$0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements in the interacting boson model with isospin restoration

We introduce a method for isospin restoration in the calculation of nuclear matrix elements (NMEs) for $0\nu \beta \beta$ and $2\nu \beta \beta$ decay within the framework of the microscopic interacting boson model (IBM-2). With this method, we calculate the NMEs for all processes of interest in $0\nu {\beta }^{-}{\beta }^{-}$ and $2\nu {\beta }^{-}{\beta }^{-}$ and in $0\nu {\beta }^{+}{\beta }^{+}$, $0\nu \mathrm{EC}{\beta }^{+}$, $R0\nu \mathrm{ECEC}$, $2\nu {\beta }^{+}{\beta }^{+}$, $2\nu \mathrm{EC}{\beta }^{+}$, and $2\nu \mathrm{ECEC}$. With this method, the Fermi matrix elements for $2\nu \beta \beta$ vanish, and those for $0\nu \beta \beta$ are considerably reduced.

Figure 1

Neutrinoless double-$\beta$ decay mechanism for (a) light neutrino exchange and (b) heavy neutrino exchange.

Figure 2

Double-$\beta$ decay mechanism with the emission of $2\overline{\nu }$.

Figure 3

IBM-2 isospin-restored results for $0\nu {\beta }^{-}{\beta }^{-}$ decay compared with QRPA-Tü [11] and the ISM [19].

Figure 4

IBM-2 (Argonne) results for $0\nu {\beta }^{-}{\beta }^{-}$ NMEs compared with QRPA-Tü (Argonne) [11], ISM (UCOM) [19], QRPA-Jy (UCOM) [25, 26], QRPA-deformed (CD-Bonn) [27], DFT (UCOM) [23], and HFB (M-S) [24].

Figure 5

Value of $g_{A,\mathrm{eff}}$ extracted from experiment for IBM-2 and the ISM.

Figure 6

Expected half-lives for $〈m_{\nu }〉=1$ eV, $g_A=1.269$, and IBM-2 isospin-restored NMEs. The points for ${}^{128}\mathrm{Te}$, ${}^{134}\mathrm{Xe}$, and ${}^{148}\mathrm{Nd}$ decays are not included in this figure. The figure is in semilogarithmic scale.

Figure 7

Current limits to $〈m_{\nu }〉$ from the CUORICINO Collaboration [35], the IGEX Collaboration [36], the NEMO-3 Collaboration [37], the KamLAND-Zen Collaboration [38], the EXO Collaboration [39], and the GERDA Collaboration [40], and IBM-2 Argonne SRC isospin-restored NMEs and $g_A=1.269$. The value of Ref. [42] is shown by $X$. The figure is in logarithmic scale.

Figure 8

Expected half-lives for $〈m_{\nu }〉=1$ eV, $g_A=1.269$, and IBM-2 isospin-restored NMEs. The figure is in semilogarithmic scale.