Hadronic Amplitude Analysis: the $a_0(980)$ Resonance

The nature of the $a_0(980)$ scalar meson remains contested — it may be a conventional $q\bar{q}$ state, a tetraquark, or a $K\bar{K}$ molecule. We perform a coupled-channel ($\pi\eta$, $K\bar{K}$) amplitude analysis of $a_0(980)$ production in charmed meson decays using data from CLEO, BaBar, and BESIII, with two explicitly unitary amplitude models fit jointly across five experiments. Machine learning is used to assess the consistency of pole localization across models and datasets.

Finite Energy Sum Rules for $\pi\eta$ Scattering

Finite energy sum rules (FESRs) relate the low-energy partial-wave content of a scattering amplitude to its high-energy Regge behavior. We apply fixed-$t$ and fixed-$u$ FESRs to $\pi\eta \to \pi\eta$ scattering to constrain the partial-wave amplitudes and assess whether an exotic $\pi_1$ hybrid meson contribution ($J^{PC} = 1^{-+}$) is required by the data. In the forward direction only positive-signature exchanges (Pomeron and $f_2$) contribute — a consequence of the $s\leftrightarrow u$ crossing symmetry of the reaction — while in the backward direction the $a_2$ and exotic $\pi_1$ appear.

Proton-Neutron Charge Exchange Scattering

The reaction $p + n \to n + p$ at low momentum transfer is dominated by $t$-channel one-pion exchange. We compute the Born amplitude using a pseudovector $\pi N$ coupling and derive the corresponding non-relativistic potential, then extend the description with contact interactions constrained by the deuteron binding energy to reproduce the low-$t$ behavior of high-energy scattering data.