Tests of the standard electroweak model in nuclear beta decay

The current status of precision measurements in allowed nuclear beta decay is reviewed, including neutron decay, with emphasis on their potential to look for new physics beyond the standard electroweak model. Experimental results are interpreted in the framework of phenomenological model-independent descriptions of nuclear beta decay as well as in some specific extensions of the standard model. The values of the standard couplings and the constraints on the exotic couplings of the general beta decay Hamiltonian are updated. The ratio between the axial and vector couplings obtained is $C_A∕C_V=-1.26992\left(69\right)$ under standard model assumptions. Particular attention is devoted to the discussion of the sensitivity and complementarity of different precision experiments in direct beta decay. The prospects and impact of recent developments of precision tools and of high intensity low-energy beams are also addressed.

Figure 1

The $\beta$ decay at the quark-lepton level, mediated by the exchange of a weak boson.

Figure 2

Contact interaction of four fermions. The hadronic and leptonic currents interact at a single point.

Figure 3

Leptoquark exchanges contributing to nuclear $\beta$ decay. Top: $\mid Q\mid =1∕3$ leptoquarks; bottom: $\mid Q\mid =2∕3$ leptoquarks.

Figure 4

Contours of constant ${\chi }^2$ around the two minima obtained for the fit case 3. The lines correspond to $1\sigma$, $2\sigma$, and $3\sigma$ confidence levels.

Figure 5

Projections of contours of constant ${\chi }^2$ on the plane of parameters $C_S∕C_V$ and $C_T∕C_A$ for the fit case 4.

Figure 6

Projections of contours of constant ${\chi }^2$ on the plane of parameters $C_A∕C_V$ and $C_S∕C_V$ for the fit case 4.

Figure 7

Projections of contours of constant ${\chi }^2$ on the plane of parameters $C_A∕C_V$ and $C_T∕C_A$ for the fit case 4.

Figure 8

Projections of contours of constant ${\chi }^2$ for the combination of parameters $(C_S-C_S^{\prime })∕C_V$ and $(C_S+C_S^{\prime })∕C_V$.

Figure 9

Projections of contours of constant ${\chi }^2$ for the combination of parameters $(C_T-C_T^{\prime })∕C_A$ and $(C_T+C_T^{\prime })∕C_A$.

Figure 10

$\mathcal{F}t$ values for superallowed $0^{+}\to 0^{+}$ transitions. The shaded band is the $1\sigma$ result from the best least-squares one-parameter fit. From 155.

Figure 11

Input data for the world average value of $\lambda$ from measurements in neutron decay (see also Table ). The most precise results are from measurements of the $\beta$ asymmetry parameter $A$ [1, 55; 2, 326; 3, 206; 4, 7; 6, 6]. Data points 7 [289] and 8 [61] refer to measurements of the $\beta \text{−}\nu$ correlation coefficient $a$ and data point 5 [227)] is from a simultaneous measurement of the $\beta$ and $\nu$ asymmetry parameters $A$ and $B$. The band indicates the weighted average adopted by the Particle Data Group (102).

Figure 12

Input data for the world average value of ${\tau }_n$ (see also Table ). 1, 284; 2, 213; 3, 232; 4, 214; 5, 60; 6, 24; 7, 97; and 8, 266. The upper band shows the weighted average of the first seven values and the lower band the weighted average of all values.

Figure 13

Values for $\mid V_{ud}\mid$ obtained from the average $\mathcal{F}t$ value for $0^{+}\to 0^{+}$ superallowed Fermi $\beta$ decays (156), from neutron decay (see text), and from pion $\beta$ decay (244).

Figure 14

Values for $\mid V_{us}\mid$ from the Particle Data Group analysis [1, 102] and from recent results in $K$ decays [2, 275; 3, 16; 4, 202; 5, 21; 6, preliminary result from KLOE, 121]. The shaded band indicates the weighted average of the published new results from $K$ decays (measurements 2–5). See also Table .

Figure 15

Schematic drawing of the NIST Penning trap neutron lifetime experiment. Details are given in the text. From 97.

Figure 16

(Color online) Schematic view of the PERKEO-II spectrometer. The neutron beam passes through the apparatus. Electrons from neutron decays in the center of the chamber are focused by a strong magnetic field on two scintillator detectors. Adapted from 250.

Figure 17

Schematic of the proposed setup to measure the spin-proton asymmetry coefficient $C$ at NIST. Details are given in the text [see also 151]. From 96.

Figure 18

Schematic of the aspect spectrometer. Details are given in the text. From 335.

Figure 19

Top: Shapes of the $\beta$ delayed proton group from ${}^{32}\mathrm{Ar}$ $0^{+}\to 0^{+}$ decay for $a=+1$, $b=0$ (pure $V$ interaction; flat curve) and $a=-1$, $b=0$ (pure $S$ interaction; “Gaussian-like” curve). Bottom: Fit (upper panel) and residuals (lower panel) of the proton peak $(0.500\mathrm{keV}∕\text{channel})$. The narrow pulser peak in the upper panel shows the electronic resolution. From 9.

Figure 20

(Color online) Top: Top view of the TRINAT two-MOT apparatus. The ion beam is implanted in a neutralizer Zr foil in the trap at the left. Atoms that leave the foil after heating are trapped with six laser beams in three mutually perpendicular directions. At regular intervals the trapped atom cloud is transferred to the measurement trap at the right where decay $\beta$ particles and recoil ions are observed. The second MOT chamber is $15\mathrm{cm}$ in diameter. Bottom: Time-of-flight of Ar recoils from ${}^{38}\mathrm{K}^m$ decay. Ar charge states are separated by a $800\mathrm{V}∕\mathrm{cm}$ electric field. From 144, 145.

Figure 21

(Color online) Schematic layout of the LPC Caen transparent Paul trap setup with the beta and recoil detectors, and the ion cloud monitor. The system is mounted on the low-energy beam line of the SPIRAL facility at GANIL (see text for details).

Figure 22

Spectrometer section of the WITCH setup. Details are given in the text. From 36.

Figure 23

Results of the early $\beta -\nu$ correlation measurements of 17 for ${}^{23}\mathrm{Ne}$ and ${}^{35}\mathrm{Ar}$, compared to more recent measurements. Only results with a precision better than 10% are included while, in addition, for a given isotope only the most precise result is shown. The $3\sigma$ deviation from the standard model for ${}^{21}\mathrm{Na}$ could be caused by a systematic dependence of the result on the ion-trap population, or by a problem with the value of the branching ratio that was used to calculate the $ft$ value (263) (see text). [${}^6\mathrm{He}$, 186; ${}^{18}\mathrm{Ne}$, 100; ${}^{23}\mathrm{Ne}$, 17; $n$, 289 and 61; ${}^{21}\mathrm{Na}$, 263; ${}^{35}\mathrm{Ar}$, 17; ${}^{32}\mathrm{Ar}$, 9; ${}^{38}\mathrm{K}^m$, 145.]

Figure 24

Results of the $\beta$ asymmetry parameter measurements for mixed transitions of the $T=1∕2$ mirror nuclei. For the neutron the weighted average value (102) is shown. The standard model values were calculated from the experimental $ft$ values (231). Note that the second result for ${}^{19}\mathrm{Ne}$ (260) was never published. More details can be found in Table . [1, 102; 2, 271; 3, 66; 4, 260; 5, 217; 6, 137; 7, 83.]

Figure 25

Experimental setup to measure the longitudinal polarization of positrons emitted in the decay of polarized ${}^{107}\mathrm{In}$ nuclei. Radioactive ions delivered by the isotope separator are implanted and oriented in an iron foil at a temperature of $10\mathrm{mK}$ inside a dilution refrigerator. Positrons emitted in the decay of the polarized nuclei are energy selected with a spectrometer and then slowed down and stopped in a MgO pellet. One plastic and two $\mathrm{Ba}{\mathrm{F}}_2$ scintillator detectors observe the decay of the positronium that is formed in the MgO, from which the longitudinal polarization of positrons is then obtained. From 272.

Figure 26

Constraints (90% C.L.) on the right-handed current parameters $\delta$ and $\zeta$ from the nuclear $\beta$ decay experiments discussed. The allowed regions are those containing $(\delta ,\zeta )=(0,0)$. The narrow vertical band around $\zeta =0$ is the region allowed by unitarity and the $\mathcal{F}t$ value for superallowed Fermi transitions (Sec. 4C1). Adapted from 291.

Figure 27

Experimental apparatus for measuring the $B$ parameter in neutron decay. (1) Electron detector, (2) proton detector, (3) vacuum chamber, (4) decay region, (5) cylindrical electrode, (6) time-of-flight chamber, (7) spherical electrode, (8) spherical grid, and (9) LiF diaphragm. From 201.

Figure 28

Exclusion plots on parameters of generalized left-right symmetric extensions of the standard model. The parameter ${\kappa }_{RL}=g_R∕g_L$ characterizes the intrinsic gauge coupling of the right-handed sector relative to the left-handed one, while ${\lambda }_{RL}=\mid V_{ud}^R\mid ∕\mid V_{ud}^L\mid$ denotes the relative coupling strength of first generation quarks to a hypothetical right-handed gauge boson with mass $M\left(W_R\right)$. The hatched areas are excluded either by direct searches at colliders (PDG2002) or by precision experiments in nuclear $\beta$ decay. The horizontal bands in the left panel are bounds from theory. The contours in the left panel assume $\mid V_{ud}^R\mid =\mid V_{ud}^L\mid$; those in the right panel assume $g_R=g_L$. Adapted from 291.

Figure 29

(Color online) Principle of the emiT experiment to test time-reversal violation using an octagonal array of four each proton $\left(P\right)$ and electron $\left(E\right)$ detectors. Adapted from 208.

Figure 30

Vertical cross section through the Mott polarimeter used in the ${}^8\mathrm{Li}$ $R$-correlation experiment. The direction of incidence of the polarized deuteron beam is perpendicular to the figure. The central arrow indicates the direction of the ${}^8\mathrm{Li}$ spin in the target. A trajectory of an electron scattered on the lead analyzer foil is also shown. The labels $\delta$, $\Delta$, and $E$ refer to two delta-$E$ detectors and energy detector. Details are given in the text. From 173.

Figure 31

(Color online) Principle of the $R$-correlation experiment in neutron decay determining the amplitude of $\mathbf{\sigma }\bullet (\mathbf{J}\times {\mathbf{p}}_e)$. The labels $E$ and $V$ refer to the energy detector and veto detector. Details are given in the text. Adapted from 50.

Figure 32

(Color online) Results of measurements of $m_{{\overline{\nu }}_e}^2$ from tritium $\beta$ decay experiments since 1990. From 218.

Figure 33

Schematic drawing of the MAC-E filter used at Mainz for tritium $\beta$ spectroscopy. From 53.