Tensor interaction constraints from $\beta$-decay recoil spin asymmetry of trapped atoms

We have measured the angular distribution of recoiling daughter nuclei emitted from the Gamow-Teller $\beta$ decay of spin-polarized ${}^{80}\mathrm{Rb}$. The asymmetry of this distribution vanishes to lowest order in the standard model (SM) in pure Gamow-Teller decays, producing an observable very sensitive to new interactions. We measure the non-SM contribution to the asymmetry to be $A_T=0.015\pm 0.029$ (stat) ±0.019 (syst), consistent with the SM prediction. We constrain higher-order SM corrections using the measured momentum dependence of the asymmetry, and their remaining uncertainty dominates the systematic error. Future progress in determining the weak magnetism term theoretically or experimentally would reduce the final errors. We describe the resulting constraints on fundamental four-Fermi tensor interactions.

Figure 1

The ${\beta }^{+}$-decay scheme for ${}^{80}\mathrm{Rb}$, showing literature values of the spin, parity, branching ratio, l${\mathrm{og}}_{10}$(ft), and excitation energy of the final levels in ${}^{80}\mathrm{Kr}$, along with the $Q$ value (maximum kinetic energy) for ${\beta }^{+}$ decay and the parent half-life. Energies in keV.

Figure 2

TRINAT detection apparatus. The MCP for ion detection has position-sensitive resitive anode readout. Given the known uniform electric field, measurement of the recoil ion TOF and impact position determines the initial momentum. The apparatus is similar to that of Ref. [22], with an MCP for electron detection added for the ${}^{80}\mathrm{Rb}$ decay asymmetry. The ${}^{80}\mathrm{Rb}$ is spin-polarized by optical pumping with light resonant to the $D1$ transition from a 50 mW diode laser. The polarization is monitored with $\beta \Delta E-E$ phoswiches using plastic/C${\mathrm{aF}}_2$(Eu) fast/slow scintillators (which are at $\text{−}{30}^{°}$ and ${150}^{°}$ out of the plane shown here).

Figure 3

Energy diagram of the atomic levels for optical pumping of the Rb atom, along with the photoionization scheme for position determination. The atomic hyperfine structure is not to scale. The frequency splittings were taken from Ref. [26].

Figure 4

(a) Time-of-flight (TOF) spectra for recoil coincidences with shakeoff atomic electrons, showing decomposition into ${\beta }^{+}$ decay and backgrounds. The small electron capture (EC) branch produces large corrections for the higher charge states and is modeled here assuming charge-state distributions from x-ray photoionization [29]. A background of order 1% from ${\beta }^{+}$'s striking the electron detector is determined by biasing the detector to exclude low-energy electrons (see text). The simulation for charge state $+$3 is highlighted; the TOF for $+$3 was cut above $0.63\hspace{0.5em}\mu$s to help exclude EC events. (b) Expanded TOF scale of the top figure, showing the charge states 9, 10, and 11 that are dominated by EC and used for polarization determination (Section 2d).

Figure 5

Nuclear polarization determined from the $\beta$ asymmetry in coincidence with Kr recoils charge states 4–9 in the C${\mathrm{aF}}_2$(Eu) detectors.

Figure 6

Nuclear polarization determined from recoils from electron capture (EC) decay (see text), which has a large spin asymmetry. (a) Counts as a function of $\cos \theta$ for opposite signs of polarization. (b) The resulting asymmetry of events from (a); the line is a fit with $P{A}_{\mathrm{EC}}=0.29\pm 0.02$ (see text).

Figure 7

An example of the recoil asymmetry fit as a function of angle, with angle reconstructed from the impact location and the ion TOF. Here the asymmetry is for the charge state 2 data, summed over all recoil momentum.

Figure 8

The dependence on recoil momentum of the experimental recoil asymmetries $A_1$. Charge states 1, 2, and 3 are shown to be in statistical agreement. (The points for charge states 1 and 3 are offset horizontally for clarity.)

Figure 9

$A_1$ as a function of recoil momentum, determined with no correction for $\beta$'s and after the correction for ${\beta }^{+}$'s described in Sec. 2c. The correction is small. Lines are drawn only to direct the eye.

Figure 10

Exclusion plot at 90% confidence showing complementarity of the present constraints to other measurements. Allowed regions are inside: ${}^6\mathrm{He}$ $\beta \text{−}\nu$ [5, 6], red concentric circles (hashed in between); ${\beta }^{+}$ polarization in ${}^{14}\mathrm{O}$, ${}^{10}\mathrm{C}$ [7] (assuming no scalar interaction), blue solid vertical lines (hashed in between); present work, letting $b_M$, $d$, and both $A_T$ and $b_T$ float, black dashed hyperbolae. For $b_T$ set to 0 (consistent with Ref. [7]), weak magnetism $b_M/({\mathit{AM}}_{\mathrm{GT}})=4.7\pm 4.7$, and $d$ left floating, then the green rectangular area indicates the present limit $|(C_T-C_T^{\text{'}})/C_A|<0.36$.

Figure 11

The dependence on recoil momentum of the recoil asymmetries for the best fit with $b_M$, $d$ and both chiralities of tensor floating. $\sqrt{{\chi }^2/N}=1.37$ for this fit. The cyan medium-dash line “r.o.” is a small exact recoil-order correction given when recoil energy is included in the energy conservation equation.

Figure 12

The dependence on recoil momentum of the recoil asymmetries for the best fit with $C_T+C_T^{\text{'}}=0$ (i.e., assuming the result of Ref. [7]) and $b_M$, $d$ and $C_T-C_T^{\text{'}}$ floating. The fit has $\sqrt{{\chi }^2/N}=1.41$, and the result is $|(C_T-C_T^{\text{'}})/C_A|=0.{42}_{-0.32}^{+0.15}$ at 90% confidence.

Figure 13

The dependence on recoil momentum of the recoil asymmetries for the best fit with $C_T+C_T^{\text{'}}=0$ (i.e., assuming the result of Ref. [7]), but $b_M/({\mathit{AM}}_{\mathrm{GT}})=4.7\pm 4.7$, with $d$ and $C_T-C_T^{\text{'}}$ floating. The result is $A_T=0.015\pm 0.029\pm 0.019$ (see text).