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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 $D$-wave admixture in quarkonium wave functions is acquired from the photonlike structure of $V\to Q\bar Q$ transition in the light-front frame widely used in the literature. Such a $D$-wave ballast is not justified by any nonrelativistic model for $Q-\bar Q$ interaction potential and leads to falsified predictions for the cross sections in heavy quarkonium production in ultra-peripheral nuclear collisions. We analyze this negative role of $D$-wave contribution by comparing with our previous studies based on a simple non-photon-like "$S$-wave-only" $V\to Q\bar Q$ transition in the $Q\bar Q$ rest frame., Comment: 13 pages including 4 figures and 1 table. The version for resubmission to Physical Review D. arXiv admin note: text overlap with arXiv:2008.05116

Ultra-peripheral collisions (UPCs) involving heavy ions and protons are the energy frontier for photon-mediated interactions. UPC photons can be used for many purposes, including probing low-$x$ gluons via photoproduction of dijets and vector mesons, probes of beyond-standard-model processes, such as those enabled by light-by-light scattering, and studies of two-photon production of the Higgs., Comment: Letter of Interest submitted to Snowmass 2021

We present a revision of predictions for nuclear shadowing in deep-inelastic scattering at small Bjorken $x_{Bj}$ corresponding to kinematic regions accessible by the future experiments at electron-ion colliders. The nuclear shadowing is treated within the color dipole formalism based on the rigorous Green function technique. This allows incorporating naturally color transparency and coherence length effects, which are not consistently and properly included in present calculations. For the lowest $|q\bar q\rangle$ Fock component of the photon, our calculations are based on an exact numerical solution of the evolution equation for the Green function. Here the magnitude of shadowing is tested using a realistic form for the nuclear density function, as well as various phenomenological models for the dipole cross section. The corresponding variation of the transverse size of the $q\bar q$ photon fluctuations is important for $x_{Bj}\gtrsim 10^{-4}$, on the contrary with the most of other models, which use frequently only the eikonal approximation with the "frozen" transverse size. At $x_{Bj}\lesssim 0.01$ we calculate within the same formalism also a shadowing correction for the higher Fock component of the photon containing gluons. The corresponding magnitudes of gluon shadowing correction are compared adopting different phenomenological dipole models. Our results are tested by available data from the E665 and NMC collaborations. Finally, the magnitude of nuclear shadowing is predicted for various kinematic regions that should be scanned by the future experiments at electron-ion colliders., Comment: Datasets at https://zenodo.org/record/3470138 , fixed figure and misprints

Hadronization of heavy quarks reveals various unusual features. Gluon radiation by a heavy quark originated from a hard process, ceases shortly on a distance of the order of few fm. Due to the dead-cone effect a heavy quark radiates only a small fraction of its energy. This is why the measured fragmentation function D(z) peaks at large z. Hadronization finishes at very short distances, well shorter than 1 fm, by production of a colorless small-size Qq-bar dipole. This ensures dominance of a perturbative mechanism and makes possible factorization of short and long distances. The latter corresponds to final state interactions of the produced dipole propagating through a dense medium. The results provide good description of data on beauty and charm suppression in heavy ion collisions, fixing the transport coefficient for b-quarks about twice smaller than for charm, and both significantly lower that the values determined from data on suppression of high-pT light hadrons. We relate this to reduction of the QCD coupling at higher scales, and suppression of radiation by the dead-cone effect., Comment: 9 pages, 6 figures

We analyze the validity of a commonly used identification between structures of the virtual photon $\gamma^*\to Q\bar Q$ and vector meson $V\to Q\bar Q$ transitions. In the existing studies of $S$-wave vector-meson photoproduction in the literature, such an identification is typically performed in the light-front (LF) frame while the radial component of the meson wave function is rather postulated than computed from the first principles. The massive photon-like $V\to Q\bar Q$ vertex, besides the $S$-wave component, also contains an extra $D$-wave admixture in the $Q\bar Q$ rest frame. However, the relative weight of these contributions cannot be justified by any reasonable nonrelativistic $Q\bar Q$ potential model. In this work, we investigate the relative role of the $D$-wave contribution starting from the photon-like quarkonium $V\to Q\bar Q$ transition in both frames: in the $Q\bar Q$ rest frame (with subsequent Melosh spin transform to the LF frame) and in the LF frame (without Melosh transform). We show that the photon-like transition imposed in the $Q\bar Q$ rest frame leads to significant discrepancies with the experimental data. In the second case we find that the corresponding total $J/\psi(1S)$ photoproduction cross sections are very close to those obtained with the "$S$-wave only" $V\to Q\bar Q$ transition, both leading to a good description of the data. However, we find that the "$S$-wave only" transition leads to a better description of photoproduction data for excited heavy quarkonium states, which represent a more effective tool for study of $D$-wave effects. Consequently, the predictions for production of excited states based on the photon-like structure of $V\to Q\bar Q$ transition should be treated with a great care due to a much stronger sensitivity of the $D$-wave contribution to the nodal structure of quarkonium wave functions., Comment: 18 pages of Latex including 6 figures. The modified version which has been accepted for publication by European Physical Journal C

The color field of a quark, stripped off in a hard reaction, is regenerated via gluon radiation. The space-time development of a jet is controlled by the coherence time of gluon radiation, which for heavy quarks is subject to the dead-cone effect, suppressing gluons with small transverse momenta. As a result, heavy quarks can radiate only a small fraction of the initial energy. This explains the peculiar shape of the measured heavy quark fragmentation function, which strongly peaks at large fractional momenta z. The fragmentation length distribution, related to the fragmentation function in a model independent way, turns out to be concentrated at distances much shorter than the confinement radius. This implies that the mechanisms of heavy quark fragmentation is pure perturbative., Comment: 5 pages, 4 figures

In this work, we revise the conventional description of J/Psi(1S), Y(1S), Psi'(2S) and Y'(2S) elastic photo- and electroproduction off a nucleon target within the color dipole picture and carefully study various sources of theoretical uncertainties in calculations of the corresponding electroproduction cross sections. For this purpose, we test the corresponding predictions using a bulk of available dipole cross section parametrisations obtained from deep inelastic scattering data at HERA. Specifically, we provide the detailed analysis of the energy and hard-scale dependencies of quarkonia yields employing the comprehensive treatment of the quarkonia wave functions in the Schroedinger equation based approach for a set of available c-\bar{c} and b-\bar{b} interquark interaction potentials. Besides, we quantify the effect of Melosh spin rotation, the Q^2-dependence of the diffractive slope and an uncertainty due to charm and bottom quark mass variations., Comment: 43 pages of Latex including 29 figures

In this work we present for the first time the comprehensive study of the Melosh spin rotation effects in diffractive electroproduction of S-wave heavy quarkonia off a nucleon target. Such a study has been performed within the color dipole approach using, as an example and a reference point, two popular parametrizations of the dipole cross section and two potentials describing the interaction between Q and bar{Q} and entering in the Schroedinger equation based formalism for determination of the quarkonia wave functions. We find a strong onset of spin rotation effects in 1S charmonium photoproduction which is obviously neglected in present calculations of corresponding cross sections. For photoproduction of radially excited Psi'(2S) these effects are even stronger leading to an increase of the photoproduction cross section by a factor of 2-3 depending on the photon energy. Even in production of radially excited Y'(2S) and Y"(3S) they can not be neglected and cause the 20-30% enhancement of the photoproduction cross section. Finally, we predict that the spin effects vanish gradually with photon virtuality Q^2 following universality properties in production of different heavy quarkonia as a function of Q^2 + M_V^2., Comment: 23 pages of Latex including 10 figures. The version for resubmission to European Physical Journal C

We present a detailed study of open heavy flavor production in high-energy $pp$ collisions at the LHC in the color dipole framework. The transverse momentum distributions of produced $b$-jets, accounting for the jet energy loss, as well as produced open charm $D$ and bottom $B$ mesons in distinct rapidity intervals relevant for LHC measurements are computed. The dipole model results for the differential $b$-jet production cross section are compared to the recent ATLAS and CMS data while the results for $D$ and $B$ mesons production cross sections -- to the corresponding LHCb data. Several models for the phenomenological dipole cross section have been employed to estimate theoretical uncertainties of the dipole model predictions. We demonstrate that the primordial transverse momentum distribution of the projectile gluon significantly affects the meson spectra at low transverse momenta and contributes to the largest uncertainty of the dipole model predictions., Comment: 22 pages, 9 figures

In this work, we investigate production of Drell-Yan (DY) pairs in proton-nucleus collisions in kinematic regions where the corresponding coherence length does not exceed the nuclear radius, $R_A$, and the quantum coherence effects should be treated with a special care. The results for the nucleus-to-nucleon production ratio available in the literature so far are usually based on the assumption of a very long coherence length (LCL) $l_c\gg R_A$. Since the onset of coherence effects is controlled by the coherence length $l_c$, we estimated its magnitude in various kinematic regions of the DY process and found that the LCL approximation should not be used at small and medium c.m. collision energies ($\sqrt{s} \lesssim 200$ GeV) as well as at large dilepton invariant masses. In order to obtain realistic predictions, we computed for the first time the DY cross section using the generalised color dipole approach based on the rigorous Green function formalism, which naturally incorporates the color transparency and quantum coherence effects and hence allows to estimate the nuclear shadowing with no restrictions on the CL. In addition to the shadowing effect, we studied a complementary effect of initial state interactions (ISI) that causes an additional suppression at large values of the Feynman variable. Numerical results for the nuclear modification factor accounting for the ISI effect and the finite $l_c$ are compared to the data available from the fixed-target FNAL measurements and a good agreement has been found. Besides, we present new predictions for the nuclear suppression as a function of dilepton rapidity and invariant mass in the kinematic regions that can be probed by the RHIC collider as well as by the planned AFTER@LHC and LHCb fixed-target experiments., Comment: 14 pages, 10 figures

The Drell-Yan (DY) process of dilepton pair production off nuclei is not affected by final state interactions, energy loss or absorption. A detailed phenomenological study of this process is thus convenient for investigation of the onset of initial-state effects in proton-nucleus ($pA$) collisions. In this paper, we present a comprehensive analysis of the DY process in $pA$ interactions at RHIC and LHC energies in the color dipole framework. We analyse several effects affecting the nuclear suppression, $R_{pA}<1$, of dilepton pairs, such as the saturation effects, restrictions imposed by energy conservation (the initial-state effective energy loss) and the gluon shadowing, as a function of the rapidity, invariant mass of dileptons and their transverse momenta $p_T$. In this analysis, we take into account besides the $\gamma^*$ also the $Z^0$ contribution to the production cross section, thus extending the predictions to large dilepton invariant masses. Besides the nuclear attenuation of produced dileptons at large energies and forward rapidities emerging due to the onset of shadowing effects, we predict a strong suppression at large $p_T$, dilepton invariant masses and Feynman $x_F$ caused by the Initial State Interaction effects in kinematic regions where no shadowing is expected. The manifestations of nuclear effects are investigated also in terms of the correlation function in azimuthal angle between the dilepton pair and a forward pion $\Delta\phi$ for different energies, dilepton rapidites and invariant dilepton masses. We predict that the characteristic double-peak structure of the correlation function around $\Delta \phi\simeq \pi$ arises for very forward pions and large-mass dilepton pairs., Comment: 16 pages, 11 figures; discussion extended, typos corrected; published version

An extensive phenomenological study of the Drell-Yan (DY) process in $pp$ collisions at various energies is performed in the color dipole framework. Besides previously studied $\gamma^*$ production we have also included the $Z^0$ contribution relevant at large dilepton invariant masses. We investigate the DY cross section differential in invariant mass, rapidity and transverse momentum of the dilepton pair in $pp$ collisions at RHIC and LHC. We consider three different phenomenological models for the dipole cross section and found a reasonable agreement with the available data. As a further test of the color dipole formalism, we also study the correlation function in azimuthal angle between the dilepton pair and a forward pion $\Delta\phi$ for different energies, dilepton rapidites and invariant masses. The characteristic double-peak structure of the correlation function around $\Delta \phi\simeq \pi$ found for very forward pions and low-mass dilepton pairs is sensitive to the saturation effects and can be tested by future DY measurements in $pp$ collisions., Comment: 16 pages, 12 figures; typos corrected, references added, conclusions unchanged

Using a simplified model for in-medium dipole evolution accounting for color filtering effects we study production of hadrons at large transverse momenta $p_T$ in heavy ion collisions. In the framework of this model, several important sources of the nuclear suppression observed recently at RHIC and LHC have been analysed. A short production length of the leading hadron $l_p$ causes a strong onset of color transparency effects manifested themselves as a steep rise of the nuclear modification factor $R_{AA}(p_T)$ at large hadron $p_T$'s. A dominance of quarks with higher $l_p$ leads to a weaker suppression at RHIC than the one observed at LHC. In the RHIC kinematic region we include an additional suppression factor steeply falling with $p_T$, which is tightly related to the energy conservation constraints. The latter is irrelevant at LHC up to $p_T\lesssim 70$ GeV while it causes a rather flat $p_T$ dependence of the $R_{AA}(p_T)$ factor at RHIC c.m. energy $\sqrt{s} = 200$ GeV and even an increasing suppression with $p_T$ at $\sqrt{s} = 62$ GeV. The calculations contain only a medium density adjustment, and for an initial time scale $t_0$ = 1 fm we found the energy-dependent maximal values of the transport coefficient, $\hat{q}_0 = 0.7, 1.0$ and 1.3 GeV$^2$/fm corresponding to $\sqrt{s} = 62, 200$ GeV and 2.76 TeV, respectively. We present a broad variety of predictions for the nuclear modification factor and the azimuthal asymmetry which are in a good agreement with available data from experiments at RHIC and LHC., Comment: 14 pages, 17 figures; extra clarifications added in Sects. II and III (with additional Figs. 1-6) and in the extended Sect. V B (with additional Fig.11), references added, conclusions unchanged

We study nuclear shadowing at small Bjorken x < 0.01 in the color dipole approach. Such a light-cone quantum-chromodynamics formalism based on the Green function technique incorporates naturally color transparency and coherence length effects. The nuclear shadowing for the barq-q Fock component of the photon is calculated using exact numerical solution of the evolution equation for the Green function. At x < 0.01 we demonstrate that a contribution of higher Fock states containing gluons to overall nuclear shadowing becomes effective. Numerical results for nuclear shadowing are compared with available data from the E665 and NMC collaborations. Model calculations are finally tested with the results obtained from other models., Comment: 16 pages, 5 figures, talk given at the Workshop on High-pT Physics at LHC (LHC07), Jyvaskyla, Finland, 23-27 Mar 2007. Published in PoS(LHC07)028