The zero-energy astrophysical S-factor for the fusion process \(p+p\rightarrow d+e^{+}+\nu _{e}\) is calculated using pionless effective field theory (\(~/\!\!\pi \)EFT). In the present study, the order-by-order results are reproduced according to a new suggested power counting. The short range interactions in the S-wave pp scattering at leading order and the corrections in the next-to-leading order including the Coulomb interaction are introduced. In addition the Coulomb interaction between the incoming protons has been considered. The new nuclear \(~/\!\!\pi \)EFT amplitude is compatible with renormalization-group invariance.

中文翻译：

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质子-质子融合在新的无离子电离功率计算中

融合过程\（p + p \ rightarrow d + e ^ {+} + \ nu _ {e} \）的零能天体S因子是使用无偶有效场理论（\（〜/ \！\ ！\ pi \） EFT）。在本研究中，根据新的建议功率计数重现了按订单结果。介绍了S波pp散射中前导顺序的短程相互作用以及包括库仑相互作用在内的下一个先导修正。另外，已经考虑了传入质子之间的库仑相互作用。新的核（〜/ \！\！\ pi \） EFT振幅与重归一化组不变性兼容。