Models, measurements, and effective field theory: Proton capture on Be7 at next-to-leading order
Models, measurements, and effective field theory: Proton capture on
Be7
at next-to-leading order
复制标题
模型、测量和有效场论：Be7 上次领先级的质子捕获
作者：
Xilin Zhang;K. Nollett;D. Phillips
我们采用有效场论 (EFT)，利用 p 波晕核 $^8mathrm{B}$ 中的尺度分离来描述 $^7mathrm{Be}(p,gamma)^8mathrm{B}$ 直至质心能量为 500 keV 的过程。我们为此开发了拉格朗日和功率计数，计算在 EFT 展开中一直执行到次前导阶 (NLO)。我们采用的功率计数意味着库仑相互作用必须包含在 $alpha_{ 中的所有阶次中
我em}$。我们通过时序微扰理论计算的 EFT 费曼图来实现这一点，从而恢复现有的量子力学技术，例如用于处理库仑核干涉的二势形式主义。同时，强相互作用和 E1 算子是通过动量幂的 EFT 展开来处理的，分解尺度由 ${}^7$Be 核心的大小设置，$Lambda 约为 70$ MeV。直到 NLO，进入辐射捕获反应的不同通道中的相关物理现象被编码为十种不同的 EFT 耦合。结果是对感兴趣的能量范围内的反应振幅进行与模型无关的参数化。为了显示与之前结果的联系，我们使用文献中的许多潜在模型和微观计算的结果来修复 EFT 耦合。这些模型中的每一个都对应于 EFT 空间中的一个特定点。因此，EFT 结构提供了一种非常通用的方法来量化 $^7mathrm{Be}(p,gamma)^8mathrm{B}$ 计算中的模型不确定性。我们还证明，$^7mathrm{Be}(p,gamma)^8mathrm{B}$ 中唯一的 N$^2$LO 修正来自于感兴趣的能量范围内实际上为 N$^3$LO 大小的非弹性，因此我们计算中的截断误差实际上是 N$^3$LO。我们还讨论了推断的 $S(0)$ 与之前标准评估的关系。
We employ an effective field theory (EFT) that exploits the separation of scales in the p-wave halo nucleus $^8mathrm{B}$ to describe the process $^7mathrm{Be}(p,gamma)^8mathrm{B}$ up to a center-of-mass energy of 500 keV. The calculation, for which we develop the lagrangian and power counting, is carried out up to next-to-leading order (NLO) in the EFT expansion. The power counting we adopt implies that Coulomb interactions must be included to all orders in $alpha_{
m em}$. We do this via EFT Feynman diagrams computed in time-ordered perturbation theory, and so recover existing quantum-mechanical technology such as the two-potential formalism for the treatment of the Coulomb-nuclear interference. Meanwhile the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta, with a breakdown scale set by the size of the ${}^7$Be core, $Lambda approx 70$ MeV. Up to NLO the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings. The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest. To show the connection to previous results we fix the EFT couplings using results from a number of potential model and microscopic calculations in the literature. Each of these models corresponds to a particular point in the space of EFTs. The EFT structure therefore provides a very general way to quantify the model uncertainty in calculations of $^7mathrm{Be}(p,gamma)^8mathrm{B}$. We also demonstrate that the only N$^2$LO corrections in $^7mathrm{Be}(p,gamma)^8mathrm{B}$ come from an inelasticity that is practically of N$^3$LO size in the energy range of interest, and so the truncation error in our calculation is effectively N$^3$LO. We also discuss the relation of our extrapolated $S(0)$ to the previous standard evaluation.