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Phenomenological analysis of near-threshold periodic modulations of the proton timelike form factor

机译：质子时代形状因子的近阈值周期性调制的现象学分析

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We have recently highlighted the presence of a periodically oscillating 10% modulation in the BABAR Collaboration data on the proton timelike form factors, expressing the deviations from the pointlike behavior of the proton -antiproton electromagnetic current in the reaction e(+) + e(-) -> (p) over bar + p. Here we deepen our previous data analysis and confirm that in the case of several standard parametrizations it is possible to write the form factor in the form F-0 + F-osc, where F-0 is a parametrization expressing the long-range trend of the form factor (for q(2) ranging from the pp threshold to 36 GeV2), and Fos, is a function of the form exp(-Bp) cos(Cp), where p is the relative momentum of the final pp pair. Error bars allow for a clean identification of the main features of this modulation for q(2) < 10 GeV2. Assuming this oscillatory modulation to be an effect of final-state interactions between the forming proton and the antiproton, we propose a phenomenological model based on a double-layer imaginary optical potential. This potential is flux absorbing when the distance between the proton and antiproton centers of mass is less than or similar to 1.7-1.8 fm and flux generating when it is less than or similar to 1.7-1.8 fm. The main features of the oscillations may be reproduced with some freedom in the potential parameters, but the transition between the two layers must be sudden (0-0.2 fm) to get the correct oscillation period. The flux -absorbing part of the pp interaction is well known in the phenomenology of small -energy antiproton interactions and is due to the annihilation of <(p)over bar>p pairs into multimeson states. We interpret the flux -creating part of the potential as due to the creation of a 1/q-ranged state when the virtual photon decays into a set of current quarks and antiquarks. This short-lived compact state may be expressed as a sum of several hadronic states including the ones with large mass Q(n) q, that may exist for a time t similar to 1/(Q(n) - q). The decay of these large -mass states leads to an intermediate -stage regeneration of the (p) over barp channel.
机译：我们最近突出显示了在质子时代形状因子上的禁阳协作数据中定期振荡的10％调制，表达与反应E（+）+ E（ - ） - >（p）在酒吧+ p。在这里，我们深化了我们之前的数据分析，并确认在几个标准参数化的情况下，可以在F-0 + F-OSC中写入形状因子，其中F-0是表达远程趋势的参数化从PP阈值到36 GEV2的Q（2）和FOS的形状因子是EXP（-BP）COS（CP）的函数，其中P是最终PP对的相对动力。误差条允许清洁识别Q（2）<10 GEV2调制的主要特征。假设该振荡调制是形成质子和抗罗本之间的最终状态相互作用的影响，我们提出了一种基于双层假导光学电位的现象学模型。当质子和防罗罗顿的距离小于或类似于1.7-1.8 fm和磁通量小于或类似于1.7-1.8 fm时，这种电位是磁通吸收。振荡的主要特征可以在潜在参数中以某种自由度再现，但两层之间的过渡必须是突然（0-0.2 fm）以获得正确的振荡周期。 PP相互作用的助熔剂部分在小 - 型抗腐蚀相互作用的现象学中是众所周知的，并且是由于湮灭<（p）在棒> p对中到多×oonson状态。当虚拟光子衰减成一组当前夸克和古董时，我们解释潜在的势势的助焊部分。这种短寿命的紧凑型状态可以表示为包括具有大质量Q（n） q的若干辐射状态的总和，其可能存在类似于1 /（q（n）-q）的时间t。这些大型国家的衰变导致（P）上的中间级再生。

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