Proton-Proton Fusion and Tritium $\beta$ Decay from Lattice Quantum Chromodynamics

Journal Article · 10 August 2017 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.119.062002 · OSTI ID:1393535

Savage, Martin J.; Shanahan, Phiala E.; Tiburzi, Brian C.; Wagman, Michael L.; Winter, Frank; Beane, Silas R.; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Kostas

The nuclear matrix element determining the $$pp\to d e^+ \nu$$ fusion cross section and the Gamow-Teller matrix element contributing to tritium $$\beta$$-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 $$m_\pi$$ ~ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within $$2\sigma$$ 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 $$pp\to d e^+ \nu$$ 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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
• Sponsoring Organization: USDOE Office of Science (SC); USDOE
• Contributing Organization: NPLQCD Collaboration
• Grant/Contract Number: NSF PHY11-25915; PHY1206498; PHY15-15738; AC02-05CH11231; AC05-00OR22725; SC001347; SC00-10337; FG02-00ER41132; SC0010495; SC0011090; FG02-04ER41302; AC05-06OR23177
• OSTI ID: 1393535
• Alternate ID(s): OSTI ID: 1374773
• Report Number(s): JLAB-THY-16-2362; DOE/OR/23177-3961; arXiv:1610.04545; PRLTAO; TRN: US1702835
• Journal Information: Physical Review Letters, Vol. 119, Issue 6; ISSN 0031-9007
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English