外磁场与有限介子动量下π⁰道的q\bar{q}散射相移及π⁰介子谱函数
$q\bar{q}$ scattering phase shift in the $π^0$ channel and $π^0$ meson spectral function under external magnetic field and finite meson momentum
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中文总结 AI 辅助
该研究在NJL模型下，分析外磁场与有限介子动量对π⁰道q\bar{q}散射相移及π⁰介子谱函数的影响，揭示了外磁场、手征相变、泡利阻塞等因素对多峰结构与相移跳变的作用。
中文摘要 AI 辅助
在两味Nambu-Jona-Lasinio（NJL）模型框架下，研究了外磁场eB和有限介子动量k_⊥²、k₃²下π⁰道的q\bar{q}散射相移Φ_{π⁰}(ω²,k_⊥²,k₃²)与π⁰介子谱函数ρ_{π⁰}(ω²,k_⊥²,k₃²)，二者密切相关。研究涵盖三种情形：手征破缺相（T=μ=0）、手征恢复相（T>T_{pc}, μ=0）、手征恢复相（T=0, μ>μ_{pc}）。对于T=μ=0和T>T_{pc}, μ=0的情形，π⁰介子谱函数ρ_{π⁰}呈现δ峰、多个Breit-Wigner峰及多个非Breit-Wigner峰；δ峰对应π⁰介子的束缚态，Breit-Wigner峰对应其共振态。对于T=0, μ>μ_{pc}的情形，泡利阻塞效应发挥作用，改变了Breit-Wigner峰与非Breit-Wigner峰的内部结构，这种多峰结构由外磁场导致。π⁰道的q\bar{q}散射相移Φ_{π⁰}在π⁰介子为束缚态时从0跳变至π；为共振态时取值π/2且连续变化；在大ω区域，谱函数宽峰的起止点处，Φ_{π⁰}发生 abrupt跳变（从π跳至有限值或从有限值跳至0），此类跳变同样由外磁场导致。有限动量k_⊥²或k₃²会修正谱函数ρ_{π⁰}与散射相移Φ_{π⁰}，体现出外磁场诱导的系统各向异性。
英文摘要
$q\bar{q}$ scattering phase shift in the $π^0$ channel $Φ_{π^0}(ω^2,\mathbf{k}_\perp^2,k^2_3)$ and $π^0$ meson spectral function $ρ_{π^0}(ω^2,\mathbf{k}_\perp^2,k^2_3)$ under external magnetic field $eB$ and finite meson momentum $\mathbf{k}_\perp^2,k^2_3$ are studied in the framework of a two-flavor Nambu-Jona-Lasinio (NJL) model. The $q\bar{q}$ scattering phase shift in the $π^0$ channel $Φ_{π^0}$ is closely related to $π^0$ spectral function $ρ_{π^0}$. We consider three situations, chiral broken phase ($T=μ=0$), chiral restoration phase ($T>T_{pc},\ μ=0$) and chiral restoration phase ($T=0,\ μ>μ_{pc}$). For $T=μ=0$ and $T>T_{pc},\ μ=0$ cases, $π^0$ meson spectral function $ρ_{π^0}$ shows a delta peak, several Breit-Wigner peaks and several non-Breit-Wigner peaks. The delta peak indicates the bound state of $π^0$ meson, and the Breit-Wigner peak means the resonant state of $π^0$ meson. For $T=0,\ μ>μ_{pc}$ case, Pauli blocking effect plays a role, which changes the inner structure of these Breit-Wigner peaks and non-Breit-Wigner peaks. Such multiple peak structure is caused by the external magnetic field. The $q\bar{q}$ scattering phase shift in the $π^0$ channel $Φ_{π^0}$ shows a jump from $0$ to $π$ when $π^0$ meson is in bound state. When $π^0$ meson is in resonant state, $Φ_{π^0}$ has the value $π/2$ and changes continuously. In large $ω$ region, at the starting and end points of wide peaks of spectral function, $Φ_{π^0}$ jumps abruptly (from $π$ to finite value or from finite value to $0$), and such jumps are caused by the external magnetic field. Finite momentum $\mathbf{k}_\perp^2$ or $k^2_3$ modifies the spectral function $ρ_{π^0}$ and scattering phase shift $Φ_{π^0}$, which demonstrates the anisotropy in the system induced by external magnetic field.
