uuencoded postscript file containing 4 text pages with three embedded figures (hard copy available from authors). Talk presented by L.H. Orr at DPF'94, Albuquerque, NM, August 2-6, 1994
Top pairs produced at the Tevatron may be accompanied by extra jets due to radiation of soft gluons. Whether these jets should be included in top momentum reconstruction depends on the source of the gluons, which can be radiated off the initial partons, the final state $b$ quarks, or the intermediate top quarks. We compute soft gluon distributions and discuss their implications for top mass measurements.
We address aspects of jet physics at the Large Hadron Collider focusing on features of recent jet measurements which challenge the theory. We discuss examples illustrating the role of QCD parton showers, nonperturbative corrections, soft multi-gluon emission.
We study the effect of soft gluon resummation on the gaps-between-jets cross-section at the LHC. We review the theoretical framework that enables one to sum logarithms of the hard scale over the veto scale to all orders in perturbation theory. We then present a study of the phenomenological impact of Coulomb gluon contributions and super-leading logarithms on the gaps between jets cross-section at the LHC.
The perturbative QCD approach, based on Modified Leading Log Approximation and Local Parton Hadron Duality, is shown to describe inclusive features of multiparticle production in the soft region. Further predictions of this approach are discussed.
Recently, an exact conformal mapping between soft gluons emitted from jets at large angle in e+e- annihilation and those in the BFKL evolution of a high energy hadron has been proposed. We elucidate some remarkable aspects of this correspondence and use them to analytically compute the distribution and correlation of gluons in the interjet region. We also establish the timelike counterpart of Mueller's dipole model and discuss the resulting linear and nonlinear evolution equations.
We present a method to calculate the soft function in Soft-Collinear Effective Theory to NLO for N-jet events, defined with respect to arbitrarily complicated observables and algorithms, using a subtraction-based method. We show that at one loop the singularity structure of all observable/algorithm combinations can be classified as one of two types. Type I jets include jets defined with inclusive algorithms for which a jet shape is measured. Type II jets include jets found with exclusive algorithms, as well as jets for which only the direction and energy are measured. Cross sections that are i…
A scaling law for the one-particle invariant density E dn/d^3p at small momenta is observed in experimental data. We show that these results are consistent with the predictions of the analytical QCD approach, based on Modified Leading Log Approximation plus Local Parton Hadron Duality, which includes colour coherence in soft gluon bremsstrahlung.
Explicit applications of factorization theorems for processes at hadron colliders near the hadronic endpoint have largely focused on simple final states with either no jets (e.g., Drell-Yan) or one inclusive jet (e.g., deep inelastic scattering and prompt photon production). Factorization for the former type of process gives rise to a soft function that depends on timelike momenta, whereas the soft function for the latter type depends on null momenta. We derive in soft-collinear effective theory a factorization theorem that allows for an arbitrary number of jets, where the jets are defined wit…
Using the framework of soft-collinear effective theory (SCET), we factorize and calculate $e^+e^-$ angularity distributions, including perturbative resummation and the incorporation of a universal model for the nonperturbative soft function. Angularities $τ_a$ are a class of event shapes varying in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter $a<2$. We calculate the jet and soft functions in factorized angularity distributions for all $a<1$ to first order in the strong coupling $α_s$ and resum large logarithms to next-to-leading logarit…
We calculate the cross section for production of a soft photon and two hard jets in the forward rapidity region in proton-nucleus collisions at high energies. The calculation is performed within the hybrid formalism. The hardness of the final particles is defined with respect to the saturation scale of the nucleus. We consider both the correlation limit of small momentum imbalance and the dilute target limit where the momentum imbalance is of the order of the hardness of the jets. The results depend on the first two transverse-momentum-dependent (TMD) gluon distributions of the nucleus.
An $η$-elongated same-side 2D peak ("soft ridge") in minimum-bias angular correlations from heavy ion collisions has been attributed both to jet formation and to initial-state geometry structure coupled to radial flow. We consider evidence for both interpretations.
We study Kaluza-Klein (KK) graviton production in the large extra dimensions model via 2 jets plus missing transverse momentum signatures at the LHC. We make predictions for both the signal and the dominant Zjj and Wjj backgrounds, where we introduce missing P_T-dependent jet selection cuts that ensure the smallness of the 2-jet rate over the 1-jet rate. With the same jet selection cuts, the distributions of the two jets and their correlation with the missing transverse momentum provide additional evidence for the production of an invisible massive object.
It is well known that cross-sections in perturbative QCD receive large corrections from soft and collinear radiation, whose properties must be resummed to all orders in the coupling. Whether or not the universal properties of this radiation can be extended to next-to-leading power (NLP) in the threshold expansion has been the subject of much recent study. In this paper, we consider two types of NLP effects: the interplay of next-to-soft and collinear radiation in processes with final state jets and the NLP contributions stemming from soft quarks. We derive an NLP amplitude for soft gluons and …
To offer a possible resolution to the apparent discrepancy between the experimental and the theoretical values of the $W + 1$ jet to $W + 0$ jets ratio reported by the \D0 group, we examine the effects of the multiple soft gluon radiation on the $W$ boson production at the Tevatron. Based on the calculation of the $W$ boson transverse momentum ($Q_T$) distribution in the Collins-Soper-Sterman resummation formalism, we conclude that the effect of the soft gluon radiation is important in the region of $Q_T < 50$ GeV, and it can be better tested by a more inclusive observable $R_{CSS}(Q_T^{\min})…
We study the correlation between two soft particles in QCD jets. We extend the Fong--Webber analysis to the region away from the hump in the single inclusive energy spectrum and show that the correlation function should flatten off and then decrease for large values of l=ln(1/x).
The energy evolution of average multiplicities and multiplicity fluctuations in jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark gluon plasma. The leading contribution of the standard production of soft hadrons is enhanced by a factor $\sqrt{N_s}$ while next-to-leading order (NLO) corrections are suppressed by $1/\sqrt{N_s}$, where the parameter $N_s>1$ accounts for the induced-soft gluons in the medium. Ou…
We make a brief presentation of the soft colour interactions models, the Soft Colour Interaction and the Generalised Area Law, and summarise the results when they are applied to p-pbar scattering. The models give a good description of the Tevatron data on production of W, bottom and jets in diffractive events, as well as jets with two rapidity gaps, alternatively leading particles. We also give predictions for diffractive J/psi production and discuss diffractive Higgs production at the Tevatron and LHC.
The energy evolution of medium-modified average multiplicities and multiplicity fluctuations in quark and gluon jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark gluon plasma. The leading contribution of the standard production of soft hadrons is found to be enhanced by the factor $\sqrt{N_s}$ while next-to-leading order (NLO) corrections are suppressed by $1/\sqrt{N_s}$, where the nuclear parameter $N_s>1$ …
In all modern hadronic colliders, jets recieve a large contribution from a soft background: pileup in the case of proton-proton collisions at the LHC, or the underlying event for heavy-ion collisions at RHIC or the LHC. In these proceedings, we present a generic and simple method, based on jet areas, to subtract the contribution of the soft background from the jets. This allows for more precise kinematic reconstruction of jets in dense environments.
Modification of the hard jet substructure in terms of the Soft Drop jet grooming algorithm observables is studied for three different scenarios of jet quenching in a quark-gluon plasma: i) an explicit enhancement of the parton splitting functions, ii) increased soft gluon emissions induced by an in-medium virtuality gain, and iii) energy loss due to a drag force. Despite the fact that first two scenarios both correspond to a radiative energy loss mechanism and lead to similar modifications of parton showers, they are shown to have very different impacts on the momentum balance of hard subjets.…
One of the greatest challenges in quantum chromodynamics is understanding the hadronization mechanism, which is also crucial for carrying out precision physics with jet substructure. In this Letter, we combine recent advancements in our understanding of the field theory-based nonperturbative structure of the soft drop jet mass with precise perturbative calculations of its multi-differential variants at next-to-next-to-leading logarithmic (NNLL) accuracy. This enables a systematic study of its hadronization power corrections in a completely model-independent way. We calibrate and test hadroniza…
An extension to the Soft-Collinear-Effective Theory (SCET) description of hard jets is motivated to include the leading contributions between the propagating partons within the jet with partons radiated from a dense extended medium. The resulting effective Lagrangian, containing both a leading and a power suppressed (in the hard scale $Q^2$) contribution, arises primarily from interactions between the hard collinear modes in the jet with Glauber modes from the medium. In this first attempt, the interactions between the hard jet and soft and collinear partonic modes have been ignored, in an eff…
QCD equations for the generating functions are applied to separate soft and hard jets in $e^+e^-$-processes of multiparticle production. The dependence of average multiplicities and higher moments of multiplicity distributions of particles created in a "newly born" soft subjets on the share of energy devoted to them is calculated in fixed coupling gluodynamics. This dependence is the same as for the total multiplicity up to a constant factor if soft jets are defined as those carrying out a fixed share of initial energy at all energies. The constant factor depends on this share in a non-trivial…
Hard diffractive production of di-jets in the Tevatron and HERA are explored. It is argued that a consistent pQCD description of these data can be attained after s-channel unitarity re-scattering screening corrections are incorporated in the calculation. To this end a simple procedure is presented in which information derived from the measured soft total, elastic and diffractive cross sections simplifies the calculation and makes it parameter free. The above approach eliminates the inconsistencies seemingly observed when comparing the rates of diffractive di-jets production in different channe…
The different modifications of quark- and gluon-initiated jets in the quark-gluon plasma (QGP) produced in heavy-ion collisions is a long-standing question that has not yet received a definitive answer from experiments. In particular, the relative sizes of the modification of quark and gluon jets differ between theoretical models. Therefore, a fully data-driven technique is crucial for an unbiased extraction of the quark and gluon jet spectra and substructure. We perform a proof-of-concept study based on proton-proton and heavy-ion collision events from the \textsc{Pyquen} generator with stati…
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom which are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for th…
We derive the leading non-global logarithms (NGLs) of ratios of jet masses m_{1,2} and a jet energy veto Λdue to soft gluons splitting into regions in and out of jets. Such NGLs appear in any exclusive jet cross section with multiple jet measurements or with a veto imposed on additional jets. Here, we consider back-to-back jets of radius R produced in e^+e^- collisions, found with a cone or recombination algorithm. The leading NGLs are of the form α_s^2 \ln^2(Λ/m_{1,2}) or α_s^2\ln^2(m_1/m_2). Their coefficients depend both on the algorithm and on R. We consider cone, \kt, anti-\kt, and Cambri…
The difference between the ratio of multiplicities and the ratio of their derivatives on energy for gluon and quark jets is calculated up to next-to-next-to leading order of perturbative QCD. Its non-zero value is uniquely defined by the running property of the QCD coupling constant. It is shown that this difference is rather small compared to values which can be obtained from experimental data. This disagreement can be ascribed either to strong non-perturbative terms or to experimental problems with a scale choice, jets separation and inadequate assignement of soft particles to jets.
The modification of quark- and gluon-initiated jets in the quark-gluon plasma produced in heavy-ion collisions is a long-standing question that has not yet received a definitive answer from experiments. In particular, the size of the modifications in the quark-gluon plasma differs between theoretical models. Therefore a fully data-driven technique is crucial for an unbiased extraction of the quark and gluon jet spectra and substructure. Corroborating past results, I demonstrate the capability of a fully data-driven technique called topic modeling in separating quark and gluon contributions to …
Diffusion wake is an unambiguous part of the jet-induced medium response in high-energy heavy-ion collisions that leads to a depletion of soft hadrons in the opposite direction of the jet propagation. New experimental data on $Z$-hadron correlation in Pb+Pb collisions at the Large Hadron Collider show, however, an enhancement of soft hadrons in the direction of both the $Z$ and the jet. Using a coupled linear Boltzmann transport and hydro model, we demonstrate that medium modification of partons from the initial multiple parton interaction (MPI) gives rise to a soft hadron enhancement that is …
Superposition of jets of different flavors as well as superposition of jets of different topologies describe well observed structures (shoulder, H_q oscillations) in e+e- annihilation. The analysis of similar effects seen in experimental data in hadron-hadron collision is performed successfully by superimposing soft and semi-hard contributions at various energies. Negative Binomial multiplicity distributions are chosen in all examined classes of collisions as elementary substructures, i.e., as QCD inspired genuine self-similar fractal processes. Predictions on final particle multiplicity distr…
We present results for mass effects coming from secondary radiation of heavy quark pairs related to gluon splitting in the thrust distribution for e+e- collisions. The results are given in the dijet limit where the hard interaction scale and the scales related to collinear and soft radiation are widely separated. We account for the corresponding fixed-order corrections at O(alpha_s^2) and the summation of all logarithmic terms related to the hard, collinear and soft scales as well as the quark mass at N3LL order. We also remove the O(Lambda_QCD) renormalon in the partonic soft function leading…
A same-side (SS, on azimuth $ϕ$) 2D peak in measured angular correlations from 200 GeV \pp collisions exhibits properties expected for jet formation. In more-central \auau collisions the SS peak becomes elongated on pseudorapidity $η$ and the transverse momentum $p_t$ structure is modified. In the latter case the SS 2D peak has been referred to as a "Soft Ridge", and arguments have been presented that the elongated peak represents flow phenomena ("triangular" and "higher harmonic" flows), possibly related to the initial-state ågeometry. In this presentation I demonstrate that "higher harmonic …
Probing compressed triplet scalars with ISR jets and soft leptons at the LHC
Uppsala University（乌普萨拉大学）；Regional Centre for Accelerator-based Particle Physics, Harish-Chandra Research Institute（哈立斯·钱德拉研究所加速器基础粒子物理区域中心）；Homi Bhabha National Institute（霍米·巴巴国立学院）；School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学促进会科学院物理科学学院）；Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata（印度科学教育与研究大学加尔各答分校物理科学系）；Department of Physics, Bharat Institute of Engineering and Technology（巴拉特工程技术学院物理系）
We address the production of black holes at LHC in space times with compactified space-like large extra dimensions (LXD). Final state black hole production leads to suppression of high-P_T jets, i.e. a sharp cut-off in the cross section for pp->jet+X. This signal is compared to the jet plus missing energy signature due to graviton production in the final state as proposed by the ATLAS collaboration. Time evolution and lifetimes of the newly created black holes are calculated based on the microcanonical formalism. It is demonstrated that previous lifetime estimates of micro black holes have bee…
We compute in the heavy quark effective theory the soft coefficient D_2 entering the resummation of next-to-next-to-leading threshold logarithms for jets initiated by a quark with a small mass compared to the hard scale of the process. We find complete agreement with a previous computation in full QCD. Contrary to our previous guess, this coefficient turns out to be different from that one entering heavy flavor decay or heavy flavor fragmentation.
Jets are an important probe to identify the hard interaction of interest at the LHC. They are routinely used in Standard Model precision measurements as well as in searches for new heavy particles, including jet substructure methods. In processes with several jets, one typically encounters hierarchies in the jet transverse momenta and/or dijet invariant masses. Large logarithms of the ratios of these kinematic jet scales in the cross section are at present primarily described by parton showers. We present a general factorization framework called SCET$_+$, which is an extension of Soft-Collinea…
We demonstrate the consistency at the next-to-leading-logarithmic (NLL) level of a factorization theorem based on Soft-Collinear Effective Theory (SCET) for jet shapes in e+e- collisions. We consider measuring jet observables in exclusive multijet final states defined with cone and k_T-type jet algorithms. Consistency of the factorization theorem requires that the renormalization group evolution of hard, jet, and soft functions is such that the physical cross-section is independent of the factorization scale mu. The anomalous dimensions of the various factorized pieces, however, depend on the …
The pull vector is a jet observable sensitive to the distribution of soft radiation controlled by the color flow in a collider event. We present calculations to leading order in the soft and collinear limits for the pull vector measured between pairs of jets that do not form a color-singlet dipole. Our calculations are presented within the context of $e^+e^-\to$ three jets events, on which pull is measured between the two subleading jets. A subset of these calculations can be re-interpreted as a bottom--anti-bottom quark jet pair in a color octet configuration, which can be a background to Hig…
In the paper experimental results obtained by studying of collective and fractal properties of soft pion jets in the space of relative four-dimensional velocities in intermediate energy domain 2 - 20 GeV are presented. Fractional values of cluster dimension are indicated on manifestation of fractal-like properties by pion jets. The changes of the mean square of the distance between secondary particles and jet axis, the mean kinetic energy of particles in jets and the cluster dimension with increasing of collision energy agree with the hypothesis of manifestation of quark degrees of freedom in …
Color Coherence and the Soft Structure of QCD Jets in Vacuum and the QGP
SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS)（苏巴泰克联合研究实验室（南特高等矿业学院、南特大学、法国国家科学研究中心））；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）
The paper generalizes the results on soft - hard decomposition of the characteristics of QCD jets obtained in [1] by taking into account the effects of fermions and running coupling constant.
We present the complete physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma (QGP) by analytical and numerical investigation of thermalization of the soft components of the jet. Our results support the following physical picture: the leading particle emits a significant number of mini-jets which promptly evolve via multiple branching and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature $T$. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equili…
Quantum chromodynamics is the theory of the strong interaction between quarks and gluons; the coupling strength of the interaction, $α_S$, is the least precisely-known of all interactions in nature. An extraction of the strong coupling from the radiation pattern within jets would provide a complementary approach to conventional extractions from jet production rates and hadronic event shapes, and would be a key achievement of jet substructure at the Large Hadron Collider (LHC). Presently, the relative fraction of quark and gluon jets in a sample is the limiting factor in such extractions, as th…
The effect of recoils on soft-drop-groomed observables in $γ$-tagged jets in a multistage approach
Akita International University（秋田国际大学）；Duke University（杜克大学）；Wayne State University（韦恩州立大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Vanderbilt University（范德堡大学）；Massachusetts Institute of Technology（麻省理工学院）；McGill University（麦吉尔大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We argue that contemporary jet substructure techniques might facilitate a more direct measurement of hard medium-induced gluon bremsstrahlung in heavy-ion collisions, and focus specifically on the "soft drop declustering" procedure that singles out the two leading jet substructures. Assuming coherent jet energy loss, we find an enhancement of the distribution of the energy fractions shared by the two substructures at small subjet energy caused by hard medium-induced gluon radiation. Departures from this approximation are discussed, in particular, the effects of colour decoherence and the conta…
We consider top-quarks produced at large energy in e+e- collisions, and address the question of what top-mass can be measured from reconstruction. The production process is characterized by well separated scales: the center-of-mass energy, Q, the top mass, m, the top decay width, Gamma_t, and also LambdaQCD; scales which can be disentangled with effective theory methods. In particular we show how the mass measurement depends on the way in which soft radiation is treated, and that this can shift the mass peak by an amount of order Q LambdaQCD/m. We sum large logs for Q >> m >> Gamma_t > LambdaQ…
Energy and momentum loss of jets in heavy ion collisions can affect the fluid dynamic evolution of the medium. We determine realistic event-by-event averages and correlation functions of the local energy-momentum transfer from hard particles to the soft sector using the jet-quenching Monte-Carlo code JEWEL combined with a hydrodynamic model for the background. The expectation values for source terms due to jets in a typical (minimum bias) event affect the fluid dynamic evolution mainly by their momentum transfer. This leads to a small increase in flow. The presence of hard jets in the event co…
We complete the physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma by investigating the thermalization of the soft components of the jet. We argue that the following scenario should hold: the leading particle emits a significant number of mini-jets which promptly evolve via quasi-democratic branchings and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature T. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equilibrium with the plasma over a time…
We introduce collinear drop jet substructure observables, which are unaffected by contributions from collinear radiation, and systematically probe soft radiation within jets. These observables can be designed to be either sensitive or insensitive to process-dependent soft radiation originating from outside the jet. Such collinear drop observables can be exploited as variables to distinguish quark, gluon, and color neutral initiated jets, for testing predictions for perturbative soft radiation in Monte Carlo simulations, for assessing models and universality for hadronization corrections, for e…
We present three case studies at a 100 TeV proton collider for how jet analyses can be improved using new jet (sub)structure techniques. First, we use the winner-take-all recombination scheme to define a recoil-free jet axis that is robust against pileup. Second, we show that soft drop declustering is an effective jet grooming procedure that respects the approximate scale invariance of QCD. Finally, we highlight a potential standard candle for jet calibration using the soft-dropped energy loss. This latter observable is remarkably insensitive to the scale and flavor of the jet, a feature that …
A persistent and fascinating problem at the high energy colliders are jets. Often trying to observe physics underlying the hard interactions at colliders requires experimental cuts in phase space, defining several jet or beam regions. QCD being a gauge theory that readily decays into infra-red modes, correlations between jet regions is almost inevitable, spoiling the predictivity of fixed order QCD calculations. One is faced with the task of calculating the evolution of a reduced density matrix, where successively less energetic (jet) regions are integrated out, to gain control of the calculat…
Experimental results obtained by studying the properties of soft jets in the 4-velocity space at $\sqrt{s} \sim 2-20$ GeV are presented. The changes in the mean distance from the jet axis to the jet particles, the mean kinetic energy of these particles, and the cluster dimension in response to the growth of the collision energy are consistent with the assumption that quark degrees of freedom manifest themselves in processes of pion jet production at intermediate energies. The energy at which quark degrees of freedom begin to manifest themselves experimentally in the production of soft pion jet…
