Title: A Unified Approach to High Density: Pion Fluctuations in Skyrmion Matter Show Chinese title

Title: 高密度统一方法：介子涨落在Skyrmion物质中的表现

Abstract: As the first in a series of systematic work on dense hadronic matter, we study the properties of the pion in dense medium using Skyrme's effective Lagrangian as a unified theory of the hadronic interactions applicable in the large $N_c$ limit. Dense baryonic matter is described as the ground state of a skyrmion matter which appears in two differentiated phases as a function of matter density: i) at high densities as a stable cubic-centered (CC) half-skyrmion crystal; ii) at low densities as an unstable face-centered cubic (FCC) skyrmion crystal. We substitute the latter by a stable inhomogeneous phase of lumps of dense matter, which represents a naive Maxwell construction of the phase transition. This baryonic dense medium serves as a background for the pions whose effective {\em in-medium} Lagrangian we construct by allowing time-dependent quantum fluctuations on the classical dense matter field. We find that the same parameter which describes the phase transition for baryonic matter, the expectation value of the $\sigma$ field, also describes the phase transition for the dynamics of the {\em in-medium} pion. Thus, the structure of the baryonic ground state $crucially$ determines the behavior of the pion in the medium. As matter density increases, $<\sigma>$ decreases, a phenomenon which we interpret to signal, in terms of the parameters of the effective pion Lagrangian $f_\pi^*$ and $m_\pi^*$, the restoration of chiral symmetry at high density. Our calculation shows also the important role played by the higher powers in the density as it increases and chiral symmetry is being restored. This feature is likely to be generic at high density although our ground state may not be the true ground state. Show Chinese abstract

Abstract: 作为对致密强子物质系统研究的第一部分，我们使用Skyrme的有效拉格朗日量作为适用于大$N_c$极限的强子相互作用统一理论，研究介子在致密介质中的性质。 致密重子物质被描述为一种skyrmion物质的基态，它随着物质密度的不同而呈现出两种不同的相：i) 在高密度下作为稳定的体心立方（CC）半skyrmion晶体；ii) 在低密度下作为不稳定的面心立方（FCC）skyrmion晶体。 我们将后者替换为一个稳定的不均匀的致密物质团块相，这代表了相变的简单麦克斯韦构造。 这种致密的重子介质作为介子的背景，我们通过允许经典致密物质场的时间依赖量子涨落来构建其有效的{\em 介质中}拉格朗日量。 我们发现，同样描述重子物质相变的参数，即$\sigma$场的期望值，也描述了{\em 介质中}介子动力学的相变。 因此，重子基态$crucially$的结构决定了介子在介质中的行为。 随着物质密度的增加，$<\sigma>$减小，这一现象我们解释为在有效介子拉格朗日量$f_\pi^*$和$m_\pi^*$的参数下，高密度下手征对称性的恢复。 我们的计算也显示了随着密度增加和手征对称性被恢复时，密度的高次幂所起的重要作用。 这一特性在高密度下可能是普遍的，尽管我们的基态可能不是真正的基态。