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

Abstract

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.

arXiv comment30 pages, 12 figures

References in corpus (55)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Color Glass Condensate
• The Wilson renormalization group for low x physics: towards the high density regime
• Green's Functions in the Color Field of a Large Nucleus
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• Unitarity at small Bjorken x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Single and Double BFKL Pomeron Exchange and a Dipole Picture of High Energy Hard Processes
• Unitarity and the BFKL Pomeron
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• Factorization and high-energy effective action
• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Evolution at small x_bj: The Color Glass Condensate
• Quark contribution to the small-$x$ evolution of color dipole
• Triumvirate of Running Couplings in Small-x Evolution
• Evidence for polarization of gluons in the proton
• Fock Space Distributions, Structure Functions, Higher Twists and Small x
• QCD Analysis of Polarized Deep Inelastic Data and Parton Distributions
• Gluon saturation and initial conditions for relativistic heavy ion collisions
• The Calculation of the Two-Loop Spin Splitting Functions $P_{ij}^{(1)}(x)$
• Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus
• The Color Glass Condensate and High Energy Scattering in QCD
• Odderon in the Color Glass Condensate
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Flavor Singlet Contribution to the Structure Function $g_1$ at Small-x
• Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
• On the Behaviour of Non--Singlet Structure Functions at Small $x$
• Perturbative Odderon in the Dipole Model
• Quark loop contribution to BFKL evolution: Running coupling and leading-N_f NLO intercept
• Helicity Evolution at Small-x
• Small-$x$ asymptotics of the quark helicity distribution
• Baryon Stopping and the Valence Quark Distribution at Small x
• The Singlet Contribution to the Structure Function $g_1(x,Q^2)$ at Small $x$
• Regge Asymptotics of Scattering with Flavour Exchange in QCD
• HERA-data in the light of small x evolution with state of the art NLO input
• Polarized DIS in N=4 SYM: Where is spin at strong coupling?
• Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution
• Intercepts of the non-singlet structure functions
• Unveiling the Proton Spin Decomposition at a Future Electron-Ion Collider
• Reggeon Interactions in Perturbative QCD
• Studying the Perturbative Reggeon
• Running coupling effects for the singlet structure function g_1 at small x
• Nonsinglet Contributions to the Structure Function g1 at Small-x
• QCD running coupling effects for the non-singlet structure function at small x
• Classical Gluon Production Amplitude for Nucleus-Nucleus Collisions: First Saturation Correction in the Projectile
• Neutron spin-dependent structure function, Bjorken sum rule, and first evidence for singlet contribution at low $x$
• Neutron spin-dependent structure function, Bjorken sum rule, and first evidence for singlet contribution at low x

Cited by in corpus (47)

• Parton distributions and lattice QCD calculations: a community white paper
• Mining for Gluon Saturation at Colliders
• The Spin Structure of the Nucleon
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Sub-eikonal corrections to scattering amplitudes at high energy
• Small-$x$ Helicity Evolution: an Operator Treatment
• Small-$x$ asymptotics of the quark helicity distribution
• Helicity-dependent generalization of the JIMWLK evolution
• Transverse momentum dependent factorization for lattice observables
• Small-$x$ Asymptotics of the Quark Helicity Distribution: Analytic Results
• Hunting BFKL in semi-hard reactions at the LHC
• Proton Spin Structure at Small-$x$
• Low $x$ physics as an infinite twist (G)TMD framework: unravelling the origins of saturation
• High-energy Operator Product Expansion at sub-eikonal level
• Quarks at next-to-eikonal accuracy in the CGC I: Forward quark-nucleus scattering
• Helicity-dependent extension of the McLerran-Venugopalan model
• Quark Sivers Function at Small $x$: Spin-Dependent Odderon and the Sub-Eikonal Evolution
• Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated
• Helicity at Small $x$: Oscillations Generated by Bringing Back the Quarks
• Quark and scalar propagators at next-to-eikonal accuracy in the CGC through a dynamical background gluon field
• Non-eikonal corrections to multi-particle production in the Color Glass Condensate
• Rapidity loss, spin and angular asymmetries in scattering of a quark from color field of a proton (nucleus)
• TMD gluon distributions at small x in the CGC theory
• Helicity Evolution at Small $x$: the Single-Logarithmic Contribution
• First analysis of world polarized DIS data with small-$x$ helicity evolution
• Effect of non-eikonal corrections on azimuthal asymmetries in the Color Glass Condensate
• DIS dijet production at next-to-eikonal accuracy in the CGC
• Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_c$: New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept
• T-odd Leading-Twist Quark TMDs at Small $x$
• Single Inclusive Hadron Production in DIS at Small $x$: Next to Leading Order Corrections
• Valence Quark Transversity at Small $x$
• Accessing the nucleon transverse structure in inclusive deep inelastic scattering
• Gluon distributions and their applications to Ioffe-time distributions
• Baseline predictions of elliptic flow and fluctuations at the RHIC Beam Energy Scan using response coefficients
• Sea quark Sivers distribution
• Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics
• Multiparticle production in proton-nucleus collisions beyond eikonal accuracy
• Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\&N_f$
• On the small-$x$ behavior of the orbital angular momentum distributions in QCD
• Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• Can sea quark asymmetry shed light on the orbital angular momentum of the proton?
• JAM small-$x$ helicity phenomenology
• How EIC can help us to understand heavy-ion collisions
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Proton spin from small-$x$ with constraints from the valence quark model