Search

We study all the possible spin asymmetries that can arise in back-to-back electron-jet production, $ep\rightarrow e+\text{jet}+X$, as well as the associated jet fragmentation process, $ep\rightarrow e+ \text{jet} (h)+X$, in electron-proton collisions. We derive the factorization formalism for these spin asymmetries and perform the corresponding phenomenology for the kinematics relevant to the future electron ion collider. In the case of unpolarized electron-proton scattering, we also give predictions for azimuthal asymmetries for the HERA experiment. This demonstrates that electron-jet production is an outstanding process for probing unpolarized and polarized transverse momentum dependent parton distribution functions and fragmentation functions., 46 pages, 10 figures, 5 tables

Within the theoretical framework of the generalized factorization of perturbative QCD, i.e., the higher-twist expansion formalism, we perform the first global analysis of the jet transport coefficient ($\hat q$) in cold nuclear matter, in which analysis we take into account the available data on various types of transverse momentum broadening in $e$A and $p$A collisions, as well as the nuclear modification of the structure functions in DIS. The global analysis suggests a universal and kinematics-dependent $\hat q=\hat q\,(x,Q^2)$ in cold nuclear matter, which would be instructive for understanding the jet quenching phenomena and the property of quark-gluon plasma in a more accurate way. Further more, utilizing the Hessian matrix, we evaluate the uncertainty of the extracted $\hat q\,(x,Q^2)$ under the constraints of the current data and generate the error evaluation sets of $\hat q\,(x,Q^2)$, with which we make preliminary predictions for the future EIC experiments at three facilities covering a wide kinematic range.

Using Soft-Collinear Effective Theory, we develop the transverse-momentum-dependent factorization formalism for heavy flavor dijet production in polarized-proton-electron collisions. We consider heavy flavor mass corrections in the collinear-soft and jet functions, as well as the associated evolution equations. Using this formalism, we generate a prediction for the gluon Sivers asymmetry for charm and bottom dijet production at the future Electron-Ion Collider. Furthermore, we compare theoretical predictions with and without the inclusion of finite quark masses. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry., 25 pages, 6 figures; journal version

We perform global fit to the quark Sivers function within the transverse momentum dependent (TMD) factorization formalism in QCD. We simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from $W/Z$ boson at RHIC. This extraction is performed at next-to-leading order (NLO) and next-to-next-to leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tension arises when trying to describe the spin asymmetries of $W/Z$ bosons at RHIC. We carefully assess the situation, and we study in details the impact of the RHIC data and their implications through different ways of performing the fit. In addition, we find that the quality of the description of $W/Z$ vector boson asymmetry data could be strongly sensitive to the DGLAP evolution of Qiu-Sterman function, besides the usual TMD evolution. We present discussion on this and the implications for measurements of the transverse-spin asymmetries at the future Electron Ion Collider., 48 pages, 21 figures

We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution ($j_T$) for the single hadron production with the thrust axis in electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit $j_T \ll Q$, and joint transverse momentum and threshold limit $j_T \ll Q(1-z_h) \ll Q$, where $Q$ and $z_h$ are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms $\ln(Q/j_T)$ and $\ln(1-z_h)$ to all orders. In the end we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration., Comment: 25 pages, 5 figures

We present predictions and projections for hadron-in-jet measurements and electron-jet azimuthal correlations at the future electron-ion collider (EIC). These observables directly probe the three-dimensional structure of hadrons, in particular, the quark transversity and Sivers parton distributions and the Collins fragmentation functions. We explore the feasibility of these experimental measurements by detector simulations and discuss detector requirements. We conclude that jet observables have the potential to enhance the three-dimensional imaging EIC program.

We study the single hadron inclusive production in the forward rapidity region in proton-nucleus collisions. We find the long-standing negative cross section at next-to-leading-order (NLO) is driven by the large negative threshold logarithmic contributions. We established a factorization theorem for resumming these logarithms with systematically improvable accuracy within the color glass condensate formalism. We demonstrate how the threshold leading logarithmic accuracy can be realized by a suitable scale choice in the NLO results. The NLO spectrums with the threshold logarithms resummed remain positive and impressive agreements with experimental data are observed., Comment: 6 pages, 3 figures, add comments on resummation and scale independence. Published in PRD as a rapid communication

In this paper we perform the first simultaneous QCD global analysis of data from semi-inclusive deep inelastic scattering, Drell-Yan, $e^+e^-$ annihilation into hadron pairs, and proton-proton collisions. Consequently, we are able to extract a universal set of non-perturbative functions that describes the observed asymmetries in these reactions. The outcome of our analysis indicates single transverse-spin asymmetries in high-energy collisions have a common origin. Furthermore, we achieve the first phenomenological agreement with lattice QCD on the up and down quark tensor charges., Comment: 8 pages, 6 figures, matches published version

We propose the jet charge observable as a novel probe of flavor structure in the nucleon spin program at the electron ion collider (EIC) and develop the underlying framework from first principles. We show that jet charge measurements can substantially enhance the sensitivity of spin asymmetries to different partonic flavors in the nucleon. This sensitivity can be further improved by constructing the jet charge using only a subset of hadron species (pions or kaons) in the jet. As an example, we use the Sivers asymmetry in back-to-back electron-jet production at the EIC to show that the jet charge can be a unique tool in constraining the Sivers function for different partonic flavors.

The study of transverse momentum dependent parton distributions (TMDs) features prominently among the goals of the EIC program. During Week 2, several topics related to TMDs have been discussed, offering complementary information with respect to the original EIC white paper. In this introduction to Week 2, we mention the main ideas and include some developments that occurred even after the conclusion of the program.

We present results for the soft drop groomed jet radius $R_g$ at next-to-leading logarithmic accuracy. The radius of a groomed jet which corresponds to the angle between the two branches passing the soft drop criterion is one of the characteristic observables relevant for the precise understanding of groomed jet substructure. We establish a factorization formalism that allows for the resummation of all relevant large logarithms, which is based on demonstrating the all order equivalence to a jet veto in the region between the boundaries of the groomed and ungroomed jet. Non-global logarithms including clustering effects due to the Cambridge/Aachen algorithm are resummed to all orders using a suitable Monte Carlo algorithm. We perform numerical calculations and find a very good agreement with Pythia 8 simulations. We provide theoretical predictions for the LHC and RHIC., Comment: 32 pages, 8 figures

We study the single spin asymmetry in the back-to-back dijet production in transversely polarized proton-proton collisions. Such an asymmetry is generated by the Sivers functions in the incoming polarized proton. We propose a QCD formalism in terms of the transverse momentum dependent parton distribution functions, which allow us to resum the large logarithms that arise in the perturbative calculations. We make predictions for the Sivers asymmetry of hadronic dijet production at the kinematic region that is relevant to the experiment at the Relativistic Heavy Ion Collider (RHIC). We further compute the spin asymmetries in the selected positive and negative jet charge bins, to separate the contributions from $u$- and $d$-quark Sivers functions. We find that both the sign and size of our numerical results are roughly consistent with the preliminary results from the STAR collaboration at the RHIC., Comment: 26 pages, 5 figures, 4 tables, section on polarized hard functions rewritten and numerics updated, additional clarification and references added

We study jet mass distributions measured in the single inclusive jet production in proton-proton collisions $pp\to \text{jet}+X$ at the LHC. We consider both standard ungroomed jets as well as soft drop groomed jets. Within the Soft Collinear Effective Theory (SCET), we establish QCD factorization theorems for both cases and we study their relation. The developed framework allows for the joint resummation of several classes of logarithmic corrections to all orders in the strong coupling constant. For the ungroomed case, we resum logarithms in the jet radius parameter and in the small jet mass. For the groomed case, we resum in addition the logarithms in the soft threshold parameter $z_{\text{cut}}$ which is introduced by the soft drop grooming algorithm. In this way, we are able to reliably determine the absolute normalization of the groomed jet mass distribution in proton-proton collisions. All logarithmic corrections are resummed to the next-to-leading logarithmic accuracy. We present numerical results and compare with the available data from the LHC. For both the groomed and ungroomed jet mass distributions we find very good agreement after including non-perturbative corrections., Comment: 38 pages, 9 figures, published version

We present a framework that describes the energy distribution of subjets of radius $r$ within a jet of radius $R$. We consider both an inclusive sample of subjets as well as subjets centered around a predetermined axis, from which the jet shape can be obtained. For $r \ll R$ we factorize the physics at angular scales $r$ and $R$ to resum the logarithms of $r/R$. For central subjets, we consider both the standard jet axis and the winner-take-all axis, which involve double and single logarithms of $r/R$, respectively. All relevant one-loop matching coefficients are given, and an inconsistency in some previous results for cone jets is resolved. Our results for the standard jet shape differ from previous calculations at next-to-leading logarithmic order, because we account for the recoil of the standard jet axis due to soft radiation. Numerical results are presented for an inclusive subjet sample for $pp \to {\rm jet}+X$ at next-to-leading order plus leading logarithmic order., 39 pages, 7 figures, v2: journal version

We develop a new formalism to describe the inclusive production of small radius jets in heavy-ion collisions, which is consistent with jet calculations in the simpler proton-proton system. Only at next-to-leading order (NLO) and beyond, the jet radius parameter $R$ and the jet algorithm dependence of the jet cross section can be studied and a meaningful comparison to experimental measurements is possible. We are able to consistently achieve NLO accuracy by making use of the recently developed semi-inclusive jet functions within Soft Collinear Effective Theory (SCET). In addition, single logarithms of the jet size parameter $\alpha_s^n\ln^n R$ are resummed to next-to-leading logarithmic (NLL$_R$) accuracy. The medium modified semi-inclusive jet functions are obtained within the framework of SCET with Glauber gluons that describe the interaction of jets with the medium. We present numerical results for the suppression of inclusive jet cross sections in heavy ion collisions at the LHC and the formalism developed here can be extended directly to corresponding jet substructure observables., Comment: 8 pages, 5 figures

Within the framework of the generalized QCD factorization formalism, we perform the first global analysis of the jet transport coefficient ($\hat q$) for cold nuclear matter. The analysis takes into account the world data on transverse momentum broadening in semi-inclusive electron-nucleus deep inelastic scattering, Drell-Yan dilepton and heavy quarkonium production in proton-nucleus collisions, as well as the nuclear modification of the structure functions in deep inelastic scattering, comprising a total of 215 data points from 8 data sets. For the first time, we clarify quantitatively the universality and probing scale dependence of the nuclear medium property as encoded in $\hat q$. We expect that the determined parametrization of $\hat q$ in cold nuclear matter will have significant impact on precise identification of the transport property of hot dense medium created in heavy ion collisions., 6 pages, 4 figures

Back-to-back light and heavy flavor dijet measurements are promising experimental channels to accurately study the physics of jet production and propagation in a dense QCD medium. They can provide new insights into the path length, color charge, and mass dependence of quark and gluon energy loss in the quark-gluon plasma produced in reactions of ultra-relativistic nuclei. To this end, we perform a comprehensive study of both light and heavy flavor dijet production in heavy ion collisions. We propose the modification of dijet invariant mass distributions in such reactions as a novel observable that shows enhanced sensitivity to the QGP transport properties and heavy quark mass effects on in-medium parton showers. This is achieved through the addition of the jet quenching effects on the individual jets as opposed to their subtraction. The latter drives the subtle effects on more conventional observables, such as the dijet momentum imbalance shifts, which we also calculate here. Results are presented in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for comparison to data at the Large Hadron Collider and in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV to guide the future sPHENIX program at the Relativistic Heavy Ion Collider., Comment: 17 pages, 16 figures, 1 table. v2: subfigures and references added, version published by PRD

In this letter we study the impact of the Electron-Ion Collider (EIC) on the phenomenological extraction of the tensor charge from a QCD global analysis of single transverse-spin asymmetries (SSAs). We generate EIC pseudo-data for the Collins effect in semi-inclusive deep-inelastic scattering for proton and $^{3\!}He$ beams across multiple center-of-mass energies. We find a significant reduction in the uncertainties for the up, down, and isovector tensor charges that will make their extraction from EIC data on SSAs as precise as current lattice QCD calculations. We also analyze the constraints placed by future data from the proposed SoLID experiment at Jefferson Lab, discuss its important complementary role to the EIC, and present the combined impact from both facilities., Comment: 12 pages, 6 figures, 1 table; minor changes; version to be published in PLB

We present some recent progress in studying the jet quenching phenomena. In the first part of the talk, we study how to improve the standard energy loss picture by going beyond the “soft-gluon” (small-x) approximation and formulating the multi-gluon emission through the usual DGLAP evolution equations in the nuclear medium. We demonstrate that the numerical results based on such an approach describe well the suppression of single hadron production in A+A collisions at the LHC. In the second part of the talk, we present how to study the next-to-leading order corrections to the energy loss formalism. In particular, we compute the full next-to-leading order QCD corrections to the transverse momentum broadening in both e+A and p+A collisions, from which we identify a QCD evolution equation for the related quark-gluon correlation function, in turn, the QCD evolution of jet transport parameter qˆ.

We present theoretical predictions for the nuclear-induced attenuation of the differential cross sections for inclusive and tagged b-jet production in heavy ion collisions at the LHC. We find that for inclusive b-jet production at high transverse momentum the mass effects are negligible, and that the attenuation is comparable to the one observed for light jets. On the other hand, for isolated-photon and B-meson-tagged b-jets the sample of events with heavy quarks produced at the early stages of the collision is greatly enhanced. Thus, these tagged b-jet final-states have a much more direct connection to the physics of b-quark energy loss. We present theoretical predictions for the quenching of such tagged b-jet events at the LHC and the QGP-induced modification of the related momentum imbalance and asymmetry. We demonstrate that these tagged processes can be used to accurately study the physics of heavy quark production and propagation in dense QCD matter., Comment: 4 pages, 5 figures, talk presented by Hongxi Xing at the Hard Probes 2015 conference

In these proceedings, we review recent theoretical progress on jet substructure at the colliders. Focusing on two observables – jet mass and groomed jet radius, we perform theoretical computations for jets measured in the single inclusive jet production in proton-proton collisions, pp → jet + X. We consider both standard ungroomed jets as well as soft-drop groomed jets. Within the Soft Collinear Effective Theory (SCET), we establish QCD factorization theorems which allow for the joint resummation of several classes of logarithmic corrections to all orders in the strong coupling constant. We present numerical results and compare with the available data from the LHC.

Protons and neutrons are known to be the building blocks of matter, and also known to be the bound states of quarks and gluons the partons, whose dynamics is best described by Quantum Chromodynamics (QCD). Perturbative QCD has been very successful in interpreting and predicting high-energy hadronic scattering processes by factorizing the leading contribution to the physical cross sections into a convolution of the perturbatively calculable short-distance part and the universal long-distance parton distribution functions (PDFs) of colliding hadrons. Besides testing QCD dynamics at the short-distance, these cross sections also probe partonic structure inside a colliding hadron via PDFs, which are often interpreted as the probability densities of finding a parton inside a hadron with a given longitudinal momentum fraction. In this thesis I discuss the possibilities to explore the rich partonic dynamics inside a hadron or a large nucleus beyond the probability distributions. I will first explain why a difference of two transverse-spin dependent cross sections (or the measurement of the single transverse-spin asymmetry) can directly probe a set of new three-parton correlation functions. These correlation functions provide the first direct information on quantum correlation between quarks and gluons inside a polarized hadron. I will describe the basic formalism and the experimental measurements of these correlation functions. I will present the first derivation of evolution equations (or renormalization group equations) for these correlation functions. I will then discuss how to use the nuclear dependence of high energy nuclear collisions to extract the information on four-parton correlations inside a large nucleus or a nuclear medium. The measurements of the spin asymmetry and the anomalous nuclear dependence provide us new opportunities to explore the QCD dynamics and hadron structure beyond the parton probability distributions.

We study jet angularity measurements for single-inclusive jet production at the LHC. Jet angularities depend on a continuous parameter $a$ allowing for a smooth interpolation between different traditional jet shape observables. We establish a factorization theorem within Soft Collinear Effective Theory (SCET) where we consistently take into account in- and out-of-jet radiation by making use of semi-inclusive jet functions. For comparison, we elaborate on the differences to jet angularities measured on an exclusive jet sample. All the necessary ingredients for the resummation at next-to-leading logarithmic (NLL) accuracy are presented within the effective field theory framework. We expect semi-inclusive jet angularity measurements to be feasible at the LHC and we present theoretical predictions for the relevant kinematic range. In addition, we investigate the potential impact of jet angularities for quark-gluon discrimination., 28 pages, 7 figures

We study the production of polarized $\Lambda$-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized $\Lambda$-hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find that the QCD equation of motion plays a crucial role in our analysis. As a byproduct, assuming the validity of QCD factorization for twist-3 observables at next-to-leading order, we derive the evolution equation for the relevant twist-3 fragmentation matrix element., Comment: 43 pages, 25 figures

Jet angularities are a class of jet substructure observables where a continuous parameter is introduced in order to interpolate between different classic observables such as the jet mass and jet broadening. We consider jet angularities measured on an inclusive jet sample at the LHC where the soft drop grooming procedure is applied in order to remove soft contaminations from the jets. The soft drop algorithm allows for a precise comparison between theory and data and could be used to extract the QCD strong coupling constant $\alpha_s$ from jet substructure data in the future. We develop a framework to realize the resummation of all relevant large logarithms at the next-to-leading logarithmic (NLL) accuracy. To demonstrate that the developed formalism is suitable for the extraction of $\alpha_s$, we extend our calculations to next-to-next-to-leading logarithm (NNLL) for the jet mass case. Overall, we find good agreement between our NLL numerical results and Pythia simulations for LHC kinematics and we observe an improved agreement when the NNLL components are included. In addition, we expect that groomed jet angularities will be a useful handle for studying the modification of jets in heavy-ion collisions., Comment: 10 pages, 3 figures, published version in PLB

We study the incoherent multiple scattering effects on heavy meson production in the backward rapidity region of p+A collisions within the generalized high-twist factorization formalism. We calculate explicitly the double scattering contributions to the heavy meson differential cross sections by taking into account both initial-state and final-state interactions, and find that these corrections are positive. We further evaluate the nuclear modification factor for muons that come form the semi-leptonic decays of heavy flavor mesons. Phenomenological applications in d+Au collisions at a center-of-mass energy $\sqrt{s}=200$ GeV at RHIC and in p+Pb collisions at $\sqrt{s}=5.02$ TeV at the LHC are presented. We find that incoherent multiple scattering can describe rather well the observed nuclear enhancement in the intermediate $p_T$ region for such reactions., 10 pages, 6 figures, published version in PLB

We investigate the Collins azimuthal asymmetry of hadrons produced inside jets in transversely polarized proton-proton collisions. Recently, the quark transversity distributions and the Collins fragmentation functions have been extracted within global analyses from data of the processes semi-inclusive deep inelastic scattering and electron-positron annihilation. We calculate the Collins azimuthal asymmetry for charged pions inside jets using these extractions for RHIC kinematics at center-of-mass energies of 200 and 500 GeV. We compare our results with recent data from the STAR Collaboration at RHIC and find good agreement, which confirms the universality of the Collins fragmentation functions. In addition, we further explore the impact of transverse momentum dependent evolution effects., 12 pages, 5 figures, expanded version published in PLB

We study the transverse momentum distribution of hadrons within jets, where the transverse momentum is defined with respect to the standard jet axis. We consider the case where the jet substructure measurement is performed for an inclusive jet sample $pp\to\text{jet}+X$. We demonstrate that this observable provides new opportunities to study transverse momentum dependent fragmentation functions (TMDFFs) which are currently poorly constrained from data, especially for gluons. The factorization of the cross section is obtained within Soft Collinear Effective Theory (SCET), and we show that the relevant TMDFFs are the same as for the more traditional processes semi-inclusive deep inelastic scattering (SIDIS) and electron-positron annihilation. Different than in SIDIS, the observable for the in-jet fragmentation does not depend on TMD parton distribution functions which allows for a cleaner and more direct probe of TMDFFs. We present numerical results and compare to available data from the LHC., 28 pages, 3 figures, published version

We study the production and polarization of $J/\psi$ mesons within a jet in proton-proton collisions at the LHC. We define the $J/\psi$-jet fragmentation function as a ratio of differential jet cross sections with and without the reconstructed $J/\psi$ in the jet. We demonstrate that this is a very useful observable to help explore the $J/\psi$ production mechanism, and to differentiate between different NRQCD global fits based on inclusive $J/\psi$ cross sections. Furthermore, we propose to measure the polarization of $J/\psi$ mesons inside the jet, which can provide even more stringent constraints for the heavy quarkonium production mechanism., Comment: 5 pages, 3 figures, published version

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6. Keywords: Semi-inclusive deep inelastic scattering; Tensor charge; Transversity; Jefferson Lab 12 GeV upgrade; SoLID; JLAB-THY-16-2328, United States. Department of Energy (Contract DE-FG02-94ER40818)

We develop a version of Soft Collinear Effective Theory (SCET) which includes finite quark masses, as well as Glauber gluons that describe the interaction of collinear partons with QCD matter. In the framework of this new effective field theory, labeled SCET$_{\mathrm{M,G}}$, we derive the massive splitting functions in the vacuum and the QCD medium for the processes $Q\to Qg$, $Q\to gQ$ and $g\to Q\bar Q$. The numerical effects due to finite quark masses are sizable and our results are consistent with the traditional approach to parton energy loss in the soft gluon emission limit. In addition, we present a new framework for including the medium-induced full splitting functions consistent with next-to-leading order calculations in QCD for inclusive hadron production. Finally, we show numerical results for the suppression of $D$- and $B$-mesons in heavy ion collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV and 2.76 TeV and compare to available data from the LHC., 43 pages, 14 figures

We review the definition of semi-inclusive jet functions within Soft Collinear Effective Theory (SCET) and their application to inclusive jet cross sections. As an example, we consider both the inclusive production of jets and the jet fragmentation function in proton-proton collisions. The semi-inclusive jet functions satisfy renormalization group (RG) equations which take the form of standard timelike DGLAP evolution equations, analogous to collinear fragmentation functions. By solving these RG equations, the resummation of potentially large single logarithms $(\alpha_s \ln R)^n$ can be achieved. We present numerical results at NLO+NLL$_R$ accuracy and compare to existing data from the LHC., Comment: 8 pages, 3 figures, contribution to proceedings of QCD Evolution 2016 Workshop

The European physical journal / A 53(4), 71 (2017). doi:10.1140/epja/i2017-12251-4, A polarized ep/eA collider (Electron-Ion Collider, or EIC), with polarized proton and light-ion beams and unpolarized heavy-ion beams with a variable center-of-mass energy $\sqrt{s} ∼ 20 to ∼100 GeV$ (upgradable to $∼ 150 GeV$) and a luminosity up to $∼ 10^{34} cm^{-2}s^{-1}$, would be uniquely suited to address several outstanding questions of Quantum Chromodynamics, and thereby lead to new qualitative and quantitative information on the microscopic structure of hadrons and nuclei. During this meeting at Jefferson Lab we addressed recent theoretical and experimental developments in the spin and the three-dimensional structure of the nucleon (sea quark and gluon spatial distributions, orbital motion, polarization, and their correlations). This mini-review contains a short update on progress in these areas since the EIC White paper (A. Accardi et al., Eur. Phys. J. A 52, 268 (2016))., Published by Springer, Berlin

We propose a new method to evaluate jet substructure observables in inclusive jet measurements, based upon semi-inclusive jet functions in the framework of Soft Collinear Effective Theory (SCET). As a first example, we consider the jet fragmentation function, where a hadron $h$ is identified inside a fully reconstructed jet. We introduce a new semi-inclusive fragmenting jet function ${\mathcal G}^h_i(z= \omega_J/\omega,z_h=\omega_h/\omega_J,\omega_J, R,\mu)$, which depends on the jet radius $R$ and the large light-cone momenta of the parton `$i$' initiating the jet ($\omega$), the jet ($\omega_J$), and the hadron $h$ ($\omega_h$). The jet fragmentation function can then be expressed as a semi-inclusive observable, in the spirit of actual experimental measurements, rather than as an exclusive one. We demonstrate the consistency of the effective field theory treatment and standard perturbative QCD calculations of this observable at next-to-leading order (NLO). The renormalization group (RG) equation for the semi-inclusive fragmenting jet function ${\mathcal G}_i^h(z,z_h, \omega_J, R,\mu)$ are also derived and shown to follow exactly the usual timelike DGLAP evolution equations for fragmentation functions. The newly obtained RG equations can be used to perform the resummation of single logarithms of the jet radius parameter $R$ up to next-to-leading logarithmic (NLL$_R$) accuracy. In combination with the fixed NLO calculation, we obtain NLO+NLL$_R$ results for the hadron distribution inside the jet. We present numerical results for $pp\to(\mathrm{jet}\,h)X$ in the new framework, and find excellent agreement with existing LHC experimental data., Comment: 28 pages, 6 figures, published version

We present the nuclear transverse momentum broadening for Drell-Yan lepton pair production in p+A collisions at next-to-leading order (NLO) in powers of strong coupling constant $\alpha_s$. We verify that the transverse momentum weighted differential cross section in NLO perturbative QCD (pQCD) at twist-4 can be factorized into the convolution of parton distribution function of an active parton in the projectile proton, a twist-4 multiparton correlation function of the target nucleus, and perturbatively calculable hard coefficient function. We identify a QCD evolution equation for such a twist-4 nuclear gluon-quark correlation function, and verify its universality -- its process independence. This finding demonstrates the prediction power of pQCD factorization approach for studying parton multiple scattering in nuclear medium., Comment: 18 pages, 12 figures

We introduce a new kind of jet function: the semi-inclusive jet function $J_i(z, \omega_J, \mu)$, which describes how a parton $i$ is transformed into a jet with a jet radius $R$ and energy fraction $z = \omega_J/\omega$, with $\omega_J$ and $\omega$ being the large light-cone momentum component of the jet and the corresponding parton $i$ that initiates the jet, respectively. Within the framework of Soft Collinear Effective Theory (SCET) we calculate both $J_q(z, \omega_J, \mu)$ and $J_g(z, \omega_J, \mu)$ to the next-to-leading order (NLO) for cone and anti-k$_{\rm T}$ algorithms. We demonstrate that the renormalization group (RG) equations for $J_i(z, \omega_J, \mu)$ follow exactly the usual DGLAP evolution, which can be used to perform the $\ln R$ resummation for {\it inclusive} jet cross sections with a small jet radius $R$. We clarify the difference between our RG equations for $J_i(z, \omega_J, \mu)$ and those for the so-called unmeasured jet functions $J_i(\omega_J, \mu)$, widely used in SCET for {\it exclusive} jet production. Finally, we present applications of the new semi-inclusive jet functions to inclusive jet production in $e^+e^-$ and $pp$ collisions. We demonstrate that single inclusive jet production in these collisions shares the same short-distance hard functions as single inclusive hadron production, with only the fragmentation functions $D_i^h(z, \mu)$ replaced by $J_i(z, \omega_J, \mu)$. This can facilitate more efficient higher-order analytical computations of jet cross sections. We further match our $\ln R$ resummation at both LL$_{R}$ and NLL$_{R}$ to fixed NLO results and present the phenomenological implications for single inclusive jet production at the LHC., Comment: 35 pages, 11 figures, published version at JHEP

We review a new approach to open heavy flavor production in heavy ion collisions based on Soft Collinear Effective Theory (SCET). We include both finite heavy quark masses in the SCET Lagrangian and Glauber gluons that describe the interaction of collinear partons with the hot and dense QCD medium. From the new effective field theory, we derive massive in-medium splitting kernels and propose a new framework for including in-medium interactions consistent with next-to-leading order calculations in QCD. We present numerical results for the suppression of $D$- and $B$-mesons and compare to results obtained within the traditional approach to parton energy loss. We find good agreement when comparing to existing data from the LHC at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV and 2.76 TeV., 4 pages, 2 figures, contribution to proceedings of Strangeness in Quark Matter 2016

Predictions made in Albacete {\it et al} prior to the LHC $p+$Pb run at $\sqrt{s_{NN}} = 5$ TeV are compared to currently available data. Some predictions shown here have been updated by including the same experimental cuts as the data. Some additional predictions are also presented, especially for quarkonia, that were provided to the experiments before the data were made public but were too late for the original publication are also shown here., 55 pages 35 figures

Recently, three twist-3 spin asymmetries for single-inclusive hadron production in deep-inelastic lepton-nucleon scattering have been computed using collinear factorization and the leading order approximation. Here we summarize the main findings of these studies.

We review the relation between the QCD perturbative resummation and evolution. Particularly we emphasize briefly the idea on how to use the evolution equation to resum the important double logarithms appeared in the perturbative QCD expansion when the process involves two distinctive scales Q1 ≫ Q2. We present the resummation formalism for the single transverse spin asymmetry for both semi-inclusive deep inelastic scattering and Drell-Yan production processes.

It is possible to extend the formalism for high- p T heavy quarkonium factorization beyond leading power. This extension may be helpful in interpreting the relative roles of octet and singlet channels in the formalism of nonrelativistic QCD (NRQCD). It may enable us to understand the origin of the surprisingly large results for cross sections calculated in the color singlet sector of NRQCD.

We study the single transverse spin asymmetries in the single inclusive particle production within the framework of the generalized parton model (GPM). By carefully analyzing the initial- and final-state interactions, we include the process-dependence of the Sivers functions into the GPM formalism. The modified GPM formalism has a close connection with the collinear twist-3 approach. Within the new formalism, we make predictions for inclusive $\pi^0$ and direct photon productions at RHIC energies. We find the predictions are opposite to those in the conventional GPM approach., Comment: 12 pages, 5 figures, extended discussion on connection with twist three approach, references added

Using the opacity expansion technique we investigate the photon radiation and dilepton production induced by multiple rescattering as energetic parton jet passing through the strong interacting medium. The real photon radiation and dilepton invariant-mass spectrums of the bremsstrahlung contribution from an energetic quark jet are presented. The leading contribution of total energy loss by photon emmision in medium of a higher energy quark jet is found to be proportional to the jet energy and has a linear dependence on the thickness of the nuclear target. The rescattering contribution for the dilepton is important only for small value of the invariant-mass and for the not so fast jet. The contribution fraction of the dilepton induced by rescattering in medium is found to be nearly a constant when the ratio of jet energy to Debye screening mass $E/\mu$ is large., Comment: 10 pages, 10 figures, revised version

We introduce a generalized definition of parton distribution functions (PDFs) for a more consistent all-order treatment of power corrections. We present a new set of modified DGLAP evolution equations for nuclear PDFs, and show that the resummed $\alpha_s A^{1/3}/Q^2$-type of leading nuclear size enhanced power corrections significantly slow down the growth of gluon density at small-$x$. We discuss the relation between the calculated power corrections and the saturation phenomena.

Recent measurements of the centrality and rapidity dependence of single inclusive jet production in p+Pb collisions at the Large Hadron Collider (LHC) have revealed large and nontrivial nuclear modification of the production cross section for this process. In this paper, we explore to what extent such nuclear modification can be understood by the framework of standard cold nuclear matter effects, in particular initial-state cold nuclear matter energy loss. We demonstrate quantitatively that theoretical calculations which include medium-induced radiative corrections can describe rather reasonably the attenuation of the jet production yields in the large transverse momentum region in d+Au collisions at the Relativistic Heavy Ion Collider and p+Pb collisions at the LHC for central to semicentral collisions. We further show that the observed scaling behavior of the nuclear modification factor as a function of the total jet energy pTcosh(y) for various rapidity intervals has a natural explanation in the picture of cold nuclear matter energy loss. However, the observed enhancement in peripheral collisions is not described in this picture and could have a different origin.

Recent advances in soft-collinear effective theory with Glauber gluons have led to the development of a new method that gives a unified description of inclusive hadron production in reactions with nucleons and heavy nuclei. We show how this approach, based on the generalization of the DGLAP evolution equations to include final-state medium-induced parton showers, can be combined with initial-state effects for applications to jet quenching phenomenology. We demonstrate that the traditional parton energy loss calculations can be regarded as a special soft-gluon emission limit of the general QCD evolution framework. We present phenomenological comparison of the SCET$_{\rm G}$-based results on the suppression of inclusive charged hadron and neutral pion production in $\sqrt{s_{NN}}=2.76$ TeV lead-lead collisions at the Large Hadron Collider to experimental data. We also show theoretical predictions for the upcoming $\sqrt{s_{NN}} \simeq 5.1$ TeV Pb+Pb run at the LHC., 21 pages 6 figures; appendix, figure and references added

We introduce a modified factorization formalism in quantum chromodynamics for hadronic production of $W$ and $Z$ bosons at large transverse momentum ${p}_{T}$. When ${p}_{T}$ is much larger than the invariant mass $Q$ of the vector boson, this new factorization formalism systematically resums the large fragmentation logarithms, ${\ensuremath{\alpha}}_{s}^{m}{\mathrm{ln}}^{m}({p}_{T}^{2}/{Q}^{2})$, to all orders in the strong coupling ${\ensuremath{\alpha}}_{s}$. Using our modified factorization formalism, we present the next-to-leading-order (NLO) predictions for $W$ and $Z$ boson production at high ${p}_{T}$ at the CERN Large Hadron Collider and at a future 100 TeV proton-proton collider. Our NLO results are about 5% larger in normalization, and they show improved convergence and moderate reduction of the scale variation compared to the NLO predictions derived in a conventional fixed-order perturbative expansion.

We present the first application of a recently-developed effective theory of jet propagation in matter SCETG to inclusive hadron suppression in nucleus-nucleus collisions at the LHC. SCETG-based splitting kernels allow us to go beyond the traditional energy loss approximation and unify the treatment of vacuum and medium-induced parton showers. In the soft gluon emission limit, we establish a simple analytic relation between the QCD evolution and energy loss approaches to jet quenching. We quantify the uncertainties associated with the implementation of the in-medim modification of hadron production cross sections and show that the coupling between the jet and the medium can be constrained with better than 10% accuracy., Comment: 5 pages, 3 eps figures