Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles

TL;DR

This paper resolves the long-standing discrepancy between observed and predicted $eta$-decay rates by demonstrating that the quenching arises from two-nucleon weak coupling and nuclear correlations, using advanced first-principles calculations.

Contribution

The study provides the first comprehensive first-principles explanation for $eta$-decay rate quenching, incorporating systematic effective field theories and many-body techniques.

Findings

Theoretical $eta$-decay rates align with experimental data.

Quenching is mainly due to two-nucleon weak coupling and nuclear correlations.

Results include accurate predictions for $^{100}$Sn decay.

Abstract

$\beta$-decay, a process that changes a neutron into a proton (and vice versa), is the dominant decay mode of atomic nuclei. This decay offers a unique window to physics beyond the standard model, and is at the heart of microphysical processes in stellar explosions and the synthesis of the elements in the Universe. For 50 years, a central puzzle has been that observed $\beta$-decay rates are systematically smaller than theoretical predictions. This was attributed to an apparent quenching of the fundamental coupling constant $g_A \simeq $ 1.27 in the nucleus by a factor of about 0.75 compared to the $\beta$-decay of a free neutron. The origin of this quenching is controversial and has so far eluded a first-principles theoretical understanding. Here we address this puzzle and show that this quenching arises to a large extent from the coupling of the weak force to two nucleons as well as from strong correlations in the nucleus. We present state-of-the-art computations of $\beta$-decays from light to heavy nuclei. Our results are consistent with experimental data, including the pioneering measurement for $^{100}$Sn. These theoretical advances are enabled by systematic effective field theories of the strong and weak interactions combined with powerful quantum many-body techniques. This work paves the way for systematic theoretical predictions for fundamental physics problems. These include the synthesis of heavy elements in neutron star mergers and the search for neutrino-less double-$\beta$-decay, where an analogous quenching puzzle is a major source of uncertainty in extracting the neutrino mass scale.

Figures

Tables

Table 1. Table 1: Gamow Teller (GT) matrix elements from the extreme single-particle model (ESPM) | m GT ​ ( 𝝈 ​ 𝝉 ) | 2 superscript subscript 𝑚 GT 𝝈 𝝉 2 |m_{\rm GT}(\bm{\sigma\tau})|^{2} and EOM-CCSDT-1 | M GT ​ ( 𝝈 ​ 𝝉 ) | 2 superscript subscript 𝑀 GT 𝝈 𝝉 2 |M_{\rm GT}(\bm{\sigma\tau})|^{2} , sum of GT and 2BC from ESPM | m GT | 2 superscript subscript 𝑚 GT 2 |m_{\rm GT}|^{2} and EOM-CCSDT-1 | M GT | 2 superscript subscript 𝑀 GT 2 |M_{\rm GT}|^{2} , the log f ​ t 𝑓 𝑡 ft values, the quenching factor q 𝑞 q from 2BC from EOM-CCSDT-1 and ESPM, the energy difference between the ground-state of 100 Sn and the 1 + superscript 1 1^{+} state in 100 In, and the binding energy per particle ( B ​ E / A 𝐵 𝐸 𝐴 BE/A ) in 100 Sn for the interactions used in this work, and compared to experiment. The B ​ E / A 𝐵 𝐸 𝐴 BE/A obtained with the interactions X/Y (EM) and 2.0/2.0 (PWA) were taken from Ref.  morris2017 , the B ​ E / A 𝐵 𝐸 𝐴 BE/A for the remaining interactions were obtained by employing the same model-space as used for the calculations of | M GT | 2 superscript subscript 𝑀 GT 2 |M_{\rm GT}|^{2} , i.e., N max = 10 subscript 𝑁 max 10 N_{\rm max}=10 and E 3 ​ m ​ a ​ x = 16 subscript 𝐸 3 m a x 16 E_{\rm 3max}=16 . The energy difference Δ ​ E Δ 𝐸 \Delta E were calculated using the model-space N max = 10 subscript 𝑁 max 10 N_{\rm max}=10 and E 3 ​ m ​ a ​ x = 16 subscript 𝐸 3 m a x 16 E_{\rm 3max}=16 for the ground-state (CCSDT-1) and E ~ 3 ​ m ​ a ​ x = 11 subscript ~ 𝐸 3 m a x 11 \tilde{E}_{\rm 3max}=11 for the 1 + superscript 1 1^{+} excited state (EOM-CCSDT-1) in 100 In. All calculations used the harmonic oscillator frequency ℏ ​ ω = 12 Planck-constant-over-2-pi 𝜔 12 \hbar\omega=12 MeV.

Interaction	${\left|m_{\mathrm{GT}}\left(𝝈𝝉\right)\right|}^2$	${\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|}^2$	${\left|m_{\mathrm{GT}}\right|}^2$	${\left|M_{\mathrm{GT}}\right|}^2$	log $ft$	q	q (ESPM)	$\Delta E$ [MeV]	$BE/A$ [MeV]
NNLOsat	17.7	$8.9$	12.5	6.5	2.77	0.85	0.84	7.4	not converged
NN-N3LO+3Nlnl	16.9	$10.0$	10.6	6.9	2.74	0.83	0.79	6.1	7.6
NN-N4LO+3Nlnl	17.2	$10.1$	8.2	5.4	2.85	0.73	0.69	5.8	7.1
1.8/2.0 (EM)	17.7	$11.3$	9.8	7.0	2.73	0.79	0.74	5.1	8.4
2.0/2.0 (EM)	17.7	$10.7$	10.2	6.9	2.74	0.80	0.76	6.0	7.7
2.0/2.0 (PWA)	17.7	$9.9$	11.5	5.9	2.81	0.77	0.81	6.8	6.4
2.2/2.0 (EM)	17.7	$10.1$	10.6	6.6	2.76	0.81	0.77	6.7	7.2
2.8/2.0 (EM)	17.7	$7.4$	11.8	5.2	2.86	0.84	0.82	8.3	not converged
Batist et al. batist2010				$5.2\pm 0.6$				5.11	8.25
Hinke et al. hinke2012				${9.1}_{-3.0}^{+2.6}$	${2.62}_{-0.11}^{+0.13}$

Table 2. Table 2: Gamow Teller (GT) transition strength in 8 He to the first 1 1 + superscript subscript 1 1 1_{1}^{+} in 8 Li for the NN-N 4 LO +3N lnl interaction calculated in the EOM-CCSDT-1, VS-IMSRG(2), and NCSM approaches.

Method	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$
EOM-CCSD	0.45	0.48
EOM-CCSDT-1	0.42	0.45
VS-IMSRG(2)	0.54	0.58
NCSM	0.41	0.46

Table 3. Table 3: Gamow Teller (GT) transition strength in 14 O to the second 1 2 + superscript subscript 1 2 1_{2}^{+} in 14 N for the NNLO sat and NN-N 4 LO +3N lnl interactions calculated in the EOM-CCSDT-1, VS-IMSRG, and NCSM approaches.

Interaction	NNLOsat		NN-N4LO+3Nlnl
Method	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$
EOM-CCSD	2.15	2.08	2.26	2.06
EOM-CCSDT-1	1.77	1.69	1.97	1.86
VS-IMSRG(2)	1.72	1.76	1.83	1.83
NCSM	1.80	1.69	1.86	1.78

Table 4. Table 4: Gamow Teller (GT) transition strength in 10 C to the first 1 1 + superscript subscript 1 1 1_{1}^{+} in 10 B for the NN-N 4 LO +3N lnl interaction calculated in the VS-IMSRG(2) and NCSM approaches.

Method	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$
VS-IMSRG(2)	1.94	1.88
NCSM	2.01	1.92

Table 5. Table 5: Gamow Teller (GT) transition strengths in 34 Si and 68 Ni for the NN-N 4 LO +3N lnl interaction calculated in the EOM-CCSDT-1 and VS-IMSRG approaches.

	34Si${\to }^{34}$P${}_{1_1^{+}}$		34Si${\to }^{34}$P${}_{1_2^{+}}$		68Ni${\to }^{68}$Cu${}_{1_1^{+}}$
Method	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$	$\left|M_{\mathrm{GT}}\left(𝝈𝝉\right)\right|$	$\left|M_{\mathrm{GT}}\right|$
EOM-CCSD	0.61	0.28	1.32	1.14	0.60	0.46
EOM-CCSDT-1	0.56	0.28	1.15	0.96	0.42	0.35
VS-IMSRG(2)	0.78	0.52	1.00	0.85	0.42	0.36

Table 6. Table 6: Values of the low-energy coupling c D subscript 𝑐 𝐷 c_{D} , the combination 2 ​ c 4 − c 3 2 subscript 𝑐 4 subscript 𝑐 3 2c_{4}-c_{3} of pion-nucleon couplings, and the value of Λ χ subscript Λ 𝜒 \Lambda_{\chi} that enters the simple estimate ( 15 ) of the renormalization of the axial-vector coupling due to 2BC. The first seven EFT interactions are used in this work, and the latter are other interactions (for details see the references given).

Interaction	$c_D$	$2c_4-c_3$	${\Lambda }_{\chi }$ [GeV]	Ref.
NNLOsat	$0.817$	$11.46$	0.7	ekstrom2015
NN-N4LO +3Nlnl	$-1.8$	$13.88$	0.7
NN-N3LO +3Nlnl	$0.7$	$14.0$	0.7	leistenschneider2017
1.8/2.0 (EM)	$1.264$	$14.0$	0.7	hebeler2011
2.0/2.0 (EM)	$1.271$	$14.0$	0.7	hebeler2011
2.2/2.0 (EM)	$1.214$	$14.0$	0.7	hebeler2011
2.0/2.0 (PWA)	$-3.007$	$12.7$	0.7	hebeler2011
Pastore 500	$-1.847$	$14.0$	1.0	pastore2017
Pastore 600	$-2.03$	$14.13$	1.0	pastore2017
Ekström 450	$0.0004$	$13.22$	0.7	\citeappekstrom2014
Ekström 500	$0.0431$	$12.50$	0.7	\citeappekstrom2014
Ekström 550	$0.1488$	$11.71$	0.7	\citeappekstrom2014

Equations

$$H=\sum _{i<j}\left(\frac{({\mathbf{p}}_i-{\mathbf{p}}_j{)}^2}{2mA}+V_{\mathrm{NN}}^{(i,j)}\right)+\sum _{i<j<k}{V}_{3N}^{(i,j,k)}.$$

$$M_{\mathrm{GT}}=⟨f|O_{\mathrm{GT}}|i⟩.$$

$$O_{\mathrm{GT}}=g_{\mathrm{A}}^{-1}\sqrt{6\pi }{E}_1^A(\vec{K}=0).$$

$${\vec{J}}^A(\vec{K})=\sum _jıg_A{\mathbf{\sigma }}_j{\mathbf{\tau }}_j^{\pm }{e}^{ı\vec{K}\cdot {\vec{r}}_j}.$$

$$O_{\mathrm{GT}}=O_{\sigma \tau }^{1b}+O_{2BC}^{2b}.$$

$$⟨{\Phi }_0|(1+\Lambda ),\mathrm{with}\Lambda ={\Lambda }_1+{\Lambda }_2+\dots .$$

$$|M_{\mathrm{GT}}{|}^2=|⟨f|O_{\mathrm{GT}}|i⟩{|}^2=⟨f|O_{\mathrm{GT}}|i⟩⟨i|O_{\mathrm{GT}}^{†}|f⟩$$

$$=⟨{\Phi }_0|L_{\mu }^{1^{+}}\overline{O_N}|{\Phi }_0⟩⟨{\Phi }_0|(1+\Lambda )\overline{O_N^{†}}{R}_{\mu }^{1^{+}}|{\Phi }_0⟩.$$

$$S^{\pm }=⟨{\Phi }_0|(1+\Lambda )\overline{O_N^{†}}\cdot \overline{O_N}|{\Phi }_0⟩.$$

$$\begin{gathered} \left[\begin{array}{cc}{\overline{H}}_{PP}& {\overline{H}}_{PQ}\\ {\overline{H}}_{QP}& {\overline{H}}_{QQ}\end{array}\right]\left[\begin{array}{c}{R}_P\\ R_Q\end{array}\right]=\omega \left[\begin{array}{c}{R}_P\\ R_Q\end{array}\right] \\ . \end{gathered}$$

$${\overline{H}}_{PP}{R}_P+{\overline{H}}_{PQ}{R}_Q=\omega R_P,$$

$$\begin{gathered} {\overline{H}}_{QP}{R}_P+{\overline{H}}_{QQ}{R}_Q=\omega R_Q \\ . \end{gathered}$$

$${\overline{H}}_{PP}{R}_P+{\overline{H}}_{PQ}(\omega -{\overline{H}}_{QQ}{)}^{-1}{\overline{H}}_{QP}{R}_P=\omega R_P.$$

$$\Delta {\omega }_{\mu }=⟨{\Phi }_0|L_{\mu }{\overline{H}}_{P{Q}^{\prime }}({\omega }_{\mu }-{\overline{H}}_{Q^{\prime }{Q}^{\prime }}{)}^{-1}{\overline{H}}_{Q^{\prime }P}{R}_{\mu }|{\Phi }_0⟩.$$

$$|{\Psi }_A^{J^{\pi }T}⟩=\sum _{N=0}^{N_{\max }}\sum _i{c}_{Ni}^{J^{\pi }T}|ANi{J}^{\pi }T⟩.$$

$$q_{2BC}\approx 1-\frac{\rho }{F_{\pi }^2}\left[-\frac{c_D}{4g_A{\Lambda }_{\chi }}+\frac{I(\rho )}{3}\left(2c_4-c_3+\frac{1}{2m}\right)\right],$$

$$I(\rho )=1-\frac{3m_{\pi }^2}{k_F^2}+\frac{3m_{\pi }^3}{k_F^3}\arctan (k_F/m_{\pi })$$

$$\rho =\frac{2k_F^3}{3{\pi }^2}.$$

Full text

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appReferences

Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles

P. Gysbers1,2, G. Hagen3,4, J. D. Holt1, G. R. Jansen3,5, T. D. Morris3,4,6, P. Navrátil1, T. Papenbrock3,4, S. Quaglioni7, A. Schwenk8,9,10, S. R. Stroberg1,11,12 & K. A. Wendt7

1TRIUMF, 4004 Wesbrook Mall, Vancouver BC, V6T 2A3, Canada. 2Department of Physics and Astronomy, University of British Columbia, Vancouver BC, V6T 1Z1, Canada. 3Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 4Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA. 5National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 6Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 7Nuclear and Chemical Science Division, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA. 8Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany. 9ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany. 10Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany. 11Physics Department, Reed College, Portland, OR 97202, USA. 12Department of Physics, University of Washington, Seattle, WA 98195, USA

$\beta$-decay, a process that changes a neutron into a proton (and vice versa), is the dominant decay mode of atomic nuclei. This decay offers a unique window to physics beyond the standard model, and is at the heart of microphysical processes in stellar explosions and the synthesis of the elements in the Universe janka2006 ; schatz2013 ; engel2017 . For 50 years, a central puzzle has been that observed $\beta$-decay rates are systematically smaller than theoretical predictions. This was attributed to an apparent quenching of the fundamental coupling constant $g_{A}\simeq$ 1.27 in the nucleus by a factor of about 0.75 compared to the $\beta$-decay of a free neutron towner1987 . The origin of this quenching is controversial and has so far eluded a first-principles theoretical understanding. Here we address this puzzle and show that this quenching arises to a large extent from the coupling of the weak force to two nucleons as well as from strong correlations in the nucleus. We present state-of-the-art computations of $\beta$-decays from light and medium-mass nuclei to 100Sn. Our results are consistent with experimental data, including the pioneering measurement for 100Sn hinke2012 ; batist2010 (see Fig. 1). These theoretical advances are enabled by systematic effective field theories of the strong and weak interactions epelbaum2009 combined with powerful quantum many-body techniques barrett2013 ; hagen2015 ; stroberg2017 . This work paves the way for systematic theoretical predictions for fundamental physics problems. These include the synthesis of heavy elements in neutron star mergers korobkin2012 ; surman2016 ; pian2017 and the search for neutrino-less double-$\beta$-decay engel2017 , where an analogous quenching puzzle is a major source of uncertainty in extracting the neutrino mass scale barea2012 .

Gamow-Teller transitions are a form of $\beta$-decay in which the spins of the $\beta$-neutrino pair emitted during the nuclear decay are aligned. Remarkably, calculated Gamow-Teller strengths appear to reproduce most of the experimental data if the fundamental constant $g_{A}\simeq$ 1.27 characterizing the coupling of the weak interaction to a nucleon is quenched by a factor of $q\sim 0.75$ wilkinson1973b ; brown1985 ; chou1993 ; martinez1996 . Missing nuclear correlations (i.e. a lack of complexity in nuclear wave functions owing to limitations of nuclear models) as well as neglected contributions from meson-exchange currents (i.e. coupling of the weak force to two nucleons) have been proposed as possible causes of the quenching phenomenon towner1987 . However, a solution has so far remained elusive. To address the quenching puzzle, we carry out a comprehensive study of Gamow-Teller decays through many-body computations of nuclei based on effective field theories (EFTs) of quantum chromodynamics epelbaum2009 ; machleidt2011 , including an unprecedented amount of correlations in the nuclear wave functions. The EFT approach offers the prospects of accuracy, by encoding the excluded high-energy physics through coefficients adjusted to data, and precision from the systematically improvable EFT expansion. Moreover, EFT enables a consistent description of the coupling of weak interactions to two nucleons, via two-body currents (2BC). In the EFT approach, 2BC enter as subleading corrections to the one-body standard Gamow-Teller operator ${\bm{\sigma}}{\bm{\tau}}^{+}$ (with Pauli spin and isospin matrices ${\bm{\sigma}}$ and ${\bm{\tau}}$, respectively); they are smaller but significant corrections to weak transitions as three-nucleon forces are smaller but significant corrections to the nuclear interaction epelbaum2009 ; machleidt2011 .

In this work we focus on strong Gamow-Teller transitions, where the effects of quenching should dominate over cancellations due to fine details (as occur in the famous case of the 14C decay used for radiocarbon dating holtjw2009 ; maris2011 ). An excellent example is the super-allowed $\beta$-decay of the doubly magic 100Sn nucleus (see Fig. 1), exhibiting the strongest Gamow-Teller strength so far measured in all atomic nuclei hinke2012 . A first-principles description of this exotic decay, in such a heavy nucleus, presents a significant computational challenge. However, its equal ‘magic’ number ($Z=N=50$) of protons and neutrons arranged into complete shells makes 100Sn an ideal candidate for large-scale coupled-cluster calculations morris2017 , while the daughter nucleus 100In can be reached via novel extensions of high-order charge-exchange coupled-cluster methods developed in this work (see Methods and Figs. 5, 12, and 15 in Supplementary Information for details). This method includes correlations via a vast number of particle-hole excitations of a reference state and also employs 2BC in the transition operator.

Figure 1 shows our results for the strength (i.e., the absolute square of the transition matrix element, $M_{\rm GT}$) of the Gamow-Teller transition to the dominant $J^{\pi}=1^{+}$ state in the 100In daughter nucleus (see Table 1 and Fig. 12 in Supplementary Information for more details). To investigate systematic trends and sensitivities to the nuclear Hamiltonian, we employed a family of established EFT interactions and corresponding currents hebeler2011 ; ekstrom2015 ; leistenschneider2017 . For an increased precision, we also developed a new interaction labeled NN-N4LO+3Nlnl which is constrained to reproduce the triton half-life (see Methods for details on the Hamiltonians considered). The hollow symbols in Fig. 1 depict the decay with the standard, leading-order coupling of the weak force to a single nucleon in the non-relativistic limit (i.e., via the standard Gamow-Teller operator ${\bm{\sigma}}{\bm{\tau}}^{+}$). The differences with respect to the extreme single-particle model (ESPM), which approximates both 100Sn and its 100In daughter as a single shell-model configuration, reveals the influence of correlations among the nucleons. The full symbols include 2BC, using consistent couplings as in the employed EFT interactions. Finally, the partially filled symbols in Fig. 1 represent results from other models of Ref. hinke2012 , where the standard Gamow-Teller operator was multiplied by a quenching factor $q\sim 0.75$.

Based on our results shown in Fig. 1, we predict the range $5.2(5)\lesssim|M_{\rm GT}|^{2}\lesssim 7.0(7)$ for the Gamow-Teller strength. This range overlaps with the evaluation of Batist et al. batist2010 , based on systematic experimental trends in the tin isotopes, and the lower end of the measurement by Hinke et al. hinke2012 . The quenching factor we obtain from 2BC depends somewhat on the employed Hamiltonian, and is in the range $q_{\rm 2BC}=0.73-0.85$. This range is consistent with the value $q=0.75(2)$ from Batist et al. batist2010 . In the present work, we used the spread of results obtained with the selected set of EFT interactions and 2BC as an estimate of the systematic uncertainty. A more thorough quantification of the uncertainties associated with the many-body methods and EFT truncations is beyond the scope of this work, and will be addressed in future studies. We note that neglected higher-order correlations in our coupled-cluster approach will further reduce the Gamow-Teller strength (see Supplementary Information for details).

Moreover, we observe that the spread for the 100Sn Gamow-Teller strength obtained for the family of employed EFT interactions is significantly reduced (by a factor two) when 2BC are included. This is consistent with ideas from EFT that residual cutoff dependence is due to neglected higher-order terms in the Hamiltonian and 2BC. In addition, we find that the relative contributions to the quenching of the Gamow-Teller strength coming from correlations and 2BC vary as a function of the resolution scale of the underlying EFT interactions. Starting from the extreme single-particle model, and adding first correlations and then the effects of 2BC, we find that the quenching from correlations typically increases with increasing resolution scale of the interaction, and that most of the quenching stems from correlations. However, adding first the effects of 2BC and then correlations shows that the quenching from 2BC increases with decreasing resolution scale and that most of the quenching stems from 2BC for all but the “hardest” potentials considered in this work (see Fig. 6 in Supplementary Information for details).

For a comprehensive study, we now turn to $\beta$-decays of light and medium-mass nuclei. Using a selection of the EFT interactions and 2BC adopted for 100Sn, we achieved an overall good description of $\beta$-decays in light nuclei. Figure 2 shows theory-to-experiment ratios for large Gamow-Teller transitions in light nuclei. Here we highlight the results obtained for the high-precision NN-N4LO+3Nlnl interaction and corresponding 2BC developed in this work. As detailed in Methods, the 2BC and three-nucleon forces 3Nlnl are parametrized consistently and are constrained to reproduce the empirical value of the triton $\beta$-decay half life. Our calculations were carried out with the no-core shell model barrett2013 , a virtually exact treatment of correlations in the nuclear wave functions (see Methods for details). The role of 2BC is relatively small in light nuclei with mass numbers $A\leqslant 7$. Full nuclear wave functions already provide a rather satisfactory description of the transitions with the standard Gamow-Teller operator. Furthermore, the inclusion of 2BC may enhance (e.g., 8He$\rightarrow^{8}$Li), quench (e.g., 7Be${}_{\tfrac{3}{2}}\rightarrow^{7}$Li${}_{\tfrac{1}{2}}$), or have virtually no impact on the computed transition (e.g., 7Be${}_{\tfrac{3}{2}}\rightarrow^{7}$Li${}_{\tfrac{3}{2}}$, see also Fig. 14 in Supplementary Information). The small role of 2BC in $A\leqslant 7$ nuclei is similar to what was found in the Green’s function Monte Carlo calculations of Ref. pastore2017 . We find a rather substantial enhancement of the 8He Gamow-Teller matrix element due to the 2BC. Let us mention, though, that this transition matrix element is the smallest of those presented in Fig. 2. We note that for the other Hamiltonians employed in this work, the 2BC and 3N were not fit to reproduce the triton half-life, nevertheless the inclusion of 2BC for most of these cases also improves the agreement with data for the light nuclei considered in Fig. 2 (see Fig. 9 in Supplementary Information for results obtained with NNLO${}_{\textrm{sat}}$ and NN-N3LO+3Nlnl). The case of 10C is special because the computed Gamow-Teller transition is very sensitive to the structure of the $J^{\pi}=1^{+}$ state in the 10B daughter nucleus. Depending on the employed interaction, this state can mix with a higher-lying $1^{+}$ state, greatly impacting the precise value of this transition. We finally note that benchmark calculations between the many-body methods used in this work agree to within 5% for the large transition in 14O. For smaller transitions discrepancies can be larger (see Supplementary Information for details).

Historically, the most extensive evidence for the quenching of Gamow-Teller $\beta$-decay strength comes from medium-mass nuclei brown1985 ; langanke1995 ; martinez1996 , and we now show that our calculations with these consistent Hamiltonians and currents largely solves the puzzle here as well. We use the valence-space in-medium similarity renormalization group (VS-IMSRG) method stroberg2017 (see Methods for details) and compute Gamow-Teller decays for nuclei in the mass range between oxygen and calcium (referred to as $sd$-shell nuclei) and between calcium and vanadium (lower $pf$-shell nuclei), focusing on strong transitions. Here, we highlight the NN-N4LO+3Nlnl interaction and corresponding 2BC.

Figure 3 shows the empirical values of the Gamow-Teller transition matrix elements versus the corresponding unquenched theoretical matrix elements obtained from phenomenological shell model with the standard Gamow-Teller ${\bm{\sigma}}{\bm{\tau}}$ operator and the first-principles VS-IMSRG calculations. Perfect agreement between theory and experiment is denoted by the diagonal dashed line. The results from the phenomenological shell model clearly exemplify the state of theoretical calculations for decades wilkinson1973b ; brown1985 ; chou1993 ; langanke1995 ; martinez1996 , as an example, in the $sd$-shell shell, a quenching factor of $q\sim 0.8$ is needed to bring the theory into agreement with experiment brown1985 . The VS-IMSRG calculations without 2BC (not shown) exhibit a modest improvement, with a corresponding quenching factor of 0.89(4) for $sd$-shell nuclei and 0.85(3) for $pf$-shell nuclei, pointing to the importance of consistent valence-space wave functions and operators (see Fig.10 in Supplementary Information). As in 100Sn, the inclusion of 2BC yields an additional quenching of the theoretical matrix elements, and the linear fit of our results lies close to the dashed line, meaning our theoretical predictions agree on average with experimental values across a large number of medium-mass nuclei.

Another approach often used in the investigation of Gamow-Teller quenching is the Ikeda sum-rule: the difference between the total integrated $\beta^{-}$ and $\beta^{+}$ strengths obtained with the ${\bm{\sigma}}{\bm{\tau}}^{\mp}$ operator yields the model-independent sum-rule $3(N$ – $Z)$. We have computed the Ikeda sum-rule for 14O, 48Ca, and 90Zr using the coupled-cluster method (see Methods for details). For the family of EFT Hamiltonians used for 100Sn we obtain a quenching factor arising from 2BC, which is consistent with our results shown in Fig. 3 and the shell-model analyses from Refs. chou1993 ; brown1985 ; langanke1995 ; martinez1996 (see Fig. 7 in Supplementary Information). We note that the comparison with experimental sum-rule tests using charge-exchange reactions gaarde1981 ; wakasa1997 are complicated by the use of a hadronic probe, which only corresponds to the leading weak one-body operator, and by the challenge of extracting all strength to high energies. Here, our developments enable future direct comparisons.

It is the combined proper treatment of strong nuclear correlations with powerful quantum many-body solvers and the consistency between 2BC and three-nucleon forces that largely explains the quenching puzzle. Smaller corrections are still expected to arise from neglected higher order contributions to currents and Hamiltonians in the EFT approach we pursued, and from neglected correlations in the nuclear wave functions. For beyond-standard-model searches of new physics such as neutrinoless double-$\beta$ decay, our work suggests that a complete and consistent calculation without a phenomenological quenching of the axial-vector coupling $g_{A}$ is called for. This Letter opens the door to ab initio calculations of weak interactions across the nuclear chart and in stars.