Beta-decay measurements were key in establishing the universal vector (V)-axial-vector (A) nature of the electroweak interaction of the standard model (SM) [1,2]. Today, searches for physics beyond the SM (BSM) remain an important topic of theoretical and experimental research. It is expected that BSM physics, such as right-handed neutrinos or supersymmetry [3,4], could manifest as scalar (S), tensor (T), or pseudoscalar (P) currents. The strength of these currents is expressed through the coupling coefficients C i and C 0 i , where i can be S, T, A, V, or P, with the terms with primed coefficients being the paritynonconserving interaction [5]. The existence of exotic S and T currents can be probed in allowed nuclear β decays through their effect on β decay correlations [5,6], such as the β-ν angular correlation coefficient a βν and the BSM Fierz interference term b F . In addition, studies with mirror nuclear systems can provide further insights on the underlying β decay physics as several contributions to the decay rate-such as b F [5] and some of the SM recoil-order terms [7]-change signs for β -and β þ decays. This property of recoil-order terms has previously been taken advantage of to explore other symmetries of the SM [8], such as weak magnetism [9,10] and the existence of second-class currents [9,11,12].

Because of the difficulty in detecting the neutrino, the signature of a βν is determined from the recoil momentum imparted to the daughter nucleus from the emitted β and ν particles. The development of both atom [13,14] and ion traps [15,16] devoted to the study of nuclear beta decay has revolutionized the search for BSM physics due to their ability to directly measure the energy and momentum of the recoiling daughter nucleus [17][18][19][20][21][22]. Traps are an ideal apparatus for these precision studies as the trapped nuclides are held nearly at rest in a well-localized volume from which the decay products can emerge nearly free from scattering. An additional benefit of ion traps is their ability to trap any element; this was crucial here, allowing the study of mirror decays in detail.

In this Letter, we have employed the Beta-decay Paul Trap (BPT) [15] to perform a measurement of a βν in the Gamow-Teller (GT) decay of 8 B to investigate the possible existence of tensor-current contributions to the electroweak interaction. This Letter builds upon our work in 8 Li [20][21][22] and represents the first time that a βν has been measured in both nuclei of a mirror-system pair. By studying both members of the mirror-system pair, we have extended our results using the ãβν prescription [23,24] and demonstrate improved limits on the combined C T and C 0 T space. In both 8 Li and 8 B, the decay proceeds from a J 8 Be. Green's function Monte Carlo ab initio calculations limit the potential admixture with a Fermi decay to be ≲0.001 [25], which is below the sensitivity of this work. The 8 Be à immediately breaks up into two α particles, which then differ in energy in the laboratory frame due to the momentum imparted by the emitted leptons.

A detailed measurement of the kinematic shift between the two β-delayed fragments can be used to determine a βν [26]. The light mass of 8 B and the large Q value results in a maximum kinematic shift between the two α particles of ∼450 keV in the laboratory frame. To leading order, the decay rate for β-delayed α emission from a nonoriented nucleus is given as [7,27]

where the upper (lower) sign corresponds to β -(β þ ) emission, FðAEZ; E e Þ is the Fermi function, ðE e ; p e Þ and ðE ν ; p ν Þ are the four-vectors of the β and ν, respectively, E 0 is the decay end-point energy, m e is the electron mass, pα is the direction of the emitted α particle, τ J 0 ;J 00 ðLÞ is a coefficient that depends on the spin sequence J → J 0 → J 00 of the decay, L is the angular momentum of the α relative to the daughter, and

with α FS being the fine structure constant. For a pure GT decay, the spectral functions g i and b F are dominated by the strength of the A and T currents with small, but important, corrections that arise from recoil-order form factors. In terms of the coupling constants C T and C 0 T , and assuming C A ¼ C 0 A , a βν and b F for GT decays are defined as [5]

In this analysis, we first assume a right-handed tensor coupling C T ¼ -C 0 T and later lift this restriction. For these

, the effective β-ν angular correlation is enhanced, giving, to leading order,

effectively tripling the β-ν angular correlation. Conversely, perpendicular emission ( pe • pα ¼ 0) effectively suppresses the β-ν angular correlation. The 8 B was produced though the two-proton transfer reaction 6 Lið 3 He; nÞ 8 B at the Argonne Tandem-Linac Accelerator System (ATLAS). A 41-MeV beam of 6 Li traversed a cryogenic 3 He gas target and the reaction products were focused by a large solenoid into a gas catcher. Most of the produced 8 B reacted with residual contaminants in the gas catcher and was incorporated into a variety of molecules. This resulted in the activity being spread over many mass units. The peak in 8 B activity was located near A ¼ 42 with the most likely molecular ion candidate being

As the lifetime of 8 Be à is τ ≈ 10 -22 s, the betadelayed, MeV-energy α particles are emitted before the molecular potential can influence the 8 Be recoil momentum. Further molecular effects, such as those discussed in Ref. [28], are also negligible. Further details of the production and subsequent stopping, preparation, and injection of the reaction products into the BPT can be found in Refs. [20,29].

The larger mass of the A ¼ 42 ions required a retune of the trapping parameters relative to previous measurements that trapped 8 Li [20,21]. In order to maximize the trapped 8 B population, the axial trapping potential was set slightly shallower than in the previous 8 Li measurement, while the radial trapping was provided by a quadrupolar radio frequency (rf) field with V rf ≈ 800V pp and a frequency of 605 kHz. The ions are thermalized by a high-purity helium buffer gas at a pressure of ∼10 -5 Torr. The thermalization process is enhanced by circulating liquid nitrogen through the trapping structure, cooling the trap surfaces and He gas to ∼90 K. Surrounding the trapping region are four 64 × 64 × 1 mm 3 double-sided silicon strip detectors (DSSDs), with the front and back sides each being segmented into 32 strips. A schematic drawing of the trapping region is shown in Fig. 1. The 1-mm-thick DSSDs allow for both α and β particles to be identified by their energy deposition within a single detector pixel. The β particles typically deposit ∼300 keV, although there is a high-energy tail that extends into the region of the α spectrum above ∼500 keV. Energy summing between particles is eliminated by requiring distinct pixels for each detected α and β.

Electronic noise, largely arising from rf pickup and dead or damaged strips, led to a large number of strips that had to be excluded from the final analysis. To further reduce noise and the effects of incomplete charge collection, the outmost strips from each detector were excluded from the analysis. This led to the inclusion of 55 front and 57 back strips, or of 128 strips, from the top and bottom detectors, and 30 front and 57 back strips, or 87 of 128 strips, from the left and right detectors in the final analysis.

An average population of ≈5 8 B ions was maintained in the BPT during the 6.5 days of data collection, resulting in a total of 6.6 × 10 5 "double" events and 1.5 × 10 5 "triple" events, prior to any data cuts. A double event corresponds to opposite facing DSSDs both detecting particles with energies > 740 keV, while a triple event requires the additional detection of a particle with a deposited energy between 200 and 700 keV. Triple events were selected only if (i) more than 35 ms had passed since the last trap closing to allow the ion cloud to thermalize, (ii) two α particles were detected with energies between 740 and 5000 keV and a single β with an energy deposition between 200 and 700 keV, and (iii) the energy difference between the front and back strips was within 45 keV. Radio frequency pickup by the detectors caused clipping in the preamplifier for the highest energy α particles, leading to distortions in the detector response. Minimizing these distortions required placing an upper limit on the detected energy of 5000 keV. The front-back energy cut removes events with incomplete charge collection due to particles hitting the interstrip gap. To account for time-dependent drifts in gain and noise, the data were split into ten segments of ≈15 h each.

To fit the data, a comprehensive Monte Carlo simulation suite was developed to simulate the decay kinematics, including the effects from the recoil-order terms [7], electromagnetic corrections [30], induced Coulomb corrections [31], and order-α radiative corrections [32] modified for β-delayed α emission [33]. We use the values of the recoil-order terms from Ref. [10], the Fermi function formulation of Ref. [34] modified for a root-mean-square radius of 2.43 AE 0.24 fm [35], and the excitation energy spectrum of 8 Be à following 8 B β decay from Ref. [36]. A detailed Autodesk Inventor model of the BPT was developed and exported to a GDML format for use in Geant4. The generated β particles were then passed through Geant4 [37] using the standard electromagnetic physics list "option3," which reproduces the triple events to double events ratio, the backscattered β fractions, and the energy spectrum of the minimum-ionizing β particles in the DSSDs.

Simulated spectra for the α energy differences are then generated for pure axial-vector and pure tensor decays for comparison to the experimental data. A linear combination of these simulated spectra are fit to the experimental data, with the ratio of the couplings jC T =C A j 2 and a normalization constant being the only free parameters. The combined fit of all the detector pairs is shown in Fig. 2 and yields a value of jC T =C A j 2 ¼ -0.0047 AE 0.0059.

Many of the systematics affecting our result have been discussed previously [21], and only systematics that have significantly changed for this analysis will be discussed below. All systematic effects for the α energy difference fits at 1σ are listed in Table I.

TABLE I. Dominant sources of systematic uncertainty at 1σ. Source ΔjC T =C A j 2 Energy calibration 0.0013 α line shape 0.0007 Dead layer thickness 0.0005 Ion-cloud size 0.0005 β scattering 0.0010 Backgrounds 0.0011 Recoil and radiative 0.0048 Nondominant systematics 0.0007 Total 0.0054 FIG. 2. Energy difference spectrum along with the fit, shown in black, to the simulated spectrum and normalized residuals. Shown in blue is the expected result for a pure tensor interaction.

The number of events N, the fitted jC T =C A j 2 , and the fit χ 2 per number of degrees of freedom are also shown. FIG. 1. Cross-sectional view of the BPT and detector system in the rf plane. The directions of the α and β particles are determined by the vectors between the trap center and detector pixels.

Energy calibration and α detector response.-A precision pulser was used to monitor the detector system linearity, and a continuous in situ energy calibration was performed using 148 Gd and 244 Cm sources that emit α particles at 3182.690 (24) and 5804.77 (5) keV, respectively [38,39]. The largest calibration uncertainty arises from the thick in situ calibration sources. These sources were used in [21], and, as in that work, we find that the uncertainty in energy calibration leads to a systematic uncertainty on jC T =C A j 2 of 0.0013. Charge-collection-dependent effects, such as the detector dead layer, nonionizing energy loss, and pulse height defect were included following Ref. [40]. A high-precision α-energy-response function was developed using data from spectroscopy-grade α sources and accounts for the various detector dead layers and charge sharing between the front and back strips that occurs after an interstrip-gap hit event. Varying the widths of the Gaussian-distributed Fano and electronic noise components of the α-response function lead to an uncertainty on jC T =C A j 2 of 0.0007, while varying the detector dead layers and nonionizing energy loss lead to an uncertainty on jC T =C A j 2 of 0.0005.

Ion cloud.-Tuning the trapping electrodes to maximize the number of trappedfoot_0 B resulted in a prolate ion cloud. Using the nearly back-to-back α-α coincidences to image the ion cloud [15], the extent of the ion cloud was measured to have full width half maximums of 3.53 mm radially and 6.40 mm axially. We conservatively assume an ion-cloud size uncertainty of AE10%, which encompasses both the statistical and systematic uncertainties resulting mainly from missing strips, yielding a systematic uncertainty on jC T =C A j 2 of 0.0005.

Beta scattering.-In approximately 20% of detected triple events, the β particle scattered prior to reaching a detector. In the energy region of this Letter, the accuracy of the physics models in Geant4 have been extensively tested [41]. Based on this and the results from comparing both the ratio of double to triple events and the fraction of backscattered β events to simulation (see Refs. [21,22]), we estimate the error on β scattering to be 5% and vary the number of scattered events by this amount. This results in a systematic uncertainty on jC T =C A j 2 of 0.0010.

Recoil and radiative corrections.-Both the ≈1-MeV increase in Q value and the change of sign of some recoilorder form factors between β þ and β -decay lead to larger recoil corrections in the decay of 8 B relative to the decay of 8 Li. The values of the recoil-order terms are from the fitted results of Ref. [10], as the large excitation energy coverage E x ≈ ½1.480; 10 MeV necessitates the use of energy averaged recoil-order terms. The state specific calculations for 8 Li of Ref. [42] and used in Ref. [22] are not yet available for 8 B. The combined correction of d (induced tensor) and b WM (weak magnetism) give rise to an uncertainty on jC T =C A j 2 of 0.0028. The largest corrections arise from the large uncertainties associated with the second-forbidden j 2 and j 3 terms, leading to a combined uncertainty of 0.0038. The Z-independent radiative corrections, including the effects from bremsstrahlung emission in the final state [32], lead to an uncertainty on jC T =C A j 2 of 0.0006. The combined uncertainty from the recoil-order and radiative corrections is 0.0048.

Adding the systematic uncertainties in quadrature yields a tensor fraction of jC T =C A j 2 ¼ -0.0047 AE 0.0059 stat AE 0.0054 syst : ð4Þ A Bayesian analysis with a uniform prior for jC T =C A j 2 > 0 leads to a limit at the 95.5% confidence level of jC T =C A j 2 < 0.013 or jC T =C A j < 0.114. Expressing this in terms of the β-ν angular correlation coefficient results in a βν ¼ -0.3365 AE 0.0039 stat AE 0.0035 syst , or ðg 2 þð2=3Þg 12 Þ=g 1 ¼ -1.009 AE 0.012 stat AE 0.011 syst , and are in agreement with the SM predictions of -1=3 and -1, respectively. This result is in agreement with our previous results in 8 Li of a βν ¼ -0.3342 AE 0.0026 stat AE 0.0029 syst [21] and a βν ¼ -0.3325 AE 0.0013 stat AE 0.0019 syst [22].

In general, it is possible to reinterpret correlation term measurements made under the assumption that b F ¼ 0 (i.e., C T ¼ -C 0 T ) to include the effect of the Fierz term through the transformation [23,24]

where the upper (lower) sign corresponds to β -(β þ ) emission, hm e =E e i is the weighted average of E -1 e over the β energy spectrum, and in the present experiment was calculated to be 0.0976.

Applying this prescription to our measured a βν values for A ¼ 8, it is possible to construct the probability distributions in ðC T ; C 0 T Þ space, as shown in Fig. 3. The change in sign of b F between 8 Li and 8 B results in the centers of the ãβν distributions in opposite quadrants in ðC T ; C 0 T Þ space, providing much stronger constraints along C T ¼ C 0 T than one would expect from naively combining measurements. Although the present result for 8 B is of lower precision than the combined results for 8 Li [21,22], the joint probability distribution for ãβν reduces the allowed region by nearly a factor of 2. The high-precision measurement of both mirror systems was only possible through the use of ion traps.

In summary, we have performed the first measurement of the β-ν angular correlation coefficient in the β þ Gamow-Teller decay of 8 B, and the results are in good agreement with the standard model. The largest systematic arises from uncertainties in the recoil-order form factors. The uncertainties can be reduced with future values for 8 B with the symmetry-adapted no-core shell model, which has shown great success in the case of 8 Li [22,42]. A future joint analysis of higher statistics measurements of 8 Li and 8 B can be used to further constrain the values of these recoil-order form factors. We have demonstrated a new pathway for increasing the precision of tensor-current searches by employing the ãβν prescription to our results, which is the first time β decay angular correlations have been precisely studied in a mirrornucleus pair. With a measurement of 8 B at a level comparable to Ref. [22], the allowed area in Fig. 3 can further be reduced by nearly 40%.