Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution

Abstract

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.

56 pages, 14 figures; v2: typos corrected, references added; v3: more typos corrected, title slightly modified

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• Quark contribution to the small-$x$ evolution of color dipole
• Triumvirate of Running Couplings in Small-x Evolution
• Relations between generalized and transverse momentum dependent parton distributions
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• The Transverse-momentum-dependent Parton Distribution Function and Jet Transport in Medium
• pT-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order
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• Sivers asymmetry of Drell-Yan production in small-$x$ regime
• Inclusive Single-Spin Asymmetries, Quark-Photon, and Quark-Quark Correlations
• Transverse Force on Quarks in DIS
• The saturation scale and its x-dependence from Lambda polarization studies
• Gluon saturation and inclusive production at low transverse momenta
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Cited by in corpus (31)

• Transverse-momentum-dependent gluon distributions from JIMWLK evolution
• Transverse-momentum-dependent gluon distribution functions in a spectator model
• Gluon TMD in particle production from low to moderate x
• Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables
• Small-$x$ Helicity Evolution: an Operator Treatment
• Small-$x$ Asymptotics of the Gluon Helicity Distribution
• Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an EIC through dijet azimuthal asymmetries
• Single spin asymmetries from a single Wilson loop
• Quark branching in QCD matter to any order in opacity beyond the soft gluon emission limit
• Power corrections to TMD factorization for Z-boson production
• Helicity-dependent extension of the McLerran-Venugopalan model
• Quark Sivers Function at Small $x$: Spin-Dependent Odderon and the Sub-Eikonal Evolution
• TMD gluon distributions at small x in the CGC theory
• T-odd Leading-Twist Quark TMDs at Small $x$
• Wigner Distributions For Gluons
• Valence Quark Transversity at Small $x$
• The spin dependent odderon in the diquark model
• Space-Time Picture of Baryon Stopping in the Color-Glass Condensate
• The evolution of the small x gluon TMD
• Three-dimensional imaging in nuclei
• Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions
• Toward Initial Conditions of Conserved Charges Part I: Spatial Correlations of Quarks and Antiquarks
• Rapidity evolution of gluon TMD from low to moderate x
• The suppressions of dijet azimuthal correlations in the future EIC
• Probing short-range nucleon-nucleon interactions with an Electron-Ion Collider
• Novel Cross Section Ratios as Possible Signals of Saturation in UPCs
• Jets in evolving matter within the opacity expansion approach
• Time-Dependent Observables in Heavy Ion Collisions I: Setting up the Formalism
• Evaluating the ratio of the exclusive vector meson photoproduction to inclusive hadron/jet production cross section in ultraperipheral heavy ion collisions
• Evolution of gluon TMDs from small to moderate x
• Small-x, Diffraction and Vector Mesons