3PCF Model Reference

3ptWL-mod models the three-point correlation function of projected scalar fields on the sphere. Its primary application is weak-lensing convergence, but the harmonic construction applies more broadly to spin-zero projected fields.

Harmonic Representation

For angular separations \(\theta_1\) and \(\theta_2\), the code represents the azimuthal dependence through multipoles

\[\zeta_m(\theta_1,\theta_2), \qquad m=0,\ldots,m_{\max}.\]

The decomposition turns the angular structure into a sequence of two-dimensional matrices. The numerical pipeline computes matter-bispectrum quantities, projects them through the lensing kernel under the adopted approximations, and transforms the projected multipoles into configuration space.

Model Branches

tree_level=1: Standard perturbation-theory branch.
tree_level=2: Power-spectrum-squared approximation.
tree_level=3: Effective-field-theory inspired branch.
tree_level=4: Takahashi/Halo-model inspired branch used by the main notebook examples.

The branches are different physical approximations, not successive numerical accuracy levels. Compare them only with consistent cosmology, inputs, grids, and source kernels.

Projection Inputs

The calculation consumes a linear matter power spectrum through fnamePS. Wg=0 uses a source plane at zbin; Wg=1 reads the tabulated kernel selected by fWgchi. See Inputs and Parameter Files for formats and units.

Numerical Grids

Nell, ellmin, and ellmax define the multipole grid. chiQuadSteps and GLpoints control radial and angular integrations. mMax selects the highest output moment. Convergence must be established for the angular range and model branch used in the analysis.

Outputs

The angular grid is written to <rootDir>/<prefix>theta_array.txt and each moment to <rootDir>/<prefix>zetam<m>.txt. Bispectrum, background, and grid products are documented in Outputs and File Formats.

Scientific Reference

The modeling framework is described in Modeling the 3-point correlation function of projected scalar fields on the sphere. Record the code commit, inputs, numerical settings, and model branch whenever publishing derived results.