We present the implementation of next-to-next-to-leading order (NNLO) QCD fully-differential corrections within the G framework, for both colour-singlet and colour-singlet+jet processes at hadron colliders, by employing a nonlocal subtraction approach. In particular, we discuss the implementation details and the challenges that arise when utilizing a dynamical infrared cutoff parameter. Additionally, we combine the subtraction with the projection-to-Born method in order to include fiducial power corrections. As a test case, we provide predictions for Drell-Yan and $\textit{Z}$+jet production at the LHC, using $\textit{N}$-jettiness as resolution variable. We validate the NNLO corrections of G against finding excellent agreement. Finally, we discuss how to extend our method to calculate the N LO QCD fully-differential corrections to colour-singlet production at hadron colliders.

Italy

Simone Alioli

Switzerland

Georgios Billis

Austria

Alessandro Broggio

Giovanni Stagnitto

NNLO predictions with nonlocal subtractions and fiducial power corrections in GENEVA

We present the resummation of one-jettiness for the color-singlet plus jet production process <math><mi>p</mi><mi>p</mi><mo>→</mo><mo>(</mo><msup><mi>γ</mi><mo>*</mo></msup><mo>/</mo><mi>Z</mi><mo>→</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><mo>)</mo><mo>+</mo><mtext>jet</mtext></math> at hadron colliders up to the fourth logarithmic order (<math><msup><mi>N</mi><mn>3</mn></msup><mi>LL</mi></math>). This is the first resummation at this order for processes involving three colored partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for color-singlet plus jet production matched to parton showers in the geneva framework.

Germany

Guido Bell

Bahman Dehnadi

United Kingdom

Matthew A. Lim

Giulia Marinelli

Riccardo Nagar

Davide Napoletano

Rudi Rahn

<math><msup><mi>N</mi><mn>3</mn></msup><mi>LL</mi></math> resummation of one-jettiness for <math><mi>Z</mi></math>-boson plus jet production at hadron colliders

We present a factorization theorem of the partonic Drell-Yan off-diagonal processes   <math> <mi>g</mi> <mover> <mi>q</mi> <mo>¯</mo> </mover> <mfenced> <mi>qg</mi> </mfenced> <mo>→</mo> <msup> <mi>γ</mi> <mo>∗</mo> </msup> <mo>+</mo> <mi>X</mi> </math>  $$ g\overline{q}(qg)\to {\gamma}^{\ast }+X $$  in the kinematic threshold regime   <math> <mi>z</mi> <mo>=</mo> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>/</mo> <mover> <mi>s</mi> <mo>̂</mo> </mover> <mo>→</mo> <mn>1</mn> </math>  $$ z={Q}^2/\hat{s}\to 1 $$  at general subleading powers in the (1 − z) expansion. Focusing on the first order of the expansion (next-to-leading power accuracy with respect to the leading power   <math> <mi>q</mi> <mover> <mi>q</mi> <mo>¯</mo> </mover> </math>  $$ q\overline{q} $$  channel), we validate the bare factorization formula up to   <math> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\alpha}_s^2\right) $$ . This is achieved by carrying out an explicit calculation of the generalized soft function in d-dimensions using the reduction to master integrals and the differential equations method. The collinear function is a universal object which we compute from an operator matching equation at one-loop level. Next, we integrate the soft and collinear functions over the convolution variables and remove the remaining initial state collinear singularities through PDF renormalization. The resulting expression agrees with the known cross section in the literature.

Sebastian Jaskiewicz

Leonardo Vernazza

Threshold factorization of the Drell-Yan quark-gluon channel and two-loop soft function at next-to-leading power

In this work, we study the production of Higgs boson pairs at next-to-next-to-leading order in QCD matched to parton showers, using the Geneva framework and working in the heavy-top-limit approximation. This includes the resummation of large logarithms of the zero-jettiness   <math> <mi>T</mi> </math>  $$ \mathcal{T} $$  0 up to the next-to-next-to-next-to-leading-log accuracy. This process features an extremely large momentum transfer, which makes its study particularly relevant for matching schemes such as that employed in Geneva, where the resummation of a variable different from that used in the ordering of the parton shower is used. To further study this effect, we extend the original shower interface designed for Pythia8 to include other parton showers, such as Dire and Sherpa.

Alessandro Gavardi

Stefan Kallweit

Matthew Lim

Double Higgs production at NNLO interfaced to parton showers in GENEVA

We describe a number of improvements to the Geneva method for matching NNLO calculations to parton shower programs. In particular, we detail changes to the resummed calculation used in the matching procedure, including disentangling the cross section dependence on factorisation and beam scales, and an improved treatment of timelike logarithms. We also discuss modifications in the implementation of the splitting functions which serve to make the resummed calculation differential in the higher multiplicity phase space. These changes improve the stability of the numerical cancellation of the nonsingular term at small values of the resolution parameter. As a case study, we consider the gluon-initiated Higgs boson production process gg → H. We validate the NNLO accuracy of our predictions against independent calculations, and compare our showered and hadronised results with recent data taken at the ATLAS and CMS experiments in the diphoton decay channel, finding good agreement.

Refining the GENEVA method for Higgs boson production via gluon fusion

We study the resummation of the 0-jettiness resolution variable   <math> <mi>T</mi> </math>  $$ \mathcal{T} $$  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   <math> <mi>T</mi> </math>  $$ \mathcal{T} $$  0 → 0 limit. We then calculate the   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (α  s ) 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′ (  <math> <msubsup> <mtext>NNLL</mtext> <mi>a</mi> <mo>′</mo> </msubsup> </math>  $$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ ). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the t   <math> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ \overline{t} $$ +jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at   <math> <msubsup> <mtext>NNLL</mtext> <mi>a</mi> <mo>′</mo> </msubsup> </math>  $$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ +NLO accuracy.

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

We extend the geneva Monte Carlo framework using the transverse momentum of a color-singlet system as the resolution variable. This allows us to use next-to-next-to-next-to-leading-logarithm (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LL</mi></mrow></math>) resummation via the radish formalism to obtain precise predictions for any color-singlet production process at the fully exclusive level. Thanks to the implementation of two different resolution variables within the geneva framework, we are able to assess the impact of such a choice on differential observables for the first time. As a first application, we present predictions for Drell-Yan lepton-pair production at next-to-next-to-leading order (NNLO) in QCD interfaced to a parton shower simulation that includes additional all-order radiative corrections. We provide fully showered and hadronized events using pythia8, while retaining the NNLO QCD accuracy for observables which are inclusive over the additional radiation. We also show that it is possible to obtain a numerically good agreement between showered geneva predictions and the <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LL</mi></mrow></math> resummation for the transverse momentum spectrum by choosing a more local recoil scheme. We compare our final predictions to LHC data at 13 TeV, finding good agreement across several distributions.

United States

Christian W. Bauer

Luca Rottoli

Matching NNLO predictions to parton showers using <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LL</mi></mrow></math> color-singlet transverse momentum resummation in geneva

We calculate the generalized soft functions at   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (  <math> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math>  $$ {\alpha}_s^2 $$ ) at next-to-leading power accuracy for the Drell-Yan process at threshold. The operator definitions of these objects contain explicit insertions of soft gauge and matter fields, giving rise to a dependence on additional convolution variables with respect to the leading power result. These soft functions constitute the last missing ingredient for the validation of the bare factorization theorem to NNLO accuracy. We carry out the calculations by reducing the soft squared amplitudes into a set of canonical master integrals and we employ the method of differential equations to evaluate them. We retain the exact d-dimensional dependence of the convolution variables at the integration boundaries in order to regulate the fixed-order convolution integrals. After combining the soft functions with the relevant collinear functions, we perform checks of the results at the cross-section level against the literature and expansion-by-regions calculations, at NNLO and partly at N3LO, finding agreement.

CERN

Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold

We present a novel next-to-next-to-leading order (NNLO) QCD calculation matched to parton shower for the production of a pair of Z bosons decaying to four massless leptons, <math><mi>p</mi><mi>p</mi><mo>→</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo><mspace width="0.2em"></mspace><mo>+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo><mspace width="0.2em"></mspace><mo>−</mo></mrow></msup><mo>+</mo><mi>X</mi></math>, at the LHC. Spin correlations, interferences and off-shell effects are included throughout. Our result is based on the resummed beam-thrust spectrum, which we evaluate at next-to-next-to-leading-logarithmic (NNLL<math><msubsup><mrow></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mrow><mo>′</mo></mrow></msubsup></math>) accuracy for the first time for this process, and makes use of the Geneva Monte Carlo framework for the matching to Pythia8 shower and hadronisation models. We compare our predictions with data from the ATLAS and CMS experiments at <math><mn>13</mn><mspace width="0.2em"></mspace><mtext>TeV</mtext></math>, finding a good agreement.

Next-to-next-to-leading order event generation for -boson Pair Production Matched to Parton Shower

We present the NNLL′ resummed 2-jettiness distribution for decays of the Standard Model Higgs boson to a b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$ -quark pair and to gluons. The calculation exploits a factorisation formula derived using Soft-Collinear Effective Theory, in which large logarithms of the 2-jettiness are resummed by renormalisation group evolution of the hard, soft and jet contributions to the differential decay rate. We match the resummed predictions to the fixed-order NNLO result using the Geneva framework, extending the validity of the results to all values of the resolution variable and providing a fully exclusive NNLO event generator matched to the Pythia8 parton shower.