Unified analysis of screening masses for vector and axial-vector mesons and their diquark partners in the Contact Interaction model

Abstract

We present a comprehensive study of the screening masses of vector and axial-vector mesons and their corresponding diquark partners within a symmetry-preserving vector-vector contact interaction approach. Our analysis includes mesons and diquarks composed of both light and heavy quarks, providing a unified description of their thermal behavior. The longitudinal and transverse modes of the screening masses are analyzed, and the results are systematically compared with other theoretical approaches. At $T = 0$ MeV, our predictions agree with available experimental data, and a comparison with the expected free theory limit at high temperatures is also presented. Notably, the parity partners of the lightest mesons and diquarks converge at high temperatures, signaling chiral symmetry restoration within this framework. These results provide a consistent and detailed picture of meson and diquark properties at finite temperature and lay the groundwork for extending the capabilities of the model to baryon screening masses in the quark-diquark picture.

Figures (10)

• Figure 1: Pictorical representation of the relation between chiral partners. Vector and axial-vector mesons are rotated into each other under chiral transformation.
• Figure 2: Diagrammatic illustration of the CI, constructed from the simplified gluon propagator model introduced in Eq. \ref{['eqn:contact_interaction']}.
• Figure 3: Results for the screening quark masses computed across a temperature range from $0$ to $4\, T_c$, with $T_c=155$ MeV Andronic:2017pugBazavov:2011nk. At high temperatures, the quark mass asymptotically tends toward its bare mass, $M(T)\to m$.
• Figure 4: Diagrammatic representation of the BSE. Blue (solid) circles represent dressed quark propagators $S$, red (solid) circle is the meson BSA $\Gamma$ while the blue (solid) rectangle is the dressed-quark-antiquark scattering kernel ${\mathcal{K}}$.
• Figure 5: Longitudinal and transverse screening masses for V mesons composed of the five quark flavors($\textcolor{red}{u}$, $\textcolor{darkcandyapplered}{d}$, $\textcolor{darkgreen}{s}$, $\textcolor{darkmagenta}{c}$ and $\textcolor{blue}{b}$). The longitudinal components are shown with dashed lines, while the transverse components are shown with solid lines. In the top left panel, the lightest vector meson is shown, the $\rho$ meson, The black dashed line corresponds to the free-theory limit, $m = 2\pi T/T_c$; the top center panel displays the $K_1$ screening mass results; the top right panel displays strangeonium vector mesons. The bottom left panel is dedicated to vector $D$-mesons ($D^{*0}$ and $D^{*}_s$); the bottom center panel is committed for vector $B$-mesons ($B^{+*}$, $B^{0*}_s$ and $B^{*}_c$) and, the bottom right panel shows the results for charmonium and bottomonium vector mesons. Results shown with squares and diamonds correspond to lattice results from Refs. Bazavov:2020tehAarts:2022krz, while stars and inverted triangles represent results obtained using an effective chiral Lagrangian from Refs. Montana:2021vksSong:1993af. Pentagons and right triangles correspond to predictions obtained using QCD sum rules in Refs. Veliev:2011zzDominguez:2013fca.