Multi-peak structure of meson spectral function in magnetic field

TL;DR

This study addresses how external magnetic fields modify the dynamical properties of light mesons in hot and dense QCD-like matter. Using the FRG in a two-flavor quark-meson model with Landau-level resolved propagators and carefully constructed vertex momentum relations, the authors derive flow equations for the effective potential and for meson two-point functions, then analytically continue to obtain spectral functions. The results show that σ and π⁰ acquire Landau-level–dependent threshold structures, while the π⁺ spectral function develops a universal multi-peak pattern at finite temperature due to multiple annihilation and decay channels across Landau levels; this multi-peak structure is further enhanced at finite density, where π⁺ becomes a broad resonance. The findings have significant implications for transport properties and quasi-particle content in magnetized strongly interacting fluids, relevant to heavy-ion collisions, magnetars, and the early universe.

Abstract

We investigate the spectral functions of neutral and charged mesons in a hot dense medium under a external magnetic field using the two-flavor quark-meson model within the functional renormalization group (FRG) framework. Our results show that the spectral functions of σ and π0 mesons develop new structures due to decay channels into quarks occupying different Landau levels. By consistently incorporating the momentum relations at vertices for charged particles in a magnetic field, we further show that the π+ spectral function develops a multi-peak structure at finite temperatures, resulting from the various annihilation and decay channels available to π+ in the magnetic environment. This multi-peak structure is further enhanced in a finite-density medium, causing the π+ meson to become a broad resonance at lower temperatures and densities compared to neutral mesons. Such a multi-peak pattern is expected to be universal for charged mesons under magnetic fields and carries significant implications for understanding transport properties in magnetized strongly interacting fluids

Figures (7)

• Figure 1: Phase boundaries in the $T-\mu$ plane under different magnetic fields. Dashed lines denote crossovers; solid lines indicate first-order transitions, circles mark the critical endpoints.
• Figure 2: Left: temperature dependence of meson screening masses $m_\sigma$, $m_\pi$, quark mass $m_\psi$, and the order parameter $\sigma$ at $\mu = 0$ and $eB = 10 m_\pi^2$. Right: chemical potential dependence of meson screening masses $m_\sigma$, $m_\pi$, quark mass $m_\psi$, and the order parameter $\sigma$ at $T = 56$ MeV and $eB = 20 m_\pi^2$.
• Figure 3: Spectral function of sigma and pion at $T=10$ MeV and vanishing density and magnetic field.
• Figure 4: Spectral functions of $\sigma$, $\pi_0$ (left panels) and $\pi_+$ (right panels) are shown versus external energy $\omega$ at $\mu=0$ and magnetic field $eB=10m_\pi^2$ for different temperature. Inserted annotations refer to the different processes affecting the spectral functions at the so indicated values of $\omega$, $s_1:\sigma'\rightarrow \sigma\sigma$, $s_2:\sigma'\rightarrow \pi_0\pi_0$, $s_3:\sigma'\rightarrow \pi_+\pi_-$, $s_4:\sigma'\rightarrow \psi_0\bar{\psi}_0$, $s_5:\sigma'\rightarrow d_1\bar{d}_1$, $s_6:\sigma'\rightarrow u_1\bar{u}_1$; $p_1:\pi_0'\rightarrow \pi_0\sigma$, $p_2:\pi_0' \pi_0\rightarrow\sigma$, $p_3:\pi_0'\rightarrow \psi_0\bar{\psi}_0$, $p_4:\pi_0'\rightarrow d_1\bar{d}_1$, $p_5:\pi_0'\rightarrow u_1\bar{u}_1$; $c_1: \pi_+'\sigma\rightarrow\pi_+$, $c_2: \pi_+'\pi_-\rightarrow\sigma$, $c_3^{ij}:\pi_+'\rightarrow u_i \bar{d}_j$, $c_4^{ij}:\pi_+'\bar{u}_i \rightarrow \bar{d}_j$, $c_5^{ij}:\pi_+'{d}_i\rightarrow u_j$.
• Figure 5: Spectral functions of $\sigma$, $\pi_0$ (left panel) and $\pi_+$ (right panel) are shown versus external energy $\omega$ at $T=56$MeV and magnetic field $eB=20m_\pi^2$ for various chemical potential $\mu$. Inserted annotations refer to the different processes affecting the spectral functions at the so indicated values of $\omega$, $s_1:\sigma'\rightarrow \sigma\sigma$, $s_2:\sigma'\rightarrow \pi_0\pi_0$, $s_3:\sigma'\rightarrow \pi_+\pi_-$, $s_4:\sigma'\rightarrow \psi_0\bar{\psi}_0$, $s_5:\sigma'\rightarrow d_1\bar{d}_1$, $s_6:\sigma'\rightarrow u_1\bar{u}_1$; $p_1:\pi_0'\rightarrow \pi_0\sigma$, $p_2:\pi_0' \pi_0\rightarrow\sigma$, $p_3:\pi_0'\rightarrow \psi_0\bar{\psi}_0$, $p_4:\pi_0'\rightarrow d_1\bar{d}_1$, $p_5:\pi_0'\rightarrow u_1\bar{u}_1$; $c_1: \pi_+'\sigma\rightarrow\pi_+$, $c_2: \pi_+'\pi_-\rightarrow\sigma$, $c_3^{ij}:\pi_+'\rightarrow u_i \bar{d}_j$, $c_4^{ij}:\pi_+'\bar{u}_i \rightarrow \bar{d}_j$, $c_5^{ij}:\pi_+'{d}_i\rightarrow u_j$.