REF 2018 is the 5th workshop in the series of workshops on Resummation, Evolution, Factorization. The workshop wishes to bring together experts of different communities specialized in: nuclear structure; transverse momentum dependend distributions; small-x physics; effective field theories.
On Friday the 23rd of November there will be a tutorial on the use of existing software for the calculation of hadron scattering processes. The emphasis will be on programs that employ TMDs, for example those provided by TMDlib. The fixed-order program KaTie, and the parton shower program CASCADE will be addressed, as well as their merging.
Previous meetings
Scientiffic committee:
Elke Aschenauer Daniel Boer
Igor Cherednikov Markus Diehl
Didar Dobur David Dudal
Miguel García Echevarría
Laurent Favart Francesco Hautmann
Hannes Jung Fabio Maltoni
Piet Mulders Gunar Schnell
Andrea Signori Pierre Van Mechelen
I will discuss using TMDs obtained with the Parton Branching method to create Parton Showers which follow the TMDs. Exempels of applications using TMD parton showers will be shown.
I will give an overview of recent results on low x TMDS and their systematic extension into the large x region.
In the first part of the talk I shall discuss the problem of initial conditions for the double parton distributions, and how to use the information about the momentum sum rule together with the initial conditions for the single parton distributions. In the second part of the talk I will address the transverse momentum dependence in the double parton distributions. The construction is based on the generalization of the KMR approach which uses Sudakov form factors and integrated parton distributions. I will show numerical results on the transverse momentum dependence, hard scale dependence and discuss the issues related to the factorization of the double parton distribution functions into the product of the single parton distributions.
In a double Drell–Yan process two hard interactions take place instead of a single one, leading to a more complex momentum, spin, and color structure of the diagrams involved. Higher-precision predictions for the LHC and the prospect of future high-energy colliders motivate the efforts for a rigorous field-theoretical description of these kinds of processes, as well as for the broader class of multi-parton interactions (MPI). A factorization theorem is therefore the first step, needed to legitimize the phenomenological applications of the standard factorized cross-section formulae. We present an overview of the all-order factorization proof at leading twist, with a stronger focus on the extraction of the soft factor. Our proof extends the well-known work of Collins, Soper and Sterman for single Drell–Yan, dropping one of the approximations on which their argument was based. The proof involves a recursive application of Ward identities, and some more carefulness in dealing with the more complicated color structure of our processes.
High energy inclusive processes are naturally formulated in terms of partonic distributions, but in fact all exclusive processes correepond to resonances and completeness of states requires a non-trivial relation betwenn inclusive and exclusive measurements. We review how Quark-Hadron Duality (QHD) for (u,d) flavors at high energies and in the scaling regime suggests a radial and angular behaviour of mesonic and baryonic resonance masses of the Regge form M2nJ=μ2n+β2J+M20. The radial mass dependence is asymptotically consistent with a common two-body dynamics for mesons and baryons in terms of the quark-antiquark (qq¯) and quark-diquark (qD) degrees of freedom, respectively. This formula is validated phenomenologically within an uncertainty determined by half the width of the resonances, With this error prescription we find from the non-strange PDG hadrons different radial slopes μ2q¯q=1.34(4)GeV2 and μ2qD=0.75(3)GeV2, but similar angular slopes β2q¯q∼β2qD∼1.15GeV2.
The cross section for top quark pair production factorizes at small transverse momentum of the heavy quark pair, qT. One of the key ingredients that appears in the factorization formula is the soft function, which mediates soft gluon exchanges between particles. I shall present the complete result for the small-qT soft function at the next-to-next-to-leading order. This is the last missing element needed to calculate the NNLO cross section for top quark pair production by means of the qT slicing method.
In this talk, I will start by generally introducing the non-perturbative formulation of QCD on a Euclidean lattice. Then, I will present a state-of-the-art computation of unpolarized, helicity and transversity parton distribution functions (PDFs) calculated using the so-called quasi-PDF approach introduced by Xiangdong Ji in 2013 and intensively developed thereafter. We employed lattice QCD simulations in the twisted mass formulation with light quark mass set to its physical value. The relevant matrix elements obtained on the lattice were non-perturbatively renormalized and converted to the $\overline{MS}$ scheme at the scale of 2 GeV. A matching process was applied together with target mass corrections, leading to the reconstruction of light-cone parton distribution functions. We find a similar behavior between the lattice and phenomenological data, and for both types of polarized PDFs a nice overlap for a range of Bjorken-x values. This presents a major success for the emerging field of direct calculations of quark distributions using lattice QCD.
In this talk I will first review the current status of higher-order perturbative calculations in pure QCD of the evolution/resummation of transverse-momentum-dependent functions (TMDs). Then, after introducing the proper definition of TMDs in QCDxQED, I will present new results for the QED corrections to their evolution.
We investigated to what extent jets - instead of hadrons - can be used to study Transverse Momentum Distributions. I will show that suitably defined jets behave exactly like single hadrons, the two being interchangeable in factorization theorems and obeying the same double-scale evolution. Such jets are excellent probes in processes like semi-inclusive deeply inelastic scattering, with the advantage of a reduced sensitivity to non-perturbative final-state effects. See arXiv:1807.07573 for further details.
The parton distributions obtained in lepton proton scattering experiments correspond to the Fourier transform of the quark-quark correlation function where the quark field operators are separated by a light cone distance known as Ioffe time. The Ioffe time behavior of the correlator can be determined unambiguously both in the short distance regime, through matrix elements of local operators accessible in lattice QCD, and at large distances, exceeding the proton size, using Regge asymptotics. We use this characteristic dependence of the correlation function to determine the x dependence of the u and d quark generalized parton distributions functions in the proton. We subsequently use Ioffe time distributions to study the properties of Transverse Momentum Distributions and the onset of factorization in QCD.
We present the Parton Branching (PB) method for the evolution of both collinear and transverse momentum dependent (TMD) parton distribution functions (PDFs). This method enables one to take into account explicitly the kinematics at each branching in the parton cascade and to study in detail the dynamics of QCD evolution, including different ordering scenarios (pt, virtuality, angular ordering), especially different definitions of the soft gluon resolution scale parameter and renormalization scale in the strong coupling alpha_s. The method was implemented in xFitter package and two TMD PDF sets, both with angular ordering definition to calculate kt and differing in renormalization scale choice, were obtained from a fit to precision HERA DIS data. Obtained TMDs were applied to LHC measurements. The PB method can be also used to construct parton shower (PS) algorithm which follows obtained TMDs. This is an important step towards precise predictions for high energy observables where ME and PS follows the same TMD and no adjustment of the kinematics after showering is needed. The PB method can be also compared with other methods to obtain TMDs as Collins-Soper-Sterman (CSS) approach.
Unintegrated (or transverse momentum dependent, TMD) parton distributions in a proton are important in high energy physics. Using the latest LHC data on the hadron production in pp collisions, we determine the parameters of the initial TMD gluon density, derived in the framework of quark-gluon string model at the low scale $\mu_0 \sim 1 - 2$ GeV and refine its large-x behaviour using data on the $t\bar t$ production at $\sqrt s = 13$ TeV. Then, by using the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation, we extend the obtained TMD gluon density to the whole kinematical region. We apply the proposed TMD gluon density to the inclusive Higgs production in different decay modes, t-channel single top production at the LHC and to the proton structure functions $F^c_2(x,Q^2)$ and $F^b_2(x,Q^2)$ in a wide region of $x$ and $Q^2$. A good agreement with the latest LHC and HERA data is achieved.
In the talk I will review the current status of nonperturbative estimates of nucleon's TMD structure functions using Lattice QCD.
Parton Reggeization Approach (PRA) is a generalized scheme of kT-factorization which uses the formalism of Reggeized gluons and quarks to define gauge-invariant hard-scattering matrix elements with off-shell partons in the initial state (See Ref. [1] for more detailed discussion). The calculations in PRA are performed in the framework of Lipatov's gauge invariant effective theory for Multi-Regge processes in QCD. LO calculations in PRA combine this matrix elements with unintegrated PDFs, defined by the Kimber-Martin-Ryskin (KMR) formula, which resums leading doubly-logarithmic corrections ~log^2(t/mu^2), where t is the virtuality of the parton and mu^2 is the hard scale.
The aim of PRA is to improve order-by-order stability of the predictions for multi-scale observables which are sensitive to the radiation of additional hard partons, such as azimuthal decorrelations of pairs of jets and vector bosons or mesons, containing heavy quarks or polarization observables in the Drell-Yan process. Some of these observables can be successfully described already in the LO of PRA, while in the conventional Collinear Parton Model (CPM), the NLO and even NNLO corrections to this observables are found to be significant. See Refs. [1-4] for examples.
The calculation of real and virtual NLO corrections in PRA significantly differs form the similar calculations in CPM. The discussion of real corrections has ben started in [5]. In the Lipatov's theory, one encounters the new type of divergences of loop integrals -- so called rapidity divergences, which are related with Reggeization of the parton in the t-channel. See Ref. [6] and references therein for the initial discussion of rapidity divergences in PRA.
New results to be presented in this talk include: the self-consistent implementation of regularization of rapidity divergences by tilting the Wilson lines in the Lipatov's effective action off the light cone, general classification of one-loop integrals with logarithmic rapidity divergences and some new results for the specific integrals. In particular, the 3 point functions with two scales of virtuality and one or two light-cone propagators will be discussed.
References:
[1] A. V. Karpishkov, M. A. Nefedov and V. A. Saleev,``$B{\bar B}$ angular correlations at the LHC in parton Reggeization approach merged with higher-order matrix elements,'' Phys. Rev. D96, no. 9, 096019 (2017) [arXiv:1707.04068 [hep-ph]].
[2] M. Nefedov and V. Saleev, "Diphoton production at the Tevatron and the LHC in the NLO* approximation of the parton Reggeization approach", Phys. Rev. D 92, no. 9, 094033 (2015) [arXiv:1505.01718 [hep-ph]].
[3] M.A.Nefedov, V.A.Saleev and A.V.Shipilova, "Dijet azimuthal decorrelations at the LHC in the parton Reggeization approach", Phys. Rev. D 87, no. 9, 094030 (2013) [arXiv:1304.3549 [hep-ph]].
[4] M.A.Nefedov, N.N.Nikolaev and V.A.Saleev, "Drell-Yan lepton pair production at high energies in the Parton Reggeization Approach", Phys. Rev. D 87, no. 1, 014022 (2013) [arXiv:1211.5539 [hep-ph]].
[5] M. Nefedov and V. Saleev, ``DIS structure functions in the NLO approximation of the Parton Reggeization Approach,'' EPJ Web Conf. 158, 03011 (2017) [arXiv:1709.06378 [hep-ph]].
[6] M. Nefedov and V. Saleev, ``On the one-loop calculations with Reggeized quarks,'' Mod. Phys. Lett. A 32, no. 40, 1750207 (2017) [arXiv:1709.06246 [hep-th]].
We resum the leading logarithms at subleading power of the Drell-Yan process employing soft-collinear effective theory in position space. Expansion of the resummed result leads to the prediction of the leading logarithms at fixed loop order. The corresponding results are given at N3LO and N4LO.
We present solutions of the BFKL equation with higher order corrections such as the kinematical constraint and DGLAP terms of the splitting fucntion. We use the results to evaluate relative contribution of each of the corrections. The study is a first step towards fitting the experimental proton structure function data.
In proton-proton collisions at $\sqrt{s} = 13$TeV, which are now achieved in the Large Hadron Collider, vector boson resonances, W/Z bosons, can be produced with transverse momenta $p_{\rm{T}}$ far exceeding their rest mass. Decay products of those bosons are collimated in the momentum direction of the mother particle and are merged into a jet with large cone-size and characteristic substructure. The measurement with the boosted W/Z bosons can be interesting for probing and testing the Standard Model at extreme energies. In this talk, we will present Monte Carlo predictions for the measurement with the boosted W/Z bosons. MC event generator will be used with the transverse momentum dependent parton distributions (TMDs) and the $p_{\rm{T}}$ spectrum of the boosted W/Z bosons obtained with the TMD will be reported.
At the LHC energies, top quarks are mostly produced in pairs (top-antitop), and also with a reasonable rate in the boosted regime: top jets with pt>400GeV. Increasing the pt of the top candidates, the back to back configuration is enriched, and in this region soft gluon re-summation effects play an important role and its studies are crucial in order to understand the imbalance between the jets. These soft radiations could be even directly measured in higher boosted regime. In this talk, phenomenological studies on top jet in the boosted regime are presented. Detail discussions of some theory predictions performed with different MC generators: Powheg+Pythia, Madrgraph+Pythia, and Powheg+CASCADE (TMD) are compared.
Energetic heavy quarks passing through the hot and dense medium of a quark-gluon plasma (QGP), represented by the resulting mesons, are viewed as a suitable probe for the interactions inside of the QGP, in particular the mecha- nisms of energy loss, as they are less likely to thermalize within the medium and are mostly created at early stages of the medium evolution. However, models of both, purely collisional energy loss as well as combinations of collisional and radiative energy loss are equally successful for reproducing the nuclear modifi- cation factor R AA and the elliptic flow v 2 [1]. In an attempt to discriminate between the two different energy-loss mechanisms, an alternative observable, the angular correlations between two mesons were investigated. Azimuthal cor- relations between pairs of heavy mesons, like D- D̄ pairs, allow for distinguishing the energy-loss scenarios [2]. We continue these studies by investigating the angular correlations between pairs of heavy and light mesons (D and π), originating from a heavy quark jet. This is motivated by the fact that the emitted gluon in radiative collisions hadronizes and these hadrons are correlated to the emitting heavy quark. We created a Monte-Carlo code for the parton splitting in the vacuum to- gether with an effective medium model. This program represents a consistent framework to study the influences of either collisional or radiative processes on parton propagation, and the resulting two-particle correlations. As experimen- tal data for angular correlations of soft particles has become available [3, 4], we extended our studies to angular correlations of charged particle pairs in various p T ranges and focused particularly on a qualitative understanding of the angular broadening effects at small momentum scales. References [1] P. B. Gossiaux, J. Aichelin, T. Gousset and V. Guiho, J. Phys. G 37 (2010) 094019 [arXiv:1001.4166 [hep-ph]]. [2] M. Nahrgang, J. Aichelin, P. B. Gossiaux and K. Werner, J. Phys. Conf. Ser. 509 (2014) 012047 [arXiv:1310.2218 [hep-ph]]. [3] ALICE Collaboration, Phys. Rev. Lett. 119 (2017) 102301. [4] ALICE Collaboration, Phys. Rev. C96 (2017) 034904.
In this talk, I elaborate on the way in which gluon transverse momentum dependent PDFs (TMDs) arise from the Color Glass Condensate (CGC). The latter is the effective theory that allows to calculate the nonlinear rapidity evolution of the gluon distribution at low-x in the presence of saturation. In particular, we use the CGC to compute the cross section for forward dijet or heavy-quark pair production in proton-nucleus collisions. In the so-called correlation limit, in which the jets or heavy-quarks are almost back-to-back, this cross section can be written in a TMD factorized form. For both processes, not one but many different gluon TMDs play a role, each characterized by a distinct Wilson line configuration, which guarantees gauge independence and is dependent on the underlying hard process. The different TMDs can be calculated analytically in the McLerran-Venugopalan (MV) model, and evolved numerically with the nonlinear JIMWLK equation. It is observed that, as is expected, all TMDs converge to the same unintegrated PDF (uPDF) in the linear or large-kt regime. Moreover, we note that in the case of heavy-quark production, also gluon TMDs play a role which encode the distribution of linearly polarized gluons inside the unpolarized nucleus. Finally, I comment on future developments, such as small-x gluon TMDs in multi particle production or in quarkonium studies.
The total and differential cross sections for the production of a Z boson decaying to two charged leptons in association with $N$ jets in proton-proton collisions at a center-of-mass energy of 13 TeV are measured for different jet multiplicities. The differential cross sections are obtained as functions of the transverse momentum of the Z boson, of the jet multiplicity, of the jet kinematic variables, transverse momentum and rapidity, the scalar sum of the jet momenta, which quantifies the hadronic activity, and of the balance in transverse momentum between the reconstructed jet recoil and the Z boson. The measurements are compared with predictions from four different calculations: a multileg leading-order and a multileg next-to-leading-order calculations including parton showering, a fixed order calculation with next-to-next-to-leading-order accuracy for the process with one parton in the final state and a combination of the fully-differential next-to-next-leading-order calculation with next-to-next-leading-log resummation. We discuss the low transverse momentum of the Z boson where the models with different treatment of soft gluon ressumation can by studied.
The gluon content of the proton, in the high-energy regime, is embodied by the unintegrated gluon distribution (UGD), which describes the probability that a gluon can be emitted by a colliding proton, with a given longitudinal momentum fraction and transverse momentum. The UGD, which is formulated within the kt-factorization approach, has universal validity and several models for it have been proposed so far. We will show that the polarized ρ-meson leptoproduction at HERA is a not trivial textfield for discriminating among existing models of UGD.
We present a thorough analysis of unpolarized Drell-Yan (DY) pair production in pion-nucleus scattering. On the nucleus side, we use nuclear parton distributions along with parametrisations of the nucleon partonic transverse distribution available in the literature. Partonic longitudinal and transverse distributions of the pion are those obtained in a recent calculation in a Nambu-Jona Lasinio (NJL) framework, with Pauli-Villars regularization. The scale of the NJL model is fixed by a comparison between NLO predictions based on NJL evolved pion distributions and rapidity differential DY cross sections data. The resulting distributions are then used to describe, up to next-to-leading logarithmic accuracy, the transverse momentum spectrum of dilepton pairs up to a transverse momentum of 2 GeV. With no additional parameters, fair agreement is found with available pion-nucleus data, confirming the virtues of the NJL description of pion parton structure. We find sizable evolution effects on the shape of the distributions and on the generated average transverse momentum of the dilepton pair. We discuss the possibility of extracting details on pion unpolarized transverse momentum dependent parton distribution from pion nucleus DY data. In this respect, the region of low invariant mass of the lepton pair appears to be favored to discriminate between different descriptions of the non-perturbative pion transverse structure.
We have studied production of open charm mesons in association with one or two jets at the LHC. The theoretical cross sections are calculated in the leading-order collinear approximation as well as in the kT-factorization approach, where a part of higher order corrections is effectively included. Both processes under consideration here give possibilities of detailed testing of pQCD dynamics beyond standard case of inclusive charm cross section. This opens new ways, e.g. for phenomenological verification of different models of transverse-momentum-dependent (unintegrated) parton distribution functions in the case of mulit-particle final states. For the case of charm + jet mechanism, different unintegrated gluon distribution functions are used in the kT-factorization approach. Several predictions for the LHC are presented, including various correlation observables. Integrated cross sections for D0+jet production for ATLAS detector acceptance and for different cuts on jet transverse momenta are also presented [1]. Associated production of charm with two jets is also very interesting from the point of view of searching for multiple-parton interaction effects. We have carefully examined production of D0+2jets and D0D0bar+2jets in both single-parton scatttering (SPS) and double-parton scattering (DPS) mechanisms. For both final states we indicate regions of phase-space where the DPS contributions clearly dominate over the standard SPS components. Several correlation distributions useful for measurement of the DPS effects for the LHCb experiment are proposed [2]. [1] R. Maciula, and A. Szczurek, “Charm quark and meson production in association with single-jet at the LHC”, Phys. Rev. D94, 114037 (2016). [2] R. Maciula, and A. Szczurek, "Double-parton scattering effects in associated production of charm mesons and dijets at the LHC", Phys. Rev. D96 (2017) no.7, 074013
I review the recent theory developments in the QCD Wigner distribution or its Fourier transform, the generalized TMD distribution (GTMD). I also discuss how it can be measured in experiments.
We perform calculations of Z+jet cross-section taking into account the transverse momenta of the initial partons. Transverse Momentum Dependent (TMD) parton densities obtained with the Parton Branching method are used and higher order corrections are included via TMD parton showers in the initial state. The predictions are compared to measurements of forward Z+jet production of the LHCb collaboration at $\sqrt{s}=7$ TeV. We show that the results obtained in kT-factorization are in good agreement with results obtained from a NLO calculation matched with traditional parton showers. We also demonstrate that in the forward rapidity region, kT-factorization and hybrid factorization predictions agree with each other.
The measurements of associated production of a vector boson with a top-antitop quark pair provide an important test for the Standard Model at the LHC.These are not only key processes to measure the top quark properties but also are very relevant in searches for new physics, both as being directly sensitive to it and as providing an important background. While NNLO calculations for this particular type of 2 to 3 processes are currently out of reach, a class of corrections beyond NLO can be taken into account with the help of resummation methods. In this talk we consider an application of soft gluon resummation in Mellin space to these processes at hadron colliders and discuss numerical predictions at NNLL matched to NLO precision for the LHC.
TMDs at NLO obtained with the Parton Branching method using HERA DIS measurements are presented. Two choices for the scale at which the strong coupling is evaluated are investigated. The TMDs are applied to two LHC processes: the Drell-Yan pT spectrum and the azimuthal correlation in high pT dijet events. For the Drell-Yan pT spectrum a significant effect from the α s scale choice is observed.
The talk will be based on the Les Houches proceedings: http://arxiv.org/abs/arXiv:1803.07977 contribution: "On the cross-talk of parameter optimization and perturbative variations in event generators" and a connected paper: Eur.Phys.J. C76 (2016) no.12, 665
I discussed combinations of state-of-the art calculations of top-quark pair differential cross sections at hadron colliders in fixed order (NNLO) and resummation (NNLL'). Qualitative insight is given into the issue of factorisation and resummation scale choices for the high-energy tail of the top-pair invariant mass distribution, based on the enhanced contributions of t and u channel singularities at high energy.
I was invited to present arXiv:1803.06347 on electroweak gauge boson PDFs. I would like to briefly discuss arXiv:1802.08687 as well, which discusses (the resummation of) electroweak logarithms in inclusive cross sections.
We present prospects for the direct measurement of ratios of differential cross sections for the production of Z and Higgs bosons in proton-proton collisions, using data taken by CMS during the LHC Run II. The aim of the measurement is to study soft and hard gluon emission in the initial state for Higgs and Z production mechanisms. Hence, we focus on variables known to be sensitive to the production mechanisms of heavy bosons: jet multiplicity, transverse momenta of the boson and leading jet, and momentum balance in the transverse plane. We use Monte-Carlo samples to study the feasibility of the measurement and estimate the expected precision.
We discuss production of $D$ mesons at high and low energies. The cross section at high-energies is calculated in the $k_t$-factorization or standard (collinear) pQCD approach. The unintegrated gluon distributions are the main ingredient of the $k_t$-factorization approach. Several distributions, in rapidity, transversemomentum, are calculated. The asymmetries observed in production of $D^+ D^-$ and $D_s^+ D_s^-$ mesons observed recently by the LHCb collaboration call for deeper understanding. One of a possibility is nonperturbative light quark/antiquark subleading fragmentation. We have shown that a small amount of such processes, necessary to understand the LHCb asymmetries, may lead to dramatic effects at lower energies or in very forward/backward directions at high-energies. This may also have important implications for high-energy neutrinos observed by IceCube Observatory. Some fixed-target future experiments and relevant predictions will be discussed. I will also discuss production of $\Lambda_c$ baryons and show difficulties to understand it within independent charm quark/antiquark fragmentation picture.
Drell-Yan dilepton production is a unique reaction which offers high sensitivity to the parton distribution in the hadron, being an important reference process from both experimental and theoretical points of view. Motivated by recent analyses, where forward Drell--Yan production in proton-proton collisions at the LHC has been studied in the high-energy factorization framework, we improve the calculation by introducing an unintegrated gluon density from a fit to combined HERA data at small values of Bjorken x. This gluon density was calculated within the BFKL formalism in the next-to-leading logarithmic accuracy. We show that it generates a good description of the forward Drell-Yan cross section dependence on the invariant mass of the lepton pair both for LHCb and ATLAS data.
We discuss production of Drell-Yan massive lepton pairs at hadron colliders in framework of the parton Reggeization approach, which includes off-shell initial state effects by the gauge-invariant way. We compare our results for transverse momentum and rapidity spectra as well as for angular coefficients with existing experimental data and perform predictions for NICA collider at the total energy $\sqrt{S}=24$ GeV. We have found sufficient difference between our calculations, which include off-shell initial state effects, and predictions of conventional TMD factorization approach for helicity structure functions when transverse momenta of lepton pairs are much smaller they invariant masses.