Latin American Strategy Forum for Research Infrastructure (III LASF4RI Contribution)

The glue that binds us all – Latin America and the Electron-Ion Collider

A. C. Aguilar Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas,13083-859 Campinas, São Paulo, Brasil A. Bashir Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán 58040, México J. J. Cobos-Martínez Departamento de Física, Universidad de Sonora, Boulevard Luis Encinas J. y Rosales, Hermosillo, Sonora 83000, México A. Courtoy Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México B. El-Bennich Departamento de Física, Universidade Federal de São Paulo, Rua São Nicolau 210, 09913-030 Diadema, São Paulo, Brasil D. de Florian International Center for Advanced Studies (ICAS) and IFICI, Universidad Nacional de San Martín, 25 de Mayo y Francia, Buenos Aires, Argentina T. Frederico Instituto Tecnológico de Aeronáutica, Departamento de Ciência e Tecnologia Aeroespacial, 12228-900 São José dos Campos, Brasil V. P. Gonçalves Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, 96010-900 Pelotas, Rio Grande do Sul, Brasil M. Hentschinski Departamento de Actuaria, Física y Matemáticas, Universidad de las Américas Puebla, Ex-Hacienda Santa Catarina Martir S/N, San Andrés Cholula, 72820 Puebla, México R. J. Hernández-Pinto Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Sinaloa, Ciudad Universitaria, Culiacán, Sinaloa 80000, México G. Krein Instituto de Física Teórica, Universidade Estadual Paulista, 01140-070 São Paulo, São Paulo, Brazil M. V. T. Machado Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051,91501-970 Porto Alegre, Rio Grande do Sul, Brasil J. P. B. C. de Melo Laboratório de Física Teórica e Computacional, Universidade Cidade de São Paulo, Rua Galvão Bueno 868, 01506-000 São Paulo, São Paulo, Brasil W. de Paula Instituto Tecnológico de Aeronáutica, Departamento de Ciência e Tecnologia Aeroespacial, 12228-900 São José dos Campos, Brasil R. Sassot Departamento de Física and IFIBA, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1 (1428) Buenos Aires, Argentina F. E. Serna Departamento de Física, Universidad de Sucre, Barrio Puerta Roja, Sincelejo 700001, Colombia
Supporting authors outside Latin America: L. Albino Departamento de Sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, E-41013 Sevilla, Spain I. Borsa Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany L. Cieri Department of Theoretical Physics & Instituto de Física Corpuscular, Universitat de València & Consejo Superior de Investigaciones Científicas, E-46980 Paterna, València, Spain J. Mazzitelli Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Á. Miramontes Department of Theoretical Physics & Instituto de Física Corpuscular, Universitat de València & Consejo Superior de Investigaciones Científicas, E-46980 Paterna, València, Spain K. Raya Department of Integrated Sciences and Center for Advanced Studies in Physics, Mathematics and Computation, University of Huelva, E-21071 Huelva, Spain F. Salazar Institute for Nuclear Theory, University of Washington, Seattle WA 98195-1550, USA G. Sborlini Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca, 37008 Salamanca, Spain P. Zurita Departamento de Física Teórica & IPARCOS, Universidad Complutense de Madrid, E-28040 Madrid, Spain

Abstract

The Electron-Ion Collider (EIC), a next generation electron-hadron and electron-nuclei scattering facility, will be built at Brookhaven National Laboratory. The wealth of new data will shape research in hadron physics, from nonperturbative QCD techniques to perturbative QCD improvements and global QCD analyses, for the decades to come. With the present proposal, Latin America based physicists, whose expertise lies on the theory and phenomenology side, make the case for the past and future efforts of a growing community, working hand-in-hand towards developing theoretical tools and predictions to analyze, interpret and optimize the results that will be obtained at the EIC, unveiling the role of the glue that binds us all. This effort is along the lines of various initiatives taken in the U.S., and supported by colleagues worldwide, such as the ones by the EIC User Group which were highlighted during the Snowmass Process and the Particle Physics Project Prioritization Panel (P5).

1 Hadron Physics in the wake of the Electron-Ion Collider

It is nowadays firmly established that Quantum Chromodynamics (QCD) is the fundamental theory of strong interactions [1, 2, 3] that describes the interaction of colored degrees of freedom: quarks and gluons. The theory has been tested over several decades and continuous progress has been made in verifying its accuracy against experimental data. But at the core of this theory lies the phenomenon of color confinement, which is still not understood. Confinement implies that quarks and gluons cannot be observed freely in nature, as they are always spatially bound within hadrons. We know that this phenomenon exists, and our own existence is its proof, but elucidating its mechanism is one of the most important problems in modern physics [4]. Understanding this fundamental question will allow us to answer the question of how observable hadrons are made of Nature’s fundamental and unobservable degrees of freedom.

A closely related problem is dynamical chiral symmetry breaking (DCBS). While hadrons make up most of the visible mass of our universe, this mass cannot be accounted for with the mass of light current quarks and perturbatively mass-less gluons. Instead, the interactions between quarks and gluons and between the gluons themselves must be so strong that an effective dynamical mass is produced within the hadrons. Only through the generation of such a dynamical mass can the spectrum of experimentally observed hadron masses be explained.

In applying the theory to understand the hadron’s bound-state properties, one immediately realizes that nonperturbative quantum effects play a key role. It is therefore crucial to probe the behavior of the theory’s strong coupling in the infrared domain, so to shed light on confinement confronting theoretical predictions with experimental observables. This is the current objective and the motivation for using electromagnetic probes of mesons, protons, and nuclei to measure the rich spectrum of excited and exotic states and the momentum distribution of quarks and gluons within them at the upgraded Thomas Jefferson National Accelerator Facility (JLab) [5, 6, 7], as well as at COMPASS++ [8]. On the other hand, the indirect role that hadron structure plays in most hadron colliders has been exploited for years, where the aim now is to overcome challenges at the precision level [9, 10].

In electron-hadron processes, the scattered particles interact predominantly through the exchange of a virtual photon, which at sufficiently large virtuality serves as a probe to resolve quark degrees of freedom inside the hadron. While the hadronic structure resolved at low momentum transfer is different from that in deep-inelastic processes, both can be related via evolution equations in QCD. On the other hand, though electron scattering off a fixed hadron target allows us to probe their valence-quark structure, larger collider energies are required to gain access to the gluon-field distribution. Since gluons are the force carrier of strong interactions, it is believed that they and their interplay with valence and sea quarks are responsible for the bulk of the aforementioned phenomena and puzzles.

Parton distribution functions (PDFs) are universal, one-dimensional objects that characterize the light-front momentum fraction of partons (quarks and gluons) inside a hadron of a given spin configuration. A PDF can phenomenologically be determined at higher energies through global analyses in QCD, for which past (e.g. DESY) and present facilities play an important role; see Ref. [11] for a review. Moreover, they provide an indispensable tool for any kind of quantitative phenomenological studies at hadron-hadron colliders, such as the Large Hadron Collider (LHC). In particular, the lack of precise knowledge of PDFs is often a limiting factor in reaching high-precision theory predictions at the LHC. On the other hand, to explore color confinement and chiral symmetry breaking, it is necessary to go beyond these one-dimensional distributions. To do so, the challenge at the EIC will be to measure appropriate observables that provide information on the spatial distribution and motion of the quarks and gluons in the hadron. Indeed, these longitudinal and transverse momentum distributions can be studied with different quantum-correlation functions that can be related to observable scattering amplitudes. Notable amongst them are the transverse momentum distribution (TMD) [12] and the generalized parton distribution (GPD). With these objects it becomes possible to understand how quarks and gluons are distributed in coordinate and momentum space and how spin and angular momentum are carried by them inside mesons and nucleons. In doing so, several key questions in hadron physics and QCD can be addressed: what is the internal multi-dimensional landscape of the nucleon? What is the role of gluons and their self-interactions in the nucleon? What role do collective effects of gluons play in atomic nuclei? How can emergent properties, such as DCBS and confinement, be responsible for more than 90% of the hadron mass?

A slightly different, but related topic, is the possible formation of a very dense and over-occupied system of gluons, carrying a small longitudinal momentum fraction $x$ at large center-of-mass energies, which will eventually saturate. Due to a large relative boost factor between the colliding virtual photon and hadron, pair creation and annihilation of gluons is time dilated in such reactions. Since each created gluon is a color source and can therefore create further gluons, one observes a power-like growth of the gluon distribution in this region of phase space. If such a growth is extrapolated to infinite high energies, it would lead to the violation of unitary bounds. The growth with energy must therefore slow down at sufficiently high energies. According to our current understanding, this takes place through recombination effects in this dense and over-occupied system of gluons, thus slowing down the growth with energy and resulting in a phenomenon known as gluon saturation [13]. The systematic exploration of such a saturated system is expected to be possible in collisions of electrons with large nuclei, where densities will be further increased through the nuclear mass number $A$ as $\sim A^{\frac{1}{3}}$ , providing the opportunity to investigate the full non-linear dynamics of QCD in a weak coupling limit. The color glass condensate [14] provides an effective description of this saturated regime with many experimental consequences [15]. Furthermore, understanding these systems is also of high importance to control the initial state before the formation of a quark-gluon plasma in relativistic heavy-ion collisions.

Recent research activities further emphasize the close connection between color confinement and entanglement of microscopic degrees of freedom in the hadron wave function. In this context, confinement is understood as the limit of maximal entanglement since colored degrees of freedom cannot exist in isolation, see Ref. [16] for a recent review. From this perspective, the DIS process can be interpreted as a sudden quench of the hadronic wave function, due to the interaction with the virtual photon. This leads to a reduced hadronic density matrix and corresponding entropy production, which can be measured in experiment [17, 18].

All of these questions are at the core of the science program of the future Electron-Ion Collider (EIC) [4, 19, 20] at Brookhaven National Lab in New York. The U.S. Department of Energy (DOE) granted Critical Decision 3A (CD-3A), i.e. the project’s final design has been approved and its construction has been authorized. This collider will be a groundbreaking research machine, pushing the boundaries of our understanding in accelerator science, particle detector design, high-performance computing, and beyond. The most pressing questions that motivated the construction of this new-generation collider are:

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How do quarks and gluons make up nearly all of the visible matter in the universe?
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What is the internal three-dimensional landscape of protons and nuclei?
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How do the proton’s constituent quarks and gluons and their interactions contribute to its spin?
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Does the interplay of quarks and gluons with the vacuum lead to confinement?
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How do quark and gluon distributions differ in a proton and in nuclei?
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Does gluon saturation into a color glass condensate exist?

For a more detailed presentation, we refer to the review in Ref. [19] and the official EIC page: https://www.bnl.gov/eic/.

2 Latin American physicists and the Electron-Ion Collider

Despite the pandemic, the scientific activity dedicated to the planning of the EIC continued and many advances and physics predictions were made [19] to clear the path for future “golden” physics measurements and to detail the accelerator and detector concepts required to achieve them. Most of the major conferences in hadron physics dealt with recent developments around the EIC and a Yellow Report was prepared [19], signed by more than 400 experts in the field from various parts of the world, including theorists and experimentalists from Argentina (Universidad de Buenos Aires), Brazil (Universidade Federal do Rio Grande do Sul, Universidade Federal de Pelotas, Instituto Tecnológico de Aeronáutica), Chile (Universidad Técnica Federico Santa María, Universidad Andres Bello) and Mexico (Universidad Nacional Autónoma de México).

Faculty and Staff Scientists at Latin American universities and labs who are members of the EIC user group (EICUG)(https://www.eicug.org) can be found in the EICUG phone book. The EICUG is an international affiliation of scientists dedicated to developing and promoting the scientific, technological, and educational goals and motivations for a new high-energy EIC. In particular, it acts as a mediator between the different entities and funding bodies of the participating countries thanks to the EIC User Group Steering Committee International Representative. This committee contacts the Scientific agencies of each country for various meetings, including meetings with the DOE. Most Latin-American institutions reported here rely on an institutional representatives in the EICUG Council. It is the case for UAS, UDLAP, UMSNH and UNAM in Mexico, as well as ITA, UNICID, UFPel, UNIFESP and UFRGS in Brazil.

More generally, the hadron, nuclear, and particle physicists of this white paper who have participated in research projects related to the EIC are: {labeling}Outside LA

Adnan Bashir (Universidad de Huelva & Universidad Michoacana de San Nicolás de Hidalgo), Javier Cobos-Martínez (Universidad de Sonora), Aurore Courtoy (Universidad Nacional Autónoma de México), Martin Hentsch-inski (Universidad de las Américas Puebla), Roger Hernández-Pinto (Universidad Autónoma de Sinaloa).

Arlene Cristina Aguilar (Universidade Estadual de Campinas), Bruno El-Bennich (Universidade Federal de São Paulo), Tobias Frederico (Instituto Tecnológico de Aeronáutica), Victor Paulo Gonçalves (Universidade Federal de Pelotas), Gastão Krein (Instituto de Física Teórica, Universidade Estadual Paulista), Magno V. T. Machado (Universidade Federal do Rio Grande do Sul), João Pacheco B. C. de Melo (Universidade Cidade de São Paulo), Wayne de Paula (Instituto Tecnológico de Aeronáutica).

Fernando Serna (Universidad de Sucre).

Daniel de Florian (Universidad Nacional de San Martín), Rodolfo Sassot (Universidad de Buenos Aires).

Support from a broader community outside Latin America is shown by the following participants of this proposal: Luis Albino (Universidad Pablo de Olavide, Spain), Ignacio Borsa (University of Tübingen), Leandro Cieri (Universitat de València, Spain), Javier Mazzitelli (Paul Scherrer Institute, Switzerland), Ángel Miramontes (Universitat de València, Spain), Khépani Raya (Universidad de Huelva, Spain), Farid Salazar (University of Washington, USA), German Sborlini (Universidad de Salamanca, Spain), Pia Zurita (Universidad Complutense de Madrid, Spain).

3 Scientific activities and current status

In this Section we summarize the research activities of the Latin-American community in phenomenology, perturbative and nonperturbative QCD.

3.1 Contributions to EIC physics within Latin America

In Brazil, several groups in the State of São Paulo are very active in hadron phenomenology, studying spectroscopy, hadrons at finite temperature and in dense matter, functional approaches to nonperturbative QCD and light-front quantum field theory.

At the Universidade Estadual de Campinas, the group of Arlene Cristina Aguilar is interested in nonperturbative QCD phenomena and employs Schwinger-Dyson equations [21, 22] to compute the nonperturbative propagators and vertices of QCD [23, 24, 25, 26]. It is known that even small quantitative changes in the quark and gluon propagators or in the fundamental quark-gluon, three-gluon, and four-gluon vertices can lead to qualitative changes in the description of bound states, resonances, and PDFs, which may eventually leave significant experimental signatures.

At the Universidade Federal de São Paulo, Bruno El-Bennich studies mass generation due to dynamical chiral symmetry breaking in the QCD gap equation. To that end, the general nonperturbative structure of the quark-gluon vertex is explored with the Schwinger-Dyson equation and generalized Slavnov-Taylor identities [27, 28, 29, 30]. In the past, the meson and nucleon resonance spectrum, including the Roper and the parity partner of the nucleon, were studied with Poincaré covariant Bethe-Salpeter and Faddeev equations [31, 32, 33, 34]. More recently, the group’s focus has been on light-front projection of Bethe-Salpeter amplitudes in order to compute the parton distribution amplitude (PDA), PDF and TMD of a wide array of mesons including heavy mesons and quarkonia [35, 36, 37, 38]. Quark fragmentation and jet functions into light and heavy mesons are currently being calculated within the same functional approach.

Since pion targets are an experimentally challenging task, whether at JLab or at the EIC, indirect approaches are explored with the Sullivan process by João Pacheco de Melo’s group at the Universidade Cidade de São Paulo. In order to probe the pion-structure, off-shell effects in electromagnetic form factors of light pseudoscalar mesons are explored [39, 40, 41], which involves the extrapolation of the meson’s wave function off their mass-shell. These studies are in view of the pion and kaon elastic form factors which will be measured at large momenta and small virtualities at the EIC [42].

At the Instituto de Física Teórica, the group of Gastão Krein has been investigating the interactions of heavy quarkonia with atomic nuclei. As nucleons and quarkonia have no valence quarks in common, there is no short-range repulsion due the Pauli exclusion principle (responsible for the nucleon-nucleon hard-core repulsion) and the interaction must involve gluonic van der Waals forces [43]. Such interactions allows us to access a matrix element related to the QCD trace anomaly, a quantum effect that is key to our understanding of the origin of the proton’s mass and its distribution within the hadron [44]. In a nuclear medium, the strong scalar and vector mean fields enhance such interactions and likely lead to the formation of an exotic nuclear bound state, for which the EIC provides promising perspectives [45, 46].

Tobias Frederico and Wayne de Paula, both at the Instituto Tecnológico de Aeronáutica in São José dos Campos, investigate a dynamical continuum formulation of generalized TMDs [47, 48] in Minkowski space. To that end, they solve the Bethe-Salpeter equation [49] with the concomitant quark dressing [50, 51] to take into account the Goldstone boson nature of the pion and kaon. They demonstrated with the light-front projection of the Bethe-Salpeter amplitude that higher Fock components of the hadron states implicitly contribute to their dynamics, For example, at the pion scale, 30% of its state is distributed beyond the valence component. In the future, they intend to amend their light-front calculations in Minkowski space with an improved quark-gluon vertex in the corresponding quark Dyson-Schwinger equation [52, 53, 54].

Victor Paulo Gonçalves of the Universidade Federal de Pelotas has focused during the last two decades on improving the description of inclusive, diffractive and exclusive processes in electron-ion collisions [55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67]. In recent years, his group has updated its predictions for the diffractive processes [68] and the exclusive production of vector mesons and photons in coherent and incoherent interactions [69, 70, 71, 72, 73] considering the kinematical range that will be probed by the EIC and LHeC. Such studies have demonstrated that the future experimental data will be able to improve the description of the QCD dynamics at high energies and constrain the magnitude of saturation effects. He is now also interested in the precise determination of the $J/\Psi$ and $\Upsilon$ photo-production at low energies, motivated by the fact that theoretical studies indicate that the near-threshold production of heavy quarkonium is sensitive to the trace anomaly contribution to the nucleon mass. This is also motivated by the observation that photon-induced interactions can also be used to study the production and properties of exotic charmonium-like states [74, 75, 76, 77], which are a class of hadrons that decay to final states that contain a heavy quark and a heavy antiquark but cannot be easily accommodated in the remaining unfilled states in the $c\bar{c}$ level scheme. His group is improving the description of the photo-production of exotic states and derive predictions for its production, considering $ep$ and $eA$ collisions at the EIC, motivated by narrow, hidden heavy-quark pentaquark states $P_{c}(4312)$ , $P_{c}(4440)$ and $P_{c}(4457)$ , which were reported by the LHCb Collaboration [78]. Recently, the particle production by $\gamma\gamma$ interactions in future electron-ion collisions was discussed in detail in Refs. [79, 80, 81], which indicated that the properties of QCD and QED bound states could be constrained at the EIC and LHeC.

At the Universidade Federal do Rio Grande do Sul, Magno Machado’s research deals with exclusive particle production and diffractive deep-inelastic scattering at the EIC. In Ref. [82], the proton structure functions and vector meson production were investigated in $ep$ processes and later extended to nuclear targets in $eA$ collisions [83]. The very same approach in momentum representation is able to predict the cross section for exclusive $Z^{0}$ production [84] as well as the time-like Compton scattering [85]. The diffractive gluon jet production can be described in the context of a QCD dipole picture, considering the $q\bar{q}g$ contribution to diffractive deep inelastic scattering. Predictions for such a process at the EIC were presented in Ref. [86]. Moreover, Coulomb corrections can be important in inclusive and diffractive $eA$ interactions. It was shown in Ref. [87] that these corrections to the total cross sections are important at low- $Q^{2}$ and small values of $x$ and are larger for diffractive interactions. The group also studies entanglement entropy in $ep$ and $eA$ collisions at small- $x$ , where this entropy is contrasted to other entropic notions, such as the parton entropy calculated in the color glass condensate formalism and the semi-classical Wehrl entropy [88].

In Colombia, high-energy and LHC physics dominates the research activities in most physics departments. However, at the Universidad de Sucre, Fernando Serna has focused on the one-dimensional structure of hadrons [35, 36, 37] and is currently exploring their three-dimensional distributions. From the projections of the Bethe-Salpeter wave functions on the light front, Serna and his collaborators have recently obtained Light-Front Wave Functions (LFWFs) of pseudoscalar mesons. These wave functions provide a comprehensive framework to describe probability amplitudes in a more general context. Using these LFWFs, the group has for the first time calculated TMDs and PDFs of the more challenging $D$ - and $B$ -mesons.

In Mexico, the hadron physics community is involved in various aspects of hadron structure and spectroscopy. Adnan Bashir’s group in Morelia (UMSNH) carries out continuum studies through Schwinger-Dyson equations in QCD to predict observables for Jlab and the EIC. The group has done extensive studies on the quark propagator, the quark-gluon and quark-photon vertices as well as the gluon propagator [27, 28, 29, 30, 89, 90, 91, 92]. An effective field-theory model of QCD based on a vector-vector contact interaction was put forward in Ref. [93] and has been studied extensively to compute the mass spectrum, decay constants, electromagnetic form factors, transition form factors and charge radii of pseudoscalar and vector meson form factors of light, heavy as well as heavy-light mesons [94, 95, 96, 97, 98, 99, 100]. The masses of the first radial excitations of these mesons and the corresponding diquarks were also computed [101]. More realistic studies in collaboration with Khépani Raya yielded predictions for the pion and kaon electromagnetic form factors [102], transition form factor of pseudo-scalar mesons to two photons [103, 104] pion and kaon form factors in the time-like region [105].

In Northern Mexico, Javier Cobos-Martínez and his students compute LFWFs of unflavored vector mesons, as well as electromagnetic form factors, PDFs and GPDs of heavy-light pseudoscalar mesons. They are currently extending these calculations to the distribution functions of diquarks and nucleons with the Schwinger-Dyson equation approach to QCD. Also in the North, at the Universidad Autónoma de Sinaloa, Roger Hernández-Pinto has recently been interested in phenomenological analyses of electromagnetic and two-photon transition form factors of pseudoscalar mesons within an algebraic model. These analyses, in collaboration with Adnan Bashir and Khépani Raya, predict the pion and kaon form factors for $Q^{2}$ up to 40 GeV², which corresponds to the projected EIC and JLab $Q^{2}$ -range [106].

Martin Hentschinski at the Universidad de las Américas Puebla contributed recently to the exploration of entanglement entropy in inclusive [107] and diffractive [108, 109] DIS. Additional research activities comprise phenomenological studies of vector meson production in exclusive photoproduction at the LHC [110, 111, 112, 113], which are closely connected to corresponding studies at the EIC as well as formal studies of high energy factorization.

At the Universidad Nacional Autónoma de México, various groups focus on phenomenological or global QCD analyses, either on the spectroscopy [114, 115, 116] or structure [10, 117, 118, 119] side, with contributions to the Joint Physics Analysis Center (JPAC) collaboration (César Fernández) and CTEQ-Tung et al. (CT) collaboration (Aurore Courtoy). Global analyses constitute the bridge between data and theory, which is nowadays also supplemented with lattice-QCD studies, in extracting and determining non-perturbative functions or characteristics in a data-driven manner. The UNAM groups are hence very active in providing predictions for the EIC [20] and together with the Argentinian groups, they form the core of global analyses in Latin America. This specific field of expertise is evolving towards precision and accuracy in the determination of the ubiquitous proton PDFs, that enter many theoretical predictions for hadron colliders. The group of Aurore Courtoy has also interest in the phenomenological determination of sub-leading twist distributions [117].

The Argentinian groups at Universidad Nacional de San Martín and Universidad de Buenos Aires have focused on different aspects of spin physics and hadronization at the EIC. These include both the computation of EIC observables beyond next-to-leading order approximation in QCD [120, 121, 122, 123] as well as impact studies based on the foreseen experimental precision [124, 125].

3.2 Latin American physicists outside Latin America

An important part of the Latin-American community is also based outside Latin America, while contributing substantially to building a connection with the region.

A Spanish node, composed of IFIC-València (Leandro Cieri), Universidad Complutense de Madrid (Pia Zurita) and the Universidad de Salamanca (German Sborlini), is mainly devoted to the development of novel computational techniques to obtain high-precision theoretical predictions in high energy physics [126, 127, 128, 129, 130]. They are interested in developing novel Quantum Monte Carlo (QMC) methods specifically tailored to address complex problems in this field. Moreover, these groups are currently working on optimizing the calculation of PDFs and fragmentation functions with the aim to reduce computational costs of hadron-collision simulations.

Also in Spain, at the Universidad de Huelva, Khépani Raya is dedicated to examining the structure of pseudoscalar mesons via electromagnetic and gravitational form factors, PDFs, and GPDs [131, 103, 104, 132, 133, 134]. His group has recently proposed new methods for deriving PDFs and GPDs of pions and kaons employing probabilistic methods [135, 136]. The Schwinger-Dyson and Bethe-Salpeter equation framework provides access to a variety of pseudoscalar meson distributions, and a similar degree of sophistication is expected for the nucleon in upcoming years. These techniques have also allowed for the computation of accurate hadronic light-by-light contributions to the anomalous magnetic moment of the meson, which was done in collaboration with Ángel Miramontes at the Universitat de València and Adnan Bashir [102, 137]. They also resulted in realistic predictions for space-like [102] and time-like [105] electromagnetic form factors of the pion and kaon. Luis Albino of the Universidad Pablo de Olavide in Sevilla has developed algebraic models for LFWFs and derived therefrom pion and kaon PDFs and GPDs [138]. He also contributed to the derivation of the nonperturbative quark-gluon vertex structure [92, 28, 29].

Farid Salazar is working at the Institute for Nuclear Theory, University of Washington, on various aspects of gluon saturation within color glass condensate effective theory. His recent efforts are focused on addressing the consistent resummation of high-energy and Sudakov/threshold-type logarithms in deep inelastic scattering in the saturation regime [139, 140, 141], as well as the phenomenology of vector meson production in high-energy photon-nucleus reactions in ultra-peripheral heavy-ion collisions [142, 143, 144]. He is also interested in elucidating the correspondence between different formalisms for multiple scattering in nuclei [145, 146].

Javier Mazzitelli, at the Paul Scherrer Institute in Switzerland, works on the computation of higher-order QCD corrections for collider phenomenology. His recent works mainly deal with Higgs boson and heavy-quark phenomenology [147, 148]. Besides computing corrections at fixed-order in perturbation theory, he also developed methods to match higher-order calculations to parton showers [149, 150] in order to provide accurate multi-purpose Monte Carlo event generators, a cornerstone of experimental analyses at colliders.

Ignacio Borsa has mainly focused on spin physics at the EIC, including the computation of higher-order QCD corrections for polarized processes [122, 151, 120, 121] and, more recently, on the matching of higher-order corrections to parton showers [152]. Part of his work has also been centered in the determination of helicity parton distributions functions beyond next-to-leading order [153].

4 The building of a community

In 2019, members of the EICUG from the Universidad de las Américas Puebla (Martin Hentschinski) co-organized the international “Workshop on Forward Physics and QCD at the LHC, the future Electron-Ion Collider, and Cosmic Ray Physics” in the city of Guanajuato. This small meeting of 47 participants aimed at connecting Mexican graduate students with international researchers in this area. In July 2021, the “19th International Conference on Hadron Spectroscopy and Structure” (HADRON 2021) was held online at the Universidad Nacional Autónoma de México, co-organized by the local EICUG members Aurore Courtoy and César Fernández.

Bruno El-Bennich was the chair of the tenth international conference on the “Physics Opportunities at an Electron-Ion Collider” (POETIC 2023) at the Instituto Principia in São Paulo, supported by the ICTP-SAIFR, Jlab and Brookhaven National Lab, while Tobias Frederico was the chair of the 2023 edition of the Light-Cone Conference Series “Light-Cone 2023: Hadrons and Symmetries”, hosted by the Centro Brasileiro de Pesquisas Físicas (CBPF) in Rio de Janeiro. Most recently, Adnan Bashir and Bruno El-Bennich co-organized the workshop “From Quarks and Gluons to the Internal Dynamics of Hadrons”, while Tobias Frederico was the co-organizer of “Elucidating the Structure of Nambu-Goldstone Bosons”, both at the Center for Frontiers in Nuclear Science, Stony Brook University. The primary objective of these in-person workshop was to discuss open questions related to momentum distributions, form factors, masses, and other observables that are of paramount interest to the EIC community.

With support from the DOE, the “38th Annual Hampton University Graduate Studies” (HUGS) Summer School was held at Jlab from May 30 to June 16, 2023. Adnan Bashir delivered six lectures on “Non-perturbative methods in continuum QCD”. He also gave lectures on “Hadron Physics in the Modern Era: A Continuum QCD Approach” to international students during the “Summer School on the Physics of the EIC” at the Center for Frontiers in Nuclear Science.

Fernando Serna took advantage of the EIC Theory Institute visitor program and spent a month at Brookhaven National Lab in September of 2023. He gave a departemnt seminar on light-front distribution amplitudes.

In July 2022 and June 2024, Martin Hentschinski co-organized two meetings, “Saturation and Diffraction at the LHC and the EIC” and “Diffraction and gluon saturation at the LHC and the EIC”, at the European Center for Theoretical Studies in Nuclear Physics and Related Areas ECT* in Trento, Italy. The EIC was also a relevant topic at the “International workshop on the physics of Ultra Peripheral Collisions (UPC 2023)”, organized in December 2023 in Playa del Carmen, Mexico.

The QCD4EIC workshop series is jointly organized by the Buenos Aires group (Daniel de Florian and Rodolfo Sassot) and Werner Vogelsang of Tübingen University at the Center for Frontiers in Nuclear Science at Stony Brook. Those workshops include the participation of other members of the Latin American community (e.g. Aurore Courtoy). The discussions of these workshop series featured the following topics:

•

Precision fixed-order calculations of polarized and unpolarized hard-scattering cross sections for the EIC. This includes QCD corrections at NLO and beyond for inclusive and semi-inclusive scattering for jet, hadron or photon final states;
•

QCD threshold resummation for EIC cross sections and their impact on phenomenology;
•

Techniques for extraction of PDFs and form factors from future EIC data in the context of global analyses, and the status and prospect for “joint” global analyses that aim at simultaneous extractions of PDFs and FFs;
•

High- $p_{T}$ observables at the EIC and their interplay with TMD physics.

5 Perspectives and challenges of Latin-American groups

The Latin American groups have mostly worked on their own or within limited national collaborations (Morelia–Sinaloa, Morelia–UNAM, São Paulo-Pelotas, for example) or international ones (Morelia–São Paulo, Sucre–São Paulo), while individual collaborations with colleagues in Europe and in the U.S. are more common. Thus far, lack of logistics and coordination have not permitted the creation of schools and workshop series specifically dedicated to the EIC. Joining efforts would be valuable given the large number of young researchers and students involved in most groups.

To that end, we shall resume the alternating workshop series, “Many manifestations of nonperturbative QCD” and “Nonperturbative Aspects of Field Theories”, which took place in São Paulo and Morelia, respectively, and were interrupted by the pandemic. We also foresee a continuity in the organization of international workshops, in particular at the Center for Frontiers in Nuclear Science in Stony Brook, but also at the Institute for Nuclear Theory in Seattle, the European Center for Theoretical Studies in Nuclear Physics and Related Areas in Trento, at the ICTP South American Institute for Fundamental Research in São Paulo and at the Mesoamerican Centre for Theoretical Physics in Chiapas.

The financial support of the Inter-American Network of Networks of QCD challenges (I.ANN-QCD) has been very valuable in the past, though this U.S. initiative ought to be supplemented by Latin American agencies. Scientific visits, student and postdoc exchanges should therefore be coordinated within the framework of bilateral or multilateral agreements. In this context, the SPRINT calls of the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) can serve as a blueprint for future initiatives [154]: proposals for inter-institutional or thematic collaborations must be submitted to the different national funding agencies, for instance FAPESP and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) in Brazil, the Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCyT) in México and the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) in Argentina. Such international calls for projects lasting two to three years would be extremely helpful to maintain long-term collaborations in Latin America. Visits can in principle also be financed by the Centro Latino-Americano de Física (CLAF), though its financial situation appears to be precarious.

We foresee publications, related to and motivated by the EIC, in peer-reviewed Q1 journals by the aforementioned groups. Those will be supplemented by talks in dedicated international workshops and conferences, as well as lectures in schools, that will take place in Latin America in the coming years. To that end, we estimate the financial needs as follows.

•

Based on the experience of organizing POETIC 2023 in São Paulo, the Latin American EIC community anticipates that each large event will cost about US$30,000, comprising of about 40-50 invited speakers and including accommodation, airfares, venue and coffee breaks. Medium-size events attended by fewer speakers, or using more economic lodging (e.g. summer schools for students), are expected to cost about US$15,000 per week (we divide the cost of typical US-based schools by two) for 50-60 students, in addition to a similar amount to cover the lodging and travel costs of lecturers. Hence, between schools and conferences, an annual budget of about $US50,000-60,000 is necessary for the organization of Latin American EIC events that would consolidate the community.
•

The I.ANN-QCD supports projects between Latin American and U.S. institutions, as well as the participation of Latin-America based speakers in conferences and workshops in the U.S. Supplementing this I.ANN-QCD support would amount to about US$30,000 per year.
•

The Center for Frontiers in Nuclear Science, dedicated to the EIC experimental program, provides 25% of funding for joint postdoctoral fellowship. However, it has proven difficult in the past to justify and/or find complementary support from Latin-American institutions. Any effort, even bureaucratic, in that direction would be useful.
•

Student exchanges and scientific visits of collaborators have mostly been financed with individual grants. We recommend more coordinated actions involving State and Federal agencies in Latin America that result in calls for bi- or multilateral projects dedicated to EIC physics.

6 Acknowledgements

We acknowledge financial support by the following Science and Research Agencies:
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), grant nos. 2023/00195-8 and 2018/25225-9, Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), grant nos. 309262/2019-4, 313030/2021-9, 409032/2023-9, 401565/2023-8 and 310763/2023-1, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, grant no. 88881.309870/ 2018-01, Instituto Nacional de Ciência e Tecnologia: Física Nuclear e Aplicações (INCT-FNA), grant no. 464898/2014-5, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCyT), project CBF2023-2024-3544 and Ciencia de Frontera 2019 No. 51244 (FORDECYT-PRON-ACES), Universidad Nacional Autónoma de México, grant no. DGAPA-PAPIIT IN111222, Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo, grant no. 4.10, Generalitat Valenciana GenT Excellence Programme, grant no. CIDEGENT/2020/011, ILINK22045, Programme PROMETEO of the Generalitat Valenciana, grant no. CIPROM/2022/66., “Atracción de Talento” of the Comunidad de Madrid, grant no. 2022-T1/TIC-24024, Agencia Estatal de Investigación, grant nos. PID2020-113334GB-I00, PID2023-151418NB-I00 and PID2022-140440NB-C22, Regional Andalusian project P18-FR-5057, Deutsche Forschungsgesellschaft (DFG) research unit FOR 2926.

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Latin American Strategy Forum for Research Infrastructure (III LASF4RI Contribution) The glue that binds us all – Latin America and the Electron-Ion Collider