Continuation and termination of the secondary finite-yield node branch

Determine whether the secondary higher-$q_T$ finite-yield crossing branch in the $M=3$ OAM channel moves beyond the scanned $q_T$ range, merges with another solution, or terminates as the collinear beam--target offset $B_{\rm ax}$ increases.

Background

The paper studies finite-yield zeros of the normalized elliptic response $S_M=D_M-C_M$ for localized Bessel--Gaussian OAM analyzers in diffractive dijet deep inelastic scattering. In the $M=3$ channel, the response can vanish while the baseline diffractive weight remains nonzero, producing a projection node generated by cancellation between the direct response and the normalization contribution.

When the beam--target offset is varied in the collinear geometry, the authors identify a primary, lowest-$q_T$ node branch that migrates substantially. They also find a secondary higher-$q_T$ crossing for small offsets, approximately $q_T^\ast\simeq0.77\text{--}0.78$ GeV for $B_{\rm ax}\lesssim0.6$ GeV. The secondary branch has a comparatively small baseline weight, and its behavior at larger offsets is not resolved by the reported scan, leaving its continuation, merger, or termination as an explicit unresolved question.