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.
Threshold resummation for gluon fusion $ZH$ production at the LHC
RWTH Aachen University（亚琛工业大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Guwahati（古瓦哈提印度理工学院）；Durham University（杜伦大学）
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.
We construct an evolution equation for the invariant-mass distribution of light-quark and gluon jets in the framework of QCD resummation. The solution of the evolution equation exhibits a behavior consistent with Tevatron CDF data: the jet distribution vanishes in the small invariant-mass limit, and its peak moves toward the high invariant-mass region with the jet energy. We also construct an evolution equation for the energy profile of the light-quark and gluon jets in the similar framework. The solution shows that the energy accumulates faster within a light-quark jet cone than within a gluo…
We calculate resummed perturbative predictions for gaps-between-jets processes and compare to HERA data. Our calculation of this non-global observable needs to include the effects of primary gluon emission (global logarithms) and secondary gluon emission (non-global logarithms) to be correct at the leading logarithm (LL) level. We include primary emission by calculating anomalous dimension matrices for the geometry of the specific event definitions and estimate the effect of non-global logarithms in the large $N_c$ limit. The resulting predictions for energy flow observables are consistent wit…
The production of vector bosons in association with jets contains at least two unrelated scales. The first is the mass of the vector boson m_V and the second is the hard interaction scale giving rise to large transverse momenta of the produced jets. The production cross sections depend logarithmically on the ratio of these scales, which can lead to a poor convergence in fixed order perturbation theory. We illustrate how to resum all leading logarithmic terms using effective theory methods, and show that they can be resummed by a simple choice of the factorization scale. Implementing this scale…
A quantity that promises to reveal important information on perturbative and non-perturbative QCD dynamics is the azimuthal decorrelation between jets in different hard processes. In order to access this information fixed-order NLO predictions need to be supplemented by resummation of logarithmic terms which are large in the region where the jets are nearly back-to-back in azimuth. In the present letter we carry out this resummation to next-to--leading logarithmic accuracy explaining the important role played by the recombination scheme in general resummations for such jet observables.
We summarize recent developments in the study of high-energy resummation effects in Mueller-Navelet jets production at the LHC and discuss possible relations with multiparton interactions.
After inserting the heavy quark mass dependence into QCD partonic evolution equations, we determine the mean charged hadron multiplicity of jets produced in high energy collisions. We thereby extend the so-called dead cone effect to the phenomenology of multiparticle production in QCD jets and find that the average multiplicity of heavy-quark initiated jets decreases significantly as compared to the massless case, even taking into account the weak decay products of the leading primary quark. We emphasize the relevance of our study as a complementary check of $b$-tagging techniques at hadron co…
The region of small transverse momentum in q-qbar- and gg-initiated processes must be studied in the framework of resummation to account for the large, logarithmically-enhanced contributions to physical observables. In this letter, we study resummed differential cross-sections for Higgs production via bottom-quark fusion. We find that the differential distribution peaks at approximately 15 GeV, a number of great experimental importance to measuring this production channel.
We present version 2.1 of the High Energy Jets (HEJ) event generator for hadron colliders. HEJ is a Monte Carlo generator for processes at high energies with multiple well-separated jets in the final state. To achieve accurate predictions, conventional fixed-order perturbative QCD is supplemented with an all-order resummation of large high-energy logarithms. The new version 2.1 now supports processes with final-state leptons originating from a charged or neutral vector boson together with multiple jets, in addition to processes available in earlier versions. Furthermore, the all-order resummat…
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…
More than 25 years ago, Mueller and Navelet proposed to study the production of two jets separated by a large interval of rapidity at hadron colliders to look for high-energy resummation effects. We here present the results of a next-to-leading logarithmic BFKL study of the azimuthal decorrelation of these jets. This includes next-to-leading corrections both to the Green's function and to the jet vertices. We compare our results with recent LHC data and results obtained in a fixed order treatment.
We study the transverse momentum resummation for dijet correlation in hadron collisions based on the Collins-Soper-Sterman formalism. The complete one-loop calculations are carried out in the collinear factorization framework for the differential cross sections at low imbalance transverse momentum between the two jets. Important cross checks are performed to demonstrate that the soft divergences cancelled out between different diagrams, and in particular, those associated with final state jets. The leading and sub-leading logarithms are identified. All order resummation is derived following th…
We present a flexible Monte Carlo implementation of the perturbative framework of High Energy Jets, describing multi-jet events at hadron colliders. The description includes a resummation which ensures leading logarithmic accuracy for large invariant mass between jets, and is matched to tree-level accuracy for multiplicities up to 4 jets. The resummation includes all-order hard corrections, which become important for increasing centre-of-mass energy of the hadronic collision. We discuss observables relevant for confronting the perturbative framework with 7 TeV data from the LHC, and the impact…
We provide a novel development in jet physics by predicting the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large-Hadron-Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. The predicted peak positions and heights in jet mass distributions are consistent with CDF data within uncertainties induced by parton dis…
The study of the production of two forward jets with a large interval of rapidity at hadron colliders was proposed by Mueller and Navelet as a possible test of the high energy dynamics of QCD. We analyze this process within a complete next-to-leading logarithm framework, supplemented by the use of the Brodsky-Lepage-Mackenzie procedure extended to the perturbative Regge dynamics, to find the optimal renormalization scale. This leads to a very good description of the recent CMS data at LHC for the azimuthal correlations of the jets.
We consider the quark beam function that describes collinear initial-state radiation that is constrained by a veto on reconstructed jets. As the veto is imposed on the transverse momenta of the jets, the beam function is subject to rapidity divergences, and we use the collinear-anomaly framework to extract the perturbative matching kernels to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on a novel framework that automates the computation of beam functions in Mellin space and it provides the ingredients to extend jet-veto resummations for quark…
We quantify the magnitude of the parton energy loss in jets in lead-lead collisions at the LHC. We extract the effective color factor characterizing the difference between the in-medium radiation of quark-initiated jets and gluon-initiated jets from the data. Then, we examine the energy loss of prompt charmonia and we point to a remarkable similarity between the quenching of light-quark-initiated jets and the prompt charmonia suppression. Finally, we discuss possible sources of this similarity.
Starting from a factorization theorem in effective field theory, we present resummed results for two non-global observables: the invariant-mass distribution of jets and the energy distribution outside jets. Our results include the full next-to-leading-order corrections to the hard, jet and soft functions and are implemented in a parton-shower framework which generates the renormalization-group running in the effective theory. The inclusion of these matching corrections leads to an improved description of the data and reduced theoretical uncertainties. They will have to be combined with two-loo…
We present HEJ 2, a new implementation of the High Energy Jets formalism for high-energy resummation in hadron-collider processes as a flexible Monte Carlo event generator. In combination with a conventional fixed-order event generator, HEJ 2 can be used to obtain greatly improved predictions for a number of phenomenologically important processes by adding all-order logarithmic corrections in $\hat{s}/p_\perp^2$. A prime example for such a process is the gluon-fusion production of a Higgs boson in association with widely separated jets, which constitutes the dominant background to Higgs boson …
Mueller Navelet jets were proposed more than 25 years ago as a decisive test of BFKL dynamics at hadron colliders. We here present a complete next-to-leading BFKL study of the azimuthal decorrelation of these jets. This includes both next-to-leading corrections to the Green's function and next-to-leading corrections to the jet vertices. We compare our results with recent data taken at the LHC and results obtained in a fixed order next-to-leading-order (NLO) calculation.
We resum the invariant mass distribution of jets initiated by massive quarks in next-to-leading logarithmic approximation and beyond in heuristic way. We find that the inclusion of mass terms, in the N-moment space, results in the universal factor delta_N(Q^2;m^2), taking into account dead-cone effects and soft radiation characteristic of massive charges. This factor multiplies the massless jet distribution function J_N(Q^2). The variable N is rescaled by the mass correction parameter r = m^2/Q^2 << 1 with respect to the standard massless case, being m the quark mass and Q the hard scale. The …
We derive the gluon initiated contribution to the initial condition for the perturbative fragmentation function of a heavy quark through order O(α_s^2) in the MS-bar scheme. This result is needed for the resummation with next-to-next-to-leading logarithmic accuracy of quasi-collinear logarithms ln^k(m^2) in heavy quark differential distributions by solving the complete DGLAP equation. Together with the previously evaluated fermion initiated components, this result completes the derivation of the initial condition for the perturbative fragmentation function at next-to-next-to-leading order.
The measurement of azimuthal correlations of Mueller-Navelet jets is generally considered as a decisive test to reveal the effect of BFKL dynamics at hadron colliders. The first experimental study of these correlations at the LHC has been recently performed by the CMS collaboration. We show that the ratios of cosine moments of the azimuthal distribution are successfully described within our next-to-leading logarithmic BFKL treatment. The whole set of CMS data for the azimuthal correlations can also be consistently described provided that one uses a larger renormalization/factorization scale th…
In this paper, we report our results on charged hadron multiplicities of heavy quark initiated jets produced in high energy collisions. After implementing the so-called dead cone effect in QCD evolution equations, we find that the average multiplicity decreases significantly as compared to the massless case. Finally, we discuss on the transverse momentum distribution of light quark initiated jets and emphasize on the comparison between our predictions and CDF data.
We show that a resummation of infrared logarithms is needed to obtain a sensible theoretical description of dijet rates when symmetric cuts are applied to the transverse energies of both jets. We also present the next-to-leading logarithmic (NLL) resummation we carried out for DIS production of two jets selected with the cone algorithm.
Resummation in QCD provides insight into the evolution of final state jets from short to long distances, and of accompanying interjet radiation. Applications to event shapes, including the recently-proposed angularities, suggest experimental tests of the interrelations between weak- and strong-coupling dynamics.
The region of small transverse momentum in q qbar- and gg-initiated processes must be studied in the framework of resummation to account for the large, logarithmically-enhanced contributions to physical observables. In this paper, we will calculate the fixed order next-to-leading order (NLO) perturbative total and differential cross-sections for both a Standard Model (SM) scalar Higgs boson and the Minimal Supersymmetric Standard Model's (MSSM) pseudoscalar Higgs boson in the Heavy Quark Effective Theory (HQET) where the mass of the top quark is taken to be infinite. Resummation coefficients B…
We derive a factorization theorem for production of an arbitrary number of color-singlet particles accompanied by a fixed number of jets at the LHC. The jets are defined with the standard anti-$k_T$ algorithm, and the fixed number of jets is obtained by imposing a veto on additional radiation in the final state. The formalism presented here is useful for current Higgs boson analyses using exclusive jet bins, and for other studies using a similar strategy. The derivation uses the soft-collinear effective theory and assumes that the transverse momenta of the hard jets are larger than the veto sc…
A number of phenomenologically relevant processes at hadron colliders, such as Higgs and Z boson production in association with b quarks, can be conveniently described as scattering of heavy quarks in the initial state. We present a detailed analysis of this class of processes, identifying the form of the leading initial-state collinear logarithms that allow the relation of calculations performed in different flavour schemes in a simple and reliable way. This procedure makes it possible to assess the size of the logarithmically enhanced terms and the effects of their resummation via heavy-quar…
We revisit the impact of the jet algorithm on predictions of energy flow into gaps between hard jets, defined using the kt clustering procedure. The resulting prediction has two distinct components: a primary emission piece that is related to independent emission of soft gluons by the hard jets and a correlated emission (non-global) piece known only in the large N_c limit. We analytically compute the dependence of the primary emission term on the jet algorithm, which gives significantly more insight than our previous numerical study of the same. We also point out that the non-global component …
We consider jet-shape observables of the type proposed recently, where the shapes of one or more high-pT jets, produced in a multi-jet event with definite jet multiplicity, may be measured leaving other jets in the event unmeasured. We point out the structure of the full next-to-leading logarithmic resummation specifically including resummation of non-global logarithms in the leading-Nc limit and emphasising their properties. We also point out differences between jet algorithms in the context of soft gluon resummation for such observables.
We investigate the stability under variation of the renormalization, factorization and energy scales entering the calculation of the cross section, at next-to-leading order in the BFKL formalism, for the production of Mueller-Navelet jets at the Large Hadron Collider, following the experimental cuts on the tagged jets. To find optimal values for the scales involved in this observable it is possible to look for regions of minimal sensitivity to their variation. We show that the scales found with this logic are more natural, in the sense of being more similar to the squared transverse momenta of…
Multijet cross sections at the LHC and Tevatron are sensitive to several distinct kinematic energy scales. When measuring the dijet invariant mass m_jj between two signal jets produced in association with other jets or weak bosons, m_jj will typically be much smaller than the total partonic center-of-mass energy Q, but larger than the individual jet masses m, such that there can be a hierarchy of scales m << m_jj << Q. This situation arises in many new-physics analyses at the LHC, where the invariant mass between jets is used to gain access to the masses of new-physics particles in a decay cha…
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…
Higgs Boson plus Quark Pair Production at High Energies as di-Higgs Background
The Henryk Niewodniczański Institute of Nuclear Physics（亨利克·涅沃德尼茨基核物理研究所）；Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology（高等物理研究所（IFAE），巴塞罗那科学技术研究院）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心 DESY）
Endpoint divergences in the convolution integrals appearing in next-to-leading-power factorization theorems prevent a straightforward application of standard methods to resum large logarithmic power-suppressed corrections in collider physics. We study the power-suppressed configuration of the thrust distribution in the two-jet region, where a gluon-initiated jet recoils against a quark-antiquark pair. With the aid of operatorial endpoint factorization conditions, we derive a factorization formula where the individual terms are free from endpoint divergences and can be written in terms of renor…
The precise knowledge of parton distribution functions (PDFs) is indispensable to the accurate calculation of hadron-initiated QCD hard scattering observables. Much of our information on PDFs is extracted by comparing deep inelastic scattering (DIS) and lepton pair production (LPP) data to convolutions of the PDFs with the partonic cross sections of these processes. It is known that partonic cross sections receive large corrections in regions of phase space near partonic thresholds that can be resummed using threshold resummation techniques. The effect of threshold resummation on DIS and LPP d…
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…
Exploiting the substructure of jets observed at the LHC to better understand and interpret the experimental data has recently been a very active area of research. In this thesis we study the substructure of high-p$_T$ QCD jets, which form a background to many new physics searches. In particular, we explore in detail the perturbative distributions of a certain class of observables known as non-global jet shapes. More specifically, we identify and present state-of-the-art calculations, both at fixed-order and to all-orders in the perturbative expansion, of a set of large logarithms known as non-…
Several searches for new physics at the LHC require a fixed number of signal jets, vetoing events with additional jets from QCD radiation. As the probed scale of new physics gets much larger than the jet-veto scale, such jet vetoes strongly impact the QCD perturbative series, causing nontrivial theoretical uncertainties. We consider slepton pair production with 0 signal jets, for which we perform the resummation of jet-veto logarithms and study its impact. Currently, the experimental exclusion limits take the jet-veto cut into account by extrapolating to the inclusive cross section using parto…
The asymptotic behaviour at large N of the MS-bar quark anomalous dimensions is derived to all orders assuming only MS-bar factorization and standard results for the exponentiation of soft logarithms in the quark initiated bare cross sections for deep inelastic scattering and Drell-Yan. The result is then used to write the MS-bar quark coefficient functions in a form in which all terms of $O(\ln^m N)$ are resummed.
The lack of convergence of the convolution integrals appearing in next-to-leading-power (NLP) factorization theorems prevents the applications of existing methods to resum power-suppressed large logarithmic corrections in collider physics. We consider thrust distribution in the two-jet region for the flavour-nonsinglet off-diagonal contribution, where a gluon-initiated jet recoils against a quark-antiquark pair, which is power-suppressed. With the help of operatorial endpoint factorization conditions, we obtain a factorization formula, where the individual terms are free from endpoint divergen…
We study the QCD charge asymmetry in t\bar{t} production at the Tevatron. We investigate the role of higher orders in perturbation theory by considering the resummation of potentially large logarithmic corrections that arise near partonic threshold. This requires us to employ the rapidity-dependent anomalous dimension matrices that describe color mixing due to soft gluon emission in both quark- and gluon-initiated processes. The charge asymmetry appears directly in the resummed cross section at next-to-leading logarithm (NLL), and we find that the first-order expansion of the NLL resummed char…
We thoroughly investigate both transverse momentum and threshold resummation effects on scalar-pseudoscalar pair production via quark-antiquark annihilation at the $13~ \text{TeV}$ Large Hadron Collider at QCD NLO+NLL accuracy. A factorization method is introduced to properly supplement the soft-gluon (threshold) resummation contribution from parton distribution functions to the resummed results obtained by the Collins-Soper-Sterman resummation approach. We find that the impact of the threshold-resummation improved PDFs is comparable to the resummation effect of the partonic matrix element and…
The properties of quark and gluon jets, and the differences between them, are increasingly important at the LHC. However, Monte Carlo event generators are normally tuned to data from $e^+e^-$ collisions which are primarily sensitive to quark-initiated jets. In order to improve the description of gluon jets we make improvements to the perturbative and the non-perturbative modelling of gluon jets and include data with gluon-initiated jets in the tuning for the first time. The resultant tunes significantly improve the description of gluon jets and are now the default in Herwig 7.1.
We present a calculation of non-global logs at finite $\mathrm{N_c}$ for the hemisphere mass distribution in $e^+e^-\to 2$ jets at single log accuracy up to fifth order in the strong coupling constant. Our results suggest a possible all-orders resummation of these large logs into an exponential. Comparing our results to those at large $\mathrm{N_c}$, recently reported in literature, we find an agreement. We additionally compare our findings with the numerical all-orders resummation at large $\mathrm{N_c}$ and discuss the significance of neglected finite-$\mathrm{N_c}$ corrections on the said d…
We introduce an infinite set of jet substructure observables, derived as projections of $N$-point energy correlators, that are both convenient for experimental studies and maintain remarkable analytic properties derived from their representations in terms of a finite number of light ray operators. We show that these observables can be computed using tracking or charge information with a simple reweighting by integer moments of non-perturbative track or fragmentation functions. Our results for the projected $N$-point correlators are analytic functions of $N$, allowing us to derive resummed resu…
We discuss the GENEVA Monte Carlo framework, which combines higher-order resummation (NNLL) of large Sudakov logarithms with multiple next-to-leading-order (NLO) matrix-element corrections and parton showering (using PYTHIA8) to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolution scales. Results for e+e- -> jets compared to LEP data and for Drell-Yan production are presented.
In this paper, the soft gluon resummation effect in double heavy quarkonium production at the LHC is studied. By applying the transverse momentum dependent factorization formalism, the large logarithms introduced by the small total transverse momentum of heavy quarkonium pair final state system, are resummed to all orders in the expansion of the strong interaction coupling at the Next-to-Leading Logarithm accuracy. We also compare our result with the LHC data. We find that the distribution shape predicted by resummation calculation is consistent with experimental data very well. Since this pro…
The moments of the single inclusive momentum distribution of hadrons in QCD jets, are studied in the next-to-modified-leading-log approximation (NMLLA) including next-to-leading-order (NLO) corrections to the alpha_s strong coupling. The evolution equations are solved using a distorted Gaussian parametrisation, which successfully reproduces the spectrum of charged hadrons of jets measured in e+e- collisions. The energy dependencies of the maximum peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution are computed analytically. Comparisons of all the existing jet data m…
Several key processes at the LHC in the standard model and beyond that involve $b$ quarks, such as single-top, Higgs, and weak vector boson associated production, can be described in QCD either in a 4-flavor or 5-flavor scheme. In the former, $b$ quarks appear only in the final state and are typically considered massive. In 5-flavor schemes, calculations include $b$ quarks in the initial state, are simpler and allow the resummation of possibly large initial state logarithms of the type $\log \frac{{\cal Q}^2}{m_b^2}$ into the $b$ parton distribution function (PDF), ${\cal Q}$ being the typical…
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…
