We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.
We present a general method to match fully differential next-to-next-to-leading (NNLO) calculations to parton shower programs. We discuss in detail the perturbative accuracy criteria a complete NNLO+PS matching has to satisfy. Our method is based on consistently improving a given NNLO calculation with the leading-logarithmic (LL) resummation in a chosen jet resolution variable. The resulting NNLO$+$LL calculation is cast in the form of an event generator for physical events that can be directly interfaced with a parton shower routine, and we give an explicit construction of the input "Monte Ca…
We present results for the Higgsstrahlung process within the GENEVA Monte Carlo framework. We combine the fully differential NNLO calculation with the higher-order resummation in the 0-jettiness resolution variable (beam-thrust). The resulting parton-level events are further showered and hadronised by Pythia8. The beam-thrust resummation is carried out to NNLL$'$ accuracy, which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment …
We discuss how the UN2LOPS scheme for matching NNLO calculations to parton showers can be applied to processes with large higher-order perturbative QCD corrections. We focus on Higgs-boson production through gluon fusion as an example. We also present an NNLO fixed-order event generator for this reaction.
We present results for Drell-Yan production from the GENEVA Monte-Carlo framework. We combine the fully-differential NNLO calculation with higher-order resummation in the 0-jettiness resolution variable. The resulting parton-level events are further combined with parton showering and hadronization provided by PYTHIA8. The 0-jettiness resummation is carried out to NNLL', which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment of …
We report the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account of the precise NNLO QCD corrections to the evolution equations kernel. The value of strong coupling constant α_s^{NNLO}(M_Z)=0.1141(14), in fair agreement with one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using obtained PDFs are in agreement to the latest Run II results.
I describe MiNNLO$_{\rm PS}$, a novel method to match NNLO QCD computations with Parton Showers, and present a selection of results for color-singlet production at the LHC.
We present a parton-shower matched NNLO QCD calculation for hadronic final state production in Deep Inelastic Scattering. The computation is based on the UNLOPS method and is implemented in the publicly available event generation framework SHERPA. Results are compared to measurements performed by the H1 collaboration.
We present a simple approach to combine NNLO QCD calculations and parton showers, based on the UNLOPS technique. We apply the method to the computation of Drell-Yan lepton-pair production at the Large Hadron Collider. We comment on possible improvements and intrinsic uncertainties.
We discuss the impact of the treatment of NMC structure function data on parton distributions in the context of the NNPDF2.1 global PDF determination at NLO and NNLO. We show that the way these data are treated, and even their complete removal, has no effect on parton distributions at NLO, and at NNLO has an effect which is below one sigma. In particular, the Higgs production cross-section in the gluon fusion channel is very stable.
In this talk, we discuss recent developments in combining parton showers and fixed-order calculations. We focus on the UNNLOPS method for matching next-to-next-to-leading order computations to the parton shower, and we present results from Sherpa for Drell-Yan lepton-pair and Higgs-boson production at the LHC.
We present a new set of parton distributions obtained at NNLO. These differ from the previous sets available at NNLO due to improvements in the theoretical treatment. In particular we include a full treatment of heavy flavours in the region near the quark mass. In this way, an essentially complete set of NNLO partons is presented for the first time. The improved treatment leads to a significant change in the gluon and heavy quark distributions, and a larger value of the QCD coupling at NNLO, alpha_S(M_Z^2) = 0.1191 +/- 0.002(expt.) +/- 0.003(theory). Indirectly this also leads to a change in t…
We present a novel method to combine QCD calculations at next-to-next-to-leading order (NNLO) with parton shower (PS) simulations, that can be applied to the production of heavy systems in hadronic collisions, such as colour singlets or a $t\bar{t}$ pair. The NNLO corrections are included by connecting the MiNLO$^\prime$ method with transverse-momentum resummation, and they are calculated at generation time without any additional reweighting, making the algorithm considerably efficient. Moreover, the combination of different jet multiplicities does not require any unphysical merging scale, and…
In this study we tried to emphasize the role parton shower plays in event generation, and in the physics of high energy event generation. We achieved this task by comparing the next-to-leading order and next-to-next-to-leading order results from EERAD3 with the next-to-leading order plus parton shower results from Vincia, and comparing both with real data.
It is shown that the previously noted extreme perturbative NNLO/NLO instability of the longitudinal structure function F_L(x,Q^2) is a mere artefact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be perturbatively rather stable already for Q^2 $\geq$ O(2-3 GeV^2).
Based on our recent NNLO dynamical parton distributions as obtained in the `fixed flavor number scheme', we generate radiatively parton distributions in the `variable flavor number scheme' where also the heavy quark flavors (c,b,t) become massless partons within the nucleon. Only within this latter factorization scheme NNLO calculations are feasible at present, since the required partonic subprocesses are only available in the approximation of massless initial-state partons. The NNLO predictions for gauge boson production are typically larger (by more than 1 sigma) than the NLO ones, and rates…
NNLOJET: a parton-level event generator for jet cross sections at NNLO QCD accuracy
CERN（欧洲核子研究组织）；Universität Zürich（苏黎世大学）；University of Durham（杜伦大学）；ETH（苏黎世联邦理工学院）；Shandong University（山东大学）；Max-Planck-Institut für Physik, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所）；KIT（卡尔斯鲁厄理工学院）；TU Dresden（德累斯顿工业大学）；LIP（葡萄牙粒子与核物理研究所）；Universidade de Lisboa（里斯本大学）；University of Wuppertal（伍珀塔尔大学）；Georg-August-Universität Göttingen（哥廷根大学）
The parton distributions functions (PDFs) derived from the NNLO QCD analysis of existing light-targets deep-inelastic-scattering data are presented. The NLO and NNLO PDFs are compared in order to analyze perturbative stability of the analysis and estimate impact of the higher-order QCD corrections. The main theoretical uncertainties and experimental uncertainties in PDFs due to all sources of experimental errors in data are estimated and used to assess corresponding uncertainties in the cross sections of other hadronic processes.
At the next generation of linear colliders, forward-backward asymmetries will be involved again in the precise determination of the neutral current couplings of heavy quarks in inclusive heavy-quark production. The theoretical understanding of these observables at the level of NNLO radiative corrections is required. We review a recent calculation of the two-parton contribution to the heavy-quark A_FB at NNLO QCD in e+e- collisions. The results are valid for arbitrary values of the momentum transfer and non-vanishing heavy-quark mass m_Q.
A detailed study of nucleon parton distribution functions is performed within a radiative Next-to-Next-to Leading Order (NNLO) parton model whose low-scale input is rigidly described by wave functions which include quarks and dressing meson-cloud. The light-front Hamiltonian dynamics fixes the three-quark wave functions and the meson cloud is introduced by means of high-order Fock component in time-ordered perturbation theory in the infinite momentum frame. Non-strange as well as strange mesons-baryon fluctuations are considered ($π$, $ρ$, $ω$, $K$ and $K^*$, together with $N$, $Δ$, $Λ$ and $Σ…
Parton distributions in the virtual photon target are investigated in perturbative QCD up to the next-to-next-to-leading order (NNLO). In the case $Λ^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NNLO, but they are factorisation-scheme-dependent. We analyse parton distributions in two different factorisation schemes, namely $\bar{\rm MS}$ and ${\rm DIS}_γ$ schemes, and discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-$x$ behavio…
We show at NNLO that the soft factors for double parton scattering (DPS) for both integrated and unintegrated kinematics, can be presented entirely in the terms of the soft factor for single Drell-Yan process, i.e. the transverse momentum dependent (TMD) soft factor. Using the linearity of the logarithm of TMD soft factor in rapidity divergences, we decompose the DPS soft factor matrices into a product of matrices with rapidity divergences in given sectors, and thus, define individual double parton distributions at NNLO. The rapidity anomalous dimension matrices for double parton distributions…
We determine at NNLO (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (Q_0^2<1 GeV^2) by employing the "fixed flavor number factorization scheme" (FFNS). These are compared with "standard" NNLO distributions, generated at some fixed and higher resolution scale (Q_0^2>1 GeV^2). The NNLO corrections imply in both approaches an improved value of χ^2, typically χ^2_{NNLO} \sim 0.9χ^2_{NLO}. The dynamical NNLO uncertainties are somewhat smaller than the NLO ones and both …
We present a determination of parton distribution functions (ABM11) and the strong coupling constant alpha_s at next-to-leading order and next-to-next-to-leading order (NNLO) in QCD based on world data for deep-inelastic scattering and fixed-target data for the Drell-Yan process. The analysis is performed in the fixed-flavor number scheme for n_f=3,4,5 and uses the MSbar-scheme for alpha_s and the heavy-quark masses. At NNLO we obtain the value alpha_s(M_Z) = 0.1134 +- 0.0011. The fit results are used to compute benchmark cross sections at hadron colliders to NNLO accuracy and to compare to da…
We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function $F_L$ and the cross sections $σ_W, σ_Z$ for $W$ and $Z$ hadroproduction as examples. For $F_L$ we find relatively poor convergence, with increasing order, at small $x$; whereas $σ_{W,Z}$ are much more reliably predict…
We present predictions for hadronic decays of the Higgs boson at next-to-next-to-leading order (NNLO) in QCD matched with parton shower based on the POWHEG framework. Those include decays into bottom quarks with full bottom-quark mass dependence, light quarks, and gluons in the heavy top quark effective theory. Our calculations describe exclusive decays of the Higgs boson with leading logarithmic accuracy in the Sudakov region and next-to-leading order (NLO) accuracy matched with parton shower in the three-jet region, with normalizations fixed to the partial width at NNLO. We estimated remaini…
We present the new preliminary MRST parton distributions at NLO and NNLO. The analysis includes some new data and there is an improvement in the theoretical treatment at NNLO. Essentially complete NNLO partons are presented for the first time, together with uncertainties.
We perform a NNLO (and a LO) global parton analysis in which we include the new precise data for deep inelastic scattering from HERA and for inclusive jet production at the Tevatron, together with the improved knowledge of the three-loop splitting functions. The results are compared with our recent NLO analyses. The LO fit produces significantly worse results in general, but gives a surprisingly good fit to the Tevatron high-E_T jet data. For the approximate NNLO analysis we notice a slight improvement in the quality of the global fit, and find that the partons are changed by up to 10% at Q^2=…
Charge and isospin symmetry violations to valence and sea distribution functions in the nucleon are evaluated (at low resolution scale) by means of a meson cloud model and light-cone quark wave functions. Their perturbative evolution are implemented at Next-to-next-to-leading order (NNLO) using an original evolution code in order to include the perturbatively generated strange - anti-strange asymmetry typical of the three loop evolution expansion. Charge symmetry violating QED effects are also added and the distributions, evolved at the experimental scale, are compared with available informati…
A new generation of (unpolarized) dynamical parton distribution functions of the nucleon is determined. After introducing basic elements of perturbative QCD, the dynamical model is discussed and compared with the approach to parton distributions used by most other groups ("standard"). Parton distributions sets (with uncertainties) at different orders (LO, NLO, NNLO), using different factorization schemes (\overline{MS}, DIS) and different treatments of heavy quark masses (FFNS, VFNS) are extracted and compared. The astrophysical implications of the dynamical predictions are outlined before foc…
We present for first time the computation at large $q_T$ (or small $b_T$) matching coefficients of Transverse Momentum Dependent Parton Distribution Function (TMDPDF) for linearly polarised to the integrated gluon distribution at next-to-next-to leading order (NNLO). The computation is performed using the modified $δ$-regulator for rapidity divergences and dimensional regularization. This TMDPDF matriz element presnts phenomenological interest in two kind of processes. The factorization of the Higgs production transverse momentum ($q_T$) distribution through gluon-gluon fusion and the quarkoni…
We discuss the influence of fixed target Drell-Yan data on the extraction of parton distribution functions at next-to-next-to-leading order (NNLO) in QCD. When used in a parton distribution fit, the Drell-Yan (DY) data constrain sea quark distributions at large values of Bjorken x. We find that not all available DY data are useful for improving the precision of parton distribution functions (PDFs) obtained from a fit to the deep inelastic scattering (DIS) data. In particular, some inconsistencies between DIS-based parton distribution functions and DY data for large values of dilepton rapidity …
We consider Higgs boson production at hadron colliders in the gluon fusion channel and compute higher order terms in the regularization parameter $ε$. In particular, the next-to-next-to-leading order cross section is evaluated including order $ε$ terms. These results are used to compute all convolutions with the splitting functions entering the next-to-next-to-next-to-leading order cross section.
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology at LO and NNLO in perturbative QCD, thereby generalizing to these orders the NNPDF2.1 NLO parton set. Heavy quark masses are included using the so-called FONLL method, which is benchmarked here at NNLO. We demonstrate the stability of PDFs upon inclusion of NNLO corrections, and we investigate the convergence of the perturbative expansion by comparing LO, NLO and NNLO results. We show that the momentum sum rule can be tested with increasing accuracy at LO,…
We present the derivation of the NNLO two-parton final state contributions to top pair production in the quark-antiquark channel proportionnal to the leading colour factor $N_c^2$. Together with the three and four-parton NNLO contributions presented in a previous publication, this enables us to complete the phenomenologically most important NNLO corrections to top pair hadro-production in this channel. We derive this two-parton contribution using the massive extension of the NNLO antenna subtraction formalism and implement those corrections in a parton-level event generator providing full kine…
Utilizing recent DIS measurements (σ_r, F_{2,3,L}) and data on hadronic dilepton production we determine at NNLO (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (Q_0^2 < 1 GeV^2). These are compared with `standard' NNLO distributions generated from positive input distributions at some fixed and higher resolution scale (Q_0^2 > 1 GeV^2). Although the NNLO corrections imply in both approaches an improved value of χ^2, typically χ^2_{NNLO} \simeq 0.9 χ^2_{NLO}, present…
Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to leading order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are ta…
We consider $W^\pm Z$ production in hadronic collisions and present high-precision predictions in QCD and electroweak (EW) perturbation theory matched to parton showers. To this end, we match next-to-next-to-leading order QCD corrections to parton showers using the MiNNLO$_{\rm PS}$ method and consistently combine them with next-to-leading order EW corrections matched to parton showers. This is the first time such accuracy in the event generation is achieved for any collider process, and we study in detail the impact of different choices in the combination of QCD and EW corrections as well as …
We derive the integrated forms of specific initial-final tree-level four-parton antenna functions involving a massless initial-state parton and a massive final-state fermion as hard radiators. These antennae are needed in the subtraction terms required to evaluate the double real corrections to $t\bar{t}$ hadronic production at the NNLO level stemming from the partonic processes $q\bar{q}\to t\bar{t}q'\bar{q}'$ and $gg\to t\bar{t}q\bar{q}$.
Recent measurements for F_2(x,Q^2) have been analyzed in terms of the `dynamical' and `standard' parton model approach at NLO and NNLO of perturbative QCD. Having fixed the relevant NLO and NNLO parton distributions, the implications and predictions for the longitudinal structure function F_L(x,Q^2) are presented. It is shown that the previously noted extreme perturbative NNLO/NLO instability of F_L(x,Q^2) is an artifact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO an…
We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to three-jet production and related event shape observables in electron-positron annihilation. Infrared singularities due to double real radiation at tree level and single real radiation at one loop are subtracted from the full QCD matrix elements using antenna functions, which are then integrated analytically and added to the two loop contribution. Using this antenna subtraction method, we obtain numerically finite contributions from five-parton and four-parton processes, and observe an explicit analytic c…
A study is made of charm and bottom flavor matching conditions on parton densities. Starting from an $\bar{\rm MS}$ three-flavor density set, where the scale $μ< m_c$, and using the recently derived two-loop matching conditions, we provide a new set of four-flavor parton densities where $ m_c \le μ< m_b$ and five-flavor densities where $μ\ge m_b$. The effect of the next-to-next-to-leading order matching conditions on the evolution equations is important for scales just above the transition regions. This includes the small $x$ and small $Q^2$ domain studied by the H1 and ZEUS experiments at HER…
We compute the rapidity distributions of W and Z bosons produced at the Tevatron and the LHC through next-to-next-to leading order in QCD. Our results demonstrate remarkable stability with respect to variations of the factorization and renormalization scales for all values of rapidity accessible in current and future experiments. These processes are therefore ``gold-plated'': current theoretical knowledge yields QCD predictions accurate to better than one percent. These results strengthen the proposal to use W and Z production to determine parton-parton luminosities and constrain parton distri…
We compute the Next-to-Next-to-Leading Order (NNLO) QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever NNLO calculation of an observable with more than two colored partons, and/or massive fermions, at hadron colliders. Augmenting our fixed order calculation with soft-gluon resummation through Next-to-Next-to-Leading Logarithmic (NNLL) accuracy, we observe that the predicted total inclusive cross-section exhibits a very small perturbative uncertainty, estimated at +-2.7%. We expect that once all sub-dominant partonic reactions are…
We present a comprehensive study of differential distributions for Tevatron top-pair events at the level of stable top quarks. All calculations are performed in NNLO QCD with the help of a fully differential partonic Monte-Carlo and are exact at this order in perturbation theory. We present predictions for all kinematic distributions for which data exists. Particular attention is paid on the top-quark forward-backward asymmetry which we study in detail. We compare the NNLO results with existing approximate NNLO predictions as well as differential distributions computed with different parton di…
We consider the collinear limit of QCD amplitudes at one-loop order, and their factorization properties directly in colour space. These results apply to the multiple collinear limit of an arbitrary number of QCD partons, and are a basic ingredient in many higher-order computations. In particular, we discuss the triple collinear limit and its relation to flavour asymmetries in the QCD evolution of parton densities at three loops. As a phenomenological consequence of this new effect, and of the fact that the nucleon has non-vanishing quark valence densities, we study the perturbative generation …
This contribution describes the HOPPET Fortran~95 package for carrying out DGLAP evolution and other common manipulations of PDFs. The PDFs are represented on a grid in $x$-space so as to avoid limitations on the functional form of input distributions. Good speed and accuracy are obtained through the representation of splitting functions in terms of their convolution with a set of piecewise polynomial basis functions. We briefly describe the structure of the code and discuss its quantitative performance. Finally we comment of future directions for the program's development.
We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets. In addition, a set of proton baseline PDFs is fitted within the same framework with the same theoretical assumptions. The results of this global QCD analysis are compared to existing nPDF sets and to the fitted cross sections. Also, the uncertainties resulting from the limited constraining power of the included experimental data are prese…
We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order (NNLO) QCD-analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutri{-}no-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF-evolution is performed in the $N_f = 3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolati…
A non-singlet QCD analysis of the structure function $xF_3$ up to NNLO is performed based on the Bernstein polynomials approach. We use recently calculated NNLO anomalous dimension coefficients for the moments of the $xF_3$ structure function in $νN$ scattering. In the fitting procedure, Bernstein polynomial method is used to construct experimental moments from the $xF_3$ data of the CCFR collaboration in the region of $x$ which is inaccessible experimentally. We also consider Bernstein averages to obtain some unknown parameters which exist in the valence quark densities in a wide range of $x$…
We present a systematic investigation of jet production at hadron colliders from a phenomenological point of view, with the dual aim of providing a validation of theoretical calculations and guidance to future determinations of parton distributions (PDFs). We account for all available inclusive jet and dijet production measurements from ATLAS and CMS at 7 and 8 TeV by including them in a global PDF determination, and comparing to theoretical predictions at NNLO QCD supplemented by electroweak (EW) corrections. We assess the compatibility of the PDFs, specifically the gluon, obtained before and…
We detail a simulation of Higgs boson production via gluon fusion, accurate at next-to-next-to-leading order in the strong coupling, including matching to a parton shower, yielding a fully exclusive, hadron-level description of the final-state. The approach relies on the POWHEG method for merging the NLO Higgs plus jet cross-section with the parton shower, and on the MINLO method to simultaneously achieve NLO accuracy for inclusive Higgs boson production. The NNLO accuracy is reached by a reweighting procedure making use of the HNNLO program.
We consider $Z γ$ production in hadronic collisions and present the first computation of next-to-next-to-leading order accurate predictions consistently matched to parton showers (NNLO+PS). Spin correlations, interferences and off-shell effects are included by calculating the full process $pp\to\ell^+\ell^-γ$. We extend the recently developed MiNNLO$_{\rm PS}$ method to genuine $2\to 2$ hard scattering processes at the LHC, which paves the way for NNLO+PS simulations of all diboson processes. This is the first $2\to2$ NNLO+PS calculation that does not require an a-posteriori multi-differential…
We present the first calculation of inclusive jet photoproduction with next-to-next-to-leading order (NNLO) contributions, obtained from a unified threshold resummation formalism. The leading coefficients for direct photoproduction are computed analytically. Together with the coefficients pertinent to parton-parton scattering, they are shown to agree with those appearing in our full next-to-leading order calculations. For hadron-hadron scattering, numerical agreement is found with a previous calculation of jet production at the Tevatron. We show that the direct and resolved NNLO contributions …
We report the first calculation of fully differential jet production in all partonic channels at next-to-next-to leading order (NNLO) in perturbative QCD and compare to the available ATLAS 7 TeV data. We discuss the size and shape of the perturbative corrections along with their associated scale variation across a wide range in jet transverse momentum, $p_{T}$, and rapidity, $y$. We find significant effects, especially at low $p_{T}$, and discuss the possible implications for Parton Distribution Function fits.
We present a subtraction method utilizing the N-jettiness observable, Tau_N, to perform QCD calculations for arbitrary processes at next-to-next-to-leading order (NNLO). Our method employs soft-collinear effective theory (SCET) to determine the IR singular contributions of N-jet cross sections for Tau_N -> 0, and uses these to construct suitable Tau_N-subtractions. The construction is systematic and economic, due to being based on a physical observable. The resulting NNLO calculation is fully differential and in a form directly suitable for combining with resummation and parton showers. We exp…
