Extraction of low-energy constants of single- and double- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math> decays from lattice QCD: A sensitivity analysis

Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs) nuclear effective field theories (EFTs) from first-principles calculations that incorporate dynamics quarks and gluons. Given Euclidean finite-volume nature LQCD outputs, complex mappings are developed in recent years to obtain Minkowski infinite-volume counterparts observables. In particular, as is moving toward computing a set important few-nucleon matrix elements at physical values quark masses, it investigate whether anticipated precision spectra will be sufficient guarantee tighter constraints on relevant LECs than those already obtained phenomenology, considering nontrivial involved. With focus leading-order pionless EFT, ${L}_{1,A}$ ${g}_{\ensuremath{\nu}}^{NN}$, which parametrize, respectively, strength isovector axial two-body current single-$\ensuremath{\beta}$ decay (and other related processes such $pp$ fusion), isotensor contact operator neutrinoless double-$\ensuremath{\beta}$ within light neutrino exchange scenario, expected uncertainty future extractions ${g}_{\ensuremath{\nu}}^{NN}$ examined using synthetic data masses. It observed achieving small uncertainties challenging, (sub)percent-level two-nucleon essential reducing this LEC compared existing constraints. On hand, short-distance coupling decay, shown less sensitive both energies element, can likely constrained with percent-level upcoming calculations.