N-jettiness beam functions at N3LO

Ebert, M.; Mistlberger, Bernhard; Vita, Gherardo

doi:10.1007/jhep09(2020)143

“…When this paper first appeared, the T 0 beam function was only known at NNLO [85][86][87][88], while only partial results were known at N 3 LO [83,84]. By now, the complete results for the three-loop beam functions have become available [91,94], for which our results provided important cross checks. In particular, the predicted z → 1 limit was the only available check of the genuine three-loop contribution.…”

Section: Introductionmentioning

confidence: 77%

A toolbox for $$q_{T}$$ and 0-jettiness subtractions at $$\hbox {N}^3\hbox {LO}$$

Billis

¹

,

Ebert

²

,

Michel

³

et al. 2021

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We derive the leading-power singular terms at three loops for both $$q_T$$ q T and 0-jettiness, $$\mathcal {T}_0$$ T 0 , for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for $$q_T$$ q T and $$\mathcal {T}_0$$ T 0 subtractions at $$\hbox {N}^3\hbox {LO}$$ N 3 LO , which are an important ingredient for matching $$\hbox {N}^3\hbox {LO}$$ N 3 LO calculations with parton showers. We obtain the full three-loop structure of the relevant beam and soft functions, which are necessary ingredients for the resummation of $$q_T$$ q T and $$\mathcal {T}_0$$ T 0 at $$\hbox {N}^3\hbox {LL}'$$ N 3 LL ′ and $$\hbox {N}^4\hbox {LL}$$ N 4 LL order, and which constitute important building blocks in other contexts as well. The nonlogarithmic boundary coefficients of the beam functions, which contribute to the integrated subtraction terms, are not yet fully known at three loops. By exploiting consistency relations between different factorization limits, we derive results for the $$q_T$$ q T and $$\mathcal {T}_0$$ T 0 beam function coefficients at $$\hbox {N}^3\hbox {LO}$$ N 3 LO in the $$z\rightarrow 1$$ z → 1 threshold limit, and we also estimate the size of the unknown terms beyond threshold.

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“…In summary, the method of collinear expansions is a great tool to study the infrared limit of QCD. At leading power in the collinear expansion, it provides access to the universal beam functions governing the collinear limit, which we employ to calculate the T N and q T beam functions at N 3 LO in two companion papers [105,106]. We also believe that the collinear expansions will similarly shed light on the universal structure of hadron collision processes beyond the leading power.…”

Section: Discussionmentioning

confidence: 98%

“…The beam function B i (t, x, µ), sometimes also referred to as the virtuality-dependent beam function, appears in the factorization of all T N [206], deep-inelastic scattering [212], and in the factorization of color-singlet processes in the generalized threshold limit [26]. It is known at NNLO [97,195,196,208], and we compute it at N 3 LO for all partonic channels in our companion paper [106]. Previous progress towards the calculation of the quark beam function at N 3 LO was made in refs.…”

Section: Comparison To Alternative Methodsmentioning

confidence: 99%

“…Since the beam function counter term Z i B gives rise to the renormalization group equation of the beam function, in practice one can either predict Z i B from the RGEs and check that this cancels all poles in , or determine Z i B by absorbing all poles remaining after QCD UV and IR subtraction and verify that it reproduces the RGE dictated by the EFT. For the T N and q T beam functions, this is discussed in more detail in our companion papers [105,106].…”

Section: Jhep09(2020)181mentioning

confidence: 99%

“…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]. In our companion papers [105,106], we complete this task by computing the q T and T 0 beam functions in all channels at N 3 LO based on the methods outlined in this article.…”

Section: Jhep09(2020)181mentioning

confidence: 99%

See 2 more Smart Citations

Collinear expansion for color singlet cross sections

Ebert

¹

,

Mistlberger

²

,

Vita

³

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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Zero-jettiness resummation for top-quark pair production at the LHC

Alioli

¹

,

Broggio

²

,

Lim

³

2022

J. High Energ. Phys.

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We study the resummation of the 0-jettiness resolution variable $$ \mathcal{T} $$ T 0 for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the $$ \mathcal{T} $$ T 0 → 0 limit. We then calculate the $$ \mathcal{O} $$ O (αs) corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL′, NNLL and approximate NNLL′ ($$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ NNLL a ′ ). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the t$$ \overline{t} $$ t ¯ +jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at $$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ NNLL a ′ +NLO accuracy.

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N-jettiness beam functions at N3LO

Cited by 41 publications

References 109 publications

A toolbox for $$q_{T}$$ and 0-jettiness subtractions at $$\hbox {N}^3\hbox {LO}$$

A toolbox for $$q_{T}$$ and 0-jettiness subtractions at $$\hbox {N}^3\hbox {LO}$$

Collinear expansion for color singlet cross sections

Zero-jettiness resummation for top-quark pair production at the LHC

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