Search

We study the tomographic applications of a new phenomenon we dub "jet drift" -- the deflection of high-energy particles and jets toward the direction of a flowing medium -- to the quark-gluon plasma produced in heavy-ion collisions. While the physics of jet drift is quite general, for specificity we consider the case of photon-jet production at mid-rapidity. Beginning with the simplest possible model, a large slab of uniformly flowing plasma, we systematically introduce the geometrical elements of a heavy-ion collision in a simple optical Glauber model. We find that the moving medium causes the jet to drift in the direction of the flow, bending its trajectory and leaving detailed signatures of the flow pattern in the distribution of $\gamma + \: \mathrm{jet}$ acoplanarities. In the elliptical geometries produced in non-central collisions, this drift effect leads to a strong geometry coupling which persists despite the addition of event-by-event fluctuations in the jet production point, impact parameter, and acoplanarity. We propose a new observable to measure the jet drift effect through the correlation of $\gamma + \: \mathrm{jet}$ acoplanarities with the elliptic flow of soft particles. Preliminary estimates suggest this correlation may be studied at sPHENIX and the LHC., Comment: 52 pages, 18 figures

In a recent study [1] we have extended the opacity expansion approach to describe jet-medium interactions including medium motion effects in the context of heavy-ion collisions. We have computed color field of the in-medium sources, including the effects of the transverse field components and the energy transfer between the medium and jet. The corresponding contributions are sub-eikonal in nature, and were previously ignored in the literature. Here we discuss how our approach can be applied to describe the medium motion effects in the context of Deep Inelastic Scattering., Comment: 6 pages, 1 figure, DIS2021 proceedings

We calculate the leading corrections to jet momentum broadening and medium-induced branching that arise from the velocity of the moving medium at first order in opacity. These results advance our knowledge of jet quenching and demonstrate how it couples to collective flow of the quark-gluon plasma in heavy-ion collisions and to the orbital motion of partons in cold nuclear matter in deep inelastic scattering at the electron-ion collider. We also compute the leading corrections to jet momentum broadening due to transverse gradients of temperature and density. We find that these effects lead to both anisotropic transverse momentum diffusion proportional to the medium velocity and anisotropic medium-induced radiation emitted preferentially in the direction of the flow. We isolate the relevant sub-eikonal corrections by working with jets composed of scalar particles with arbitrary color factors interacting with the medium by scalar QCD. Appropriate substitution of the color factors and light-front wave functions allow us to immediately apply the results to a range of processes including $q \rightarrow q g$ branching in real QCD. The resulting general expressions can be directly coupled to hydrodynamic simulations on an event-by-event basis to study the correlations between jet quenching and the dynamics of various forms of nuclear matter., Comment: 94 pages, 12 figures, 1 table

One of the greatest uncertainties in heavy-ion collisions is the description of the initial state. Different models predict a wide range of initial energy density distributions based on their underlying assumptions. Final flow harmonics are sensitive to these differences in the initial state due to the nearly linear mapping between eccentricities and anisotropic flow harmonics. The Trento code uses a model-agnostic approach by phenomenologically parameterizing the initial state and constraining those parameters from a Bayesian analysis. There the multiplicity fluctuations were determined by a one parameter $\Gamma$ distribution. However, initial-state models arising from the Color-Glass Condensate (CGC) framework lead to an initial energy density which is outside the functional form considered in Trento and its later Bayesian analyses because they rely on log-normal multiplicity fluctuations. We compare $T_{A}T_{B}$ scaling (CGC-like) to $\sqrt{T_{A}T_{B}}$ scaling (preferred from a Trento Bayesian analysis) and find that the $T_A T_B$ form together with log-normal fluctuations is a reasonable candidate to describe the multiplicity fluctuations but leads to larger eccentricities, which would affect the extraction of viscosity in small systems., Comment: 4 pages, 2 figures, 10th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions

We present a Monte Carlo based analysis of the combined world data on polarized lepton-nucleon deep-inelastic scattering at small Bjorken $x$ within the polarized quark dipole formalism. We show for the first time that double-spin asymmetries at $x, 7 pages, 5 figures; v2: Discussion extended, typos corrected, data set expanded, figure added. To appear in Phys. Rev. D

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of nonspherical nuclei. In the case of $^{129}\mathrm{Xe}$ collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In $^{208}\mathrm{Pb}$ collisions a discrepancy exists in similar centralities, where either elliptic flow is overpredicted or triangular flow is underpredicted by hydrodynamic models; this is known as the ${v}_{2}$-to-${v}_{3}$ puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that $^{208}\mathrm{Pb}$ nuclei could have a pear-shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we reexamine the ${v}_{2}$-to-${v}_{3}$ puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio ${v}_{3}\left\{4\right\}/{v}_{3}\left\{2\right\}$ and comparing two different hydrodynamic models. We find that while an octupole deformation would slightly improve the ratio between ${v}_{2}$ and ${v}_{3}$, it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with ${\ensuremath{\beta}}_{3}\ensuremath{\lesssim}0.0375$ for $^{208}\mathrm{Pb}$, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. The ${v}_{2}$-to-${v}_{3}$ puzzle remains a challenge for hydrodynamic models.

Jets produced at a future electron-ion collider (EIC) are predominantly initiated by energetic quarks, and the subsequent branching of these quarks into systems of quarks and gluons is heavily modified by multiple scattering in the nuclear medium. In cold nuclear matter and in the quark-gluon plasma, this feature allows jet cross sections and jet substructure to be used as a probe of the medium's properties. Here we present a formalism for computing the gluon substructure of a quark jet to an arbitrary order in opacity, the average number of scatterings in the medium, while maintaining the exact kinematics of the splitting. We present explicit results at second order in opacity for the first time, along with a recursion relation which can be used to construct the solution for arbitrarily high orders in opacity. The theoretical framework demonstrated here applies equally well to light and heavy quark branching, and is easily generalizable to other systems.

In recent years the understanding of the limits of the smallest possible droplet of the quark gluon plasma has been called into question. Experimental results from both the Large Hadron Collider and the Relativistic Heavy Ion Collider have provided hints that the quark gluon plasma may be produced in systems as small as that formed in $p\mathrm{Pb}$ or $d\mathrm{Au}$ collisions. Yet alternative explanations still exist from correlations arising from quarks and gluons in a color glass condensate picture. In order to resolve these two scenarios, a system-size scan has been proposed at the Large Hadron Collider for collisions of ArAr and OO. Here we make predictions for a possible future run of ArAr and OO collisions at the Large Hadron Collider and study the system-size dependence of a variety of flow observables. We find that linear response (from the initial conditions to the final flow harmonics) becomes more dominant in smaller systems, whereas the $\text{linear}+\text{cubic}$ response can accurately predict multiparticle cumulants for a wide range of centralities in large systems.

We study a range of collision systems involving deformed ions and compare the elliptic and triangular flow harmonics produced in a hydrodynamics scenario versus a color glass condensate (CGC) scenario. For the hydrodynamics scenario, we generate initial conditions using TRENTO and work within a linear response approximation to obtain the final flow harmonics. For the CGC scenario, we use the explicit calculation of two-gluon correlations taken in the high-pT “(semi)dilute-(semi)dilute” regime to express the flow harmonics in terms of the density profile of the collision. We consider ultracentral collisions of deformed ions as a testbed for these comparisons because the difference between tip-on-tip and side-on-side collisions modifies the multiplicity dependence in both scenarios, even at zero impact parameter. We find significant qualitative differences in the multiplicity dependence obtained in the initial conditions+hydrodynamics scenario and the CGC scenario, allowing these collisions of deformed ions to be used as a powerful discriminator between models. We also find that sub-nucleonic fluctuations have a systematic effect on the elliptic and triangular flow harmonics which are most discriminating in 0–1% ultracentral symmetric collisions of small deformed ions and in 0–10% d197Au collisions. The collision systems we consider are 238U238U, d197Au, 9Be197Au, 9Be9Be, 3He3He, and 3He197Au.

QCD dynamics are directly studied in two different but intersecting contexts: high-temperature QCD in heavy-ion collisions and zero-temperature hadronic structure in electron-hadron collisions. The approaches to high-energy nuclear physics in these two contexts are very different, however, and bringing the two fields into dialogue can reveal new opportunities. In this paper I highlight one interesting intersection between the two: leveraging the sea quark chemistry of the proton to study charge transport in top-energy heavy-ion collisions.

In our previous work we established a formalism which allows one to determine the small-$x$ asymptotics of any transverse momentum-dependent parton distribution function (TMD PDF) of the proton at small values of strong coupling. In this paper we apply this formalism to the valence quark transversity TMD. We relate the valence quark transversity to the transversely polarized dipole scattering amplitude, written in terms of the fundamental transversely-polarized "Wilson line" operator, an expression for which we derive explicitly as well. We then write down the evolution equation for the transversely polarized dipole amplitude. Solving that equation we arrive at the following small-$x$ asymptotics of the valence quark transversity in the large-$N_c$ limit: \begin{align} h_{1T}^v (x, k_T^2) \sim h_{1T}^{\perp \, v} (x, k_T^2) \sim \left( \frac{1}{x} \right)^{-1 + 2 \, \sqrt{\frac{\alpha_s \, N_c}{2 \, \pi}} } . \notag \end{align} This result is in agreement with one of the two possible small-$x$ asymptotics for the transverse structure function found previously by Kirschner, Mankiewicz, Sch\"{a}fer, and Szymanowski., Comment: 18 pages, 7 figures

In this Letter we report the first calculation of all ${\cal O}(\alpha_s)$ medium-induced branching processes to any order in opacity. Our splitting functions results are presented as iterative solutions to matrix equations with initial conditions set by the leading order branchings in the vacuum. The flavor and quark mass dependence of the in-medium $q \rightarrow qg$, $g\rightarrow gg$, $q \rightarrow g q$, $g \rightarrow q\bar{q}$ processes is fully captured by the light-front wavefunction formalism and the color representation of the parent and daughter partons. We include the explicit solutions to second order in opacity as supplementary material and present numerical results in a realistic strongly-interacting medium produced in high center-of-mass energy heavy ion collisions at the Large Hadron Collider. Our numerical simulations show that the second order in opacity corrections can change the energy dependence of the in-medium shower intensity. We further find corrections to the longitudinal and angular distributions of the in-medium splitting kernels that may have important implications for jet substructure phenomenology., Comment: 10 pages, 3 figures, 1 table

In this paper, we compute a number of cross sections for the production of multiple particles at mid-rapidity in the semi-dilute / dense regime of the color-glass condensate (CGC) effective field theory. In particular, we present new results for the production of two quark-antiquark pairs (whether the same or different flavors) and for the production of one quark-antiquark pair and a gluon. We also demonstrate the existence of a simple mapping which transforms the cross section to produce a quark-antiquark pair into the corresponding cross section to produce a gluon, which we use to obtain various results and to cross-check them against the literature. We also discuss hadronization effects in the heavy flavor sector, writing explicit expressions for the production of various combinations of $D$ and $\bar D$ mesons, $J/\psi$ mesons, and light hadrons. The various multiparticle cross sections presented here contain a wealth of information and can be used to study heavy flavor production, charge-dependent correlations, and "collective" flow phenomena arising from initial-state dynamics., Comment: 51 pages, 8 figures

Cold nuclear matter effects in reactions with nuclei at a future electron-ion collider (EIC) lead to a modification of semi-inclusive hadron production, jet cross sections, and jet substructure when compared to the vacuum. At leading order in the strong coupling, a jet produced at an EIC is initiated as an energetic quark, and the process of this quark splitting into a quark-gluon system underlies experimental observables. The spectrum of gluons associated with the branching of this quark jet is heavily modified by multiple scattering in a medium, allowing jet cross sections and jet substructure to be used as a probe of the medium's properties. We present a formalism that allows us to compute the gluon spectrum of a quark jet to an arbitrary order in opacity, the average number of scatterings in the medium. This calculation goes beyond the simplifying limit in which the gluon radiation is soft and can be interpreted as energy loss of the quark, and it significantly extends previous work which computes the full gluon spectrum only to first order in opacity. The theoretical framework demonstrated here applies equally well to light parton and heavy quark branching, and is easily generalizable to all in-medium splitting processes., Comment: 41 pages, 10 figures

We determine the small-$x$ asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large $N_c$. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small $x$. We then construct and solve novel small-$x$ large-$N_c$ evolution equations for the operator related to the dipole gluon helicity TMD. Our main result is the small-$x$ asymptotics for the gluon helicity distribution: \begin{align}\label{dG_final} \Delta G \sim \left( \frac{1}{x} \right)^{\alpha_h^G} \ \ \ \mbox{with} \ \ \ \alpha_h^G = \frac{13}{4 \sqrt{3}} \, \sqrt{\frac{\as \, N_c}{2 \pi}} \approx 1.88 \, \sqrt{\frac{\as \, N_c}{2 \pi}}. \end{align} We note that the power $\alpha_h^G$ is approximately 20$\%$ lower than the corresponding power $\alpha_h^q$ for the small-$x$ asymptotics of the quark helicity distribution defined by \begin{align}\label{dq_final} \Delta q \sim \left( \frac{1}{x} \right)^{\alpha_h^q} \ \ \ \mbox{with} \ \ \ \alpha_h^q = \frac{4}{\sqrt{3}} \, \sqrt{\frac{\as \, N_c}{2 \pi}} \approx 2.31 \, \sqrt{\frac{\as \, N_c}{2 \pi}} \end{align} found in our earlier work.

In this paper, we study the spatial correlations among quarks and antiquarks produced at mid-rapidity by gluon pair production in the color glass condensate framework. This paper is the first part of a series in which we calculate a complete set of quark/quark, quark/antiquark, and antiquark/antiquark spatial correlation functions in heavy-light ion collisions, with the goal of incorporating their conserved charges into the initial conditions of hydrodynamics. The physical mechanisms captured in this calculation include geometric, entanglement, and interaction-mediated correlations. In this first paper, we construct the building blocks for the correlations arising from single- and double-pair production, studying in detail the single-pair case and the general features of the double-pair case. We find a rich correlation structure in transverse coordinate space, with different mechanisms dominating over different length scales, and we present explicit results for the quark-antiquark correlations in the single-pair production regime. We reserve a detailed discussion of the double-pair production regime for the next paper in this sequence., Comment: 49 pages, 13 figures

We rederive the small-$x$ evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods. In this work, we re-derive the double-logarithmic small-$x$ evolution equations for quark helicity in terms of the "polarized Wilson lines", the operators consisting of light-cone Wilson lines with one or two non-eikonal local operator insertions which bring in helicity dependence. For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark sub-eikonal operators. We show that the double-logarithmic small-$x$ evolution of the "polarized dipole amplitude" operators, made out of regular light-cone Wilson lines along with the polarized ones constructed here, reproduces the equations derived in our earlier works. The method we present here can be used as a template for determining the small-$x$ asymptotics of any transverse momentum-dependent (TMD) quark (or gluon) parton distribution functions (PDFs), and is not limited to helicity., Comment: 31 pages, 11 figures

We determine the small-x asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large Nc. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small x. We then construct and solve novel small-x large-Nc evolution equations for the operator related to the dipole gluon helicity TMD. Our main result is the small-x asymptotics for the quark helicity distribution

We determine the small-$x$ asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large $N_c$. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small $x$. In the process we obtain an interesting new result: in contrast to the unpolarized dipole gluon TMD case, the operator governing the small-$x$ behavior of the dipole gluon helicity TMD is different from the operator corresponding to the polarized dipole scattering amplitude (used in our previous work to determine the small-$x$ asymptotics of the quark helicity distribution). We then construct and solve novel small-$x$ large-$N_c$ evolution equations for the operator related to the dipole gluon helicity TMD. Our main result is the small-$x$ asymptotics for the gluon helicity distribution: $\Delta G \sim \left( \tfrac{1}{x} \right)^{\alpha_h^G}$ with $\alpha_h^G = \tfrac{13}{4 \sqrt{3}} \, \sqrt{\tfrac{\alpha_s \, N_c}{2 \pi}} \approx 1.88 \, \sqrt{\tfrac{\alpha_s \, N_c}{2 \pi}}$. We note that the power $\alpha_h^G$ is approximately 20$\%$ lower than the corresponding power $\alpha_h^q$ for the small-$x$ asymptotics of the quark helicity distribution defined by $\Delta q \sim \left( \tfrac{1}{x} \right)^{\alpha_h^q}$ with $\alpha_h^q = \tfrac{4}{\sqrt{3}} \, \sqrt{\tfrac{\alpha_s \, N_c}{2 \pi}} \approx 2.31 \, \sqrt{\tfrac{\alpha_s \, N_c}{2 \pi}}$ found in our earlier work., Comment: 36 pages, 9 figures; v3: minus signs and factors of 2 corrected, main results remained the same

Ultracentral collisions of heavy nuclei, in which the impact parameter is nearly zero, are especially sensitive to the details of the initial state model and the microscopic mechanism for collective flow. In a hydrodynamic “flow” picture, the final state momentum correlations are a direct response to the fluctuating initial geometry, although models of the initial geometry differ widely. Alternatively, dynamical mechanisms based in the color glass condensate (CGC) formalism can naturally lead to many-body correlations with very different systematics. Here we present a calculation of event-by-event elliptic flow in both the hydrodynamic and CGC paradigms and show that they can be qualitatively distinguished in ultracentral collisions of deformed nuclei. Specifically, the multiplicity dependence in such collisions is qualitatively opposite, with the CGC correlations increasing with multiplicity while the hydrodynamic correlations decrease. The consistency of the latter with experimental data on UU collisions appears to rule out a CGC-mediated explanation. We find that these qualitative features also persist in small deformed systems and can therefore be a valuable test of the microscopic physics in that regime. The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

In recent years, the theoretical foundations of small-x physics have made significant advances in two frontiers: higher-order (NLO) corrections and power-suppressed (sub-eikonal) corrections. Among the former are the NLO calculations of the linear (BFKL) and nonlinear (BK-JIMWLK) evolution equations, as well as cross sections for various processes. Among the latter are corrections to the whole framework of high-energy QCD, including new contributions from quarks and spin asymmetries. One common element to both of these frontiers is the appearance of collinear logarithms beyond the leading-order framework. The proper treatment of these logarithms is a major challenge in obtaining physical cross sections at NLO, and they lead to a new double-logarithmic resummation parameter which governs spin at small x. In this paper, I will focus on the role of these collinear logarithms in both frontiers of small-x physics, as well as give a brief sample of other recent advances in its theoretical foundations.The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

Here we briefly outline the calculation of the single transverse spin asymmetry due to a new perturbative, saturation-mediated mechanism in high energy QCD. We use light-cone perturbation theory to study a simple model in which a transversely polarized quark scatters on a proton or nuclear target. The spin dependence of the scattering cross section is introduced by the lowest-order q → q G splitting wave function of the polarized projectile, while the time-reversal odd property of the asymmetry is generated by the antisymmetric odderon dipole scattering amplitude. We study the properties of the obtained STSA, some of which are in qualitative agreement with experiment: STSA increases with increasing projectile x F and is a non-monotonic function of the transverse momentum k T . Our mechanism predicts that the quark STSA in polarized proton–nucleus collisions should be much smaller than in polarized proton–proton collisions. We also observe that the STSA for prompt photons due to our mechanism is zero within the accuracy of the approximation.

In this Letter, we analytically solve the evolution equations for the small-$x$ asymptotic behavior of the (flavor singlet) quark helicity distribution in the large-$N_c$ limit. These evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-$x$ asymptotics, which we exploit here to obtain an analytic solution. We find that the small-$x$ power-law tail of the quark helicity distribution scales as $\Delta q^S (x, Q^2) \sim \left(\tfrac{1}{x} \right)^{\alpha_h}$ with $\alpha_h = \tfrac{4}{\sqrt{3}} \sqrt{\tfrac{\alpha_s N_c}{2\pi}}$, in excellent agreement with the numerical estimate $\alpha_h \approx 2.31\sqrt{\tfrac{\alpha_s N_c}{2\pi}}$ obtained previously. We then verify this solution by cross-checking the predicted scaling behavior of the auxiliary "neighbor dipole amplitude" against the numerics, again finding excellent agreement., Comment: 5 pages, 2 figures

We extend our earlier results for the quark helicity evolution at small $x$ to derive the small-$x$ asymptotics of the flavor singlet and flavor non-singlet quark helicity TMDs and PDFs and of the $g_1$ structure function. In the flavor singlet case we re-derive the evolution equations obtained in our previous paper on the subject, performing additional cross-checks of our results. In the flavor non-singlet case we construct new small-$x$ evolution equations by employing the large-$N_c$ limit. All evolution equations resum double-logarithmic powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the single-logarithmic powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. We solve the linearized flavor non-singlet equation analytically, obtaining an intercept which agrees with the one calculated earlier by Bartels, Ermolaev and Ryskin using the infra-red evolution equations. Our numerical solution of the linearized large-$N_c$ evolution equations for the flavor singlet case is presented in the accompanying Letter and is further discussed here., Comment: 30 pages, 12 figures

We present the first steps in an effort to incorporate the physics of transverse spin asymmetries into the saturation formalism of high energy QCD. We consider a simple model in which a transversely polarized quark scatters on a proton or nuclear target. Using the light-cone perturbation theory the hadron production cross section can be written as a convolution of the light-cone wave function squared and the interaction with the target. To generate the single transverse spin asymmetry (STSA) either the wave function squared or the interaction with the target has to be T-odd. In this work we use the lowest-order q->qG wave function squared, which is T-even, generating the STSA from the T-odd interaction with the target mediated by an odderon exchange. We study the properties of the obtained STSA, some of which are in qualitative agreement with experiment: STSA increases with increasing projectile x_F and is a non-monotonic function of the transverse momentum k_T. Our mechanism predicts that the quark STSA in polarized proton--nucleus collisions should be much smaller than in polarized proton--proton collisions. We also observe that the STSA for prompt photons due to our mechanism is zero within the accuracy of the approximation., 10 pages, 6 figures, proceedings of the QCD Evolution Workshop, May 14 - 17, 2012, Thomas Jefferson National Accelerator Facility, Newport News, VA

We construct a numerical solution of the small-$x$ evolution equations recently derived in \cite{Kovchegov:2015pbl} for the (anti)quark helicity TMDs and PDFs as well as the $g_1$ structure function. We focus on the case of large $N_c$ where one finds a closed set of equations. Employing the extracted intercept, we are able to predict directly from theory the behavior of the helicity PDFs at small $x$, which should have important phenomenological consequences. We also give an estimate of how much of the proton's spin may be at small $x$ and what impact this has on the so-called "spin crisis.", Comment: 5 pages, 4 figures; minor changes, to appear in PRL

We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) using the tools of saturation physics. By generalizing the quasi-classical Glauber-Gribov-Mueller/McLerran-Venugopalan approximation to allow for the possibility of spin-orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large "nucleus." To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer-Mulders distribution. We observe that spin-orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon., Comment: 56 pages, 14 figures; v2: typos corrected, references added; v3: more typos corrected, title slightly modified

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function. These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $\alpha_s \, \ln (1/x)$ in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for $g_1$ structure function derived previously by Bartels, Ermolaev and Ryskin., Comment: 33 pages, 20 figures; v2: typos corrected, a reference added; v3: more corrections included

We derive the cross-section for exclusive vector meson production in high energy deeply inelastic scattering off a deuteron target that disintegrates into a proton and a neutron carrying large relative momentum in the final state. This cross-section can be expressed in terms of a novel gluon Transition Generalized Parton Distribution (T-GPD); the hard scale in the final state makes the T-GPD sensitive to the short distance nucleon-nucleon interaction. We perform a toy model computation of this process in a perturbative framework and discuss the time scales that allow the separation of initial and final state dynamics in the T-GPD. We outline the more general computation based on the factorization suggested by the toy computation: in particular, we discuss the relative role of "point-like" and "geometric" Fock configurations that control the parton dynamics of short range nucleon-nucleon scattering. With the aid of exclusive $J/\Psi$ production data at HERA, as well as elastic nucleon-nucleon cross-sections, we estimate rates for exclusive deuteron photo-disintegration at a future Electron-Ion Collider (EIC). Our results, obtained using conservative estimates of EIC integrated luminosities, suggest that center-of-mass energies $s_{NN}\sim 12$ GeV$^2$ of the neutron-proton subsystem can be accessed. We argue that the high energies of the EIC can address outstanding dynamical questions regarding the short-range quark-gluon structure of nuclear forces by providing clean gluon probes of such "knockout" exclusive reactions in light and heavy nuclei., Comment: 51 pages, 17 figures

We calculate the Sivers function in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY) by employing the quasi-classical Glauber-Mueller/ McLerran-Venugopalan approximation. Modeling the hadron as a large "nucleus" with non-zero orbital angular momentum (OAM), we find that its Sivers function receives two dominant contributions: one contribution is due to the OAM, while another one is due to the local Sivers function density in the nucleus. While the latter mechanism, being due to the "lensing" interactions, dominates at large transverse momentum of the produced hadron in SIDIS or of the di-lepton pair in DY, the former (OAM) mechanism is leading in saturation power counting and dominates when the above transverse momenta become of the order of the saturation scale. We show that the OAM channel allows for a particularly simple and intuitive interpretation of the celebrated sign flip between the Sivers functions in SIDIS and DY., Comment: 44 pages, 14 figures; v2: typos corrected, figure modified

We examine in detail the diagrammatic mechanisms which provide the change of sign between the single transverse spin asymmetries measured in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY). This asymmetry is known to arise due to the transverse spin dependence of the target proton combined with a T-odd complex phase. Using the discrete symmetry properties of transverse spinors, we show that the required complex phase originates in the denominators of rescattering diagrams and their respective cuts. For simplicity, we work in a model where the proton consists of a valence quark and a scalar diquark. We then show that the phases generated in SIDIS and in DY originate from distinctly different cuts in the amplitudes, which at first appears to obscure the relationship between the single-spin asymmetries in the two processes. Nevertheless, further analysis demonstrates that the contributions of these cuts are identical in the leading-twist Bjorken kinematics considered, resulting in the standard sign-flip relation between the Sivers functions in SIDIS and DY. Physically, this fundamental, but yet untested, prediction occurs because the Sivers effect in the Drell-Yan reaction is modified by the initial-state "lensing" interactions of the annihilating antiquark, in contrast to the final-state lensing which produces the Sivers effect in deep inelastic scattering., Comment: 40 pages, 15 figures

We propose a new mechanism for generating a single transverse spin asymmetry (STSA) in polarized proton-proton and proton-nucleus collisions in the high-energy scattering approximation. In this framework the STSA originates from the q->q G splitting in the projectile (proton) light-cone wave function followed by a perturbative (C-odd) odderon interaction, together with a C-even interaction, between the projectile and the target. We show that some aspects of the obtained expression for the STSA of the produced quarks are in qualitative agreement with experiment: STSA decreases with decreasing projectile x_F and is a non-monotonic function of the transverse momentum k_T. In our framework the STSA peaks at k_T near the saturation scale Q_s. Our mechanism predicts that the quark STSA in proton-nucleus collisions should be much smaller than in proton-proton collisions. We also observe that in our formalism the STSA for prompt photons is zero., 28 pages, 17 figues; v2: minor corrections, a subsection, discussion and references added; v3: minor corrections and a new figure added; v4: minor corrections; v5: minor corrections in figures

In this brief article we summarize the derivation of the Sivers function of a heavy nucleus, which we obtain by generalizing the quasi-classical McLerran-Venugopalan model to incorporate the role of spin and orbital angular momentum. In doing so we obtain a new channel which is capable of generating the Sivers function of the nucleus from the orbital motion of its nucleons. An essential role is played in this channel by the multiple rescatterings on spectator nucleons which screen the distribution function during the initial- or final-state interactions. The combination of orbital angular momentum together with multiple rescattering yields a new interpretation of the sign flip relation between the Sivers function measured in semi-inclusive deep inelastic scattering and the Drell-Yan process.

In this brief article, we summarize our recent work1 regarding the origin of the nucleon Sivers functions within the diquark spectator model in semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process (DY). We demonstrate that the C, P, T symmetry properties of transverse spinors always couple the spin-dependent part of the numerator algebra to the imaginary part of the denominator in the cross section. This complex phase, and its sign change under time reversal, is believed to be responsible for the predicted sign change of the Sivers functions in SIDIS and DY. We study the complex phase generated in both processes by the "color-lensing" mechanism and find that, although the phases appear to be different in structure between SIDIS and DY, they do give rise to the expected sign flip relation at leading twist.