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Topic: The COVID-19 pandemic affected adolescents' physical and psychological health. There must be specific services to cater to the needs of adolescents during COVID-19 in Indonesia. Lessons learned from previous pandemics will be beneficial for nurses and other health professionals to prepare services for future pandemics. Purpose: This mixed-method study aimed to examine 459 Indonesian adolescents' health, literacy, preventive measures, and preferred health services during the COVID-19 pandemic. This study also examines sociodemographics, respondent characteristics, health information sources, and media choices. Results: A total of 47.5% of adolescents knew about COVID-19, 26.8% experienced physical health changes, and 61.7% considered wearing masks. Adolescent health information came from teachers (26.6%) and the Internet (32.9%). Psychological changes showed 67.8% irritation. Indonesians preferred online counseling (53.8%) and WhatsApp (45.8%) for pandemic health services. COVID-19 literacy did not affect physical or mental health (p > 0.05). Conclusions: Most adolescents reported mental and physical health changes during COVID-19. Our data suggest that adolescents' strong COVID−19 knowledge did not prevent anxiety and other psychological difficulties. The longitudinal studies could be utilized if pandemic demands social and physical distance. The government, as well as nurses, might utilize WhatsApp-based remote online treatment for health services.

We study the azimuthal angle dependence of the energy-energy correlators $$\langle \mathcal{E}\left({\widehat{n}}_{1}\right)\mathcal{E}\left({\widehat{n}}_{2}\right)\rangle $$ in the back-to-back region for e+e− annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers $${\mathbb{S}}_{i}$$ in the back-to-back limit $$\langle {\mathcal{E}}_{{\mathbb{S}}_{1}}\left({\widehat{n}}_{1}\right){\mathcal{E}}_{{\mathbb{S}}_{2}}\left({\widehat{n}}_{2}\right)\rangle $$ . We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program.

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance., Comment: 44 pages, ReVTeX, White Paper on EIC Theory Alliance

The confining transition from asymptotically free partons to hadrons remains one of the most mysterious aspects of Quantum Chromodynamics. With the wealth of high quality jet substructure data we can hope to gain new experimental insights into the details of its dynamics. Jet substructure has traditionally focused on correlations, $\langle \mathcal{E}(n_1) \mathcal{E}(n_2) \cdots \mathcal{E}(n_k) \rangle$, in the energy flux of hadrons. However, significantly more information about the confinement transition is encoded in how energy is correlated between hadrons with different quantum numbers, for example electric charge. In this Letter we develop the field theoretic formalism to compute general correlations, $\langle \mathcal{E}_{R_1}(n_1) \mathcal{E}_{R_2}(n_2) \cdots\mathcal{E}_{R_k}(n_k) \rangle$, between the energy flux carried by hadrons with quantum numbers $R_i$, by introducing new universal non-perturbative functions, which we term joint track functions. Using this formalism we show that the strong interactions introduce enhanced small angle correlations between opposite-sign hadrons, relative to like-sign hadrons, identifiable as an enhanced scaling of $\langle \mathcal{E}_+(n_1) \mathcal{E}_-(n_2) \rangle$ relative to $\langle \mathcal{E}_+(n_1) \mathcal{E}_+(n_2) \rangle$. We are also able to compute the scaling of a $C$-odd three-point function, $\langle \mathcal{E}_\mathcal{Q}(n_1) \mathcal{E}_\mathcal{Q}(n_2) \mathcal{E}_\mathcal{Q}(n_3) \rangle$. Our results greatly extend the class of systematically computable jet substructure observables, pushing perturbation theory deeper into the parton to hadron transition, and providing new observables to understand the dynamics of confinement., Comment: 6 pages, 5 incredible figures

The confining transition from asymptotically free partons to hadrons remains one of the most mysterious aspects of Quantum Chromodynamics. With the wealth of high quality jet substructure data we can hope to gain new experimental insights into the details of its dynamics. Jet substructure has traditionally focused on correlations, $\langle \mathcal{E}(n_1) \mathcal{E}(n_2) \cdots \mathcal{E}(n_k) \rangle$, in the energy flux of hadrons. However, significantly more information about the confinement transition is encoded in how energy is correlated between hadrons with different quantum numbers, for example electric charge. In this Letter we develop the field theoretic formalism to compute general correlations, $\langle \mathcal{E}_{R_1}(n_1) \mathcal{E}_{R_2}(n_2) \cdots\mathcal{E}_{R_k}(n_k) \rangle$, between the energy flux carried by hadrons with quantum numbers $R_i$, by introducing new universal non-perturbative functions, which we term joint track functions. Using this formalism we show that the strong interactions introduce enhanced small angle correlations between opposite-sign hadrons, relative to like-sign hadrons, identifiable as an enhanced scaling of $\langle \mathcal{E}_+(n_1) \mathcal{E}_-(n_2) \rangle$ relative to $\langle \mathcal{E}_+(n_1) \mathcal{E}_+(n_2) \rangle$. We are also able to compute the scaling of a $C$-odd three-point function, $\langle \mathcal{E}_\mathcal{Q}(n_1) \mathcal{E}_\mathcal{Q}(n_2) \mathcal{E}_\mathcal{Q}(n_3) \rangle$. Our results greatly extend the class of systematically computable jet substructure observables, pushing perturbation theory deeper into the parton to hadron transition, and providing new observables to understand the dynamics of confinement., Comment: 6 pages, 5 incredible figures

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance., Comment: 44 pages, ReVTeX, White Paper on EIC Theory Alliance

We generalize the conventional Energy-Energy Correlator (EEC) to include the azimuthal angle dependence, so to define azimuthal angle dependent EEC observables. We study this new EEC observable in $e^+e^-$ and semi-inclusive deep inelastic scattering (SIDIS). In the back-to-back region, we find that the azimuthal angle dependent EEC is sensitive to both the unpolarized EEC jet function and a Collins-type EEC jet function. While the unpolarized EEC jet function is related to the unpolarized transverse momentum dependent (TMD) fragmentation function, the Collins-type EEC jet function is connected with the Collins fragmentation function. We further demonstrate how the new observables allow us to access to the 3D structure of nucleons, especially the spin-dependent ones., Comment: Presented at DIS2023: XXX International Workshop on Deep-Inelastic Scattering and Related Subjects, Michigan State University, USA, 27-31 March 2023

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an anti-fermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system's von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity (CP) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors., Comment: 23 pages, 16 figures

The theoretical description of observables at collider experiments relies on factorization theorems separating perturbative dynamics from universal non-perturbative matrix elements. Despite significant recent progress in extending these factorization theorems to increasingly differential jet substructure observables, the focus has been primarily on infrared safe observables sensitive only to correlations in the energy of final state hadrons. However, significant information about the dynamics of the underlying collision is encoded in how energy is correlated between hadrons of different quantum numbers. In this paper we extend the class of calculable correlations by deriving factorization theorems for a broad class of correlations, $\langle \mathcal{E}_{R_1}(n_1) \cdots \mathcal{E}_{R_k}(n_k) \rangle$, between the energy flux carried by hadrons specified by quantum numbers, $R_1, \cdots, R_k$. We show that these factorization theorems involve moments of a new class of universal non-perturbative functions, the "joint track functions", which extend the track function formalism to describe the fraction of energy carried by hadrons of multiple quantum numbers arising from the fragmentation of quarks or gluons. We study the general properties of these functions, and then apply this to the specific case of joint track functions for positive and negative electromagnetic charges. We extract these from parton shower Monte Carlo programs and use them to calculate correlations in electromagnetically charged energy flux. We additionally propose and study a C-odd $\mathcal{E}_{\mathcal{Q}}$ detector, which results in a qualitatively distinct scaling behavior compared to the standard energy correlators. Our formalism significantly extends the class of observables that can be computed at hadron colliders, with a wide range of applications from particle to nuclear physics., Comment: 25 pages, 9 fancy figures

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called "track functions", in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program., Comment: 22 pages, 8 beautiful figures

The future electron-ion collider (EIC) will produce the first-ever high energy collisions between electrons and a wide range of nuclei, opening a new era in the study of cold nuclear matter. Quarks and gluons produced in these collisions will propagate through the dense nuclear matter of nuclei, imprinting its structure into subtle correlations in the energy flux of final state hadrons. In this Letter, we apply recent developments from the field of jet substructure, namely the energy correlator observables, to decode these correlations and provide a new window into nuclear structure. The energy correlators provide a calibrated probe of the scale dependence of vacuum QCD dynamics, enabling medium modifications to be cleanly imaged and interpreted as a function of scale. Using the eHIJING parton shower to simulate electron-nucleus collisions, we demonstrate that the size of the nucleus is cleanly imprinted as an angular scale in the correlators, with a magnitude that is visible for realistic EIC kinematics. Remarkably, we can even observe the size difference between the proposed EIC nuclear targets ${}^3$He, ${}^4$He, ${}^{12}$C, ${}^{40}$Ca, ${}^{64}$Cu, ${}^{197}$Au, and ${}^{238}$U, showing that the energy correlators can image femtometer length scales using asymptotic energy flux. Our approach offers a unified view of jet substructure across collider experiments, and provides numerous new theoretical tools to unravel the complex dynamics of QCD in extreme environments, both hot and cold., Comment: 6 pages, 5 beautiful figures, and appendices

One of the greatest challenges in quantum chromodynamics is understanding the hadronization mechanism, which is also crucial for carrying out precision physics with jet substructure. In this Letter, we combine recent advancements in our understanding of the field theory-based nonperturbative structure of the soft drop jet mass with precise perturbative calculations of its multi-differential variants at next-to-next-to-leading logarithmic (NNLL) accuracy. This enables a systematic study of its hadronization power corrections in a completely model-independent way. We calibrate and test hadronization models and their interplay with parton showers by comparing our universality predictions with various event generators for quark and gluon initiated jets in both lepton-lepton and hadron-hadron collisions. We find that hadronization models perform better for quark jets relative to gluon jets. Our results provide the necessary toolkit for precision studies with the soft drop jet mass motivating future analyses using real world collider data. The nontrivial constraints derived in our framework are useful for improving the modeling of hadronization and its interface with parton showers in next generation event generators., Comment: 8 pages, 6 figures + supplemental material (4 pages, 5 figures)

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an anti-fermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system's von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity (CP) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors., Comment: 23 pages, 16 figures

We study the azimuthal angle dependence of the energy-energy correlators $\langle \mathcal{E}(\hat{n}_1)\mathcal{E}(\hat{n}_2)\rangle$ in the back-to-back region for $e^+e^-$ annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers $\mathbb{S}_i$ in the back-to-back limit $\langle \mathcal{E}_{\mathbb{S}_1}(\hat{n}_1)\mathcal{E}_{\mathbb{S}_2}(\hat{n}_2)\rangle$. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures., Comment: 36 pages, 7 figures

The theoretical description of observables at collider experiments relies on factorization theorems separating perturbative dynamics from universal non-perturbative matrix elements. Despite significant recent progress in extending these factorization theorems to increasingly differential jet substructure observables, the focus has been primarily on infrared safe observables sensitive only to correlations in the energy of final state hadrons. However, significant information about the dynamics of the underlying collision is encoded in how energy is correlated between hadrons of different quantum numbers. In this paper we extend the class of calculable correlations by deriving factorization theorems for a broad class of correlations, $\langle \mathcal{E}_{R_1}(n_1) \cdots \mathcal{E}_{R_k}(n_k) \rangle$, between the energy flux carried by hadrons specified by quantum numbers, $R_1, \cdots, R_k$. We show that these factorization theorems involve moments of a new class of universal non-perturbative functions, the "joint track functions", which extend the track function formalism to describe the fraction of energy carried by hadrons of multiple quantum numbers arising from the fragmentation of quarks or gluons. We study the general properties of these functions, and then apply this to the specific case of joint track functions for positive and negative electromagnetic charges. We extract these from parton shower Monte Carlo programs and use them to calculate correlations in electromagnetically charged energy flux. We additionally propose and study a C-odd $\mathcal{E}_{\mathcal{Q}}$ detector, which results in a qualitatively distinct scaling behavior compared to the standard energy correlators. Our formalism significantly extends the class of observables that can be computed at hadron colliders, with a wide range of applications from particle to nuclear physics., Comment: 25 pages, 9 fancy figures

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called "track functions", in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program., Comment: 22 pages, 8 beautiful figures

We generalize the conventional Energy-Energy Correlator (EEC) to include the azimuthal angle dependence, so to define azimuthal angle dependent EEC observables. We study this new EEC observable in $e^+e^-$ and semi-inclusive deep inelastic scattering (SIDIS). In the back-to-back region, we find that the azimuthal angle dependent EEC is sensitive to both the unpolarized EEC jet function and a Collins-type EEC jet function. While the unpolarized EEC jet function is related to the unpolarized transverse momentum dependent (TMD) fragmentation function, the Collins-type EEC jet function is connected with the Collins fragmentation function. We further demonstrate how the new observables allow us to access to the 3D structure of nucleons, especially the spin-dependent ones., Comment: Presented at DIS2023: XXX International Workshop on Deep-Inelastic Scattering and Related Subjects, Michigan State University, USA, 27-31 March 2023

We explore machine learning-based jet and event identification at the future Electron-Ion Collider (EIC). We study the effectiveness of machine learning-based classifiers at relatively low EIC energies, focusing on (i) identifying the flavor of the jet and (ii) identifying the underlying hard process of the event. We propose applications of our machine learning-based jet identification in the key research areas at the future EIC and current Relativistic Heavy Ion Collider program, including enhancing constraints on (transverse momentum dependent) parton distribution functions, improving experimental access to transverse spin asymmetries, studying photon structure, and quantifying the modification of hadrons and jets in the cold nuclear matter environment in electron-nucleus collisions. We establish first benchmarks and contrast the estimated performance of flavor tagging at the EIC with that at the Large Hadron Collider. We perform studies relevant to aspects of detector design including particle identification, charge information, and minimum transverse momentum capabilities. Additionally, we study the impact of using full event information instead of using only information associated with the identified jet. These methods can be deployed either on suitably accurate Monte Carlo event generators, or, for several applications, directly on experimental data. We provide an outlook for ultimately connecting these machine learning-based methods with first principles calculations in quantum chromodynamics.

The future electron-ion collider (EIC) will produce the first-ever high energy collisions between electrons and a wide range of nuclei, opening a new era in the study of cold nuclear matter. Quarks and gluons produced in these collisions will propagate through the dense nuclear matter of nuclei, imprinting its structure into subtle correlations in the energy flux of final state hadrons. In this Letter, we apply recent developments from the field of jet substructure, namely the energy correlator observables, to decode these correlations and provide a new window into nuclear structure. The energy correlators provide a calibrated probe of the scale dependence of vacuum QCD dynamics, enabling medium modifications to be cleanly imaged and interpreted as a function of scale. Using the eHIJING parton shower to simulate electron-nucleus collisions, we demonstrate that the size of the nucleus is cleanly imprinted as an angular scale in the correlators, with a magnitude that is visible for realistic EIC kinematics. Remarkably, we can even observe the size difference between the proposed EIC nuclear targets ${}^3$He, ${}^4$He, ${}^{12}$C, ${}^{40}$Ca, ${}^{64}$Cu, ${}^{197}$Au, and ${}^{238}$U, showing that the energy correlators can image femtometer length scales using asymptotic energy flux. Our approach offers a unified view of jet substructure across collider experiments, and provides numerous new theoretical tools to unravel the complex dynamics of QCD in extreme environments, both hot and cold., Comment: 6 pages, 5 beautiful figures, and appendices

The remarkably high energies of the Large Hadron Collider (LHC) have allowed for the first measurements of the shapes and scalings of multi-point correlators of energy flow operators, $\langle \Psi | \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \cdots \mathcal{E}(\vec n_k) |\Psi \rangle$, providing new insights into the Lorentzian dynamics of quantum chromodynamics (QCD). In this Letter, we use recent advances in effective field theory to derive a rigorous factorization theorem for the light-ray density matrix, $\rho= |\Psi\rangle \langle \Psi |$, inside high transverse momentum jets at the LHC. Using the light-ray operator product expansion, the scaling behavior of multi-point correlators can be computed from the expectation value of the twist-2 spin-$J$ light-ray operators, $\mathbb{O}^{[J]}$, in this state, $\text{Tr}[ \rho ~\mathbb{O}^{[J]} ]$. We compute the light-ray density matrix at next-to-leading order, and combine this with results for the next-to-leading logarithmic scaling behavior of the correlators up to six-points, comparing with CMS Open Data. This theoretical accuracy allows us to resolve the quantum scaling dimensions of QCD light-ray operators inside jets at the LHC. Our factorization theorem for the light-ray density matrix at the LHC completes the link between recent developments in the study of energy correlators and LHC phenomenology, opening the door to a wide variety of precision jet substructure studies., Comment: 5 pages, 4 colorful figures of light-ray operator scaling

We investigate all the possible spin asymmetries that can occur in back-to-back electron-jet production with hadron observed inside a jet in electron-proton collisions. We derive the factorization formalism for all spin asymmetries and perform phenomenological studies for the future electron ion collider kinematics. We illustrate that the back-to-back electron-jet production opens up new opportunities to study transverse momentum dependent fragmentation functions and distribution functions., Comment: 5 pages, 4 figures. Contribution to the 24th International Spin Symposium (SPIN2021). JPS Conference Proceedings

We report the current understanding of heavy quarkonium production at high transverse momentum ($p_T$) in hadronic collisions in terms of QCD factorization. In this presentation, we highlight the role of subleading power corrections to heavy quarkonium production, which are essential to describe the $p_T$ spectrum of quarkonium at a relatively lower $p_T$. We also introduce prescription to match QCD factorization to fixed-order NRQCD factorization calculations for quarkonium production at low $p_T$., Comment: 8 pages, 4 figures; talk given at the XVth Quark confinement and the Hadron spectrum conference, August 1st - 6th, 2022, University of Stavanger, Norway

Understanding the detailed structure of energy flow within jets, a field known as jet substructure, plays a central role in searches for new physics, and precision studies of QCD. Many applications of jet substructure require an understanding of jets initiated by heavy quarks, whose description has lagged behind remarkable recent progress for massless jets. In this Letter, we initiate a study of correlation functions of energy flow operators on beauty and charm jets to illuminate the effects of the intrinsic mass of the elementary particles of QCD. We present a factorization theorem incorporating the mass of heavy quarks, and show that the heavy quark jet functions for energy correlators have a simple structure in perturbation theory. Our results achieve the very first full next-to-leading-logarithmic calculation of the heavy quark jet substructure observable at the LHC. Using this framework, we study the behavior of the correlators, and show that they exhibit a clear transition from a massless scaling regime, at precisely the scale of the heavy quark mass. This manifests the long-sought-after dead-cone effect and illustrates fundamental effects from the intrinsic mass of beauty and charm quarks in a perturbative regime, before they are confined inside hadrons. Our theoretical framework for studying energy correlators using heavy jets has many exciting applications for improving the description of mass effects in next generation parton shower event generators, probing the QGP, and studying heavy flavor fragmentation functions., Comment: 2 beautiful figures, 2 charming figures

We explore machine learning-based jet and event identification at the future Electron-Ion Collider (EIC). We study the effectiveness of machine learning-based classifiers at relatively low EIC energies, focusing on (i) identifying the flavor of the jet and (ii) identifying the underlying hard process of the event. We propose applications of our machine learning-based jet identification in the key research areas at the future EIC and current Relativistic Heavy Ion Collider program, including enhancing constraints on (transverse momentum dependent) parton distribution functions, improving experimental access to transverse spin asymmetries, studying photon structure, and quantifying the modification of hadrons and jets in the cold nuclear matter environment in electron-nucleus collisions. We establish first benchmarks and contrast the estimated performance of flavor tagging at the EIC with that at the Large Hadron Collider. We perform studies relevant to aspects of detector design including particle identification, charge information, and minimum transverse momentum capabilities. Additionally, we study the impact of using full event information instead of using only information associated with the identified jet. These methods can be deployed either on suitably accurate Monte Carlo event generators, or, for several applications, directly on experimental data. We provide an outlook for ultimately connecting these machine learning-based methods with first principles calculations in quantum chromodynamics., Comment: Final version after journal review

Grooming techniques, such as soft drop, play a central role in reducing sensitivity of jets to e.g. underlying event and hadronization at current collider experiments. The momentum sharing fraction zg, of the two branches in a jet that pass the soft drop condition, is one of the most important observables characterizing a collinear splitting inside the jet, and directly probes the QCD splitting functions. In this work, we present a factorization framework that enables a systematic calculation of the corresponding cross section beyond modified leading-logarithmic (MLL) accuracy, showing that this measurement is not only sensitive to the QCD charge but also the spin of the parton that initiates the jet. Our results at next-to-leading logarithmic (NLL′) accuracy include non-global logarithms, and provide a first meaningful assessment of the perturbative uncertainty. We present a comparison to the available experimental data from ALICE, ATLAS, and STAR and find excellent agreement.

We investigate all the possible spin asymmetries that can occur in back-to-back electron-jet production with hadron observed inside a jet in electron-proton collisions. We derive the factorization formalism for all spin asymmetries and perform phenomenological studies for the future electron ion collider kinematics. We illustrate that the back-to-back electron-jet production opens up new opportunities to study transverse momentum dependent fragmentation functions and distribution functions., Comment: 5 pages, 4 figures. Contribution to the 24th International Spin Symposium (SPIN2021). JPS Conference Proceedings

Understanding the detailed structure of energy flow within jets, a field known as jet substructure, plays a central role in searches for new physics, and precision studies of QCD. Many applications of jet substructure require an understanding of jets initiated by heavy quarks, whose description has lagged behind remarkable recent progress for massless jets. In this Letter, we initiate a study of correlation functions of energy flow operators on beauty and charm jets to illuminate the effects of the intrinsic mass of the elementary particles of QCD. We present a factorization theorem incorporating the mass of heavy quarks, and show that the heavy quark jet functions for energy correlators have a simple structure in perturbation theory. Our results achieve the very first full next-to-leading-logarithmic calculation of the heavy quark jet substructure observable at the LHC. Using this framework, we study the behavior of the correlators, and show that they exhibit a clear transition from a massless scaling regime, at precisely the scale of the heavy quark mass. This manifests the long-sought-after dead-cone effect and illustrates fundamental effects from the intrinsic mass of beauty and charm quarks in a perturbative regime, before they are confined inside hadrons. Our theoretical framework for studying energy correlators using heavy jets has many exciting applications for improving the description of mass effects in next generation parton shower event generators, probing the QGP, and studying heavy flavor fragmentation functions., Comment: 2 beautiful figures, 2 charming figures

The remarkably high energies of the Large Hadron Collider (LHC) have allowed for the first measurements of the shapes and scalings of multi-point correlators of energy flow operators, $\langle \Psi | \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \cdots \mathcal{E}(\vec n_k) |\Psi \rangle$, providing new insights into the Lorentzian dynamics of quantum chromodynamics (QCD). In this Letter, we use recent advances in effective field theory to derive a rigorous factorization theorem for the light-ray density matrix, $\rho= |\Psi\rangle \langle \Psi |$, inside high transverse momentum jets at the LHC. Using the light-ray operator product expansion, the scaling behavior of multi-point correlators can be computed from the expectation value of the twist-2 spin-$J$ light-ray operators, $\mathbb{O}^{[J]}$, in this state, $\text{Tr}[ \rho ~\mathbb{O}^{[J]} ]$. We compute the light-ray density matrix at next-to-leading order, and combine this with results for the next-to-leading logarithmic scaling behavior of the correlators up to six-points, comparing with CMS Open Data. This theoretical accuracy allows us to resolve the quantum scaling dimensions of QCD light-ray operators inside jets at the LHC. Our factorization theorem for the light-ray density matrix at the LHC completes the link between recent developments in the study of energy correlators and LHC phenomenology, opening the door to a wide variety of precision jet substructure studies., Comment: 5 pages, 4 colorful figures of light-ray operator scaling

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the DGLAP evolution, and we show that it can suppress the PDF at large $x$. Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large $x$., Comment: 15 pages, 7 figures

We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The interaction with the environment ultimately drives the system to thermal equilibrium. In the quantum Brownian motion limit, the Lindblad equation is related to a field theoretical Caldeira-Leggett equation. By using the Stinespring dilation theorem with ancillary qubits, we perform studies of both the non-equilibrium dynamics and the preparation of a thermal state in the Schwinger model using IBM's simulator and quantum devices. The real-time dynamics of field theories as open quantum systems and the thermal state preparation studied here are relevant for a variety of applications in nuclear and particle physics, quantum information and cosmology., Comment: 18 pages, 8 figures; v2: minor change in appendix

Heavy quarkonium production at high transverse momentum ($p_T$) in hadronic collisions is explored in the QCD factorization approach. We find that the leading power in the $1/p_T$ expansion is responsible for high $p_T$ regime, while the next-to-leading power contribution is necessary for the low $p_T$ region. We present the first numerical analysis of the scale evolution of coupled twist-2 and twist-4 fragmentation functions (FFs) for heavy quarkonium production and demonstrate that the QCD factorization approach is capable of describing the $p_T$ spectrum of hadronic $J/\psi$ production at the LHC., Comment: 7 pages, 3 figures. Contribution to the XXVIII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2021). SciPost Proceedings

Grooming techniques, such as soft drop, play a central role in reducing sensitivity of jets to e.g. underlying event and hadronization at current collider experiments. The momentum sharing fraction $z_g$, of the two branches in a jet that pass the soft drop condition, is one of the most important observables characterizing a collinear splitting inside the jet, and directly probes the QCD splitting functions. In this work, we present a factorization framework that enables a systematic calculation of the corresponding cross section beyond leading-logarithmic (LL) accuracy, showing that this measurement is not only sensitive to the QCD charge but also the spin of the parton that initiates the jet. Our results at next-to-leading logarithmic (NLL$'$) accuracy include non-global logarithms, and provide a first meaningful assessment of the perturbative uncertainty. We present a comparison to the available experimental data from ALICE, ATLAS, and STAR and find excellent agreement., Comment: 7 pages, 7 figures

We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The interaction with the environment ultimately drives the system to thermal equilibrium. In the quantum Brownian motion limit, the Lindblad equation is related to a field theoretical Caldeira-Leggett equation. By using the Stinespring dilation theorem with ancillary qubits, we perform studies of both the non-equilibrium dynamics and the preparation of a thermal state in the Schwinger model using IBM's simulator and quantum devices. The real-time dynamics of field theories as open quantum systems and the thermal state preparation studied here are relevant for a variety of applications in nuclear and particle physics, quantum information and cosmology., Comment: 18 pages, 8 figures; v2: minor change in appendix; v3: minor change; v4: published version

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., Comment: 46 pages, 10 figures, 5 tables

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the DGLAP evolution, and we show that it can suppress the PDF at large $x$. Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large $x$., Comment: 15 pages, 7 figures

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., Comment: 46 pages, 10 figures, 5 tables

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the DGLAP evolution, and we show that it can suppress the PDF at large $x$. Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large $x$., Comment: 15 pages, 7 figures

We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The interaction with the environment ultimately drives the system to thermal equilibrium. In the quantum Brownian motion limit, the Lindblad equation is related to a field theoretical Caldeira-Leggett equation. By using the Stinespring dilation theorem with ancillary qubits, we perform studies of both the non-equilibrium dynamics and the preparation of a thermal state in the Schwinger model using IBM's simulator and quantum devices. The real-time dynamics of field theories as open quantum systems and the thermal state preparation studied here are relevant for a variety of applications in nuclear and particle physics, quantum information and cosmology., Comment: 18 pages, 8 figures; v2: minor change in appendix; v3: minor change; v4: published version

Grooming techniques, such as soft drop, play a central role in reducing sensitivity of jets to e.g. underlying event and hadronization at current collider experiments. The momentum sharing fraction $z_g$, of the two branches in a jet that pass the soft drop condition, is one of the most important observables characterizing a collinear splitting inside the jet, and directly probes the QCD splitting functions. In this work, we present a factorization framework that enables a systematic calculation of the corresponding cross section beyond leading-logarithmic (LL) accuracy, showing that this measurement is not only sensitive to the QCD charge but also the spin of the parton that initiates the jet. Our results at next-to-leading logarithmic (NLL$'$) accuracy include non-global logarithms, and provide a first meaningful assessment of the perturbative uncertainty. We present a comparison to the available experimental data from ALICE, ATLAS, and STAR and find excellent agreement., Comment: 7 pages, 7 figures

We develop the theoretical framework needed to study the distribution of hadrons with general polarization inside jets, with and without transverse momentum measured with respect to the standard jet axis. The key development in this paper, referred to as "polarized jet fragmentation functions", opens up new opportunities to study both collinear and transverse momentum dependent (TMD) fragmentation functions. As two examples of the developed framework, we study longitudinally polarized collinear $\Lambda$ and transversely polarized TMD $\Lambda$ production inside jets in both $pp$ and $ep$ collisions. We find that both observables have high potential in constraining spin-dependent fragmentation functions with sizeable asymmetries predicted, in particular, at the future Electron-Ion Collider., Comment: 14 pages, 5 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 the jet energy drop, which is the relative difference between the groomed and ungroomed jet energy or transverse momentum. It is one of the fundamental quantities that characterizes the impact of grooming on jets produced in high energy collisions. We consider three different grooming algorithms i) soft drop, ii) iterated soft drop, and iii) trimming. We carry out the resummation of large logarithms of the jet energy drop, the jet radius as well as relevant grooming parameters at next-to-leading logarithmic (NLL$'$) accuracy. In addition, we account for non-global and clustering logarithms, and determine the next-to-leading order corrections. For soft drop we perform a joint resummation of the jet energy drop and the groomed jet radius, which is necessary to achieve the correct all-order structure of the cross section, in particular for the Sudakov-safe case of soft drop with $\beta=0$. We present numerical results for LHC energies and compare to Pythia simulations as well as CMS data. Our factorization framework predicts the onset of nonperturbative effects in the jet energy distribution, in line with what we find in Pythia. The jet energy drop observables stand out because they only probe soft radiation, making them ideal candidates for the tuning of parton shower Monte Carlo event generators and for probing medium effects in heavy-ion collisions., Comment: 49 pages, 25 figures, published version

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 heavy quarkonium production associated with gluons in $\rm e^+e^-$ annihilation as an illustration of the perturbative QCD (pQCD) factorization approach, which incorporates the first nonleading power in the energy of the produced heavy quark pair. We show how the renormalization of the four-quark operators that define the heavy quark pair fragmentation functions using dimensional regularization induces "evanescent" operators that are absent in four dimensions. We derive closed forms for short-distance coefficients for quark pair production to next-to-leading order ($\alpha_s^2$) in the relevant color singlet and octet channels. Using non-relativistic QCD (NRQCD) to calculate the heavy quark pair fragmentation functions up to $v^4$ in the velocity expansion, we derive analytical results for the differential energy fraction distribution of the heavy quarkonium. Calculations for ${}^3S_1^{[1]}$ and ${}^1S_0^{[8]}$ channels agree with analogous NRQCD analytical results available in the literature, while several color-octet calculations of energy fraction distributions are new. We show that the remaining corrections due to the heavy quark mass fall off rapidly in the energy of the produced state. To explore the importance of evolution at energies much larger than the mass of the heavy quark, we solve the renormalization group equation perturbatively to two-loop order for the ${}^3S_1^{[1]}$ case., Comment: 44 pages, 9 figures

We develop the theoretical framework needed to study the distribution of hadrons with general polarization inside jets, with and without transverse momentum measured with respect to the standard jet axis. The key development in this paper, referred to as "polarized jet fragmentation functions", opens up new opportunities to study both collinear and transverse momentum dependent (TMD) fragmentation functions. As two examples of the developed framework, we study longitudinally polarized collinear $\Lambda$ and transversely polarized TMD $\Lambda$ production inside jets in both $pp$ and $ep$ collisions. We find that both observables have high potential in constraining spin-dependent fragmentation functions with sizeable asymmetries predicted, in particular, at the future Electron-Ion Collider., Comment: 14 pages, 5 figures

We develop the theoretical framework needed to study the distribution of hadrons with general polarization inside jets, with and without transverse momentum measured with respect to the standard jet axis. The key development in this paper, referred to as "polarized jet fragmentation functions", opens up new opportunities to study both collinear and transverse momentum dependent (TMD) fragmentation functions. As two examples of the developed framework, we study longitudinally polarized collinear $\Lambda$ and transversely polarized TMD $\Lambda$ production inside jets in both $pp$ and $ep$ collisions. We find that both observables have high potential in constraining spin-dependent fragmentation functions with sizeable asymmetries predicted, in particular, at the future Electron-Ion Collider., Comment: 14 pages, 5 figures

Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside $Z$-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction $z_h$ of the jet carried by the hadron and the transverse momentum $j_\perp$ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the $z_h$-dependence provides information on standard collinear fragmentation functions, while $j_\perp$-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate $z_h$ region. For $j_\perp$-dependence, we suggest binning in both $z_h$ and $j_\perp$, which would lead to a more direct probing of TMD fragmentation functions., Comment: 9 pages, 4 figures

We consider the one-parameter family of jet substructure observables known as angularities using the specific case of inclusive jets arising from photoproduction events at an Electron-Ion Collider (EIC). We perform numerical calculations at next-to-leading logarithmic accuracy within perturbative QCD and compare our results to PYTHIA 6 predictions. Overall, we find good agreement and conclude that jet substructure observables are feasible at the EIC despite the relatively low jet transverse momentum and particle multiplicities. We investigate the size of subleading power corrections relevant at low energies within the Monte Carlo setup. In order to establish the validity of the Monte Carlo tune, we also perform comparisons to jet shape data at HERA. We further discuss detector requirements necessary for angularity measurements at an EIC, focusing on hadron calorimeter energy and spatial resolutions. Possible applications of precision jet substructure measurements at the EIC include the tuning of Monte Carlo event generators, the extraction of nonperturbative parameters and studies of cold nuclear matter effects., Comment: 12 pages, 8 figures

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