质子-质子聚变和氚$β$衰变的晶格量子色动力学研究
Proton-proton fusion and tritium $β$-decay from lattice quantum chromodynamics
摘要：
首次用晶格量子色动力学（QCD）计算了决定$pp\to d e^+ ν$熔合截面的核矩阵元和对氚$β$衰变有贡献的Gamow-Teller矩阵元.使用一种新的背景场方法，这些量在夸克质量的SU（3）味对称值下计算，对应于$m_π$ ~ 806 MeV的π介子质量。在这些夸克质量下，氚的Gamow-Teller矩阵元为0.979（03）（10），在实验值的$2σ$范围内。假设短距离关联的两核子对矩阵元的贡献（介子交换电流）仅轻微地依赖于夸克质量，就像在类似的磁相互作用中所看到的那样，计算的$pp\to d e^+ ν$跃迁矩阵元导致在物理夸克质量处的聚变截面与其当前接受的值一致。此外，在物理π介子质量所设定的重整化尺度下，确定了无π介子有效场论的主导双核子轴向反项为$L_{1,A}=3.9(0.1)(1.0)(0.3)(0.9)\ {\rm fm}^3$，这也符合公认的唯象范围.这一工作具体地证明了可以直接从基本夸克和胶子自由度研究少核子系统中的弱跃迁振幅，并为核物理中许多重要量的后续研究开辟了道路。
英文摘要：
The nuclear matrix element determining the $pp\to d e^+ ν$ fusion cross section and the Gamow-Teller matrix element contributing to tritium $β$-decay are calculated with lattice Quantum Chromodynamics (QCD) for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3)-flavor-symmetric value of the quark masses, corresponding to a pion mass of $m_π$ ~ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within $2σ$ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated $pp\to d e^+ ν$ transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be $L_{1,A}=3.9(0.1)(1.0)(0.3)(0.9)\ {\rm fm}^3$ at a renormalization scale set by the physical pion mass, also in agreement with the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics.
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