We update a previous N LL + $$ \mathcal{O}\left({\alpha}_s^3\right) $$ determination of the strong coupling from a global fit to thrust data by including newly available perturbative ingredients, upgrading the renormalization scales to include a fully canonical scaling region, and implementing the log resummation in a way which ensures the integrated cross section is unaffected by the leading 1/$\textit{Q}$ hadronization power corrections. Detailed discussions are provided concerning the stability of the results under variations of the fit range and the importance of summing up higher-order logarithmic terms for convergence and stability. We show that high-precision results can be achieved even when carrying out a more conservative fit by restricting the dataset to a region which is more clearly dominated by dijet events. This leads to $\textit{α}$ ($\textit{m}$ ) = 0.1136 ± 0$\textit{.}$0012 with $\textit{χ}$ /dof = 0.86, fully compatible with earlier results using a larger fit range. We also demonstrate that a number of additional effects associated to power corrections have a small impact on this fit result, including modifications to the renormalon substraction scheme for dijet power corrections and the inclusion of three-jet power correction models. The fit is also shown to provide very good agreement with data outside the fit range.

Spain

Miguel Benitez

Austria

André Hoang

Vicent Mateu

United States

Iain Stewart

Switzerland

Gherardo Vita

On determining $\textit{α}$

While the current frontier in fixed-order precision for collider observables is N LO, important steps are necessary to consolidate NNLO cross-section predictions with improved stability and efficiency. Slicing methods have been successfully applied to obtain NNLO and N LO predictions, but have shown poor performance in the presence of fiducial cuts due to large kinematical power corrections. In this paper we implement Projection-to-Born-improved $\textit{q}$ (P2B $\textit{q}$ ) and jettiness (P2B $\textit{τ}$ ) subtractions for a large class of color singlet processes in MCFM. This method allows for the efficient evaluation of $\textit{fiducial}$ power corrections in any non-local subtraction scheme using a Projection-to-Born subtraction. We demonstrate the significant numerical improvements of this method based on fiducial Drell-Yan and Higgs cross-sections. Moreover, with fiducial power corrections removed via this method, the leading-logarithmic power corrections that have only been calculated without fiducial cuts can be included, further improving the calculations. For di-photon production with photon isolation, we devise a novel method in combination with P2B-improved subtractions, which we name P2B $\textit{τ}$ , and P2B $\textit{q}$ for the two subtraction schemes, respectively. This method allows the inclusion of both fiducial power corrections due to kinematic cuts on the photons and a set of isolation power corrections in the fragmentation channel where a quark may enter the isolation cone. We find significant improvements in the convergence of NNLO di-photon cross-sections with photon isolation cuts, demonstrating that it is possible to achieve a stable and efficient calculation of di-photon cross-sections using slicing methods.

John Campbell

Tobias Neumann

Projection-to-Born-improved subtractions at NNLO

We compute the leading logarithmic power corrections at next-to-next-to-next-to-leading order for 0-jettiness subtractions for Drell-Yan and Higgs production in gluon fusion differential in both the invariant mass and rapidity of the color singlet. We review how to disentangle these power corrections from those arising from the presence of fiducial and isolation cuts by using Projection-to-Born improved slicing. Our results include all the channels contributing at leading logarithmic order for these processes, including the off-diagonal channels that receive contributions from soft quark emission. We study the numerical impact of the power corrections for Drell-Yan and Higgs production and find it to become negligible compared to the size of the N3LO corrections only below τ cut ~ 10−5. We estimate that in a fully differential calculation at N3LO combining the Projection-to-Born improved slicing method and our results for the leading logarithmic power corrections may allow for keeping the slicing uncertainties under control already with τ cut ≲ 10−3, marking a significant improvement in efficiency for these methods. These results constitute a crucial ingredient for fully differential N3LO calculations based on the N-jettiness subtraction scheme.

CERN

N3LO power corrections for 0-jettiness subtractions with fiducial cuts

We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> rapidity anomalous dimensions to higher order in the dimensional regulator and make use of the soft and rapidity anomalous dimension correspondence in conjunction with the recent determination of the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>LO</mi></mrow></math> threshold anomalous dimensions to achieve our result. We show that the results for the quark and gluon rapidity anomalous dimensions at four loops are related by generalized Casimir scaling. Using the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>LO</mi></mrow></math> rapidity anomalous dimension, we perform the resummation of the energy-energy correlation in the back-to-back limit at <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>LL</mi></mrow></math>, achieving for the first time the resummation of an event shape at this logarithmic order. We present numerical results and observe a reduction of perturbative uncertainties on the resummed cross section to below 1%.

Germany

Claude Duhr

Bernhard Mistlberger

Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

We calculate soft phase-space and loop master integrals for the computation of color-singlet cross sections through N3LO in perturbative QCD. Our results are functions of homogeneous transcendental weight and include the first nine terms in the expansion in the dimensional regulator ϵ. We discuss the application of our results to the computation of deeply-inelastic scattering and e + e  −  annihilation processes. We use these results to compute the perturbative coefficient functions for the Drell-Yan and gluon-fusion Higgs boson production cross sections to higher orders in ϵ through N3LO in QCD in the limit where only soft partons are produced on top of the colorless final state. Furthermore, we extract the anomalous dimension of the inclusive threshold soft function and of the N-Jettiness beam and jet functions to N4LO in perturbative QCD.

Soft integrals and soft anomalous dimensions at N3LO and beyond

We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N3LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N3LO. We combine the newly obtained N3LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N3LL′ accuracy, resulting in a factor of ∼ 4 reduction of uncertainties in the peak region compared to N3LL predictions.

Markus Ebert

The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL′

We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit of the semi-inclusive deep inelastic scattering cross section where all final-state radiation becomes collinear to the detected hadron. The required cross section is obtained by analytically continuing our recent computation of the Drell-Yan and Higgs boson production cross section at N3LO expanded around the limit of all final-state radiation becoming collinear to one of the initial states. Our results agree with a recent independent calculation by Luo et al.

TMD fragmentation functions at N3LO

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.

Collinear expansion for color singlet cross sections

We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the q  T  subtraction methods to N3LO and to obtain resummed q  T  spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.

Transverse momentum dependent PDFs at N3LO

We present the first complete calculation for the quark and gluon N-jettiness (  <math> <msub> <mi>T</mi> <mi>N</mi> </msub> </math>  $$ {\mathcal{T}}_N $$ ) beam functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The class of functions appearing in the matching coefficents for all channels includes iterated integrals with non-rational kernels, thus going beyond the one of harmonic polylogarithms. Our results are a key step in extending the   <math> <msub> <mi>T</mi> <mi>N</mi> </msub> </math>  $$ {\mathcal{T}}_N $$  subtraction methods to N3LO, and to resum   <math> <msub> <mi>T</mi> <mi>N</mi> </msub> </math>  $$ {\mathcal{T}}_N $$  distributions at N3LL′ accuracy both for quark as well as for gluon initiated processes.