Theoretical investigation of the dependence of double beta decay tracks in a Ge detector on particle and nuclear physics parameters and separation from gamma ray events

The sizes of tracks of events of neutrinoless double-beta decay in a Germanium detector depend on particle physics and nuclear physics parameters such as neutrino mass, right-handed current parameters, etc., and nuclear matrix elements. In this paper for the first time Monte Carlo simulations of neutrino-accompanied ($2\nu \beta \beta$) and neutrinoless double-beta decay ($0\nu \beta \beta$) events, and of various kinds of background processes such as multiple and other $\gamma$ interactions are reported for a Ge detector. The time history of the evolution of the individual events is followed and the sizes of the events (partial volumes in the detector inside which the energy of the event is released) are investigated. Effects of the angular correlations of the two electrons in $\beta \beta$ decay, which again depend on the above nuclear and (for $0\nu \beta \beta$ decay) on particle physics parameters, are taken into account and have been calculated for this purpose for the first time on basis of the experimental half-life of ${}^{76}\mathrm{G}\mathrm{e}$ and of realistic nuclear matrix elements. The sizes determine, together with the location of the events in the detector, the pulse shapes to be observed. It is shown for $\beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$, that $\beta \beta$ events should be selectable with high efficiency by rejecting large size (high multiplicity) $\gamma$ events. Double-escape peaks of similar energy of $\gamma$ lines show concerning their sizes similar behavior as $0\nu \beta \beta$ events, and in that sense can be of some use for corresponding ’calibration’ of pulse shapes of the detector. The possibility to distinguish $\beta \beta$ events from $\gamma$ events is found to be essentially independent of the particle physics parameters of the $0\nu \beta \beta$ process. A brief outlook is given on the potential of future experiments with respect to determination of the particle physics parameters $⟨m_{\nu }⟩,⟨\lambda ⟩,⟨\eta ⟩$.

Figure 1

Calculated angular correlations of the single electron spectrum for the $0^{+}\to 0^{+}$ transition for the $2\nu \beta \beta$ mode for ${}^{76}\mathrm{G}\mathrm{e}$.

Figure 2

Allowed parameters for $⟨m_{\nu }⟩$, $⟨\lambda ⟩$, $⟨\eta ⟩$ from the measured half-life of $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ [5, 6] according to analysis with QRPA [28] from Table  ($CP$ parities ${\psi }_1={\psi }_2=0$ (left) and ${\psi }_1={\psi }_2=\pi$ (right)).

Figure 3

Calculated spectral-angular correlation for the neutrino mass term for $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ (left), and for the $⟨\lambda {⟩}^2$-term (right) (QRPA from 28).

Figure 4

Calculated spectral-angular distribution for the $⟨\eta {⟩}^2$-term for $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ (left), and for the values $⟨m_{\nu }⟩=0.503$ eV, $⟨\lambda ⟩=1.793·{10}^{-7}$, $⟨\eta ⟩=-2.495·{10}^{-9}$ (right). (QRPA from 28).

Figure 5

Calculated spectral-angular distribution for the parameters $⟨m_{\nu }⟩=0.33$ eV, $⟨\lambda ⟩=4.953·{10}^{-7}$, $⟨\eta ⟩=0$, for $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ (QRPA from 28).

Figure 6

Allowed parameters for $⟨m_{\nu }⟩$, $⟨\lambda ⟩$, $⟨\eta ⟩$ from the measured half-life of $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ [5] with matrix elements from the shell model from Table .

Figure 7

Calculated spectral-angular distribution for the neutrino mass term for $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ (left) and for the $⟨\lambda {⟩}^2$-term (right) (for matrix elements from SM [33]).

Figure 8

Calculated spectral-angular distribution for the $⟨\eta {⟩}^2$ -term for $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ (left) and for the parameter set $⟨m_{\nu }⟩=0.4224$ eV, $⟨\lambda ⟩=1.89·{10}^{-7}$, $⟨\eta ⟩=0.611·{10}^{-7}$ (right) (with matrix elements from shell model [33]).

Figure 9

Calculated spectral-angular distribution in $0\nu \beta \beta$-decay of ${}^{76}\mathrm{G}\mathrm{e}$ for $⟨m_{\nu }⟩=0.3554$ eV, $⟨\lambda ⟩=2.147·{10}^{-7}$, $⟨\eta ⟩=1.059·{10}^{-7}$ (matrix elements from shell model [33], see Table ).

Figure 10

Allowed parameters $⟨m_{\nu }⟩$, $⟨\lambda ⟩$, $⟨\eta ⟩$ from ${}^{76}\mathrm{G}\mathrm{e}$ $0\nu \beta \beta$ decay [5, 6] according to analysis with VAMPIR from Table .

Figure 11

Calculated spectral-angular distribution for $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$ and $⟨m_{\nu }⟩=0.3018$ eV, $⟨\lambda ⟩=1.208·{10}^{-7}$, $⟨\eta ⟩=-3.533·{10}^{-9}$, with the VAMPIR approaches.

Figure 12

The geometry of one of the five enriched Ge detectors of the HEIDELBERG-MOSCOW double-beta experiment (from 25).

Figure 13

Upper part: Typical calculated $0\nu \beta \beta$ decay event without photon emission (bremstrahlung) (left), and with photon emission (bremstrahlung) (right). Low part: Calculated photon event (the energy of the initial photon is 2614 keV) for the double-escape case (leading to a line in the detector at 1592 keV). For further explanation see text.

Figure 14

The calculated energy spectrum of $0\nu \beta \beta$ decay of ${}^{76}\mathrm{G}\mathrm{e}$, as seen in an enriched ${}^{76}\mathrm{G}\mathrm{e}$ detector. The sum of the energies of the emitted electrons is shown on the x-axis.

Figure 15

Simulation of the spectrum seen in the detector for the 2614 keV $\gamma$-transition: Upper part: the full spectrum (left) and the zoomed part for the 1500–2200 keV region (right). The middle and lower parts show in addition to the (red) full spectra also the (black) spectra consisting only of events with diameter $\le 2$ mm (for the linear and weighted sizes, respectively) (see Sec. 3d).

Figure 16

Simulation of the spectrum seen in the detector for the 2614 keV $\gamma$-transition: the full spectrum (left) and the zoomed part for the 1500–2200 keV region (right). The upper and lower parts show in addition to the (red) full spectra also the (black) spectra consisting only of events with diameter $\le 10$ mm (for the linear and weighted sizes, respectively) (see Sec. 3d).

Figure 17

Distribution of sizes (linear and weighted) in a Ge detector of various types of $0\nu \beta \beta$ events, and of the $\gamma$-line at 2614 keV, and its single and double-escape lines at 2103 keV and 1592 keV, respectively, and of the Compton events produced by this $\gamma$-transition in the range around $Q_{\beta \beta }$ (2035–2043 keV), according to Monte Carlo simulations of these events taking into account the angular correlations between the emitted electrons in $0\nu \beta \beta$ decay.

Figure 18

Calculated events sizes of $\beta \beta$ events (only mass term considered), and of $\gamma$-transitions 2614, 2204 and 1620 keV. For the first two in addition to the main line (full energy peak), also shown are the sizes of the double-escape (DE) and single escape (SE) peaks, and of Compton events in the range 2035–2043 keV.

Figure 19

Calculated event sizes of $0\nu \beta \beta$ events for the $⟨m_{\nu }⟩$, $⟨\eta ⟩$, $⟨\lambda ⟩$ parameter sets of Eq. (34) and for $⟨m_{\nu }⟩=0.33,⟨\lambda ⟩=4.95\times {10}^{-7},⟨\eta ⟩=0$.