Scattering of high energy particles from nucleons probes their structure, as was done in the experiments that established the non-zero size of the proton using electron beams¹. The use of charged leptons as scattering probes enables measuring the distribution of electric charges, which is encoded in the vector form factors of the nucleon². Scattering weakly interacting neutrinos gives the opportunity to measure both vector and axial vector form factors of the nucleon, providing an additional, complementary probe of their structure. The nucleon transition axial form factor, F_A, can be measured from neutrino scattering from free nucleons, ν_μn → μ⁻p and \({\bar{\nu }}_{\mu }p\to {\mu }^{+}n\), as a function of the negative four-momentum transfer squared (Q²). Up to now, F_A(Q²) has been extracted from the bound nucleons in neutrino–deuterium scattering^{3,4,5,6,7,8,9}, which requires uncertain nuclear corrections¹⁰. Here we report the first high-statistics measurement, to our knowledge, of the \({\bar{\nu }}_{\mu }\,p\to {\mu }^{+}n\) cross-section from the hydrogen atom, using the plastic scintillator target of the MINERvA¹¹ experiment, extracting F_A from free proton targets and measuring the nucleon axial charge radius, r_A, to be 0.73 ± 0.17 fm. The antineutrino–hydrogen scattering presented here can access the axial form factor without the need for nuclear theory corrections, and enables direct comparisons with the increasingly precise lattice quantum chromodynamics computations^12,13,14,15. Finally, the tools developed for this analysis and the result presented are substantial advancements in our capabilities to understand the nucleon structure in the weak sector, and also help the current and future neutrino oscillation experiments^{16,17,18,19,20} to better constrain neutrino interaction models.

^{来自核子的高能粒子散射探测它们的结构，正如在使用电子束1}建立质子的非零尺寸的实验中所做的那样。使用带电的轻子作为散射探针可以测量电荷的分布，这些分布被编码在核子²的矢量形状因子中。散射弱相互作用的中微子提供了测量核子矢量和轴向矢量形状因子的机会，提供了对其结构的额外、互补的探测。核子跃迁轴向形状因子F _A可以通过自由核子的中微子散射ν _μ n  →  μ ⁻ p来测量和\({\bar{\nu }}_{\mu }p\to {\mu }^{+}n\) ，作为负四动量传递平方 ( Q ² )的函数。到目前为止，F _A ( Q ² ) 已经从中微子-氘散射^{3,4,5,6,7,8,9}中的束缚核子中提取出来，这需要不确定的核校正¹⁰。据我们所知，这里我们报告了\({\bar{\nu }}_{\mu }\,p\to {\mu }^{+}n\)横截面的第一个高统计测量从氢原子中，使用 MINERvA ¹¹实验的塑料闪烁体靶，提取F _A来自自由质子靶并测量核子轴向电荷半径r _A为 0.73 ± 0.17 fm。这里介绍的反中微子-氢散射无需核理论校正即可获得轴向形状因子，并能够与日益精确的晶格量子色动力学计算^12,13,14,15进行直接比较。最后，为该分析开发的工具和所呈现的结果大大提高了我们理解弱区核子结构的能力，也有助于当前和未来的中微子振荡实验 16、17、18、19、20 更好^地约束中微子相互作用模型。