Proton-Proton Fusion and Tritium β Decay from Lattice Quantum Chromodynamics

The nuclear matrix element determining the pp→de⁺ν fusion cross section and the Gamow-Teller matrix element contributing to tritium β decay are calculated with lattice quantum chromodynamics 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[subscript 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→de⁺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[subscript 1,A]=3.9(0.2)(1.0)(0.4)(0.9) fm³ at a renormalization scale set by the physical pion mass, also agreeing within 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.National Science Foundation (U.S.) (PHY11-25915