Resummed azimuthal decorrelation and transverse momentum imbalance of dijets at the LHC
Fudan University（复旦大学）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（NSFC与复旦大学上海理论核物理研究中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；University of Vienna（维也纳大学）；Nikhef（尼赫夫国家粒子物理研究所）；University of Amsterdam（阿姆斯特丹大学）；Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所）
Rong-Jun Fu, Rudi Rahn, Ding Yu Shao, Wouter J. Waalewijn, Bin Wu
备注：
47 pages, 20 figures. v2: Revised to match the published version
We present a theoretical study of the azimuthal decorrelation $δϕ$ and transverse momentum imbalance $q_T$ in dijet production at the LHC, offering intriguing insights into the dynamics of quantum chromodynamics. We define the jet axes using the recoil-free winner-take-all (WTA) recombination scheme. For the azimuthal decorrelation $δϕ$, this axis choice eliminates non-global logarithms (NGLs) entirely. For the transverse momentum imbalance $q_T$, NGLs emerge specifically in the small jet radius limit ($R \ll 1$). In this regime, the WTA scheme simplifies the theoretical framework by restricting jet radius logarithms to the soft sector. We derive factorization formulae for both observables within soft-collinear effective theory. To address the small-$R$ NGLs in the $q_T$ distribution, we refactorize the soft function into global soft, collinear-soft, and ultra-collinear-soft modes. We perform the resummation of global large logarithms $\ln(δϕ)$ and $\ln(q_T/Q)$ up to next-to-next-to-leading logarithmic accuracy. For the $q_T$ distribution, this is combined with a leading-logarithmic resummation of the non-global $\ln R$ terms. We match our predictions to leading fixed-order $O(α_s^3)$ calculations. We also numerically investigate the structure of the first subleading power corrections. Comparisons with PYTHIA8 simulations demonstrate that the observables we consider are robust against non-perturbative multi-parton interactions and hadronization effects.
We study the azimuthal angular decorrelation of the dijet production via photon fusion in ultra-peripheral heavy ion collisions. The impact parameter dependent cross section of quark-antiquark pairs production is derived using the equivalent photon approximation, and the contribution from final-state QCD radiations to the azimuthal angular distribution are calculated within Soft-Collinear Effective Theory. We carry out the QCD resummation of large logarithms of the azimuthal angle as well as the jet radius at next-to-leading logarithmic accuracy. In the end we present the normalized differenti…
We point out an inconsistency in perturbative QCD predictions previously used for dijet azimuthal decorrelations for azimuthal angles of $Δϕ_{\rm dijet} < 2π/3$ between the two jets. We show how the inconsistency arises and how the calculations can be modified to provide more accurate results that exhibit a smaller scale dependence and give a better description of the data than the inconsistent results. We also explain how the quality of the predictions strongly depends on a perceivedly minor detail in the definition of the dijet phase space and give recommendations for future measurements.
In this talk we examine the azimuthal angle decorrelation in dijet production at large rapidity intervals at the Tevatron as a possible signature of the BFKL evolution.
We provide a description, within the High Energy Factorization formalism, of central-forward dijet decorrelation data measured by the CMS experiment and the predictions for nuclear modification ratio~$R_{pA}$ in p+Pb collisions. In our study, we use the unintegrated gluon density derived from the BFKL and BK equations supplemented with subleading corrections and a hard scale dependence. The latter is introduced at the final step of the calculation by reweighting the Monte Carlo generated events using suitable Sudakov form factors, without changing the total cross section. We achieve a good des…
We report on the status of the QCD analysis of dijet azimuthal decorrelations. We emphasise the relevance of resummation of soft and collinear enhancements in describing these observables in the region where the two jets are nearly back-to-back in the transverse plane. We also discuss the sources of theoretical uncertainties and possible research directions aimed at their reduction.
Based on the color dipole QCD approach we discuss the multiple scattering mechanism (MSM) of suppression of back-to-back azimuthal correlations of high $p_{T}$ forward dijets in DIS off nuclei. We quantify the effect in terms of acoplanarity/decorrelation momentum of jets. For hard dijets the decorrelation momentum is found to be of the order of the nuclear saturation momentum $Q_A$. Minijets with the transverse momentum below the saturation scale are proved to be completely decorrelated. The analysis of DIS indicates that in heavy ion collisions the contribution of MSM to the reactions dynami…
We introduce a new measurable quantity, $R_{Δϕ}$, for studies of the rapidity and transverse momentum dependence of dijet azimuthal decorrelations in hadron-hadron collisions. In pQCD, $R_{Δϕ}$ is computed as a ratio of three-jet and dijet cross sections in which the parton distribution functions cancel to a large extent. At the leading order, $R_{Δϕ}$ is proportional to $α_s$, and the transverse momentum dependence of can therefore be exploited to determine $α_s$. We compute the NLO pQCD theory predictions and non-perturbative corrections for $R_{Δϕ}$ at the LHC and the Tevatron and investiga…
We study inclusive dijet azimuthal decorrelations in proton-proton collisions at the CERN LHC invoking the hypothesis of parton Reggeization in t-channel exchanges at high energies. In the parton Reggeization approach, the main contribution to the azimuthal angle difference between the two most energetic jets is due to the Reggeon-Reggeon-Particle-Particle scattering, when the fusion of two Reggeized gluons into a pair of Yang-Mills gluons dominates. Using a high-energy factorization scheme with the Kimber-Martin-Ryskin unintegrated parton distribution functions and the Fadin-Lipatov effective…
In this contribution we study azimuthal angle decorrelation in inclusive dijet cross sections taking into account the next-to-leading (NLO) corrections to the BFKL kernel while keeping the jet vertices at leading order. We show how the angular decorrelation for jets with a wide relative separation in rapidity largely decreases when the NLO corrections are included.
We study saturation effects in the production of dijets in p-p and p-Pb collisions using the framework of high energy factorization. We focus on central-forward jet configurations, which allow for probing gluon density at low longitudinal momentum fraction. We find significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, which we attribute to saturation of gluon density in nuclei.
We construct dijet differential cross sections at large momentum transfer, in which threshold logarithms have been summed to all orders in perturbation theory. This extends previous work on heavy quark production, by treating collinear singularities associated with hard, massless partons in the final state. The resummed corrections enable us to define, in the sense of factorization, the underlying color exchange mechanism. The influence of color exchange on the resummed cross section is contained in the eigenvalues and eigenvectors of an anomalous dimension matrix, which describes the factoriz…
We develop the QCD description of the breakup of photons into forward dijets in small-x deep inelastic scattering off nuclei in the saturation regime. Based on the color dipole approach, we derive a multiple scattering expansion for intranuclear distortions of the jet-jet transverse momentum spectrum. A special attention is paid to the non-Abelian aspects of the propagation of color dipoles in a nuclear medium. We report a nonlinear $k_{\perp}$-factorization formula for the breakup of photons into dijets in terms of the collective Weizsäcker-Williams (WW) glue of nuclei as defined in ref. \cit…
We revisit the azimuthal decorrelation $δϕ$ between a jet and a $Z$ boson produced at hadron colliders. Employing different recombination schemes for the jets leads to significantly different NLL-resummed predictions for the distribution of this quantity. Specifically when the jets are reconstructed with the $E$-scheme (i.e., four-momentum addition) in the $k_t$ or anti-$k_t$ clustering algorithms, then the resummation becomes highly non-trivial due to the presence of non-global and/or clustering logarithms. We evaluate these logarithms analytically at two loops and numerically to all orders i…
Azimuthal angle decorrelation in inclusive dijet cross sections is studied analytically to take into account the next-to-leading corrections to the BFKL kernel while keeping the jet vertices at leading order. The spectral representation on the basis of leading order eigenfunctions is generalized to include the dependence on conformal spins. With this procedure running coupling effects and angular dependences are both included. It is shown how the angular decorrelation for jets with a wide relative separation in rapidity largely decreases at this higher order in the resummation.
We analyse the azimuthal decorrelation of Mueller-Navelet dijets produced in the collisions at Tevatron energies using a BFKL framework which incorporates dominant subleading effects. We show that these effects significantly reduce the decorrelation yet they are still insufficient to give satisfactory description of experimental data. However a good description of the data is obtained after incorporating within formalism the effective rapidity defined by Del Duca and Schmidt.
We study the azimuthal correlation distribution for dijet production in QCD hard processes. This observable is sensitive to soft and/or collinear emissions in the back-to-back region, giving rise to single and double logarithms. We provide resummed predictions to NLL accuracy for both DIS at HERA and hadronic collisions at Tevatron and perform a NLO matching to NLOJET++ results in the DIS case.
We present recently defined jet-observables for hadron-hadron dijet production, which are designed to reconcile the seemingly conflicting theoretical requirement of globalness, which makes it possible to resum them (automatically) at NLL accuracy and the limited experimental reach of detectors, so that they are measurable at the Tevatron and at the LHC.
We consider the dijet cross section in $e^+ e^-$ annihilation using the Georgi jet algorithm, or the maximizing jet algorithm. The cross section is factorized into the hard, collinear and soft parts. Each factorized function is computed to next-to-leading order, and is shown to be infrared finite. The large logarithms are resummed at next-to-leading logarithmic accuracy. By analyzing the phase space for the jet algorithm, the Georgi algorithm turns out to be equivalent to the Sterman-Weinberg and the cone-type algorithms.
We discuss the resummation of threshold logarithms for heavy quark and dijet cross sections in hadronic collisions. The resummed cross sections are presented at next-to-leading logarithmic accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We apply our formalism to the calculation of the top quark production cross section at the Fermilab Tevatron.
We review the resummation of threshold logarithms for heavy quark, dijet, direct photon, and W boson production cross sections in hadronic collisions. Beyond leading logarithms the resummed cross section is sensitive to the color exchange in the hard scattering. The resummation is formulated at next-to-leading logarithmic or higher accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We give results for the soft anomalous dimension matrices at one loop for the full range of partonic subprocesses involved in heavy quark, dij…
The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL …
We discuss central-forward dijet production at LHC energies within the framework of high energy factorization. In our study, we profit from the recent progress on consistent merging of Sudakov resummation with small-$x$ effects, which allows us to compute two different gluon distributions which depend on longitudinal momentum, transverse momentum and the hard scale of the process: one for the quark channel and one for the gluon channel. The small-$x$ resummation is included by means of the BK equation supplemented with a kinematic constraint and subleading corrections. We test the new gluon di…
We discuss a class of event shapes for e+e- dijet events that include the thrust as a special case. Large logarithmic corrections to the corresponding cross sections can be resummed to all logarithmic orders at leading power. However, irrespective of the order up to which the perturbative expansion is calculated, it has to be supplemented by nonperturbative corrections due to its at best asymptotic nature. We find that the leading power corrections are universal for the class of event shapes discussed here. Based on these findings, we provide sample numerical predictions for the distributions …
A Monte Carlo study of the azimuthal angular distribution around the virtual boson-proton beam axis for dijet events in DIS at HERA is presented. In the presence of typical acceptance cuts on the jets in the laboratory frame, the azimuthal distribution is dominated by kinematic effects rather than the typical $\cosϕ$ and $\cos 2ϕ$ dependence predicted by the QCD matrix elements. This implies that the $ϕ$ dependent part of the QCD matrix elements contributes even to the dijet production cross section. Neglecting this $ϕ$ dependence leads to an error of about 5-8\% in the production cross sectio…
We test several BFKL-like evolution equations for unintegrated gluon distributions against forward-central dijet production at LHC. Our study is based on fitting the evolution scenarios to the LHC data using the high energy factorization approach. Thus, as a by-product, we obtain a set of LHC-motivated unintegrated gluon distributions ready to use. We utilize this application by calculating azimuthal decorrelations for forward-central dijet production and compare with existing data.
We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small $x$ as a function of the relative momentum $\boldsymbol{P}_\perp$ and momentum imbalance $\boldsymbol{k}_\perp$ of the dijet system for different photon virtualities $Q^2$, and study the elliptic and quadrangular anisotropies in the relative angle between $\boldsymbol{P}_\perp$ and $\boldsymbol{k}_\perp$. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse mom…
We present an operator based factorization formula for the transverse energy-energy correlator (TEEC) hadron collider event shape in the back-to-back (dijet) limit. This factorization formula exhibits a remarkably symmetric form, being a projection onto a scattering plane of a more standard transverse momentum dependent factorization. Soft radiation is incorporated through a dijet soft function, which can be elegantly obtained to next-to-next-to-leading order (NNLO) due to the symmetries of the problem. We present numerical results for the TEEC resummed to next-to-next-to-leading logarithm (NN…
We discuss how the dijet azimuthal correlations in DIS and real photoproduction at HERA probe the differential (unintegrated) gluon distribution in the proton. We find a strong dependence of the azimuthal correlation pattern on Bjorken-$x$, photon virtuality and the cut on the jet transverse momenta. A rise of the azimuthal decorrelations is observed with decreasing Bjorken-x due to the interplay of perturbative and nonperturbative effects. We predict a strong rise of the same-side jet rate with photon energy for real photoproduction. We discuss conditions for the correlation function to be do…
We study the exclusive heavy quark dijet cross section from $e^+e^-$-annihilation using soft-collinear effective theory. In order to resum the large logarithms of small jet veto parameter $β$ and jet radius $R$, we factorize the cross section into the hard, hard-soft, collinear, and collinear-soft parts. Compared with the case of a massless quark, the jet sector with the collinear and collinear-soft parts can be modified to include the heavy quark mass. The factorization of the jet sector can be systematically achieved through matching onto the boosted heavy quark effective theory. Heavy quark…
Based on an approach to non-Abelian propagation of color dipoles in a nuclear medium we formulate a nonlinear k_t-factorization for the breakup of photons and pions into forward hard dijets in terms of the collective Weizsäcker-Williams (WW) glue of nuclei. We find quite distinct practical consequences of nonlinear nuclear k_t-factorization for interactions of pointlike photons and non-pointlike pions. In the former case the large transverse momentum p_t of jets comes from the intrinsic momentum of quarks and antiquarks in the photon and nuclear effects manifest themselves as an azimuthal deco…
The mass distribution of jets produced in hard processes at the LHC plays an important role in several jet substructure related studies involving both Standard Model and BSM physics, especially in the context of boosted heavy particle searches. We compute analytically the jet-mass distribution for both Z+jet and dijet processes, for QCD jets defined in the anti-k_t algorithm with an arbitrary radius R, to next-to-leading logarithmic accuracy and match our resummed calculation to full leading-order results. We note the important role played by initial state radiation (ISR) and non-global logari…
We study the influence of in-medium transverse momentum broadening on observables of jet pairs produced in nuclear collisions. These dijets were obtained numerically via the Monte-Carlo simulations of nuclear collisions, where the partons within the colliding nuclei were described via unintegrated parton densities, and their subsequent propagation within the medium of a quark-gluon plasma (QGP). For jet-evolution in the QGP both, kicks transverse to the momentum of the incoming particle as well as medium induced radiation were considered. After favorable comparison of our results with experime…
Calculating the distribution of jet masses in high-energy collisions is challenging because fixed-order perturbation theory breaks down near the peak region, and because multiple scales complicate the resummation. To avoid using a jet veto, one can consider inclusive observables, in which every particle is in a jet. We demonstrate that calculating the mass of the hardest jet in multijet events can be problematic, and we give an example of an inclusive observable, asymmetric thrust, which can be resummed to next-to-next-to-leading logarithmic accuracy. Exclusive observables with out-of-jet regi…
We show that saturation can manifest itself in central-forward dijet production in p-A collisions. In spite of large transverse momenta of the jets, the almost back-to-back dijet configurations are able to probe gluon density at low x and low kt. We perform our study in the framework of high energy factorization with the unintegrated gluon density given by a nonlinear QCD evolution equation. We show that the formalism can successfully account for features measured in e-p and p-p data and it predicts significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, whic…
We investigate the use of jets to measure transverse momentum dependent distributions (TMDs). The example we use to present our framework is the dijet momentum decorrelation at lepton colliders. Translating this momentum decorrelation into an angle $θ\ll 1$, we analyze the factorization of the cross section for the cases $θ\gg R$, $θ\sim R$ and $θ\ll R$, where $R$ is the jet radius. Critically, for the Winner-Take-All axis, the jet TMD has the same double-scale renormalization group evolution as TMD fragmentation functions for all radii $R$. TMD fragmentation functions in factorization theorem…
We present an innovative method to resum infrared and collinear logarithms appearing in distributions of jet observables in QCD. The method, based on a general master formula with applicability conditions, allows resummations at next-to-leading logarithmic accuracy in an automated way. As a sample application we present resummed results in hadronic dijet events.
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 previ…
We obtain a prediction for the hadron-collider event-shape variable transverse thrust in which the terms enhanced in the dijet limit are resummed to next-to-next-to-leading logarithmic accuracy. Our method exploits universality properties made manifest in the factorized expression for the cross section and only requires one-loop calculations. The necessary two-loop ingredients are extracted using known results and existing numerical codes. Our technique is general and applicable to other observables as well.
We study the factorization of the dijet cross section in $e^+ e^-$ annihilation using the generalized exclusive jet algorithm which includes the cone-type, the JADE, the $k_T$, the anti-$k_T$ and the Cambridge/Aachen jet algorithms as special cases. In order to probe the characteristics of the jet algorithms in a unified way, we consider the generalized $k_T$ jet algorithm with an arbitrary weight of the energies, in which various types of the $k_T$-type algorithms are included for specific values of the parameter. We show that the jet algorithm respects the factorization property for the para…
The Lorentz contraction of ultrarelativistic nuclei entails a spatial overlap and fusion (recombination, saturation) of partons belonging to different nucleons at the same impact parameter. In these lectures we present a consistent description of the fusion of partons in terms of nuclear attenuation of color dipole states of the photon and collective Weizsäcker-Williams (WW) gluon structure function of a nucleus. The point that all observables for DIS off nuclei are uniquely calculable in terms of the nuclear WW glue amounts to a new form of factorization in the saturation regime. We start wit…
The $D$-parameter is one of the oldest and most experimentally well-studied hadronic observables for $e^+e^-$ collisions. Nevertheless, unlike other classic observables like the $C$-parameter or thrust, the $D$-parameter has never been resummed throughout its entire singular phase space. Using insights and techniques motivated by modern multi-differential jet substructure calculations, we are able to predict the $D$-parameter distribution with no additional phase space cuts. Our approach is to measure both the $C$- and $D$-parameters on hadronic final states in $e^+e^-$ collisions. We can tune…
We compute resummed and matched predictions for jet angularities in hadronic dijet and Z+jet events with and without grooming the candidate jets using the SoftDrop technique. Our theoretical predictions also account for non-perturbative corrections from the underlying event and hadronisation through parton-to-hadron level transfer matrices extracted from dedicated Monte Carlo simulations with SHERPA. Thanks to this approach we can account for non-perturbative migration effects in both the angularities and the jet transverse momentum. We compare our predictions against recent measurements from …
University of Durham（杜伦大学）；Universität Bern（伯尔尼大学）；The Henryk Niewodniczański Institute of Nuclear Physics（亨利克·涅沃德尼茨基核物理研究所）；The University of Edinburgh（爱丁堡大学）
Heavy ion collisions at high energies can be used as an interesting way to recreate and study the medium of the quark-gluon plasma (QGP). We particularly investigate the jets produced in hard binary collisions and their interactions with a tentative medium. These jets were obtained numerically from the Monte-Carlo simulations of hard collisions using the KATIE-algorithm [1], where parton momenta within the colliding nucleons were describe by means of unintegrated parton distribution functions (uPDF). We evolved these jets within a medium that contains both, transverse kicks (yielding a broaden…
We consider the energy flow into gaps between hard jets. It was previously believed that the accuracy of resummed predictions for such observables can be improved by employing the $k_t$ clustering procedure to define the gap energy in terms of a sum of energies of soft jets (rather than individual hadrons) in the gap. This significantly reduces the sensitivity to correlated soft large-angle radiation (non-global leading logs), numerically calculable only in the large $N_c$ limit. While this is the case, as we demonstrate here, the use of $k_t$ clustering spoils the straightforward single-gluon…
Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple parameters has frustrated precision theoretic understanding. In this paper, we demonstrate that one particular groomer called soft drop actually makes precision jet substructure easier. In particular, we derive a factorization formula for a large class of soft drop jet substructure observables, including jet mass. The essential observation that …
