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arXiv 1603.01593nucl-thastro-ph.SR
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手征有效场论中质子-质子聚变的不确定性量化

Uncertainty quantification for proton-proton fusion in chiral effective field theory

B. Acharya, B. D. Carlsson, A. Ekström, C. Forssén, L. Platter

摘要:

我们使用手征有效场论($χ$ EFT)计算质子-质子($pp$)聚变反应的$S$ -因子,直到次-次-主导阶(NNLO),并对结果进行严格的不确定性分析。我们量化的不确定性,由于(i)用于计算的$pp$横截面在动量空间的计算方法,(ii)在低能量耦合常数的$χ$ EFT的统计不确定性,(iii)由于$χ$ EFT截止的系统不确定性,和(iv)用于校准核子-核子相互作用的数据库中的系统变化。我们还研究了多项式外推过程的鲁棒性,该过程通常用于提取阈值$S$因子及其能量导数。通过在几个不同的能量区间对能量相关的$S$ -因子的多项式拟合进行统计分析,我们消除了在计算中选择拟合区间可能产生的系统不确定性。此外,我们还研究了$S$因子与$^{2,3}$ H和$^3$ He的结合能和点质子半径、$^2$ H的$D$态几率和四极矩以及$^{3}$ H的$β$衰变等少核子观测量之间的统计相关性。我们发现,与国家的最先进的优化的核哈密顿量,统计不确定性的阈值$S$ -因子不能减少超过0.7%。

英文摘要:

We compute the $S$-factor of the proton-proton ($pp$) fusion reaction using chiral effective field theory ($χ$EFT) up to next-to-next-to-leading order (NNLO) and perform a rigorous uncertainty analysis of the results. We quantify the uncertainties due to (i) the computational method used to compute the $pp$ cross section in momentum space, (ii) the statistical uncertainties in the low-energy coupling constants of $χ$EFT, (iii) the systematic uncertainty due to the $χ$EFT cutoff, and (iv) systematic variations in the database used to calibrate the nucleon-nucleon interaction. We also examine the robustness of the polynomial extrapolation procedure, which is commonly used to extract the threshold $S$-factor and its energy-derivatives. By performing a statistical analysis of the polynomial fit of the energy-dependent $S$-factor at several different energy intervals, we eliminate a systematic uncertainty that can arise from the choice of the fit interval in our calculations. In addition, we explore the statistical correlations between the $S$-factor and few-nucleon observables such as the binding energies and point-proton radii of $^{2,3}$H and $^3$He as well as the $D$-state probability and quadrupole moment of $^2$H, and the $β$-decay of $^{3}$H. We find that, with the state-of-the-art optimization of the nuclear Hamiltonian, the statistical uncertainty in the threshold $S$-factor cannot be reduced beyond 0.7%.

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