  We propose a generalized left-handed (chiral) gauge choice for the genus one
Riemann surface, realized through a singular gauge transformation of worldsheet
coordinates. The transformation predominantly affects the logarithmic non-zero
modes of the Green's function, leaving non-holomorphic and non-logarithmic
modes unchanged. This procedure yields $\delta$-functions for chiral
coordinates and box-diagram-like integrals in terms of modular parameters. The
resulting $\delta$-functions formulate one-loop level Scattering Equations that
simplify to satisfy the tree-level solutions, constraining the locations of the
marked points. Subsequent integrals agree with the field-theoretic box diagram
for the four-point amplitude, in accordance with the divergent $\epsilon$
expansions derived from dimensional regularization in the infrared limit. We
conclude by highlighting potential avenues for future research, including the
exploration of methodologies that preclude the need for worldsheet coordinates
reparametrization and their implications for accurately capturing infrared
behavior from modular parameter integrals.
