Measurement of the $\beta$-asymmetry parameter of ${}^{67}\mathrm{Cu}$ in search for tensor-type currents in the weak interaction

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general $\beta$-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear $\beta$ decay are on the level of several percent.

Purpose: Extracting new information on tensor coupling constants by measuring the $\beta$-asymmetry parameter in the pure Gamow-Teller decay of ${}^{67}\mathrm{Cu}$, thereby testing the V-A structure of the weak interaction.

Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a ${}^3\mathrm{He}{\text{−}}^4\mathrm{He}$ dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic $\beta$ radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the $\beta$ asymmetry of ${}^{68}\mathrm{Cu}$ was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations.

Results: The experimental value, $\tilde{A}=0.587\left(14\right)$, is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are $-0.045<(C_T+C_T^{\prime })/C_A<0.159$ (90% C.L.).

Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear $\beta$ decay and contribute to further constraining tensor coupling constants.

Figure 1

Simplified decay scheme of ${}^{67}\mathrm{Cu}$ and ${}^{67}\mathrm{Ga}$. For ${}^{67}\mathrm{Cu}$ the $\beta$ intensities and end-point energies ($E_0$) are shown, while for ${}^{67}\mathrm{Ga}$ the EC transition intensities are indicated. The accompanying $\gamma$ rays in ${}^{67}\mathrm{Zn}$ are also shown.

Figure 2

Simplified decay scheme of ${}^{68}\mathrm{Cu}$ and ${}^{68}\mathrm{Ga}$ with $\beta$ branch intensities, $\beta$-end-point energies ($E_0$), and accompanying $\gamma$ rays being shown. For clarity, two weak branches in the decay of ${}^{68}\mathrm{Cu}$ (with total intensity of 5%) decaying to levels in ${}^{68}\mathrm{Zn}$ between the two higher-lying ones, as well as other, low-end-point branches, are not shown.

Figure 3

Schematic view of the NICOLE LTNO setup, located at ISOLDE, CERN. The sample foil is soldered to the sample holder, which is in direct thermal contact with the dilution unit. The incoming radioactive beam from ISOLDE is perpendicular to the sample foil. The right (left) particle detector is directly facing the sample foil containing the implanted nuclei at an angle of ${15}^{\circ }$ (${165}^{\circ }$).

Figure 4

The $\beta$ spectrum of ${}^{67}\mathrm{Cu}$ as observed by the left particle detector. The very weak $\gamma$ line at 692.4 keV is from the ${}^{57}\mathrm{Co}$ thermometer, while the large peak at the end of the spectrum is the pulser peak.

Figure 5

The $\beta$ spectrum of ${}^{68}\mathrm{Cu}$ as observed by the right particle detector. The 511-keV annihilation peak is from the ${\beta }^{+}$ decay of ${}^{68}\mathrm{Ga}$. Above the high-energy end of the spectrum the pulser peak is visible.

Figure 6

Anisotropy of the 136-keV $\gamma$ line of the ${}^{57}\mathrm{Co}$ thermometer [count rate normalized to isotropic “warm” data, Eq. (7)] during the ${}^{67}\mathrm{Cu}$ measurement, showing the six “cold” and three “warm” data sets. Every data point represents a measurement time of 300 s.

Figure 7

Difference between the experimental and simulated isotropic spectrum of ${}^{67}\mathrm{Cu}$ (left detector), normalized to the experimental spectrum. The region of interest is between 470 and 560 keV, where ${\chi }_{\text{red}}^2=1.24$ for 91 degrees of freedom.

Figure 8

Fit of the fraction $f$ to the double ratio $R$ [Eq. (8)] determined at different temperatures, for the energy range of 3600–3700 keV. The fit resulted in $f=1.002\left(4\right)$ with ${\chi }_{\text{red}}^2=1.1$ for 4 degrees of freedom. The fit function is not continuous because of the different values of $\tilde{Q}$ at different temperature points.

Figure 9

Results of the fit of the fraction $\tilde{f}$ to the experimental double ratio $R$ in the different energy regions. The weighted average for the total region from 3400 to 4000 keV is 1.0003(26), which is indicated by the dashed line and the gray band.

Figure 10

Ratio $\tilde{A}/A_{\mathrm{SM}}$ as a function of energy in 20-keV-wide energy bins for the different sample temperatures. Weighted averages are shown as horizontal lines (with the gray bands indicating the $1\sigma$ error bar) in the regions from 410 to 470 keV and from 470 to 510 keV. The energy region between 410 and 470 keV also contains events from the second most energetic $\beta$ branch in the decay of ${}^{67}\mathrm{Cu}$ (see Fig. 1 and Table 2). No temperature or time-dependent effects are observed (the temperature points are ordered chronologically).

Figure 11

Limits (90% C.L.) on time-reversal invariant tensor-type coupling constants $C_T$ and $C_T^{\prime }$ normalized to the axial-vector coupling constant $C_A$. The result of this work is shown together with results from other experiments in nuclear $\beta$ decay: the $a_{\beta \nu }$ measurement of ${}^6\mathrm{He}$ [61, 62], the $\alpha \text{−}\beta \text{−}\nu$ correlation of ${}^8\mathrm{Li}$ [18], the longitudinal positron polarization in the decays of ${}^{14}\mathrm{O}$ and ${}^{10}\mathrm{C}$ ($P_F/P_{\mathrm{GT}}$) [63], and the $\tilde{A}$ measurement of ${}^{60}\mathrm{Co}$ [16].