Multipoles of the galaxy bispectrum on a light cone: wide-separation and relativistic corrections

The galaxy bispectrum provides access to correlations among different scales that cannot be captured by the power spectrum alone, and with the Stage-IV galaxy surveys it enables the possibility of detecting both primordial non-Gaussianity (PNG) and general relativistic effects. Accounting for wide-separation corrections, which arise from the loss of symmetry in the correlation of widely separated points on the past light cone, is essential for their accurate modelling and detection. These corrections can be included perturbatively to the standard bispectrum and we compute them analytically for a generalised line of sight. We include the radial contribution to the wide-separations corrections for the first time. We show that the first-order corrections entering the odd multipoles with respect to the line of sight are large, up to $10 \%$ of the bispectrum monopole, and need to be included when considering the leading-order relativistic effects that could be detectable with surveys like DESI and Euclid. The second-order wide-separation and relativistic contributions, including their mixing terms, have implications for analysis of PNG and we show, for the local type, they can mimic $f_{\rm NL}$ of order 10 in the squeezed limit. We present full analytic expressions for all these contributions to the local bispectrum and its multipoles with a publicly available code for their computation.