Computing the gluon Sivers function at small-xx

We compute the gluon Sivers function $f_{1T}^{\perp g}(x,k_\perp)$ of the transversely polarized nucleon at small-$x$ by exploiting the known connection between the dipole gluon Sivers function and the Odderon. We numerically solve the evolution equation for the Odderon both in the linear and nonlinear regimes. While we find that the $x$ and $k_\perp$ dependences of the Sivers function do not factorize as a result of the quantum evolution, factorization breaking is not numerically significant, and is much milder than what one expects in the case of unpolarized TMDs. We also point out the possibility that, due to the presence of a node in the Sivers function, single spin asymmetry for open charm production in semi-inclusive deep inelastic scattering flips signs as the transverse momentum of D-mesons is varied. This can be tested at the future Electron-Ion Collider.Comment: 9 pages, 7 figures; minor changes, accepted in PL

Quantum Simulation of Light-Front QCD for Jet Quenching in Nuclear Environments

We develop a framework to simulate jet quenching in nuclear environments on a quantum computer. The formulation is based on the light-front Hamiltonian dynamics of QCD. The Hamiltonian consists of three parts relevant for jet quenching studies: kinetic, diffusion and splitting terms. In the basis made up of $n$-particle states in momentum space, the kinetic Hamiltonian is diagonal. Matrices representing the diffusion and splitting parts are sparse. The diffusion part of the Hamiltonian depends on classical background gauge fields, which need to be sampled classically before constructing quantum circuits for the time evolution. The cost of the sampling scales linearly with the time length of the evolution and the momentum grid volume. The framework automatically keeps track of quantum interference and thus it can be applied to study the Landau-Pomeranchuk-Migdal effect in cases with more than two splittings, which is beyond the scope of state-of-the-art analyses, no matter whether the medium is static or expanding, thin or thick, hot or cold. We apply this framework to study a toy model and gluon in-medium radiation on a small lattice. The Landau-Pomeranchuk-Migdal effect that suppresses the total radiation probability is observed in the quantum simulation results of both the toy model and the gluon case.Comment: 56 pages, 9 figures; v2: add a section on the simulation of the LPM effect in gluon radiatio

SU(2) Non-Abelian Gauge Theory on a Plaquette Chain Obeys Eigenstate Thermalization Hypothesis

We test the eigenstate thermalization hypothesis (ETH) for 2+1 dimensional SU(2) lattice gauge theory. By considering the theory on a chain of plaquettes and truncating basis states for link variables at $j=1/2$, we can map it onto a quantum spin chain with local interactions and numerically exactly diagonalize the Hamiltonian for reasonably large lattice sizes. We find energy level repulsion in momentum sectors with no remaining discrete symmetry. We study two local observables made up of Wilson loops and calculate their matrix elements in the energy eigenbasis, which are shown consistent with the ETH.Comment: 7+6 pages, 4+4 figure

Quarkonium Semiclassical Transport in Quark-Gluon Plasma: Factorization and Quantum Correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.Comment: 35 pages, 3 figures; v2: added an appendix to explain the Wilson lines at infinite time; v3: make the assumed hierarchy more genera