Magnetic thresholds and spin-resolved spectral moments of $ϕ$ and $K^{*0}$ in a hadronic model

Abstract

We study the spin-resolved spectral functions of $ϕ$ and $K^{*0}$ in a thermal hadronic model with a constant magnetic field. We construct the rest-frame retarded propagators by combining real vacuum matching with exact Landau levels, connection contacts, and thermal scattering terms. The resulting stable-daughter calculation is checked against independent collision kernels and published expressions in common limits. We find that closed transverse thresholds give rise to narrow peaks with eV-scale detunings, whose areas must be resolved in the calculation of small spin spectral moments. We test the leading threshold estimate for the peak area by an independent integration of the full kernel. Using positive compact daughter spectra, we then investigate how a finite spectral spread changes the local threshold structure. The disappearance of zeros of the real part of the inverse propagator is controlled by the spread relative to the detuning, whereas the weight integrated over a finite patch can remain nearly unchanged. We relate this redistribution to smooth accepted moments through a weighted identity with a bounded Taylor remainder, and evaluate the complete-window response to three endpoint replacements, including the patch complement. For the stable-daughter $ϕ$ spectra with a fixed smooth weight, the response at the two smallest sampled fields is negative and compatible with $b^2$ scaling. Hard-window results instead oscillate in sign, and pseudoscalar mixing substantially changes the smooth response coefficient. These results quantify the sensitivity to thresholds and spectral projection; microscopic daughter widths and source-matched experimental spin alignment require additional input.