Once subtracted Roy-like dispersion relations and a precise analysis of $ππ$ scattering data
R. Garcia-Martin, R. Kaminski, J. R. Pelaez, F. J. Yndurain
备注:
6 pages, 4 figures, to appear in the proceedings of the International Workshop On Effective Field Theories: From The Pion To The Upsilon (EFT 09), 2-6 Feb 2009, Valencia, Spain
We report our progress on the data analysis of $ππ$ scattering data in terms of Forward Dispersion Relations (FDR), as well as Roy equations (RE) and their once-subtracted counterpart, GKPY equations. The first part of the analysis consists of independent fits to the different $ππ$ channels. The GKPY equations provide a more stringent consistency check for the parametrizations of the S0-wave data in the region from 400 to 1100 MeV, In the second part we present our preliminary analysis where the fits are constrained to satisfy all dispersion relations within errors, including the new GKPY Eqs., thus providing a very precise and model independent description of data using just analyticity, causality and crossing.
我们分析了弹性π π散射的最低分波的罗伊方程,并证明了两个S波散射长度a_0^0和a_0^2是低能区的基本参数:一旦这些已知,可用的实验信息确定阈值附近的行为在非常小的不确定性。给出了S波和P波的能量依赖性的显式数值表示,并表明D波和F波的阈值参数也非常精确地固定在a_0^0和a^2_0上。与较早的工作(经过详细审查)一致,我们发现罗伊方程仅在(a_0^0,a_0^2)平面的带内存在物理上可接受的解。我们表明,反应e+e-> pi pi和tau -> pi pi nu的数据减少了这个带的宽度相当显着。此外,我们讨论了衰变K -> pi pi e nu在限制a_0^0的允许范围方面的相关性,为分析即将到来的关于这种衰变和π原子的精确数据奠定了基础。我们希望这些减少的不确定性,在两个基本的低能量参数非常大,使手征微扰理论预测的有意义的测试将成为可能。
Subtracted Dispersion Relations for Virtual Compton Scattering off the Proton
Johannes Gutenberg-Universität, Mainz(美因茨约翰内斯·古腾堡大学);Università degli Studi di Pavia(帕维亚大学);Istituto Nazionale di Fisica Nucleare, Sezione di Pavia(意大利国家核物理研究所帕维亚分部)