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Sketch of the infinite-volume spectral density $\rho(\omega)$ (left) and the finite-volume $\rho_V(\omega)$ for a specific volume $V$ (right). The height of $\rho_V(\omega)$ represents the multiplicity of the states with the same energy $\omega$.

Sketch of the infinite-volume spectral density $\rho(\omega)$ (left) and the finite-volume $\rho_V(\omega)$ for a specific volume $V$ (right). The height of $\rho_V(\omega)$ represents the multiplicity of the states with the same energy $\omega$.

Infinite volume limit (solid line) of the integral \eqref{equ:AuxilaryFunction} and its finite volume evaluation on $48^3$ (dashed line) and $256^3$ (dash-dotted line) lattices using the finite volume expressions obtained for the spectral density for $J=0$ with $l=0$ (left) and $J=1$ with $l=2$ (right) as a function of the threshold energy $\omega_{\text{th}}$.

Infinite volume limit (solid line) of the integral \eqref{equ:AuxilaryFunction} and its finite volume evaluation on $48^3$ (dashed line) and $256^3$ (dash-dotted line) lattices using the finite volume expressions obtained for the spectral density for $J=0$ with $l=0$ (left) and $J=1$ with $l=2$ (right) as a function of the threshold energy $\omega_{\text{th}}$.

Four-point correlation function for the temporal current insertion of the axial channel (left) and the spatial components (right). For both plots we fit the correlator directly to extract the ground state contribution needed to fix the prior in our model. This fit is represented by the red dashed line. The black dash-dotted line represents the fit results obtained from a fit to our model using the fit prescription \eqref{equ:ModelFitFunction}.

Four-point correlation function for the temporal current insertion of the axial channel (left) and the spatial components (right). For both plots we fit the correlator directly to extract the ground state contribution needed to fix the prior in our model. This fit is represented by the red dashed line. The black dash-dotted line represents the fit results obtained from a fit to our model using the fit prescription \eqref{equ:ModelFitFunction}.

Contribution of spatial currents to $\bar{X}_{AA}^{\perp, \parallel}(\pmb{q}^2)$ at $\pmb{q}^2 = \SI{0}{\giga\electronvolt^2}$. We show the results for two choices of the volume $L=48^3$ and $256^3$. The left panel assumes that the cut-off in the kernel function is implemented through a heaviside function, while the left panel assumes the smeared kernel. For the latter, we also compare the results with those obtained from the Chebyshev analysis of our lattice data evaluated for different choices of the threshold $\omega_{\text{th}}$ represented by the blue dots. The physical value of the threshold $\omega_{\text{th}} = \omega_{\text{th}}^{\text{Phys}}$ is denoted by the star symbol.

Contribution of spatial currents to $\bar{X}_{AA}^{\perp, \parallel}(\pmb{q}^2)$ at $\pmb{q}^2 = \SI{0}{\giga\electronvolt^2}$. We show the results for two choices of the volume $L=48^3$ and $256^3$. The left panel assumes that the cut-off in the kernel function is implemented through a heaviside function, while the left panel assumes the smeared kernel. For the latter, we also compare the results with those obtained from the Chebyshev analysis of our lattice data evaluated for different choices of the threshold $\omega_{\text{th}}$ represented by the blue dots. The physical value of the threshold $\omega_{\text{th}} = \omega_{\text{th}}^{\text{Phys}}$ is denoted by the star symbol.