The Effect Of Vector Mesons And False Vacuum Potential In Skyrme Model

This article provides a brief introduction to the effective Lagrangian of QCD and chiral symmetry,as well as a more detailed explanation of the Skyrme model and how to obtain the chiral Lagrangian with hidden local symmetry by integrating out the heavy vector and axial-vector mesons from the holographic QCD model.We also briefly introduce how to construct Skyrmions solutions using rational maps and product ansatz,and how to numer-ically solve for Skyrmions solutions.Additionally,we discuss the Skyrme model with a false vacuum potential energy term.We summarize existing research and begin the study of the transition from multi-Skyrmions to Skyrmions crystal.By introducing the false vacuum potential energy term,we calculate that Skyrmions approach each other from the infinity and eventually form two kinds of structures:one is the cluster structure which consisting of alpha particles and the other has the symmetry of the truncated octahedron.We also find that under certain parameter sets,the cluster struc-ture may be a local energy extremum.Just this past November,the molecular structure of the¹⁰Be nucleus was experimentally confirmed,confirming the significance of our work and reinforcing our determination to begin the search for the cluster structure of the heavy nucleus.We employed the hidden local symmetry approach to investigate the roles of the lightest vector mesonsρandωin the multi-skyrmion states,up to the next to leading order and including the homogeneous Wess-Zumino terms.The low energy constants in the effective field theory were determined using the Sakai-Sugimoto model and the flat-space five-dimensional Yang-Mills action.With only two inputs,m_ρand f_π,all the low energy constants could be determined without ambiguity.The vector meson effects could be probed by integrating them in,and the influence from the geometry could be clarified by comparing the results using the low energy constants estimated from the Sakai-Sugimoto model and the flat-space five-dimensional Yang-Mills action.We found that theρmeson reduces the masses of the multi-skyrmion states and increases the overlaps of the constituents of the multi-skyrmion states,while theωmeson repulses the constituents of the multi-skyrmion states and increases their masses.Therefore,these vector mesons are important in the Skyrme model approach to nuclei.We also found that the warping factor,which is an essential element in the holographic model of QCD,affects the properties of the multi-skyrmion states and cannot be ignored.This article also explores the connection between Multi-Skyrmions and Skyrmions crystal.The main contents are as follows:We propose that the nuclear force determines the structure of nuclear matter.Skyrmions can be in either an attractive or repulsive channel,providing attraction and repulsion forces,which determines their arrangement in nuclear matter.The Skyrmions crystal structure is seen as the result of forming toroidal nuclear matter in each dimension.Opening up one of these toroidal surfaces results in a lower-dimensional nuclear matter.Starting from the construction method of Multi-Skyrmions,a three-dimensional Skyrmions crystal can be gradually constructed.One-dimensional nu-clear matter can be seen as an intermediate process.We used numerical methods to sim-ulate one-dimensional nuclear matter,resulting in a ladder-like structure of Skyrmions,which may be a new type of nuclear matter structure.Increasing the density of one-dimensional nuclear matter does not lead to the observation of Half-Skyrmions.However,by numerically constructing one-dimensional Skyrmions that are in a repulsive channel,it is observed that the density between two Skyrmions is non-zero,which is one of the pos-sible conditions for Half-Skyrmions to appear.Although the Skyrmions crystal structure proposed only considers the interaction between the nearest Skyrmions,we still infer that the interaction between the second-nearest Skyrmions cannot be ignored in high-density regions.As Skyrmions have both attraction and repulsion forces,their combined effect may cause Skyrmions to deform.