arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1707.09210hep-phnucl-th
收藏

核子作为计算低能矢量-等矢量形状因子的一个测试实例

The nucleon as a test case to calculate vector-isovector form factors at low energies

Stefan Leupold

摘要:

将最近提出的超子形状因子的概念推广到核子的情况,利用色散理论将核子的低能矢量-等矢量形状因子与π矢量形状因子联系起来。另外所需的输入,即π介子-核子散射振幅是从相对论次领先级(NLO)重子手征微扰理论,包括核子和可选的Delta重子确定。比较了两种如何包含π介子再散射的方法:(a)求解Muskhelishvili-Omnes(MO)方程和(b)使用N/D方法。事实证明,结果彼此差异很大。此外,结果进行了比较的(亚阈值)π介子核子振幅的完全色散计算的基础上罗伊-施泰纳(RS)方程。与超子部分的研究结果完全一致,事实证明,包含Delta重子不是一种选择,而是获得合理结果的必要条件。磁等矢量形状因子强烈依赖于一个低能量常数的非线性光学拉格朗日。如果调整它使相应的磁半径重现,则相应的π-核子散射振幅(基于MO方程)的结果与RS结果非常一致。同样在电扇区中,需要Delta自由度来获得等矢量电荷和相应的电半径的正确数量级。然而,没有达成数量协议。如果在MO方程的解中出现的减常数不是从核子+ δ手征微扰理论中取的,而是经过调整,使得电半径重现,那么在这个扇区中也得到与RS结果完全一致的π-核子散射振幅。

英文摘要:

Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods how to include pion rescattering are compared: (a) solving the Muskhelishvili-Omnes (MO) equation and (b) using an N/D approach. It turns out that the results differ strongly from each other. Furthermore the results are compared to a fully dispersive calculation of the (subthreshold) pion-nucleon amplitudes based on Roy-Steiner (RS) equations. In full agreement with the findings from the hyperon sector it turns out that the inclusion of Delta baryons is not an option but a necessity to obtain reasonable results. The magnetic isovector form factor depends strongly on a low-energy constant of the NLO Lagrangian. If it is adjusted such that the corresponding magnetic radius is reproduced, then the results for the corresponding pion-nucleon scattering amplitude (based on the MO equation) agree very well with the RS results. Also in the electric sector the Delta degrees of freedom are needed to obtain the correct order of magnitude for the isovector charge and the corresponding electric radius. Yet quantitative agreement is not achieved. If the subtraction constant that appears in the solution of the MO equation is not taken from nucleon+Delta chiral perturbation theory but adjusted such that the electric radius is reproduced, then one obtains also in this sector a pion-nucleon scattering amplitude that agrees well with the RS results.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑