NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $$\epsilon $$

Baranowski, Daniel

doi:10.1140/epjc/s10052-020-8047-y

Cited by 22 publications

(23 citation statements)

References 39 publications

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“…Specifically, we investigate the transverse momentum (q T ) dependent beam functions and N -jettiness (T N ) beam function. We illustrate our method by computing these quantities through NNLO, up to the second order in the dimensional regularization parameter , confirming recent results in the literature [98][99][100]. These results are necessary input for the calculation of aforementioned beam functions at N 3 LO in QCD, where much progress has been already made for the quark T N beam function [101][102][103], and which has already been achieved for the quark q T beam function and TMDPDF [104].…”

Section: Jhep09(2020)181supporting

confidence: 82%

“…This approach was used in refs. [100][101][102][103], where the required splitting function at N 3 LO was obtained following the method of ref. [205].…”

Section: Comparison To Alternative Methodsmentioning

confidence: 99%

“…[195,196], and the higher-order terms in agree with ref. [100]. Our bare results are provided as supplementary material.…”

Section: Jhep09(2020)181mentioning

confidence: 99%

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Collinear expansion for color singlet cross sections

Ebert

Mistlberger

Vita

2020

J. High Energ. Phys.

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We demonstrate how to efficiently expand cross sections for color-singlet production at hadron colliders around the kinematic limit of all final state radiation being collinear to one of the incoming hadrons. This expansion is systematically improvable and applicable to a large class of physical observables. We demonstrate the viability of this technique by obtaining the first two terms in the collinear expansion of the rapidity distribution of the gluon fusion Higgs boson production cross section at next-to-next-to leading order (NNLO) in QCD perturbation theory. Furthermore, we illustrate how this technique is used to extract universal building blocks of scattering cross section like the N-jettiness and transverse momentum beam function at NNLO.

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Section: Jhep09(2020)181supporting

confidence: 82%

“…This approach was used in refs. [100][101][102][103], where the required splitting function at N 3 LO was obtained following the method of ref. [205].…”

Section: Comparison To Alternative Methodsmentioning

confidence: 99%

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Collinear expansion for color singlet cross sections

Ebert

Mistlberger

Vita

2020

J. High Energ. Phys.

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“…Furthermore angular integrals in the Somogyi parametrization make their appearance in the determination of beam and soft functions (see ref. [73]).…”

Section: Jhep06(2021)066mentioning

confidence: 99%

New ideas for handling of loop and angular integrals in D-dimensions in QCD

Lyubovitskij

Wunder

Zhevlakov

2021

J. High Energ. Phys.

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We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

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“…However, it is not clear how to directly apply the regular IBP method to integrals with cuts. In a recent paper [3], theta functions were written as integrals of delta functions. The resulting integrals were reduced by combining the reverse unitarity [4] and the IBP method.…”

Section: Introductionmentioning

confidence: 99%

Reduction of Feynman integrals in the parametric representation III: integrals with cuts

Chen

2020

Eur. Phys. J. C

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Phase space cuts are implemented by inserting Heaviside theta functions in the integrands of momentum-space Feynman integrals. By directly parametrizing theta functions and constructing integration-by-parts (IBP) identities in the parametric representation, we provide a systematic method to reduce integrals with cuts. Since the IBP method is available, it becomes possible to evaluate integrals with cuts by constructing and solving differential equations.

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NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $$\epsilon $$

Cited by 22 publications

References 39 publications

Collinear expansion for color singlet cross sections

Collinear expansion for color singlet cross sections

New ideas for handling of loop and angular integrals in D-dimensions in QCD

Reduction of Feynman integrals in the parametric representation III: integrals with cuts

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