P. Aurenche, M. Fontannaz
The reaction e + p ---> photon + jet + X is studied in QCD at the next-to-leading order. Previous studies on inclusive distributions showed a good agreement with ZEUS data. To obtain a finer understanding of the dynamics of the reaction, several correlation functions are evaluated for ZEUS kinematics.
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We give an overview of jet physics in deeply inelastic scattering at HERA. The problem of jet definitions, the scale dependence of jet cross sections and some applications are discussed. (Talk presented at the Workshop on Deeply Inelastic Scattering and QCD, Paris, April 1995. To appear in the proceedings.)
The recent results of Forshaw and Sabio Vera on small-$x$ jet rates to order $α_s^3$ are extended to all orders, for any number of jets. A simple generating function is obtained.
We use the BFKL equation to calculate the rate of deep inelastic scattering events containing two forward jets (adjacent to the proton remnants) at HERA. We compare the production of two forward jets with that of only one forward jet (the "Mueller" process). We obtain a stable prediction for this two to one jet ratio, which may serve as a measure of the BFKL vertex function.
We study the azimuthal angle decorrelation of forward jets in Deep Inelastic Scattering. We make predictions for this observable at HERA describing the high energy limit of the relevant scattering amplitudes with quasi-multi-Regge kinematics together with a collinearly improved evolution kernel for multiparton emissions.
For theoretically consistent determination of $α_s$ from jet rates in deep inelastic scattering the dependence on $α_s$ of parton distribution functions is in principle as important as that of hard scattering cross--sections. For the kinematical region accessible at HERA we investigate in detail numerical importance of these two sources of the $α_s$ dependence of jet rates.
We present the calculation for single-inclusive jet production in (longitudinally) polarized deep-inelastic lepton-nucleon scattering at next-to-next-to leading order (NNLO) accuracy, based on the Projection-to-Born method. As a necessary ingredient to achieve the NNLO results, we also introduce the next-to-leading-order (NLO) calculation for the production of di-jets in polarized DIS. Our di-jet calculation is based on an extension of the dipole subtraction method to account for polarized initial-state partons. We analyze the phenomenological consequences of higher order QCD corrections for t…
For theoretically consistent determination of $α_s$ from jet rates in deep inelastic scattering the dependence on $α_s$ of parton distribution functions is in principle as important as that of hard scattering cross-sections. For the kinematical region accessible at HERA we investigate in detail numerical importance of these two sources of the $α_s$ dependence of jet rates.
We calculate the O(α_s) corrections to the production of a hard and isolated photon accompanied by one or two jets in deep inelastic lepton nucleon scattering at HERA. Numerical results are presented and the potential of this process for studies of parton distribution functions is discussed.
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.
The production of jets in charged-current deep-inelastic scattering (CC DIS) probes simultaneously the strong and the electroweak sectors of the Standard Model; its measurement provides important information on the quark flavour structure of the proton. We compute third-order (N3LO) perturbative QCD corrections to this process, fully differential in the jet and lepton kinematics. We observe a substantial reduction in the theory uncertainty, to sub-percent level throughout the relevant kinematical range, thus enabling precision phenomenology with jet observables.
The main experimental results on jet production at HERA are reviewed. A study of jet shapes shows that the internal structure of jets is well understood. The potential to accurately determine the strong coupling constant using jet rates is discussed. First attempts to extract the gluon density in next-to-leading order are presented. Although fixed order perturbative QCD is able to describe the shape of most variables associated to the hard subprocess leading to jets, it does not reproduce the absolute dijet rate over a large phase space region.
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.
The production of jets in charged current deep inelastic scattering (CC DIS) constitutes a class of observables that can be used to simultaneously test perturbative predictions for the strong and the electroweak sectors of the Standard Model. We compute both single jet and di-jet production in CC DIS for the first time at next-to-next-to-leading order (NNLO) in the strong coupling. Our computation is fully differential in the jet and lepton kinematics, and we observe a substantial reduction of scale variation uncertainties in the NNLO predictions compared to next-to-leading order (NLO). Our ca…
We argue that the production of forward jets in polarised deep inelastic scattering can be a useful tool for probing the double $ln^2(1/x)$ resummation effects which control the polarised deep inelastic scattering for small values of the Bjorken parameter $x$. We solve the corresponding integral equations generating the double $ln^2(1/x)$ resummation and calculate the differential structure function describing the forward jet production in the small $x$ regime which can possibly be probed by the polarised HERA measurements. We show that these structure functions should exhibit the characterist…
Hadronic jets in deeply inelastic electron-proton collisions are produced by the scattering of a parton from the proton with the virtual gauge boson mediating the interaction. The HERA experiments have performed precision measurements of inclusive single jet production and di-jet production in the Breit frame, which provide important constraints on the strong coupling constant and on parton distributions in the proton. We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to these processes, and assess their size and impact. A detailed comparison with data fro…
We compare different next-to-leading order calculations of jet cross sections in deep-inelastic scattering as implemented in the programs DISASTER++, DISENT, JETVIP and MEPJET. In all phase space regions under study DISENT and DISASTER++ agree better than 2%. MEPJET shows systematic deviations of being typically 5-8% lower than the other programs. The JETVIP results show a significant dependence on the phase space slicing parameter $y_{\rm cut}$. In the cases where the $y_{\rm cut}$ dependence within $10^{-4} \le y_{\rm cut} \le 10^{-3}$ is smaller than 3% the JETVIP results are often comparab…
We predict the rate of deep inelastic scattering (DIS) events containing an identified forward $π^0$ that is expected in the experiments at the HERA electron-proton collider, in order to see if this process can be used as an indicator of the underlying small $x$ dynamics. We determine the background due to deep inelastic events containing forward photons which are fragments of the forward jet. We compare the DIS + $π^0$ cross section with that of the DIS + parent jet process.
We present a new parton level Monte Carlo program for the calculation of jet cross sections in Deep Inelastic Scattering based on Born and next-to-leading order matrix elements. Using a class of invariant jet definition schemes, the program allows for the calculation of differential distributions of jet cross sections in the basic kinematical variables (like s, x, y, W^2, Q^2...) as well as for total jet cross sections. Various kinematical cuts can be chosen from an input file.
We have implemented a systematic procedure for combining parton shower algorithms with next-to-leading order QCD calculations for the case of jet production in deep-inelastic electron-proton scattering. Using this method we have computed inclusive jet cross sections and jet shapes for the case of single-jet production and compared them to data from the ZEUS collaboration at HERA. We found good agreement between the data and our calculations, both for the jet shapes and the inclusive spectra.
Multi-Jet Merging in Deep Inelastic Scattering with Pythia
本研究在Pythia的Vincia部分子簇射中实现多喷注合并，以改进深度非弹性散射建模，结合不同多重数样本无重复计数，对比HERA实验数据证实其能提升喷注建模效果，尤其低虚度事件。
We perform the calculation of the fully differential single-jet production in longitudinally polarized deep inelastic scattering (DIS) at the next-to-next-to-leading order (NNLO) accuracy, featuring both neutral current and charged current processes. The computation is done with the projection-to-Born method (P2B), using the next-to-leading order (NLO) dijet calculation and the NNLO DIS structure functions as its main ingredients. We also analyze its phenomenological consequences in the kinematics of the future Electron-Ion Collider (EIC).
Jet cross sections in deeply inelastic scattering in the case of transverse photon exchange for the production of (1+1) and (2+1) jets are calculated in next-to-leading order QCD (here the `+1' stands for the target remnant jet, which is included in the jet definition for reasons that will become clear in the main text). The jet definition scheme is based on a modified JADE cluster algorithm. The calculation of the (2+1) jet cross section is described in detail. Results for the virtual corrections as well as for the real initial- and final state corrections are given explicitly. Numerical resu…
Two-jet cross sections in deep inelastic scattering at HERA are calculated in next-to-leading order. The importance of higher order corrections and recombination scheme dependencies is studied for various jetalgorithms. Some implications for the determination of $α_s(μ_R^2)$, the determination of the gluon density and the associated forward jet production in the low $x$ regime at HERA are briefly discussed.
NLO corrections to jet cross sections in DIS at HERA are studied, with particular emphasis on the two jet final state. High jet transverse momenta are a good criterion for the applicability of fixed order perturbation theory. A ``natural'' scale choice is the average $k_T^B$ of the jets in the Breit frame, which suggest analyzing the data in different $<k_T^B>$ intervalls.
The size of non-perturbative corrections to high E_T jet production in deep-inelastic scattering is reviewed. Based on predictions from fragmentation models, hadronization corrections for different jet definitions are compared and the model dependence as well as the dependence on model parameters is investigated. To test whether these hadronization corrections can be applied to next-to-leading order (NLO) calculations, jet properties and topologies in different parton cascade models are compared to those in NLO. The size of the uncertainties in estimating the hadronization corrections is compa…
The contributions to the deep inelastic scattering structure function which arise from emission of zero, one, two or three resolvable gluons and any number of unresolvable ones are computed to order ${\bar α}_{S}^{3}$. Coherence effects are taken into account via angular ordering and are demonstrated to yield (at the leading logarithm level) the identical results to those obtained assuming the multi-Regge kinematics of BFKL.
Multi-Jet Production in Deep Inelastic Scattering with Pythia
本文在 Pythia 8 的 Vincia 部分子簇射中实现深度非弹性散射的多喷注合并，并通过 H1 数据验证其可改善低虚度事例描述并促进喷注截面收敛。
We analyse the dissociation of a photon in diffractive deep inelastic scattering in the kinematic regime where the diffractive mass is much bigger than the photon virtuality. We consider the dominant q\bar{q}g component keeping track of the transverse momentum of the gluon which can be measured as a final-state jet. We show that the diffractive gluon-jet production cross-section is strongly sensitive to unitarity constraints. In particular, in a model with parton saturation, this cross-section is sensitive to the scale at which unitarity effects become important, the saturation scale. We argue…
A QCD analysis of jet production in deep-inelastic scattering is presented. The studies are based on recent measurements of jet cross sections in the H1 experiment at HERA which are directly sensitive to the gluon density in the proton. The inclusion of H1 data on the inclusive deep-inelastic scattering cross section enables us to perform a consistent, simultaneous determination of the quark and gluon densities in the proton. The gluon density has been determined at fairly large values of $0.01 < x < 0.1$ at a scale of the order of the transverse jet energies $μ^2_f = 200\GeV^2$. The result is…
We estimate the cross-section and asymmetry relevant for the production of forward jets in polarised deep inelastic scattering in the region of small values of $x$ which can be probed at possible polarised HERA measurements. The kinematical cuts implemented in our analysis are the same as those which were used in the unpolarised deep inelastic scattering at HERA. The calculations are based on the double ln^2(1/x) resummation which controls the polarised deep inelastic scattering for small values of the Bjorken parameter x. We show that this resummation substantially enhances the corresponding …
The production of a hard and isolated photon accompanied by one or two jets in large-Q2 deep inelastic ep scattering is calculated at next-to-leading order. We include consistently contributions from quark-to-photon fragmentation and study various differential cross sections and their dependence on isolation cut parameters. Numerical results relevant for HERA experiments are presented.
Jet substructure in neutral current deep inelastic e+p scattering at upcoming Electron-Ion Collider
针对未来电子-离子对撞机上的电子-质子中性流深度非弹性散射单喷注事件，用蒙特卡洛生成器模拟数据，研究不同算法与参数下的喷注子结构，并结合HERA数据对比两种聚类算法。
The prospects of a direct extraction of the proton's gluon density in next-to-leading order via jet rates in deeply inelastic scattering are studied. The employed method is based on the Mellin transform, and can be applied, in principle, to all infra-red-safe observables of hadronic final states. We investigate the dependence of the error band on the extracted gluon distribution on the statistical and systematic error of the data.
Recent results for the total and inelastic hadronic cross-sections from LHC experiments are compared with predictions from a single channel PDF driven eikonal mini-jet model and from an empirical model. The role of soft gluon resummation in the infrared region in taming the rise of mini-jets and their contribution to the increase of the total cross-sections at high energies are discussed. Survival probabilities at LHC, whose theoretical estimates range from circa 10 percent to a few per mille, will be estimated in this model and compared with results from QCD inspired models and from multi cha…
We present results from NLO QCD calculations on the production of jets in ep collisions at HERA in a continuous range of photon virtuality Q^2. Special attention is given to the collinear singularities from the virtual photon and the resolved virtual photon component of the cross sections. Comparisons with dijet data from H1 are shown and the infrared sensitivity of dijet cross sections is discussed.
Most of the models of jet quenching generally assumes that a jet always travels in a straight eikonal path, which is indeed true for sufficiently hard jet but may not be a good one for moderate and low momentum jet. In this article an attempt has been made to relax part of this approximation for 2 --> 3 processes and found a (15-20)% suppression in the differential cross-section for moderately hard jets because of the noneikonal effects. In particular, for the process qq' --> qq'g in the centre of momentum frame the scattering with an angle wider than \pm 0.52π, is literally forbidden unlike t…
We present the complete next-to-leading order calculation of isolated prompt photon production in association with a jet in deep-inelastic scattering. The calculation involves, direct, resolved and fragmentation contributions. It is shown that defining the transverse momenta in the proton virtual-photon frame (CM*), as usually done, or in the laboratory frame (LAB), as done in some experiments, is not equivalent and leads to important differences concerning the perturbative approach. In fact, using the latter frame may preclude, under certain conditions, the calculation of the next-to-leading …
We analyze the order alpha_s^2 corrections to the single inclusive jet cross section in lepton-nucleon deep inelastic scattering. The full calculation is done analytically, in the small cone approximation, obtaining finite NLO partonic level cross sections for these processes. A detailed study of the different underlying partonic reactions is presented focusing in the size of the corrections they get at NLO accuracy, their relative weight, and the residual scale uncertainty they leave in the full cross section depending on the kinematical region explored. The dominant partonic process in very …
Recent results on dijet production in deep-inelastic scattering from the H1 experiment at the ep-collider HERA are presented. Internal jet structure has been studied in terms of jet shapes and subjet multiplicities in the Breit frame. Both observables are seen to be well described by QCD models. We observe a broadening of the jets towards the proton direction and at lower transverse jet energies. Dijet rates and dijet cross sections have been measured over a wide range of four momentum transfers (5 < Q^2 < 5000 GeV^2) and transverse jet energies (25 < E^2_t,Breit < 1200 GeV^2) with different j…
Complete next-to leading order QCD predictions for (2+1) jet cross sections and jet rates in deep inelastic scattering (DIS) based on a new parton level Monte Carlo program are presented. All relevant helicity contributions to the total cross section are included. Results on total jet cross sections as well as differential distributions in the basic kinematical variables $x,W^2$ and $Q^2$ are shown for HERA energies and for the fixed target experiment E665 at FERMILAB. We study the dependence on the choices of the renormalization scale $μ_R$ and the factorization scale $μ_F$ and show that the …
The recent CDF single jet inclusive measurements at Fermilab are incorporated in a global next-to-leading order parton analysis of the available deep inelastic and related data. We find that it is impossible to achieve a simultaneous QCD description of both the CDF jet distribution for transverse energies $E_T > 200$~GeV and the deep inelastic structure function data for $x > 0.3$. However, the CDF data for $E_T < 200$~GeV and the deep inelastic data are adequately described provided that the QCD coupling $α_S(M_Z^2)$ is increased from its preferred deep inelastic value to $α_S (M_Z^2) \simeq …
PROJET is a parton level Monte Carlo program for the calculation of jet cross sections in deeply inelastic electron proton scattering. In its present version it contains the Born level diagrams for the production of (1+1), (2+1) and (3+1) jets and the next-to-leading order corrections for the production cross sections of (1+1) and (2+1) jets for all polarisations of the exchanged virtual photon. In particular, the full angular correlations between the lepton and jet momenta are implemented. The program permits the application of acceptance cuts on all external momenta. For this purpose, the pr…
We suggest that, if current measurements of inclusive jet production for central rapidities at the LHC are extended to lower transverse momenta, one could define a visible cross section sensitive to the unitarity bound set by the recent determination of the inelastic proton-proton cross section.
We show that the onset and rise of QCD mini-jets provide the dynamical mechanism behind the appearance of a soft edge in pp collisions around ISR energies and thus such a soft edge is built in our mini-jet model with soft gluon resummation. Here the model is optimized for LHC at $\sqrt{s} = 7, 8 TeV$ and predictions made for higher LHC and cosmic ray energies. Further, we provide a phenomenological picture to discuss the breakup of the total cross-section into its elastic, uncorrelated and correlated inelastic pieces in the framework of a one-channel eikonal function.
We use all the available new precise data for deep inelastic and related hard scattering processes to perform NLO global parton analyses. These new data allow an improved determination of partons and, in particular, the inclusion of the recent measurements of the structure functions at HERA and of the inclusive jets at the Tevatron help to determine the gluon distribution and alpha_S better than ever before. We find a somewhat smaller gluon at low x than previous determinations and that alpha_S(M_Z^2) = 0.119 +/- 0.002 (expt.) +/- 0.003 (theory).
Different methods to reconstruct the quark-gluon fusion product and current jet are tried in deep-inelastic e-p scattering events with instanton as background generated by QCDINS Monte Carlo code. A comparison of these methods are performed and a good method is found which can reconstruct well the energies of current jet and instanton product as well as the mass of the latter. The isotropy property of the instanton product and jet are calculated and compared. A parameter characterizing the degree of ``hardness'' of the instanton product is presented.
Computations of higher-order QCD corrections for processes with exclusive final states require a subtraction method for real-radiation contributions. We present the first-ever generalisation of a subtraction method for third-order (N3LO) QCD corrections. The Projection-to-Born method is used to combine inclusive N3LO coefficient functions with an exclusive second-order (NNLO) calculation for a final state with an extra jet. The input requirements, advantages, and potential applications of the method are discussed, and validations at lower orders are performed. As a test case, we compute the N3…
We derive the two-loop QCD helicity amplitudes for the processes $l q \to l qg$ ($l \bar q \to l \bar q g$) and $l g \to l q\bar q$, which are the partonic reactions yielding $(2+1)$-jet final states in deep inelastic lepton nucleon scattering. The amplitudes are obtained by analytic continuation of the known helicity amplitudes for $e^+e^- \to q\bar q g$. We separate the infrared divergent and finite parts of the amplitudes using Catani's infrared factorization formula. The analytic results for the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic poly…
The production of two-jet final states in deep inelastic scattering is an important QCD precision observable. We compute it for the first time to next-to-next-to-leading order (NNLO) in perturbative QCD. Our calculation is fully differential in the lepton and jet variables and allows one to impose cuts on the jets both in the laboratory and the Breit frame. We observe that the NNLO corrections are moderate in size, except at kinematical edges, and that their inclusion leads to a substantial reduction of the scale variation uncertainty on the predictions. Our results will enable the inclusion o…
In deeply inelastic lepton-nucleus scattering (DIS), the average jet transverse momentum is broadened because of the multiple scattering in the nuclear medium. The size of jet broadening is proportional to the multi-parton correlation functions inside nuclei. We show that at leading order, jet broadening in DIS and nulcear enhancement in di-jet momentum imbalance and Drell-Yan $< q_T^2 > $ share the same four-parton correlation functions. We argue that jet broadening in DIS provide an indenpendent measurement of the four-parton correlation functions and a test of QCD treatment of multiple scat…
We discuss predictions for the total inelastic gamma-gamma cross-section and their model dependence on the input parameters. We compare results from a simple extension of the Regge Pomeron exchange model as well as predictions from the eikonalized mini-jet model with recent LEP data.
We study the transverse momentum ($p_T$) spectrum of charged particles produced in deep inelastic scattering (DIS) at small Bjorken $x$ in the central region between the current jet and the proton remnants. We calculate the spectrum at large $p_T$ with the BFKL $\ln (1/x)$ resummation included and then repeat the calculation with it omitted. We find that data favour the former. We normalize our BFKL predictions by comparing with HERA data for DIS containing a forward jet. The shape of the $x$ distribution of DIS + jet data are also well described by BFKL dynamics.
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical studies of saturation and unitarity effects at small $x$ in quarkonium scattering; Renormalons and higher twist contributions; Next-to-leading-order calculations of jet cross sections; Forward jet production as a probe of small-$x$ dynamics.
The concept of resolved virtual photons in addition to direct deep inelastic $ep$ scattering is used to simulate the 2+1 jet - rate and the forward jet cross section, which cannot be described by direct LO/NLO processes. With standard DGLAP evolution of the parton densities of the virtual photon and the proton the HERA data can be described, provided a sufficiently large scale for the hard scattering matrix element is used.
A generalised-$k_t$ jet algorithm for Deep Inelastic Scattering
在Breit框架下引入一种包含广义-$k_t$喷注算法的家族，通过参数p和R控制，研究其与 struck夸克关联的喷注识别及非微扰效应敏感性，并与Centauro算法比较。
We derive a modified form of the BFKL equation which enables the structure of the gluon emissions to be studied in small $x$ deep inelastic scattering. The equation incorporates the resummation of the virtual and unresolved real gluon emissions. We solve the equation to calculate the number of small $x$ deep-inelastic events containing 0,1,2 ...resolved gluon jets, that is jets with transverse momenta $q_{T} > μ$. We study the jet decomposition for different choices of the jet resolution parameter $μ$.
The status of the calculation of next-to-leading-order QCD corrections to hadronic final states in deeply inelastic scattering is reviewed, and an overview of the phenomenology (including the measurement of the strong coupling constant and the gluon density via jet rates) is given. We also describe a new universal program (DISASTER++) for the calculation of (2+1)-jet observables.
Treatment of QED corrections in jet production in deep inelastic scattering at ZEUS
本文讨论 ZEUS 深度非弹性散射喷注产生测量中高阶 QED 效应的处理，以实现与 NNLO QCD + NLO 电弱预测的直接比较。
The sensitivity of the Deep Inelastic Compton (DIC) scattering at HERA to the structure of the virtual photon is discussed. It is demonstrated that the gluonic content of the virtual photon can be pinned down by measuring the photons with $p_T \sim 5 $ GeV in the proton direction.
The distribution of a suitably defined azimuthal angle in diffractive deep inelastic scattering contains information on the polarisation of the exchanged photon. In particular it allows one to constrain the longitudinal diffractive structure function. We investigate the potential of such bounds in general and for particular diffractive final states.
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