrated parton distribution (beam function) at next-to-next-to-leading order (NNLO). We obtain the fully-differential beam function for quark-initiated processes by matching it onto standard parton distribution functions (PDFs) at two loops. The fully-differential beam function is a universal ingredient in resummed predictions of observables probing both the virtuality as well as the transverse momentum of the incoming quark in addition to its usual longitudinal momentum fraction. For such double-differential observables our result provides the part of the NNLO singular cross section related to collinear initial-state radiation (ISR), and is important for the resummation of large logarithms through N3LL.

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Invariant Operators in Collinear Effective Theory

Iain W. Stewart, Christian W Bauer (2001)

We consider processes which produce final state hadrons whose energy is much greater than their mass. In this limit interactions involving collinear fermions and gluons are constrained by a symmetry, and we give a general set of rules for constructing leading and subleading invariant operators. Wilson coefficients C(mu,P) are functions of a label operator P, and do not commute with collinear fields. The symmetry is used to reproduce a two-loop result for factorization in B -> D pi in a simple way.

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JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes

L. Theussl, C. Kaufhold, J. Collins … (2008)

A new version of the Feynman graph plotting tool JaxoDraw is presented. Version 2.0 is a fundamental re-write of most of the JaxoDraw core and some functionalities, in particular importing graphs, are not backward-compatible with the 1.x branch. The most prominent new features include: drawing of Bezier curves for all particle modes, on-the-fly update of edited objects, multiple undo/redo functionality, the addition of a plugin infrastructure, and a general improved memory performance. A new LaTeX style file is presented that has been written specifically on top of the original axodraw.sty to meet the needs of this this new version.

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Treating the b quark distribution function with reliable uncertainties

Frank Tackmann, Iain W. Stewart, Zoltan Ligeti (2008)

The parton distribution function for a b quark in the B meson (called the shape function) plays an important role in the analysis of the B -> X_s gamma and B -> X_u l nu data, and gives one of the dominant uncertainties in the determination of |Vub|. We introduce a new framework to treat the shape function, which consistently incorporates its renormalization group evolution and all constraints on its shape and moments in any short distance mass scheme. At the same time it allows a reliable treatment of the uncertainties. We develop an expansion in a suitable complete set of orthonormal basis functions, which provides a procedure for systematically controlling the uncertainties due to the unknown functional form of the shape function. This is a significant improvement over fits to model functions. Given any model for the shape function, our construction gives an orthonormal basis in which the model occurs as the first term, and corrections to it can be studied. We introduce a new short distance scheme, the "invisible scheme", for the kinetic energy matrix element, lambda_1. We obtain closed form results for the differential rates that incorporate perturbative corrections and a summations of logarithms at any order in perturbation theory, and present results using known next-to-next-to-leading order expressions. The experimental implementation of our framework is straightforward.

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Publication date Created: 2014-09-29

Publication date Updated: 2015-01-02

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DOI: 10.1007/JHEP12(2014)146

ArXiV ID: 1409.8281

SO-VID: 57fb4a2e-07da-49ec-a27c-15e48db600bf

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Report No DESY 14-170

Journal reference JHEP 1412 (2014) 146

Comments 17 pages, 1 figure; v2: journal version

Categories hep-ph

ScienceOpen disciplines: High energy & Particle physics

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ScienceOpen disciplines: High energy & Particle physics

The Fully-Differential Quark Beam Function at NNLO

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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory

Most cited references 13

Invariant Operators in Collinear Effective Theory

JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes

Treating the b quark distribution function with reliable uncertainties

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