A look into mirrors: A measurement of the β -asymmetry in 19 Ne decay and searches for new physics
Dustin Combs, Gordon Jones, William Anderson, Frank Calaprice, Leendert Hayen, Albert Young
AA look into mirrors: A measurement of the β -asymmetry in Ne decay and searches for newphysics
Dustin Combs , , Gordon Jones , William Anderson ,Frank Calaprice , Leendert Hayen , , Albert Young , Department of Physics,North Carolina State University Raleigh, NC 27695, USA Triangle Universities Nuclear Laboratory Durham, NC 27708, USA Department of Physics, Hamilton College Clinton, NY , USA Johns Hopkins University, School of Medicine Baltimore, MD, USA Department of Physics, Princeton University Princeton, NJ, USAHigh precision measurements of isospin T = 1 / decays in the neutron and nuclei providestrong model-independent constraints on extensions to the standard model of particle physics.A measurement of the β -asymmetry in Ne decay between the initial nuclear spin and thedirection of the emitted positron is presented which determined the zero intercept of the asym-metry parameter to be A = − . / − sys (26) stat . This result establishes Ne asthe most precisely characterized nuclear mirror and fixes the Fermi-to-Gamow-Teller mixingratio to ρ = 1 . / − sys (8) stat . The mixing ratio presented here is consistent withthe previous, most precise measurement ( ), produces a value of the CKM unitarity parameter V ud in agreement with the nuclear mirror, neutron and superallowed β -decay data sets, showsno evidence for second class currents, and can be effectively used with neutron decay data toplace a limits on exotic tensor couplings. 1 a r X i v : . [ nu c l - e x ] N ov ntroduction Beta decay measurements provide precise and useful information concerning the weak interac-tions of quarks. For these decays, the standard model (SM) of particle physics predicts vector(V) and axial-vector (A) couplings with a maximal parity violating, V-A Lorentz structure. Wepresent a measurement (which is sensitive to this helicity structure) of the angular correlationbetween the initial nuclear spin and the positron momentum, or β -asymmetry, in the isobaricanalog decay of Ne to F. The results reinforce the usefulness of nuclear mirrors for be-yond standard model (BSM) constraints, substantiate the current consistency of the data setfor nuclear mirrors with the SM, address previous evidence for second class currents in Nedecays, provide constraints (when taken together with neutron decay data) on tensor couplingsand highlight the possible impact for future measurements.Data from beta decays are the basis, through tests of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix and through constraints on exotic couplings, for some of ourmost stringent probes for BSM physics ( ). For couplings to the up quark, the expectationof unitarity in the SM is given by Σ u = | V ud | + | V us | + | V ub | = 1 , where V ud , V us and V ub represent the strength of the coupling of the up quark to the down, strange and bottom quark,respectively. The experimental uncertainty for this test is 0.05%, with the most precise experi-mental input coming from “superallowed” + → + nuclear decays (
7, 8 ). The Σ u unitarity testprobes model-independent BSM interactions at energy scales up to 11 TeV for interactions with(V,A) symmetry, assuming there are no right-handed neutrinos (
9, 10 ), while from the LargeHadron Collider (LHC) they are expected to reach 7 TeV. Recent improvements in the elec-troweak radiative corrections (EWRC) for neutron and nuclear decays by Seng et al. (
11, 12 )and cross-checked by Czarnecki et al. ( ), feature a reduced uncertainty for V ud (improvingthe reach of a unitarity test with Σ u ), but also of shift the central value of the EWRC by about 42tandard deviations from it’s previously quoted value. The potential impact of this shift, about0.1% in the unitarity sum, motivates careful scrutiny of other aspects of the analysis of thesuperallowed data set, including the nuclear structure-based corrections ( ).Mirror decays in nuclei and the neutron offer a range of nuclear structure cases, permittinga complementary extraction of | V ud | to the superallowed data set (
15, 16 ) and provide oppor-tunities to optimize sensitivity for tests of specific BSM physics scenarios, for example exoticscalar (S) and tensor (T) couplings. The isotope Ne has played an important role in funda-mental symmetries studies since the 1950’s (
1, 17–21 ), in part because of the simplicity of itsdecay scheme and in part due to the sensitivity of some angular correlations measurements inthis decay to the ratio of Gamow-Teller to Fermi amplitudes ( ). A current review of the physicsimpact of high precision decay data from Ne is presented in Rebeiro et al. ( ), with decayparameters included in Table I. For a measurement of the positron distribution from polarized Ne decay, the leading order angular distribution ( ) is given by Γ = 1 + β (cid:104) P (cid:105) A ( W ) cosθ (1)with β = v/c of the positron, (cid:104) P (cid:105) the average Ne nuclear polarization, θ the angle betweenthe nuclear spin and the positron momentum, and A ( W ) , the angular correlation parameter,determines the magnitude of the β -asymmetry as a function of relativistic energy, W . The A parameter is specified to leading order for Ne by ¯ A ≈ . ρ − . ρ ) / (1 + ρ )) ≈ − . ,with ρ ≡ g A M GT /g V M F ≈ . (2)(using the sign convention of (
24, 25 ) for ρ , with g V and g A denoting the vector and axial vectorweak coupling constants, and M GT and M F denoting the Gamow-Teller and Fermi matrix ele-ments). The accidental cancellation which leads to the small value of A ( W ) also leads to a verystrong dependence of A ( W ) on the ρ parameter: δ ¯ A/ ¯ A ≈ − δρ/ρ . For a given relative preci-3 Source Slit
220 cm 69 cm 0 cm
Not Drawn to Scale
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Selector Slit
Stern-Gerlach Magnet
Goniometer
100 cm
Det. 2
N Pole S Pole
Mylar foil Magnetic Field 0.675 T e + Decay Rate vs. Selector Slit Position
Det. 1
Magnet Bore 25 cm
Figure 1: Schematic of the experimental apparatus. Spin selection was accomplished using aStern-Gerlach magnet and three slits: the atomic beam source slit, the movable selector slit andthe entrance to the decay cell. The inset depicts a scan over the movable selector slit, with redvertical lines indicating the operational settings for each spin state and for the Stern-Gerlachmagnet on and off.sion level for A , this leads to over an order of magnitude higher relative precision for ρ , easingthe requirements for the systematic uncertainties due to, for example, the Ne polarization.
Experimental Apparatus
In 1995, an experiment to determine the β -asymmetry in the decay of Ne was performedat Princeton ( ). Due to inconsistencies in the simulated and measured timing spectrum ofscattered positrons, the results were not published immediately. In this work we developeda new simulation and analysis of that experiment and a more detailed model of the detectorsignals which successfully reproduced the experimentally measured data. We also incorporateda correction for Ne depolarization based on noble gas relaxation rates not available when our4xperimental data was obtained.The Ne polarized atomic beam apparatus was developed at Berkeley ( ) and then movedto Princeton where it was used in a series of measurements until 1997 (
1, 28, 29 ). The apparatusis described in detail in these publications, so we provide only a brief overview of the apparatus.The Ne gas is created from the F(p,n) Ne reaction utilizing 12 MeV protons from thePrinceton cyclotron in a flowing gas target, separated from the SF target gas in a LN trap,and pumped into a recirculation chamber containing a 2.5 cm copper atomic beam source heldat 38-40 K. For this work, a 1 in diffusion pump was added as the final compression stage forthe oven, increasing the flux of Ne in the atomic beam by a factor of about 5 over previouslyreported work.The experiment after the Ne beam exits the “source” is depicted in Fig. 1. The gas waspolarized using a 44.8 cm long Stern-Gerlach magnet of the two-wire type described by Ram-sey ( ). The polarized atomic beam was defined by the three slits with vertical dimension of1 cm: source (0.64 mm width), selector (0.71 mm width) and cell entrance (0.89 mm width).The selector slit was positioned so that only atoms of a single spin state can enter the cell.Solenoidal magnetic fields positioned along the beam axis between the Stern-Gerlach magnetand the spectrometer magnet ensured that the polarization of the beam was preserved whiletraversing a differentially pumped buffer volume and the fringe fields of the spectrometer. Cellalignment was fine-tuned using a goniometer system to ensure optimum cell loading and po-larizer conditions. A BGO scintillator detector was used to monitor the atomic beam sourcestrength, to provide normalization for the backgrounds measured before and after the Ne de-cay runs.The polarized gas entered the decay cell through a glass capillary array (Galileo Electro-Optics C25S10M10) into a 2 cm × ×
12 cm decay cell constructed of 0.5 µ m thickmylar. The mean residency time for Ne was 3.5 s. The decay trap sat inside a homogeneous,5.675 T solenoidal magnetic field with its axis perpendicular to the atomic beam axis. Themagnetic field was manually shimmed to reduce inhomogeneities to less than 0.1% over central40 cm of the decay volume. When the Ne decayed, positrons from the decay were guided bythe magnetic field to a pair of lithium-drifted silicon (Si(Li)) detectors separated by a distanceof 1.0 m. The detectors were 7.46 cm diameter and 0.3 cm thick, with an active region 6.18cm in diameter. The detectors were divided into four quadrants, with each quadrant read outseparately to reduce capacitance and rise time. The detectors had a low energy threshold of4 keV and resolution of about 2 keV for energy spectroscopy.In this experimental geometry it is possible for a beta particle, initially emitted towards oneof the detectors, to “back-scatter” from that detector and then to traverse the spectrometer andhit the opposite detector (see the inset in Fig. 2). In these cases, the relative timing between thefirst “hit” on the two detectors was used to determine the initial emission direction. This wasaccomplished by performing leading edge discrimination of the the detector pulses and thenapplying a “walk-correction” to account for the dependence of the timing on the amplitude ofthe recorded pulse. Detector timing versus energy curves were measured in separate, dedicatedruns using Co source with decays “tagged” by a fast plastic scintillator to provide a quantita-tive determination of the walk correction. Ultimately, knowledge of the polarization of the Neand the corrections required for event timing reconstruction (backscattering) proved the sourcesof limiting uncertainty for this measurement.Data collection was arranged in 8-section cycles with the spin states in the following order ↑↓↓↑↓↑↑↓ . A total of 38 hours of usable data comprised of approximately 6 million events werecollected. Data from the different spin cycles are first reconstructed by summing the energyover all hit quadrants and then using the relative timing to determine whether the intial decaywas directed towards detector 1 or 2. After background subtraction, the resultant event rates ineach detector were used to construct a super-ratio R = N ↑ N ↓ N ↓ N ↑ , where the N is the number of6ounts (corrected for background) and the subscripts refer to the detector number and spin state.The ratio R gives the asymmetry in each energy bin using the following relation A i = √ R i − √ R i +1 .This analysis allows for first order cancellation in systematic errors associated with differencesin detector efficiencies and variations in the decay rate. This ordering of the spin states providedadditional suppression of drift in backgrounds and any residual dependence on drifts in detectorthresholds, gain varations, etc... .Approximately 30% of all events scatter from one detector into the other, leaving someamount of energy in both detectors. A timing spectrum is produced using the difference in the“hit” time of pulses from events leaving energy in both detectors: ∆ t = t − t , where t and t are the earliest times the positron hits detector 1 and detctor 2, respectively. The measuredtiming spectrum is depicted in Fig. 2. Because the minimum transit time from one detectorto another is 3.5 ns but charge collection times are of order 30 ns, the timing distributions fordetectors 1 and 2 were not fully separated, and a simulation was developed to determine thecorrection required for mis-reconstructed events. Monte Carlo Simulation
The simulation assumes the decays occur uniformly throughout the interior volume of the hold-ing cell, propagates positrons through the magnetic field using the approximation method ofBielajew ( ) and incorporates interactions between the positrons and materials through theMonte Carlo calculations using the PENELOPE code ( ). Energy pulses were created by prop-agating charge through the electric field within the detector assuming an ideal planar geome-try ( ) and then through a fast amplifier with a 20 ns shaping time. A separate simulation wasperformed for the ex situ Co timing data. All timing data from both the asymmetry runs inthe spectrometer and Co data were fit to determine detector timing characteristics. This jointfitting procedure resulted in timing parameters which reproduced both data sets and provided7 − − − − - t t05000100001500020000250003000035000 C oun t s Full parameter space95% confidenceBest fitBest fit (sum)Measured timing (sum)
Figure 2: The measured timing distribution for backscattering events in which a positron hitsboth detectors (see inset). The relative timing distribution is defined by ∆ t = t − t , with t and t the earliest times in which a given positron hits the detectors. Also shown is the best fit tothe timing distribution with the Monte Carlo model of positron energy deposition and the 95%confidence intervals for parameter variations in the timing response model.8he necessary predictions for incorrectly reconstructed backscattering events.The measured timing spectrum is depicted in Fig. 2. The analysis of the simulated timingdata used five parameters: the detector energy threshold for timing signals, the electronic noiseand a timing walk correction specified as a function of kinetic energy, E , as w ( E ) = p + p p + E (
26, 34 ). The parameters were allowed to vary in order to simultaneously fit the Co data andthe positron coincidence timing spectrum from the asymmetry measurement using a χ metric.The fit was strongly dominated by the constraints placed by the coincidence timing data from Ne decays, defining allowed ranges for the timing correction consistent with the measureddata. The results of this analysis are also depicted in Fig. 2. The fit indicates that 14(1)% of thescattered decays or 4.1(3)% of the total decays were incorrectly reconstructed.Table 1: List of corrections to the asymmetry and their uncertainties. All values are multiplesof − . Systematic Correction ( − ) Uncertainty ( − ) Monte Carlo Corrections:Above threshold in both detectors:Backscatter correction -14.5 ± ± ± ± ± ± ± ± ± ± Total systematic -19.8 +6.5 -8.7
Statistical – ± Total – +7.0 -9.1
Results
The β -asymmetry parameter as a function of relativistic energy, A ( W ) , is definedin Eq. 3 with input constants collected in Tab. 2, based on expressions from Behrens andBuehring ( ). In these expressions, we use an effective form-factor notation consistent with( ), where F V = g V M F SM = 1 and F A = g A M GT are the leading order vector and axial-vector form-factors ( a and − c in ( )), and F Vσ and F Aσ are recoil order terms correspondingto the weak magnetism and induced tensor form factors ( − b and − d in ( )), with radiativecorrections, some smaller terms due to recoil order matrix elements and radiative correctionsincluded ( ). The expression below is accurate to an order of magnitude higher precisionthan required for the analysis of experiment. Further corrections depend on nuclear structureinput and the experimental geometry, and are discussed elsewhere ( ). Because the vectorcoupling constants are very precisely specified and the induced tensor term is negligible in theSM ( F Aσ is produced by second class currents), the only free parameter in the SM in Eq. 3is ρ = F A /F V (equivalent to Eq. 2 but with the new notation). When a one parameter fitfor A ( W ) as a function of ρ is performed, the zero kinetic energy intercept is found to be A = − . / − sys (26) stat and ρ = 1 . / − sys (8) stat , in agreementwith the most precise measurement to date of Calaprice et al. ( ). The χ /DOF for this fit was1.12, with a probability of 31% of measuring greater than this χ /DOF, indicating reasonableagreement with the SM functional form. The measured asymmetry and fit results are shown in10
00 1000 1500 2000Energy [keV]0.05 - - - - C o rr ec t e d A sy mm e t r y = 0 s A = 1.6014(8), F r = -140(130) s A = 1.5965(54), F r
500 1000 1500 20000.05 - - - - - U n c o rr ec t e d A sy mm e t r y
500 1000 1500 2000 00.050.10.150.2 M on t e C a r l o C o rr ec t i on Analysis Window
Figure 3: (top) The uncorrected asymmetry (statistical error bars) and the Monte Carlo cor-rection to the magnitude of the asymmetry ( δAA ) as a function of energy, (bottom) Correctedasymmetry with one and two parameter fit (bottom). In the one parameter fit, only ρ is varied(as per the SM) and in the two parameter fit, both ρ and the induced tensor, second class currentcoupling are varied. 11he bottom half of Fig. 3. A ( W ) = − √ ρ (1 + C ) + ρ (1 + C ) + C D + ρ (1 + D ) RC (3) C = 10 − (cid:16) −
287 + 3 . F Vσ + 1 . F Aσ + (cid:16) . − . F Vσ + 0 . F Aσ (cid:17) W (cid:17) (4) C = 10 − (cid:16) −
335 + 6 . F Vσ + 3 . F Aσ + (cid:16) . − . F Vσ (cid:17) W (cid:17) (5) C = 10 − (cid:16) − . F Vσ − . F Aσ (cid:17) W (6) D = 10 − (cid:16) −
221 + 48 . W + 3 . /W − . W (cid:17) (7) D = 10 − (cid:16) −
328 + 6 . F Vσ + 3 . F Aσ + (cid:16) . − . F Vσ (cid:17) W + (cid:16) − . . F Vσ − . F Aσ (cid:17) /W − . W (cid:17) (8) RC = 1 − . × − + 2 . × − /W + 1 . × − W − . × − W (9) Corrections
In order to quantify the fidelity of the Monte Carlo corrections to the asymmetrydue to scattering effects, an assessment was made of the simulation results for events whichhit more than one detector. The reconstructed energy spectra and the fraction of events whichundergo at least one, at least two and at least three or more scatters ( ) were investigated, withthe measured total hit fractions proving the most stringent test of the simulation. These data,as well as more detailed investigations of β scattering by the UCNA collaboration ( ),indicate a relative uncertainty of about 25% is a conservative and appropriate estimate for ourMonte Carlo corrections to the asymmetry with the largest relative discrepancy between simu-lation and measurement applied to the ratio of (two or more scatters)/(three or more scatters) of21%.Table 1 lists the systematic corrections to the asymmetry and their associated uncertainties.For the scattering corrections, each correction listed in the table is the difference between the12ncorrected experimental A and the value found after applying the Monte Carlo correction forthat class of event and then performing a fit to the asymmetry to extract A . In what followswe provide a brief description of our evaluation of the leading sources of systematic correctionsand uncertainty.The Stern-Gerlach magnet provided a uniform 24 kG/cm gradient over the entire beamheight. For Ne at a temperature of 38 K, this gradient causes a typical deflection of 640 µ mover the length of the magnet, with 97% of the beam being deflected by more than 250 µ m. Theselection slit can block the line of sight between the source and cell, allowing only atoms whosetrajectories are bent by the magnet to enter the cell. Larger slits before and after the magnet, andbefore the solenoid, are used to reduce the number of unpolarized Ne atoms that diffuse intothe solenoid chamber. The inset in Fig. 1 shows the count rate in the decay cell as a functionof the selection slit position with the magnet on and off. Vertical lines show the positions usedduring the experiment(4.93 mm and 6.58 mm). The glass channels of the MCP cell entrance slitwas slightly rotated with respect to the beam, causing a slight asymmetry in the beam profilewith the magnet on.To determine the uncertainty in the polarization, the background-subtracted, beta detectionrate was measured with the magnet on and off (see the inset in Fig. 1). For spin-down selectionat slit position 6.58 mm, the magnet off rate is 2.2% of the magnet on rate. For spin-up selectionat slit position 4.93 mm, the magnet off rate falls to 0.7% of the magnet on rate. In order to seta lower limit on the polarization, it is assumed that the unpolarized atoms detected with magnetoff are still present with the magnet on, causing on average 1.5% of the beam to be unpolarized.This is a conservative limit because atoms with the wrong spin are actually deflected away fromthe slit with the magnet on, even if there is a line of sight between source and cell. A simplemodel of the beam found that there should be no spin contamination in the cell by a 0.25 mmmargin. In practice, any background would far more likely be of the correct spin state as most13f the wrong spin state is blocked by a differential pumping slit well upstream of the entranceslit.The depolarization rate was not measured for the cell used in this experiment, howeverstringent limits on Ne depolarization were determined through measurements performed bySchreiber ( ). They used the same atomic beams machine, solenoidal magnetic field geometryand a very similar cell (with an MCP entrance channel, roughly the same dimensions and plasticwith the same elemental constituents), with no Ne relaxation observed. These measurements,scaling for the difference in expected wall collision rates and holding times due to cell geometry,place an upper limit of 2.3% (95% C.L.) for spin depolarization in the cell. During the time sincethis experiment and the first analysis were complete, a relaxation time of 900 s was measuredfor He on mylar by Heil ( ), which we scale for Ne in our geometry assuming dipole-dipolerelaxation in the wall material dominates the depolarization (
43, 44 ) to obtain a correction of1.4%. Given the possibility of relaxation at this level, we apply a correction to the asymmetryof 1.4(1.4) % accounting for depolarization over a larger range than covered by the relaxationlimits from the measurements of Schreiber.The linearity of the detector’s energy response was checked with sources
Am,
Ba, Co and
Ba. The maximum non-linearity was measured to be 1% at 1550 keV, the Comptonedge of the
Bi gamma line. The asymmetry is very insensitive to linearity errors, leading toan upper limit for the uncertainty in A due to the non-linearity of 0.14%. Backgrounds in thebeta signals are determined by moving a brass flag to cover the entrance slit to the cell, withthe background dominated by polarized Ne decaying outside the cell but also with a smallerunpolarized component due to ambient background. The ratio of signal to background in theanalysis window is greater than 100 when determined in this way, with a 6% correction dueto the component of the atomic beam which actually enters the cell when the brass flag is notpresent. The resultant correction to the asymmetry is found to be 0.2(2)%.14able 2: Parameters used to calculate F t and A . Constant Value Units Reference K/ (¯ hc ) . × − GeV − s ( ) G F / (¯ hc ) . × − GeV − ( ) ∆ VR . × − ( ) Q EC . MeV ( ) f V . ( ) f A /f V . ( ) δ VC − δ VNS . × − ( ) BR . ( ) P EC . (
25, 49 ) t / . s (
50, 51 ) F Vσ . (
24, 52 ) W . MeV ( ) m e . MeV ( ) M . amu ( ) Two Parameter Fit
Analysis of the energy dependence of the asymmetry in ref. ( ) deter-mined a non-zero value for F Aσ = 250(100) . The primary motivation for using Si(Li) de-tectors in this work was to permit more reliable modeling of the energy dependent responsethan previous experiments performed with plastic scintillators. A two parameter fit was per-formed, in which ρ and F Aσ were both allowed to vary, with the variation in χ used to deter-mine the 67% confidence level assuming Gaussian statistics. The results of the analysis are ρ = 1 . / − sys (54) stat and F Aσ = − / − sys (130) stat , in nominal agree-ment with the SM and the one parameter fit, and in disagreement with Ref. ( ) which measureda slope with opposite sign. The uncertainty in the slope is dominated by uncertainties in theMonte Carlo corrections to the asymmetry. We find no evidence for second class currents. Weidentify no obvious origin for the disagreement with Ref. ( ), but the small magnitude of theslope makes measurements of the energy dependence very sensitive to the detector responsefunction (linearity, scattering contributions, possible dead layers) and backgrounds. With the15mproved signal-to-background ratio and the ability to reliably model the energy response forour measurement, we believe it represents an improvement in the understanding of the asym-metry’s energy dependence. Discussion
To compare to other nuclei, the quantity F t is defined in Naviliat-Cuncic and Severijns ( ), F t ≡ f V t / (cid:18) P EC BR (cid:19) (1 + δ NC − δ C ) (1 + δ (cid:48) R ) (cid:32) f A f V (cid:33) ρ (10)using quantities from Tab. 2. The mean value and uncertainty in the lifetime of Ne wascalculated from the error weighted average of all published experimental results (
50, 51 ) witha scale factor of 1.9 for scatter. The value of f V was calculated using the parameterization ofTowner and Hardy ( ) with the Q EC value of Ref. ( ). We find that F t = 6142(17) s for Ne, dominated by the uncertainty in ρ . From this value of F t , F t = (cid:34) KG F | V ud | (1 + ∆ VR ) (cid:35) (11)the EWRC of Seng et al ( ) and the new analysis of Gamow-Teller decays of Hayen (
48, 56 ),we can extract the value of | V ud | from Ne decay, | V ud | ( Ne) = 0 . and compare it tothe value from other decays, summarized in Fig. 4, finding good agreement with the other mirrordecays, the neutron and the superallowed data set. For neutron data we used all published valuesand particle data group methods to determine averages and global uncertainties, obtaining aneutron lifetime of . s, with scale factor of 2.0 for scatter and g A = 1 . , witha scale factor of 2.2 for scatter, resulting in F t (neutron) = 6148(10) s. Our result does notinclude recently discovered contributions from quasi-elastic processes to the EWRC ( ), whichare expected to contribute at the × − level.The value of F t is sensitive to exotic tensor couplings, primarily through Fierz interfer-ence terms that impact the measured decay rate, β spectra, and angular correlations (
10, 58, 59 ).16igure 4: A global summary of | V ud | determined from nuclear decays. Mirror decay valuestaken from ( ) except for Al ( ) (technically a T = 1 isotriplet decay) and Ne (this work).Also presented are | V us | = 0 . from Ref. (
8, 13 ) for the “unitarity” band, | V ud | (0 + → + ) = 0 . from Ref. ( ) with the previous vertex correction values of Marciano andSirlin ( ), | V ud | (0 + → + ) = 0 . with the new nuclear and EWRC corrections ofSeng et al. (
11, 12 ) and | V ud | = 0 . for the neutron with the new EWRC (see text).17able 3: Summary of results. Observable Value A (SM) − . / − sys (26) stat ρ (SM: F Aσ = 0) . / − sys (8) stat ρ (BSM: F Aσ (cid:54) = . / − sys (54) stat F Aσ − / − sys (130) stat f t . . s F t s V ud . T ≡ (174 GeV ) / √ (cid:15) T > . TeVBeta decays are competitive with the LHC for left-handed neutrino couplings ( ), with a par-ticularly sensitive constraint for these produced from the ratio of | V ud | determined from theneutron to that from Ne, R = | V ud | (neutron)/ | V ud | ( Ne ) ( ). To illustrate the impactof this constraint, for model independent analysis, one can take C S = ( G F / √ V ud g S (cid:15) S and C T = ( G F / √ V ud g T (cid:15) T , with the g S = 1 . , and g T = 0 . the isovector scalarand tensor charges (or form factors) of the nucleon and (cid:15) S and (cid:15) T are effective BSM scalar andtensor couplings ( ), giving R ≈ . (cid:15) S − . (cid:15) T = 0 . . L . ) . In this ex-pression, the current limits on scalar couplings are taken from the superallowed data set ( ) andthe impact of the Fierz term on asymmetry measurements is assumed to be an average dilutionfactor, consistent with the analysis procedures of the three most recent neutron β -asymmetryexperiments which perform single parameter fits of the asymmetry to determine ρ (
59, 61, 62 ).This analysis yields (cid:15) T = 2 . . × − (at 90% C.L.), which corresponds to an energy scalefor new tensor interactions of Λ T ≡ (174 GeV ) / √ (cid:15) T > . TeV. Details of this analysis can befound in Ref. ( ).Exotic coupling limits such as these are the natural output of global fits to the beta decay dataset. The sensitivity quoted here is less strong than the global fit to all beta decay data by Wauters et al. , with a “sensitivity scale” determined by the precision of the constraints of about 7.8 TeV,18nd comparable to that of Gonzalez-Alonso et al. ( ). We did, however, incorporate morerecent neutron decay data than these earlier publications which should improve their quotedlimits somewhat. Current, model independent limits for tensor couplings from the LHC arealso about 7.8 TeV ( ), which are expected to improve to about 11 TeV when the full LHCdata set is analyzed.If it is possible to push the precision of the F t values for the neutron and Ne to levelscomparable to the superallowed decays ( 1s), one can establish a model-independent sensitivityscale with “discovery potential” for BSM tensor couplings ( ) above 20 TeV. These measure-ments would also probe uncertainty scales well below the recent shifts in the EWRC, relevant toboth the uncertainties in the isospin-mixing nuclear-structure corrections for the superalloweddecays ( ) and proposed new structure corrections to the EWRC ( ). These shifts have sharp-ened motivation to develop a systematic nuclear structure analysis of nuclear beta decay over awide range of nuclei, an activity already underway with promising approaches in the mass rangeof < A < using effective field theory approaches (
64, 65 ). From an experimental per-spective, all of the ingredients for this improvement in precision are in place. For the neutron,the next generation of measurements are planned at the sensitivity level of the superallowed de-cays. For Ne, using optical trapping methods, Fenker et al. (
66, 67 ) has already demonstratedit is possible to measure the β -asymmetry with systematic errors an order of magnitude smallerthan those presented here, at about the 0.3% level, with improvements to 0.1% precision under-way ( ). Such a measurement of Ne would involve a significant focus on the Neon isotopes,but exactly such an experimental program is underway at the Hebrew University ( ).The results in this article are summarized in Table 3, and establish Ne decay as the mostprecise asymmetry measurement from a nuclear mirror. The value of the zero-intercept of theasymmetry was determined to be A = − . / − sys (26) stat , with the energy de-pendence of the asymmetry showing no evidence for second class currents, disagreeing with19he results of ref. ( ). When taken together with recent theoretical progress, the nuclear mirrordata set for | V ud | is internally consistent, and also consistent with the neutron and superalloweddecays. The sensitivity of β -asymmetry measurements to the mixing ratio ρ , when taken to-gether with all other details of the decay already being known to roughly two parts in ,makes this a unique target of opportunity for fundamental symmetries studies. State-of-the-artexperimental technique could already, in principle, probe precision levels comparable to thesuper-allowed decays. The ratio of the F t value for Ne with that from the neutron providesstrong, model-independent constraints for BSM tensor couplings and opens a path to unprece-dented sensitivity.
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