The quark beam function at NNLL

By Iain W. Stewart, F. Tackmann, W. Waalewijn. 2010

134 citations recorded by the source corpus.

In hard collisions at a hadron collider the most appropriate description of the initial state depends on what is measured in the final state. Parton distribution functions (PDFs) evolved to the hard collision scale Q are appropriate for inclusive observables, but not for measurements with a specific number of hard jets, leptons, and photons. Here the incoming protons are probed and lose their identity to an incoming jet at a scale μB ≪ Q, and the initial state is described by universal beam functions. We discuss the field-theoretic treatment of beam functions, and show that the beam function has the same RG evolution as the jet function to all orders in perturbation theory. In contrast to PDF evolution, the beam function evolution does not mix quarks and gluons and changes the virtuality of the colliding parton at fixed momentum fraction. At μB, the incoming jet can be described perturbatively, and we give a detailed derivation of the one-loop matching of the quark beam function onto quark and gluon PDFs. We compute the associated NLO Wilson coefficients and explicitly verify the cancellation of IR singularities. As an application, we give an expression for the next-to-next-to-leading logarithmic order (NNLL) resummed Drell-Yan beam thrust cross section.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1a2518782ce21dfdf0b75b39d07c18bd7a5ecc50

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In Nuclear and High Energy Physics

Citations in the corpus

Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA (2012, background): “J H E P 0 9 ( 2 0 1 3 ) 1 2 0 be further factorized into a convolution between the parton distribution functions fj and perturbatively calculable Wilson coefficients Iij [34, 89], Bi(t, x, µ) = ∑ j ∫ 1 x dξ ξ Iij ( t, x ξ , µ ) fj(ξ, µ) .”
Calculation of the transverse parton distribution functions at next-to-next-to-leading order (2014, background): “Popular examples are virtuality dependent factorization [13, 14], transverse momentum dependent (TMD) factorization [4, 5, 15–26], as well as virtuality and transverse momentum dependent factorization [27– 29].”
N-jettiness subtractions for NNLO QCD calculations (2015, background): “For the quark jet and beam functions in MS we have [90, 96]”
Higgs production with a central jet veto at NNLL+NNLO (2010, methodology): “The renormalized matrix elements Bg/j(t, z, μ) are given in terms of the bare ones as [68]”
An effective field theory for forward scattering and factorization violation (2016, background): “) For event shape observables such as beam thrust [102, 127, 128], transverse thrust [101, 129], and ET [130–132] the importance of this type of diagram for the violation of factorization was first discussed in [103].”
Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis) (2009, methodology): “enormalization Structure of the Beam Function In this appendix we derive the general structure of the beam function RGE in Eq. (3.25) to all orders in perturbation theory, which was presented in Ref. [168]. The two essential ingredients will be the known all-order renormalization properties of light”