Anti-$k_T$ jet function at next-to-next-to-leading order
Hao-yu Liu, Xiaohui Liu, Sven-Olaf Moch
备注：
12 pages, update the references, add a plot to demonstrate the fully differential nature of the calculated jet function, match the punished version, corrected an unnecessary approximation, numbers updated
Jets constructed via clustering algorithms (e.g., anti-$k_T$, soft-drop) have been proposed for many precision measurements, such as the strong coupling $α_s$ and the nucleon intrinsic dynamics. However, the theoretical accuracy is affected by missing QCD corrections at higher orders for the jet functions in the associated factorization theorems. Their calculation is complicated by the jet clustering procedure. In this work, we propose a method to evaluate jet functions at higher orders in QCD. The calculation involves the phase space sector decomposition with suitable soft subtractions. As a concrete example, we present the quark-jet function using the anti-$k_T$ algorithm with E-scheme recombination at next-to-next-to-leading order.
We compute the ${\cal O}(α^2α_s^2)$ perturbative corrections to inclusive jet production in electron-nucleon collisions. This process is of particular interest to the physics program of a future Electron Ion Collider (EIC). We include all relevant partonic processes, including deep-inelastic scattering contributions, photon-initiated corrections, and parton-parton scattering terms that first appear at this order. Upon integration over the final-state hadronic phase space we validate our results for the deep-inelastic corrections against the known next-to-next-to-leading order (NNLO) structure …
We demonstrate that jet observables are highly sensitive to the characteristics of the vacuum and the in-medium QCD parton showers and propose techniques that exploit this sensitivity to constrain the mechanism of quark and gluon energy loss in strongly-interacting plasmas. As a first example, we calculate the inclusive jet cross section in high-energy nucleus-nucleus collisions to ${\cal O}(α_s^3)$. Theoretical predictions for the medium-induced jet broadening and the suppression of the jet production rate due to cold and hot nuclear matter effects in Au+Au and Cu+Cu reactions at RHIC are pre…
We present the complete calculation of $W$-boson production in association with a jet in hadronic collisions through next-to-next-to-leading order in perturbative QCD. To cancel infrared divergences we introduce a new subtraction method that exploits the fact that the $N$-jettiness event-shape variable fully captures the singularity structure of QCD amplitudes with final-state partons. This method holds for processes with an arbitrary number of jets, and is easily implemented into existing frameworks for higher-order calculations. We present initial phenomenological results for $W$+jet product…
Analytic predictions for the energy dependence of the mean multiplicities in gluon and quark jets are presented at the next-to-next-to-next-to-leading order (3NLO) of perturbative QCD and are compared to experiment. The 3NLO correction to the gluon jet multiplicity is found to be small. The corresponding theoretical expression provides a good description of available gluon jet measurements. In contrast, the 3NLO correction to the quark jet multiplicity is large and the theoretical expression does not describe the data accurately. It is shown that the well known success of the next-to-leading o…
I report results from a next-to-leading order event generator of purely gluonic jet production. This calculation, is the first step in the construction of a full next-to-leading order calculation of three jet production at hadron colliders.
We calculate the $N$-jettiness soft function for $tW$ production up to next-to-next-to-leading order in QCD, which is an important ingredient of the $N$-jettiness subtraction method for predicting the differential cross sections of massive coloured particle productions. The divergent parts of the results have been checked using the renormalization group equations controlled by the soft anomalous dimension.
We present a general framework for the calculation of soft functions for SCET_I observables through next-to-next-to-leading order (NNLO) in the strong coupling constant. As an example of our formalism we show how it can be used to obtain the complete NNLO soft function for the $N$-jettiness event shape variable. We present numerical results for two examples with phenomenological impact: the one-jettiness soft function for both electron-proton and proton-proton collisions.
We present results for associated Higgs+n-jet production in bottom quark annihilation, for n=0 and n>=1 at NNLO and NLO accuracy, respectively. We consider both the cases with and without b-tagging. Numerical results are presented for parameters relevant for experiments at the LHC.
We report the results of a next-to-leading order event generator of purely gluonic jet production. This calculation is the first step in the construction of a full next-to-leading order calculation of three jet production at hadron colliders. Several jet-algorithms commonly used in experiments are implemented and their numerical stability is investigated.
The next-to-leading corrections to the jet vertex which is relevant for the Mueller-Navelet jets production in hadronic collisions and for the forward jet cross section in lepton-hadron collisions are presented in the context of a k_t factorizazion formula which resums the leading and next-to-leading logarithms of the energy.
We report on QCD radiative corrections to the processes p pbar --> W + 2 jets and p pbar --> Z + 2 jets at the Tevatron. These processes are included in the Monte Carlo program MCFM, which allows the calculation of any infra-red finite variable at next-to-leading order. Due to a better theoretical description of jets at next-to-leading order, some distributions exhibit significant corrections. As expected, the unphysical dependence of theoretical predictions upon the renormalization and factorization scales is greatly reduced compared to leading order. As an example of the predictions that may…
We present a new QCD event generator for hadron collider which can calculate one-, two- and three-jet cross sections at next-to-leading order accuracy. In this letter we study the transverse energy spectrum of three-jet hadronic events using the kT algorithm. We show that the next-to-leading order correction significantly reduces the renormalization and factorization scale dependence of the three-jet cross section.
We present a new subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-leading order accuracy in perturbative QCD. The new scheme is motivated by problems emerging in extending the subtraction scheme to the next-to-next-to-leading order. The new scheme is tested by comparing predictions for three-jet event-shape distributions to those obtained by the standard program EVENT.
I present results of a next-to-leading order calculation of three jet production at hadron colliders. This calculation will have many applications. In addition to computing three-jet observables (spectra, mass distributions), this calculation permits the first next-to-leading order studies (at hadron colliders) of jet and event shape variables.
We present results of a next-to-leading order calculation of three jet production at hadron colliders. This calculation will have many applications. In addition to computing such three-jet observables as spectra, mass distributions, this calculation permits the first next-to-leading order studies at hadron colliders of jet and event shape variables.
We report preliminary results for a next-to-leading order event generator for hadronic three jet production. We demonstrate the stability of the calculation and present preliminary results for the jet transverse energy spectra. This is the first calculation of three jet production at this order to include all parton sub-processes.
We compute the next-to-leading order (NLO) QCD corrections to the gluon-fusion subprocess of diphoton-plus-jet production at the LHC. We compute fully differential distributions by combining two-loop virtual corrections with one-loop real radiation using antenna subtraction to cancel infrared divergences. We observe significant corrections at NLO which demonstrate the importance of combining these corrections with the quark-induced diphoton-plus-jet channel at next-to-next-to-leading order (NNLO).
Jet production cross-sections in polarized proton-proton and electron-proton collisions are studied to next-to-leading order accuracy. Phenomenological results are presented for RHIC and HERA kinematics.
We discuss a calculation of the next-to-leading order QCD corrections to the process $e^+e^-\to 3$ jets with massive quarks, and show numerical results for the three jet fraction and the differential two jet rate.
The $N$-jettiness subtraction has proven to be an efficient method to perform differential QCD next-to-next-to-leading order (NNLO) calculations in the last few years. One important ingredient of this method is the NNLO soft function. We calculate this soft function for one massive colored particle production at hadron colliders. We select the color octet and color triplet cases to present the final results. We also discuss its application in NLO and NNLO differential calculations.
The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The longitudinally-invariant $k_\perp$ jet-clustering algorithm is used. The important property of reduced renormalization and factorization scale dependence of the next-to-leading order physical cross section as compared to the Born cross section is demonstrated.
We present in detail a calculation of the next-to-leading order QCD corrections to the process $e^+e^-\to 3$ jets with massive quarks. To isolate the soft and collinear divergencies of the four parton matrix elements, we modify the phase space slicing method to account for masses. Our computation allows for the prediction of oriented three jet events involving heavy quarks, both on and off the Z resonance, and of any event shape variable which is dominated by three jet configurations. We show next-to-leading order results for the three jet fraction, the differential two jet rate, and for the t…
The reaction $e^+e^-$ annihilation into three jets was recently computed for massive quarks at next-to-leading order in perturbative QCD. We discuss some results of our calculation for b jets produced at the Z resonance.
We compute the two-loop heavy quark jet-function in the heavy quark limit. This is one of the key ingredients in next-to-next-to-leading order (NNLO) and next-to-next-to-leading-log order (NNLL) computations of the invariant mass distribution of top-jets at a future e+e- collider. The shape of the top invariant mass distribution is affected by large logs which we compute at NNLL order. Exploiting the non-abelian exponentiation theorem, a definition of the top jet-mass is given which is transitive and whose renormalization group evolution is determined by the cusp-anomalous dimension to all ord…
We present a next-to-leading order QCD calculation for the single-inclusive production of collimated jets at hadron colliders, when the jet is defined by maximizing a suitable jet function that depends on the momenta of final-state particles in the event. A jet algorithm of this type was initially proposed by Georgi and subsequently further developed into the class of "$J_{E_T}$ algorithms". Our calculation establishes the infrared safety of the algorithms at this perturbative order. We derive analytical results for the relevant partonic cross sections. We discuss similarities and differences …
I present results from a next-to-leading order event generator of purely gluonic jet production. This calculation is the first step in the construction of a full next-to-leading order calculation of three jet production at hadron colliders. Several jet algorithms commonly used in experiments are implemented and their numerical stability is investigated. A numerical instability is found in the iterative cone algorithm which makes it inappropriate for use in fixed order calculations beyond leading order.
We compute production rates for two, three, four and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order (NNLO) in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order (N$^3$LO). Our results yield an improved perturbative description of the dependence of jet multiplicity on the jet resolution parameter, $\ycut$, particularly at small values of $\ycut$.
We present the first next-to-next-to-leading logarithmic resummation for the two-jet rate in $e^+e^-$ annihilation in the Durham and Cambridge algorithms. The results are obtained by extending the ARES method to observables involving any global, recursively infrared and collinear safe jet algorithm in e^+e^- collisions. As opposed to other methods, this approach does not require a factorization theorem for the observables. We present predictions matched to next-to-next-to-leading order, and a comparison to LEP data.
We present the perturbative prediction for three-jet production cross section in DIS at the NLO accuracy. We study the dependence on the renormalization and factorization scales of exclusive three-jet cross section. The perturbative prediction for the three-jet differential distribution as a function of the momentum transfer is compared to the corresponding data obtained by the H1 collaboration at HERA.
We consider within QCD collinear factorization the process $p+p\to {\rm jet} +{\rm jet} +X$, where two forward high-$p_T$ jets are produced with a large separation in rapidity $Δy$ (Mueller-Navelet jets). In this case the (calculable) hard part of the reaction receives large higher-order corrections $\sim α^n_s (Δy)^n$, which can be accounted for in the BFKL approach with next-to-leading logarithmic accuracy, including contributions $\sim α^n_s (Δy)^{n-1}$. We calculate several observables related with this process, using the next-to-leading order jet vertices, recently calculated in the appro…
Top-quark pair production with an additional jet is an important signal and background process at the LHC. We present the next-to-leading order QCD calculation for this process and show results for integrated as well as differential cross sections.
We calculate the cross section for $e^+ e^-$ annihilation into three jets for massive quarks at next-to-leading order in perturbative QCD, both on and off the $Z$ resonance. Our computation allows the implementation of any jet clustering algorithm. We give results for the three-jet cross section involving $b$ quarks for the JADE and Durham algorithm at c.m. energies $\sqrt s = m_Z$. We also discuss a three-jet observable that is sensitive to the mass of the $b$ quark.
A new next-to-leading order Monte Carlo program for the calculation of jet cross sections in photoproduction is described. The contributions from both resolved and direct components are included to O(αα_s^2). Properties of the predictions for various inclusive jet and dijet observables are discussed and comparisons with HERA data are presented.
We have calculated inclusive two-jet cross sections in next-to-leading order QCD for low Q^2 ep collisions superimposing direct and resolved contributions. Infrared and collinear singularities in the virtual and real contributions are cancelled with the phase space slicing method. Various inclusive two-jet distributions have been computed. The results are compared with recent data from the ZEUS collaboration at HERA.
We present phenomenological results for the production of a Higgs boson in association with two jets at the LHC. The calculation is performed in the limit of large top mass and is accurate to next-to-leading order in the strong coupling, i.e. ${\cal O}(α_s^6)$
We report on a method for matching the next-to-leading order calculation of QCD jet production in e+e- annihilation with a Monte Carlo parton shower event generator (MC) to produce realistic final states. The final result is accurate to next-to-leading order (NLO) for infrared-safe one-scale quantities, such as the Durham 3-jet fraction y_3, and agrees well with parton shower results for multi-scale quantities, such as the jet mass distribution in 3-jet events. For our numerical results, the NLO calculation is matched to the event generator Pythia, though the method is more general. We compare…
The production of four jets in electron-positron annihilation allows for measuring the strong coupling and the underlying group structure of the strong interaction simultaneously. This requires next-to-leading order perturbative prediction for four-jet observables. In this paper we describe the theoretical formalism of such a calculation with sufficient details. We use the dipole method to construct a Monte Carlo program that can be used for calculating any four-jet observable at the NLO accuracy. As new results, we present the NLO prediction for the thrust minor, y_4 and C parameter (at C > 0…
We present the calculation of the next-to-next-to-leading order (NNLO) zero-jettiness beam and soft functions, up to the second order in the expansion in the dimensional regularization parameter $ε$. These higher order terms are needed for the computation of the next-to-next-to-next-to-leading order (N$^3$LO) zero-jettiness soft and beam functions. As a byproduct, we confirm the $O(ε^0)$ results for NNLO beam and soft functions available in the literature.
Based upon a next-to-leading order perturbative calculation of the four-jet production rate in electron-positron annihilation and assuming 8 % for the theoretical error emerging from hadronization effects in the $0.002\le \ycut \le 0.004$ range for the Durham clustering algorithm, we exclude the existence of the light gluinos at the 95 % confidence level.
In this thesis we describe the calculation of the process e+ e- --> Z/gamma -> Q Qbar + X, where Q is a heavy quark, X is anything else at order alpha_s^2.
We determine dominant next-to-next-to-leading order QCD corrections to single-inclusive jet production at the LHC and Tevatron, using the established threshold resummation framework. In contrast to previous literature on this topic, our study incorporates all of the following features: (1) It properly accounts for the way a jet is defined in experiment and treated in available full next-to-leading order calculations, (2) It includes the three leading classes of logarithmic terms in the perturbative expansion, and (3) It is adapted to the full kinematics in jet transverse momentum and rapidity …
I present a general purpose Monte Carlo program for calculating the next-to-leading order corrections to arbitrary four-jet quantities in electron-positron annihilation. In the current version of the program, some subleading in color terms are neglected. As an example, I calculate the four-jet rate in the Durham scheme as well as the Bengtsson-Zerwas angular distribution at $O(α_s^3)$ and compare the results to existing data.
We calculate the rate for $e^+e^-$ annihilation into four jets at next-to-leading order in perturbative QCD, but omitting terms that are suppressed by one or more powers of $1/\Nc^2$, where $\Nc$ is the number of colors. The $\cO(α_s^3)$ corrections depend strongly on the jet resolution parameter $\ycut$ and on the clustering and recombination schemes, and they substantially improve the agreement between theory and data.
We have calculated inclusive two-jet production in photon-photon collisions superimposing direct, single-resolved and double-resolved cross sections for center-of-mass energies of TRISTAN and LEP1.5. All three contributions are calculated up to next-to-leading order. The results are compared with recent experimental data. Three NLO sets of parton distributions of the photon are tested.
In the cross section for single-inclusive jet production in electron-nucleon collisions, the distribution of a quark in an electron appears at next-to-next-to-leading order. The numerical calculations in Ref. [1] were carried out using a perturbative approximation for the distribution of a quark in an electron. We point out that that distribution receives nonperturbative QCD contributions that invalidate the perturbative approximation. Those nonperturbative effects enter into cross sections for hard-scattering processes through resolved-electron contributions and can be taken into account by d…
A next-to-leading order QCD calculation for single-inclusive jet photoproduction in unpolarized and longitudinally polarized lepton-hadron collisions is presented which consistently includes ``direct'' and ``resolved'' photon contributions. The computation is performed within the ``small-cone approximation'' in a largely analytical form. Phenomenological aspects of jet production at future ep colliders such as the CERN-LHeC and the polarized BNL-eRHIC are discussed, placing particular emphasis on the perturbative stability of the predictions and the possibility to constrain the parton content …
A complete next-to-leading order QCD calculation of deep inelastic electron-photon scattering including direct and resolved real photon components is presented. Soft and collinear singularities are extracted using the phase space slicing method. Application of the results for the prediction of single- and dijet cross sections at the LEP e+e- collider are presented, using the Snowmass jet definition. The dependence of the cross sections on the transverse momentum and on the rapidities of the jets are discussed.
We consider within QCD collinear factorization the process p+p to jet + jet +X, where two forward high-$p_T$ jets are produced with a large separation in rapidity $Δy$ (Mueller-Navelet jets). In this case the (calculable) hard part of the reaction receives large higher-order corrections $\sim α^n_s (Δy)^n$, which can be accounted for in the BFKL approach. In particular, we calculate in the next-to-leading order the impact factor (vertex) for the production of a forward high-$p_T$ jet, in the approximation of small aperture of the jet cone in the pseudorapidity-azimuthal angle plane. The final …
One- and two-jet inclusive quantities in hadron collisions have already been calculated to next-to-leading order accuracy, using both the subtraction and the cone method. Since the one-loop corrections have recently been obtained for all five-parton amplitudes, three-jet inclusive quantities can also be predicted to next-to-leading order. The subtraction method presented in the literature is based on a systematic use of boost-invariant kinematical variables, and therefore its application to three-jet production is quite cumbersome. In this paper we re-analyze the subtraction method and point o…
We present the next-to-leading order calculation of two four-jet event shape variables, the D parameter and acoplanarity differential distributions. We find large, more than 100% radiative corrections. The theoretical prediction for the D parameter is compared to L3 data obtained at the Z peak and corrected to hadron level.
We present a next-to-next-to-leading order (NNLO) QCD calculation of the bottom-induced contributions to the production of a Higgs boson plus a jet, i.e. the process $p p \rightarrow H +j$ to $\mathcal{O}(y_b^2 α_s^3)$. We work in the five-flavor scheme (5FS) in which the bottom quark mass is retained only in the coupling to the Higgs boson. Our calculation uses $N$-jettiness slicing to regulate infrared divergences, allowing for fully-differential predictions for collider observables. After extensively validating the methodology, we present results for the 13 TeV LHC. Our NNLO predictions sho…
In this talk we discuss the implementation of the full next-to-leading order QCD corrections to electroweak Higgs boson plus three jet production at the LHC within the Matchbox framework of the Herwig++ event generator. We also present numerical results for integrated cross sections and kinematic distributions.
The cross section for Higgs+jet production in bottom quark annihilation is calculated through NLO QCD. The five-flavour scheme is used to derive this contribution to the Higgs+jet production cross section which becomes numerically important in the MSSM for large values of tan(beta). We present numerical results for a proton collider with 14 TeV center-of-mass energy. The NLO matrix elements for d(sigma)/d(pT) are then combined with the total inclusive cross section in order to derive the integrated cross section with a maximum cut on pT at next-to-next-to-leading order.
We present the first complete calculation of Z-boson production in association with a jet in hadronic collisions through next-to-next-to-leading order in perturbative QCD. Our computation uses the recently-proposed N-jettiness subtraction scheme to regulate the infrared divergences that appear in the real-emission contributions. We present phenomenological results for 13 TeV proton-proton collisions with fully realistic fiducial cuts on the final-state particles. The remaining theoretical uncertainties after the inclusion of our calculations are at the percent-level, making the Z+jet channel r…
