Two-loop anomalous dimension for the resummation of non-global observables

Becher, Thomas; Rauh, Thomas; Xu, Xiaofeng

doi:10.48550/arxiv.2112.02108

Cited by 2 publications

(3 citation statements)

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“…For the ln(R) resummation, the α 2 s corrections to P q→γ (z) and P g→γ (z) are as of yet unknown and would need to be computed. For the resummation of ln( γ ) the most important ingredient, namely the two-loop evolution, is available [63,66,67]. Only the one-loop boundary conditions, in particular the jet function with an additional parton, will need to be determined and implemented.…”

Section: Discussionmentioning

confidence: 99%

“…The "evolution time" t measures the separation of the scales µ j and µ 0 . The relevant one-loop anomalous dimension Γ (1) can be found in [41] (by now also the two-loop result is known [63]) and the solution of the evolution equation is detailed in [44,46]. The shower starts with a quark along the direction n which fragments into a photon and a quark along the n q direction with angular separation Θ q .…”

Section: Resummation Of Ln( γ ) Termsmentioning

confidence: 99%

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QCD anatomy of photon isolation

Becher¹,

Favrod²,

Xu³

2022

Preprint

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To separate the energetic photons produced in hard scattering processes from those from other sources, measurements impose isolation requirements which restrict the hadronic radiation inside a cone around the photon. In this paper, we perform a detailed factorization analysis of the QCD effects associated with photon isolation. We show that for small cone radius R, photon isolation effects can be captured by a fragmentation function describing the decay of a parton into a photon accompanied by hadronic radiation. We compute this fragmentation function for different isolation criteria and solve the associated renormalization group equations to resum logarithms of R. For small isolation energy, the cone fragmentation function factorizes further, into collinear functions describing energetic quarks and gluons near the cone boundary and functions encoding their soft radiation emitted into the cone. Based on this factorization we also resum the non-global logarithms of the ratio of the photon energy and the isolation energy, so that we control all logarithmically enhanced terms in the cross section. Finally, we provide a simple formula to convert NNLO cross section results from smooth-cone isolation to fixed-cone isolation.

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Section: Discussionmentioning

confidence: 99%

Section: Resummation Of Ln( γ ) Termsmentioning

confidence: 99%

QCD anatomy of photon isolation

Becher¹,

Favrod²,

Xu³

2022

Preprint

Self Cite

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show abstract

“…[697]); and d) performing analytic or semi-analytic calculations that provide references and/or validations of the many different kinds of logarithmic contributions that need to be included in the shower (e.g. recent advances in subleading-logarithmic calculations for non-global logarithms [698][699][700]).…”

Section: Qcd Parton Showers and Dipole Showersmentioning

confidence: 99%