Abstract
The nuclear matrix element determining the fusion cross section and the Gamow-Teller matrix element contributing to tritium 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 . The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within 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 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 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.
- Received 21 November 2016
DOI:https://doi.org/10.1103/PhysRevLett.119.062002
© 2017 American Physical Society
Physics Subject Headings (PhySH)
Synopsis
Strong Force Calculations for Weak Force Reactions
Published 10 August 2017
Theorists have used lattice-QCD calculations to predict two weak-force-driven reactions—proton fusion and tritium decay.
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