Dijet Differential Cross Sections Research Articles

NNLO QCD corrections in full colour for jet production observables at the LHC

Calculations for processes involving a high multiplicity of coloured particles often employ a leading colour approximation, where only the leading terms in the expansion of the number of colours Nc and the number of flavours nf are retained. This approximation of the full colour result is motivated by the 1/ {N}_c^2 suppression of the first subleading terms and by the increasing complexity of including subleading colour contributions to the calculation. In this work, we present the calculations using the antenna subtraction method in the NNLOjet framework for the NNLO QCD corrections at full colour for several jet observables at the LHC. The single jet inclusive cross section is calculated doubly differential in transverse momentum and absolute rapidity and compared with the CMS measurement at 13 TeV. A calculation for dijet production doubly differential in dijet mass and rapidity difference is also performed and compared with the ATLAS 7 TeV data. Lastly, a triply differential dijet cross section in average transverse momentum, rapidity separation and dijet system boost is calculated and compared with the CMS 8 TeV data. The impact of the subleading colour contributions to the leading colour approximation is assessed in detail for all three types of observables and as a function of the jet cone size. The subleading colour contributions play a potentially sizable role in the description of the triply differential distributions, which probe kinematical configurations that are not easily accessed by any of the other observables.

Triple Differential Dijet Cross Section at the LHC.

The measurement of the triple-differential dijet production cross section as a function of the average transverse momentum p_{T,avg}, half the rapidity separation y^{*}, and the boost y_{b} of the two leading jets in the event enables a kinematical scan of the underlying parton momentum distributions. We compute for the first time the second-order perturbative QCD corrections to this triple-differential dijet cross section, at leading color in all partonic channels, thereby enabling precision studies with LHC dijet data. A detailed comparison with experimental CMS 8TeV data is performed, demonstrating how the shape of this differential cross section probes the parton densities in different kinematical ranges.

Mass limits for the chiral color symmetry G′-boson from LHC dijet data

The contributions of [Formula: see text]-boson predicted by the chiral color symmetry of quarks to the differential dijet cross-sections in pp-collisions at the large hadron collider (LHC) are calculated and analyzed in dependence on two free parameters of the model, the [Formula: see text] mass [Formula: see text] and mixing angle [Formula: see text]. The exclusion and consistency [Formula: see text] regions imposed by the ATLAS and CMS data on dijet cross-sections are found. Using the CT10 (MSTW2008) parton distribution function (PDF) set we show that the [Formula: see text]-boson for [Formula: see text], i.e. the axigluon, with the masses [Formula: see text] TeV and [Formula: see text] TeV is excluded at the probability level of 95% by the ATLAS and CMS dijet data, respectively. For the other values of [Formula: see text] the exclusion limits are more stringent. The [Formula: see text] regions consistent with these data at CL = 68% and CL = 90% are also found.

Jet shapes in dijet events at the LHC in SCET

We consider the class of jet shapes known as angularities in dijet production at hadron colliders. These angularities are modified from the original definitions in e+e- collisions to be boost invariant along the beam axis. These shapes apply to the constituents of jets defined with respect to either k_T-type (anti-k_T, C/A, and k_T) algorithms and cone-type algorithms. We present an SCET factorization formula and calculate the ingredients needed to achieve next-to-leading-log (NLL) accuracy in kinematic regions where non-global logarithms are not large. The factorization formula involves previously unstudied "unmeasured beam functions," which are present for finite rapidity cuts around the beams. We derive relations between the jet functions and the shape-dependent part of the soft function that appear in the factorized cross section and those previously calculated for e+e- collisions, and present the calculation of the non-trivial, color-connected part of the soft-function to O(\alpha_s). This latter part of the soft function is universal in the sense that it applies to any experimental setup with an out-of-jet p_T veto and rapidity cuts together with two tagged jets and it is independent of the choice of jet (sub-)structure measurement. In addition, we implement the recently introduced soft-collinear refactorization to resum logarithms of the jet size, valid in the region of non-enhanced non-global logarithm effects. While our results are valid for all 2 \to 2 channels, we compute explicitly for the qq' \to qq' channel the color-flow matrices and plot the NLL resummed differential dijet cross section as an explicit example, which shows that the normalization and scale uncertainty is reduced when the soft function is refactorized. For this channel, we also plot the jet size R dependence, the p_T^{\rm cut} dependence, and the dependence on the angularity parameter a.

Measurements of jet vetoes and azimuthal decorrelations in dijet events produced in [Formula: see text] collisions at [Formula: see text] using the ATLAS detector.

Additional jet activity in dijet events is measured using {pp} collisions at ATLAS at a centre-of-mass energy of 7,mathrm{TeV}, for jets reconstructed using the {mathrm{anti}hbox {-}{k_t}} algorithm with radius parameter {R=0.6}. This is done using variables such as the fraction of dijet events without an additional jet in the rapidity interval bounded by the dijet subsystem and correlations between the azimuthal angles of the dijet s. They are presented, both with and without a veto on additional jet activity in the rapidity interval, as a function of the scalar average of the transverse momenta of the dijet s and of the rapidity interval size. The double differential dijet cross section is also measured as a function of the interval size and the azimuthal angle between the dijet s. These variables probe differences in the approach to resummation of large logarithms when performing QCD calculations. The data are compared to powheg, interfaced to the pythia 8 and herwig parton shower generators, as well as to hej with and without interfacing it to the ariadne parton shower generator. None of the theoretical predictions agree with the data across the full phase-space considered; however, powheg+pythia 8 and hej+ariadne are found to provide the best agreement with the data. These measurements use the full data sample collected with the ATLAS detector in 7,mathrm{TeV} {pp} collisions at the LHC and correspond to integrated luminosities of 36.1,mathrm{pb}^{-1} and 4.5,mathrm{fb}^{-1} for data collected during 2010 and 2011, respectively.

Di-jet production in γ γ collisions at LEP2

The production of two high-p T jets in the interactions of quasi-real photons in e + e − collisions at $\sqrt{s_{ee}}$ from 189 GeV to 209 GeV is studied with data corresponding to an integrated e + e − luminosity of 550 pb−1. The jets reconstructed by the k ⊥ -cluster algorithm are defined within the pseudo-rapidity range −1<η<1 and with jet transverse momentum, p T , above 3 GeV/c. The differential di-jet cross-section is measured as a function of the mean transverse momentum $\overline{p_{T}}$ of the jets and is compared to perturbative QCD calculations.

Dijet cross sections and parton densities in diffractive DIS at HERA

Differential dijet cross sections in diffractive deep-inelastic scattering are measured with the H1 detector at HERA using an integrated luminosity of 51.5 pb-1. The selected events are of the type ep --> eXY, where the system X contains at least two jets and is well separated in rapidity from the low mass proton dissociation system Y. The dijet data are compared with QCD predictions at next-to-leading order based on diffractive parton distribution functions previously extracted from measurements of inclusive diffractive deep-inelastic scattering. The prediction describes the dijet data well at low and intermediate zpom (the fraction of the momentum of the diffractive exchange carried by the parton entering the hard interaction) where the gluon density is well determined from the inclusive diffractive data, supporting QCD factorisation. A new set of diffractive parton distribution functions is obtained through a simultaneous fit to the diffractive inclusive and dijet cross sections. This allows for a precise determination of both the diffractive quark and gluon distributions in the range 0.05<zpom<0.9. In particular, the precision on the gluon density at high momentum fractions is improved compared to previous extractions.

Tests of QCD factorisation in the diffractive production of dijets in deep-inelastic scattering and photoproduction at HERA

Measurements are presented of differential dijet cross sections in diffractive photoproduction (Q^2<0.01 GeV^2) and deep-inelastic scattering processes (DIS, 4<Q^2<80 GeV^2). The event topology is given by ep-> e X Y, in which the system X, containing at least two jets, is separated from a leading low-mass proton remnant system Y by a large rapidity gap. The dijet cross sections are compared with NLO QCD predictions based on diffractive parton densities previously obtained from a QCD analysis of inclusive diffractive DIS cross sections by H1. In DIS, the dijet data are well described, supporting the validity of QCD factorisation. The diffractive DIS dijet data are more sensitive to the diffractive gluon density at high fractional parton momentum than the measurements of inclusive diffractive DIS. In photoproduction, the predicted dijet cross section has to be multiplied by a factor of approximately 0.5 for both direct and resolved photon interactions to describe the measurements. The ratio of measured dijet cross section to NLO prediction in photoproduction is a factor 0.5+-0.1 smaller than the same ratio in DIS. This suppression is the first clear observation of QCD hard scattering factorisation breaking at HERA. The measurements are also compared to the two soft colour neutralisation models SCI and GAL. The SCI model describes diffractive dijet production in DIS but not in photoproduction. The GAL model fails in both kinematic regions.

Inclusive-jet and dijet cross sections in deep inelastic scattering at HERA

Inclusive-jet and dijet differential cross sections have been measured in neutral current deep inelastic ep scattering for exchanged boson virtualities Q 2 > 125 GeV 2 with the ZEUS detector at HERA using an integrated luminosity of 82 pb −1. Jets were identified in the Breit frame using the k T cluster algorithm. Jet cross sections are presented as functions of several kinematic and jet variables. The results are also presented in different regions of Q 2 . Next-to-leading-order QCD calculations describe the measurements well. Regions of phase space where the theoretical uncertainties are small have been identified. Measurements in these regions have the potential to constrain the gluon density in the proton when used as inputs to global fits of the proton parton distribution functions.

Measurement of charm and beauty dijet cross sections in photoproduction at HERA using the H1 vertex detector

A measurement of charm and beauty dijet photoproduction cross sections at the ep collider HERA is presented. Events are selected with two or more jets of transverse momentum $p_t^{jet}_{1(2)}>11(8)$ GeV in the central range of pseudo-rapidity $-0.9<\eta^{jet}_{1(2)}<1.3$. The fractions of events containing charm and beauty quarks are determined using a method based on the impact parameter, in the transverse plane, of tracks to the primary vertex, as measured by the H1 central vertex detector. Differential dijet cross sections for charm and beauty, and their relative contributions to the flavour inclusive dijet photoproduction cross section, are measured as a function of the transverse momentum of the leading jet, the average pseudo-rapidity of the two jets and the observable $x_{\gamma}^{obs}$. Taking into account the theoretical uncertainties, the charm cross sections are consistent with a QCD calculation in next-to-leading order, while the predicted cross sections for beauty production are somewhat lower than the measurement.

Photoproduction of dijets with high transverse momenta at HERA

Differential dijet cross sections are measured in photoproduction in the region of photon virtualities Q^2 < 1 GeV^2 with the H1 detector at the HERA ep collider using an integrated luminosity of 66.6 pb^{-1}. Jets are defined with the inclusive k_T algorithm and a minimum transverse momentum of the leading jet of 25 GeV is required. Dijet cross sections are measured in direct and resolved photon enhanced regions separately. Longitudinal proton momentum fractions up to 0.7 are reached. The data compare well with predictions from Monte Carlo event generators based on leading order QCD and parton showers and with next-to-leading order QCD calculations corrected for hadronisation effects.

QCD analysis of dijet production at low Q 2 at HERA

Recent H1 data on triple differential dijet cross sections in $e^\pm p$ interactions in the region of low photon virtualities are shown to be in reasonable agreement with the predictions of the NLO QCD calculations obtained using the program NLOJET++. The implications of this observation for the phenomenological relevance of the concept of resolved virtual photon are discussed.

Genuine twist-3 contributions to the generalized parton distributionsfrom instantons

Triple differential dijet cross sections in e^\pm p interactions are presented in the region of photon virtualities 2<Q^2<80GeV^2, inelasticities 0.1<y<0.85, jet transverse energies E_T1>7GeV, E_T2>5GeV, and pseudorapidities -2.5 < eta_1^*, eta_2^* <0. The measurements are made in the gamma^* p centre-of-mass frame, using an integrated luminosity of 57pb^-1. The data are compared with NLO QCD calculations and LO Monte Carlo programs with and without a resolved virtual photon contribution. NLO QCD calculations fail to describe the region of low Q^2 and low jet transverse energies, in contrast to a LO Monte Carlo generator which includes direct and resolved photon interactions with both transversely and longitudinally polarised photons. Initial and final state parton showers are tested as a mechanism for including higher order QCD effects in low E_T jet production.

Measurement of dijet production at low Q 2 at HERA

Triple differential dijet cross sections in e^\pm p interactions are presented in the region of photon virtualities 25GeV, and pseudorapidities -2.5 < eta_1^*, eta_2^* <0. The measurements are made in the gamma^* p centre-of-mass frame, using an integrated luminosity of 57pb^-1. The data are compared with NLO QCD calculations and LO Monte Carlo programs with and without a resolved virtual photon contribution. NLO QCD calculations fail to describe the region of low Q^2 and low jet transverse energies, in contrast to a LO Monte Carlo generator which includes direct and resolved photon interactions with both transversely and longitudinally polarised photons. Initial and final state parton showers are tested as a mechanism for including higher order QCD effects in low E_T jet production.

Jet production in two-photon collisions at LEP

Jet and di-jet production are studied in collisions of quasi-real photons collected during the LEP2 program at e+e- center-of-mass energies from 189 to 209 GeV. OPAL reports good agreement of NLO perturbative QCD with the measured differential di-jet cross sections, which reach a mean transverse energy of the di-jet system of 25 GeV. L3, on the other hand, finds drastic disagreement of the same calculation with single jet production for transverse jet momenta larger than about 25 GeV.

Diffractive charm and jet production at HERA

A new high precision inclusive measurement of the diffractive production of D ∗±(2010) mesons in deep inelastic scattering (DIS) in the kinematic region Q 2>1.5 GeV 2, 0.02< y <0.7, χ IP < 0.035 as well as differential dijet cross sections in low-| t| diffractive photoproduction (PHP) process in the kinematic region Q 2 <0.01 GeV 2, 165< W <240 GeV 2, χ IP < 0.03 are presented. Diffractive parton densities extracted using a NLO DGLAP QCD fit are used for comparisons with diffractive DIS and PHP dijet and open charm cross sections at HERA and the Tevatron, thus testing the factorization properties of hard diffraction.

High-mass dijet cross sections in photoproduction at HERA

Dijet differential cross sections for the reaction e+p -> e+ + jet + jet + X in the photoproduction regime have been measured with the ZEUS detector at HERA using an integrated luminosity of 42.7 pb**{-1}. The cross sections are given for photon-proton centre-of-mass energies in the range 134< W <277 GeV. The differential cross sections as a function of the dijet mass, Mjj, and of the dijet angular variables have been measured for 47 < Mjj < 160 GeV and compared to next-to-leading-order QCD calculations. The dijet events in the region 75< Mjj < 100 GeV have been used to derive a 95% C.L. upper limit on the cross section for Z0 photoproduction of sigma(e+ p -> e+ Z0 X} < 5.9 pb. Upper limits on the photoproduction of new heavy resonances decaying into two jets are also presented for masses in the range between 60 GeV and 155 GeV.

Measurement of dijet production in neutral current deep inelastic scattering at high Q2 and determination of αs

Dijet production has been studied in neutral current deep inelastic e + p scattering for 470<Q 2<20 000 GeV 2 with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb −1. Dijet differential cross sections are presented in a kinematic region where both theoretical and experimental uncertainties are small. Next-to-leading-order (NLO) QCD calculations describe the measured differential cross sections well. A QCD analysis of the measured dijet fraction as a function of Q 2 allows both a precise determination of α s ( M z ) and a test of the energy-scale dependence of the strong coupling constant. A detailed analysis provides an improved estimate of the uncertainties of the NLO QCD cross sections arising from the parton distribution functions of the proton. The value of α s ( M Z ), as determined from the QCD fit, is α s ( M Z )=0.1166±0.0019(stat.) +0.0024 −0.0033(exp.) +0.0057 −0.0044(th.).

Measurement of di-jet cross-sections in photoproduction and photon structure

The production of hard di-jet events in photoproduction at HERA is dominated by resolved photon processes in which a parton in the photon with momentum fraction x γ is scattered from a parton in the proton. These processes are sensitive to the quark and gluon content of the photon. The differential di-jet cross-section d σ/dlog( x γ ) is presented here, measured in tagged photoproduction at HERA using data taken with the H1 detector, corresponding to an integrated luminosity of 7.2 pb −1. Using a restricted data sample at high transverse jet energy, E T,jet>6 GeV, the effective parton density f γ ,eff (x γ)= q(x γ)+ q ̄ (x γ)+9/4 g(x γ) in the photon in leading order QCD is measured down to x γ = 0.05 from which the gluon density in the photon is derived.

Measurement of differential cross sections for Dijet production in neutral current DIS at high Q2 and determination of αs

Dijet production has been studied in neutral current Deep Inelastic ep Scattering for 470 < Q 2 < 20000 GeV 2 with the ZEUS detector at HERA using 38 pb −1. The jet search is performed in the Breit frame using the longitudinally invariant K ⊥-luster algorithm. Dijet differential cross sections and rates have been measured in a kinematic region where both theoretical and experimental uncertainties are small. NLO QCD calculations describe in shape and magnitude the measured differential cross sections. A QCD fit to the dijet rate as a function of Q 2 allows a precise determination of the strong coupling constant.