Tritium β decay and proton-proton fusion in pionless effective field theory

The Gamow-Teller and Fermi matrix elements, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>〈</a:mo><a:mi mathvariant="bold">GT</a:mi><a:mo>〉</a:mo></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>〈</c:mo><c:mi mathvariant="bold">F</c:mi><c:mo>〉</c:mo></c:mrow></c:math>, respectively, for tritium <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>β</e:mi></e:math> decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb interactions and isospin violation giving the leading order predictions <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:msub><f:mrow><f:mo>〈</f:mo><f:mi mathvariant="bold">GT</f:mi><f:mo>〉</f:mo></f:mrow><f:mn>0</f:mn></f:msub><f:mo>=</f:mo><f:mn>0.9807</f:mn></f:mrow></f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mrow><h:mo>〈</h:mo><h:mi mathvariant="bold">F</h:mi><h:mo>〉</h:mo></h:mrow><h:mn>0</h:mn></h:msub><h:mo>=</h:mo><h:mn>1</h:mn></h:mrow></h:math>. Using an experimentally determined value for the tritium <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>β</j:mi></j:math> decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>L</k:mi><k:mrow><k:mn>1</k:mn><k:mo>,</k:mo><k:mi>A</k:mi></k:mrow></k:msub><k:mo>=</k:mo><k:mn>6.01</k:mn><k:mo>±</k:mo><k:mn>2.08</k:mn><k:mspace width="4pt"/><k:msup><k:mrow><k:mi>fm</k:mi></k:mrow><k:mn>3</k:mn></k:msup></k:mrow></k:math> at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. The impact of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>L</m:mi><m:mrow><m:mn>1</m:mn><m:mo>,</m:mo><m:mi>A</m:mi></m:mrow></m:msub></m:math> on proton-proton fusion is also discussed. Finally, the consequences of Wigner-SU(4) spin-isospin symmetry are considered for the Gamow-Teller matrix element. Published by the American Physical Society 2024