arXiv subjects

Yuri V. Kovchegov

Publications and source records attributed to Yuri V. Kovchegov.

At least 37 records · Page 2Linked to original sources

arXiv2021

First analysis of world polarized DIS data with small-$x$ helicity evolution

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 $x<0.1$ can be successfully described using only small-$x$ evolution derived from first-principles QCD, allowing predictions to be made for the $g_1$ structure function at much smaller $x$. Anticipating future data from the Electron-Ion Collider, we assess the impact of electromagnetic and parity-violating polarization asymmetries on $g_1$ and demonstrate an extraction of the individual flavor helicity PDFs at small $x$.

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arXiv2020

Helicity-dependent extension of the McLerran-Venugopalan model

We construct a generalization of the McLerran-Venugopalan (MV) model including helicity effects for a longitudinally polarized target (a proton or a large nucleus). The extended MV model can serve as the initial condition for the helicity generalization of the JIMWLK evolution equation constructed in our previous paper, as well as for calculation of helicity-dependent observables in the quasi-classical approximation to QCD.

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arXiv2020

Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow}+p$ and $p^{\uparrow}+A$ Collisions

We calculate the single transverse spin asymmetry (STSA) in polarized proton-proton ($p^{\uparrow}+p$) and polarized proton-nucleus ($p^{\uparrow}+A$) collisions ($A_N$) generated by a partonic lensing mechanism. The polarized proton is considered in the quark-diquark model while its interaction with the unpolarized target is calculated using the small-$x$/saturation approach, which includes multiple rescatterings and small-$x$ evolution. The phase required for the asymmetry is caused by a final-state gluon exchange between the quark and diquark, as is standard in the lensing mechanism of Brodsky, Hwang and Schmidt. Our calculation combines the lensing mechanism with small-$x$ physics in the saturation framework. The expression we obtain for the asymmetry $A_N$ of the produced quarks has the following properties: (i) The asymmetry is generated by the dominant elastic scattering contribution and $1/N_c^2$ suppressed inelastic contribution (with $N_c$ the number of quark colors); (ii) The asymmetry grows or oscillates with the produced quark's transverse momentum $p_T$ until the momentum reaches the saturation scale $Q_s$, and then only falls off as $1/p_T$ for larger momenta; (iii) The asymmetry decreases with increasing atomic number $A$ of the target for $p_T$ below or near $Q_s$, but is independent of $A$ for $p_T$ significantly above $Q_s$. We discuss how these properties may be qualitatively consistent with the data on $A_N$ published by the PHENIX collaboration and with the preliminary data on $A_N$ reported by the STAR collaboration.

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arXiv2020

Helicity at Small $x$: Oscillations Generated by Bringing Back the Quarks

We construct a numerical solution of the recently-derived large-$N_c \& N_f$ small-$x$ helicity evolution equations with the aim to establish the small-$x$ asymptotics of the quark helicity distribution beyond the large-$N_c$ limit explored previously in the same framework. (Here $N_c$ and $N_f$ are the numbers of quark colors and flavors.) While the large-$N_c$ helicity evolution involves gluons only, the large-$N_c \& N_f$ evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of $x$. Our numerical results in the large-$N_c \& N_f$ limit lead to the $x$-dependence of the flavor-singlet quark helicity distribution which is well-approximated by \begin{align} ΔΣ(x, Q^2)\bigg|_{\mbox{large-}N_c \& N_f} \sim \left( \frac{1}{x} \right)^{α_h^q} \, \cos \left[ ω_q \, \ln \left( \frac{1}{x} \right) + φ_q \right]. \end{align} The power $α_h^q$ exhibits a weak $N_f$-dependence, and, for all $N_f$ values considered, remains very close to $α_h^q (N_f=0) = (4/\sqrt{3}) \sqrt{α_s N_c/(2 π)}$ obtained earlier in the large-$N_c$ limit. The novel oscillation frequency $ω_q$ and phase shift $φ_q$ depend more strongly on the number of flavors $N_f$ (with $ω_q =0$ in the pure-glue large-$N_c$ limit). The typical period of oscillations for $ΔΣ$ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with $x$ seen in the strange quark helicity distribution extracted from the data.

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arXiv2020

Probing Nucleons and Nuclei in High Energy Collisions

This volume is a collection of contributions for the 7-week program "Probing Nucleons and Nuclei in High Energy Collisions" that was held at the Institute for Nuclear Theory in Seattle, WA, USA, from October 1 until November 16, 2018. The program was dedicated to the physics of the Electron Ion Collider (EIC), the world's first polarized electron-nucleon (ep) and electron-nucleus (eA) collider to be constructed in the USA. These proceedings are organized by chapters, corresponding to the weeks of the program: Week I, Generalized parton distributions; Week II, Transverse spin and TMDs; Week III, Longitudinal spin; Week IV, Symposium week; Weeks V & VI, eA collisions; Week VII, pA and AA collisions. We hope these proceedings will be useful to readers as a compilation of EIC-related science at the end of the second decade of the XXI century.

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arXiv2019

From Parton Saturation to Proton Spin: the Impact of BFKL Equation and Reggeon Evolution

Lev Lipatov was a giant in the field of strong interactions and a dominant force in high-energy QCD for many decades. His work deeply influenced both how we think about QCD and how we perform calculations in the theory. Below we describe the work in two related research directions: the physics of parton saturation and proton spin at small $x$. Both developments would have been impossible without Lipatov's groundbreaking work. Saturation physics would not have happened without the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. The recent progress in our theoretical understanding of the proton spin contribution coming from small-$x$ partons started with the seminal paper by Kirschner and Lipatov resumming double logarithms of energy in the Reggeon evolution.

hep-ph↗

arXiv2019

Helicity-dependent generalization of the JIMWLK evolution

We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived earlier. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").

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arXiv2019

Orbital Angular Momentum at Small $x$

We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of $α_s \ln^2 (1/x)$ with $α_s$ the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small $x$, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-$x$ evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-$x$ asymptotics of the quark and gluon OAM distributions in the large-$N_c$ limit: \begin{align} L_{q + \bar{q}} (x, Q^2) = - ΔΣ(x, Q^2) \sim \left(\frac{1}{x}\right)^{\frac{4}{\sqrt{3}} \, \sqrt{\frac{α_s \, N_c}{2 π}} }, \ \ \ \ \ L_G (x, Q^2) \sim ΔG (x, Q^2) \sim \left(\frac{1}{x}\right)^{\frac{13}{4 \sqrt{3}} \, \sqrt{\frac{α_s \, N_c}{2 π}}} . \end{align}

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arXiv2018

Valence Quark Transversity at Small $x$

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{α_s \, N_c}{2 \, π}} } . \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, Schäfer, and Szymanowski.

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arXiv2018

Small-$x$ Asymptotics of the Gluon 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: $ΔG \sim \left( \tfrac{1}{x} \right)^{α_h^G}$ with $α_h^G = \tfrac{13}{4 \sqrt{3}} \, \sqrt{\tfrac{α_s \, N_c}{2 π}} \approx 1.88 \, \sqrt{\tfrac{α_s \, N_c}{2 π}}$. We note that the power $α_h^G$ is approximately 20$\%$ lower than the corresponding power $α_h^q$ for the small-$x$ asymptotics of the quark helicity distribution defined by $Δq \sim \left( \tfrac{1}{x} \right)^{α_h^q}$ with $α_h^q = \tfrac{4}{\sqrt{3}} \, \sqrt{\tfrac{α_s \, N_c}{2 π}} \approx 2.31 \, \sqrt{\tfrac{α_s \, N_c}{2 π}}$ found in our earlier work.

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arXiv2018

Small-$x$ Helicity Evolution: an Operator Treatment

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.

hep-ph↗

arXiv2018

When gluons go odd: how classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions

We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions with the projectile. We evaluate the obtained expression both analytically and numerically, confirming that the odd-harmonics contribution to the two-gluon production in the saturation framework is non-zero.

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arXiv2017

Time-Dependent Observables in Heavy Ion Collisions II: in Search of Pressure Isotropization in the $φ^4$ Theory

To understand the dynamics of thermalization in heavy ion collisions in the perturbative framework it is essential to first find corrections to the free-streaming classical gluon fields of the McLerran-Venugopalan model. The corrections that lead to deviations from free streaming (and that dominate at late proper time) would provide evidence for the onset of isotropization (and, possibly, thermalization) of the produced medium. To find such corrections we calculate the late-time two-point Green function and the energy-momentum tensor due to a single $2 \to 2$ scattering process involving two classical fields. To make the calculation tractable we employ the scalar $φ^4$ theory instead of QCD. We compare our exact diagrammatic results for these quantities to those in kinetic theory and find disagreement between the two. The disagreement is in the dependence on the proper time $τ$ and, for the case of the two-point function, is also in the dependence on the space-time rapidity $η$: the exact diagrammatic calculation is, in fact, consistent with the free streaming scenario. Kinetic theory predicts a build-up of longitudinal pressure, which, however, is not observed in the exact calculation. We conclude that we find no evidence for the beginning of the transition from the free-streaming classical fields to the kinetic theory description of the produced matter after a single $2 \to 2$ rescattering.

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arXiv2017

Time-Dependent Observables in Heavy Ion Collisions I: Setting up the Formalism

We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function $G_{22}^{aμ,bν}$ due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to $G_{22}^{aμ,bν}$ coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on the ordering between the proper time of the rescattering $τ_Z$ and the proper time $τ$ when the gluon distribution is measured. For (i) $τ_Z\gg 1/Q_s$ and $τ-τ_Z\gg 1/Q_s$ (with $Q_s$ the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) $τ-τ_Z\gg τ_Z\gg 1/Q_s$ we end up with a result very different from kinetic theory and consistent with a picture of "free-streaming" particles. Due to the approximations made, our calculation is too coarse to indicate whether the ordering (i) or (ii) is the correct one: to resolve this controversy, we shall present a detailed diagrammatic calculation of the rescattering correction in the $φ^4$ theory in the second paper of this duplex.

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arXiv2017

Small-$x$ Asymptotics of the Quark Helicity Distribution: Analytic Results

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 $Δq^S (x, Q^2) \sim \left(\tfrac{1}{x} \right)^{α_h}$ with $α_h = \tfrac{4}{\sqrt{3}} \sqrt{\tfrac{α_s N_c}{2π}}$, in excellent agreement with the numerical estimate $α_h \approx 2.31\sqrt{\tfrac{α_s N_c}{2π}}$ 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.

hep-ph↗

arXiv2017

Small-$x$ asymptotics of the quark helicity distribution

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."

hep-ph↗

arXiv2016

Helicity Evolution at Small x: Summary of Recent Developments

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 $α_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the powers of $α_s \, \ln (1/x)$ 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. We construct a numerical solution of the helicity evolution equations in the large-$N_c$ limit. Employing the extracted intercept, we are able to predict directly from theory the behavior of the quark 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." Based on JHEP 1601 (2016) 072 (arXiv:1511.06737), arXiv:1610.06197 and arXiv:1610.06188.

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arXiv2016

Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables

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 $α_s \, \ln^2 (1/x)$ in the polarization-dependent evolution along with the single-logarithmic powers of $α_s \, \ln (1/x)$ 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.

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