The positron-neutrino correlation in the $0^+ \to 0^+ \beta$ decay of
$^{32}$Ar was measured at ISOLDE by analyzing the effect of lepton recoil on
the shape of the narrow proton group following the superallowed decay. Our
result is consistent with the Standard Model prediction. For vanishing Fierz
interference we find $a=0.9989 \pm 0.0052 \pm 0.0036$, which yields improved
constraints on scalar weak interactions

A. García

A. I. Boothroyd

A. S. Carnoy

C. H. Johnson

C. Ortiz

C. Stratowa

D. Schardt

E. G. Adelberger

E. T. H. Clifford

F. Glück

G. Audi

H. Behrens

H. Bichsel

H. E. Swanson

H. Wenninger

I. Martel

J. D. Jackson

M. B. Schneider

M. Beck

M. J. G. Borge

M. S. Antony

N. B. Gove

O. Tengblad

P. Herczeg

P. M. Endt

the ISOLDE Collaboration, 

W. E. Ormand

English

arXiv

4 pages, 1 table, 4 figures.-- PACS nrs.: 23.20.En, 13.30.Ce, 23.40.Bw, 24.80.+y.-- Erratum to this paper in: Phys. Rev. Lett. 83(15): 3101-3101 (1999).Erratum available at: http://digital.csic.es/handle/10261/12896The positron-neutrino correlation in the O+ -> O+ decay of Ar-32 was measured at ISOLDE by analyzing the effect of lepton recoil on the shape of the narrow proton group following the superallowed decay. Our result is consistent with the standard model prediction. For vanishing Fierz interference we find a = 0.9989 ± 0.0052 ± 0.0039, which yields improved constraints on scalar weak interactions.This work was supported in part by the DOE (at the University of Washington) and by the NSF and the Warren Foundation (at the University of Notre Dame).Peer reviewe

Adelberger, E. G.

Ortíz, C.

García, A.

Swanson, H. E.

Beck, M.

Tengblad, Olof

García Borge, María José

Martel, Ismael

Bichsel, H.

Digital.CSIC

Physical Review Letters

Positron-neutrino correlation in the O+ -> O+ decay of Ar-32

The positron-neutrino correlation in the $0^+ \to 0^+ \beta$ decay of $^{32}$Ar was measured at ISOLDE by analyzing the effect of lepton recoil on the shape of the narrow proton group following the superallowed decay. Our result is consistent with the Standard Model prediction. For vanishing Fierz interference we find $a=0.9989 \pm 0.0052 \pm 0.0036$, which yields improved constraints on scalar weak interactions.The positron-neutrino correlation in the $0^+ \to 0^+ \beta$ decay of $^{32}$Ar was measured at ISOLDE by analyzing the effect of lepton recoil on the shape of the narrow proton group following the superallowed decay. Our result is consistent with the Standard Model prediction. For vanishing Fierz interference we find $a=0.9989 \pm 0.0052 \pm 0.0036$, which yields improved constraints on scalar weak interactions

Adelberger, E.G.

Ortiz, C.

Garcia, A.

Swanson, H.E.

Tengblad, O.

Borge, M.J.G.

Martel, I.

CERN Document Server

arXiv:nucl-ex/9903002v1  5 Mar 1999Positron-neutrino correlation in the 0+ → 0+ decay of 32ArE. G. Adelberger1, C. Ortiz2, A. Garc´ıa2, H.E. Swanson1, M. Beck1, O. Tengblad3, M.J.G. Borge3, I. Martel4,H. Bichsel1 and the ISOLDE collaboration41Department of Physics, University of Washington, Seattle, Washington 98195-15602Department of Physics, University of Notre Dame, Notre Dame, Indiana 465563Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain4EP Division, CERN, Geneva, Switzerland CH-1211(February 14, 2014)The positron-neutrino correlation in the 0+ → 0+ β decayof 32Ar was measured at ISOLDE by analyzing the effect oflepton recoil on the shape of the narrow proton group follow-ing the superallowed decay. Our result is consistent with theStandard Model prediction. For vanishing Fierz interferencewe find a = 0.9989 ± 0.0052 ± 0.0036, which yields improvedconstraints on scalar weak interactions.23.20.En,13.30.CeThe e+-ν correlation in 0+ → 0+ β decay provides arobust signature of possible rare processes where parti-cles other than the usual W± boson are exchanged. Inthe Standard Model and its left-right symmetric general-izations, 0+ → 0+ decays produce the e+ and ν with op-posite chiralities. Angular momentum conservation thenprevents relativistic leptons from being emitted in op-posite directions. On the other hand, a scalar interac-tion, which could arise from exchange of a leptoquarkor a Higgs boson [1], will produce the e+ and ν withidentical chiralities so that, in the relativistic limit, theleptons cannot be emitted in the same direction. In min-imal extensions of the Standard Model, Higgs couplingsare too small to affect significantly the e-ν correlation.However, supersymmetric theories with more than onecharged Higgs doublet can accommodate sizable scalarcouplings [1] that are not ruled out by existing data [2].This paper reports new constraints on scalar weak in-teractions based on a precise measurement of the e-ν cor-relation in the 0+ → 0+ β+ decay of 32Ar, the only pureFermi transition whose e-ν correlation has been deter-mined with good precision. The simple spin structureof this decay permits tests for scalar interactions with-out complications from axial or tensor currents or fromrecoil-order effects. We consider a 0+ → 0+ β+-decayHamiltonian [3]H = (ψ¯nγµψp)(CV ψ¯νγµψe + C′V ψ¯νγµγ5ψe) +(ψ¯nψp)(CS ψ¯νψe + C′S ψ¯νγ5ψe) , (1)which gives a decay rated3ωdpdΩedΩν∝ F (Z, p)p2E2ν(1 + apEcos θeν + bmE)×MfMi − E + p cos θeν, (2)where E, p and m are the total energy, momentum andmass of the positron, Eν the energy of the neutrino, Miand Mf are the masses of the parent atom and daugh-ter nucleus, and F (Z, p) the Fermi function. We assumethat the Standard Model provides an exact descriptionof the W± exchange process and that CV = C′V [4], butmake no assumptions on the parity or time-reversal prop-erties of the scalar interaction. Then the e-ν correlationcoefficient,a =2− |C˜S |2 − |C˜′S |2 + 2Zαm/p Im(C˜S + C˜′S)2 + |C˜S |2 + |C˜′S |2, (3)and the Fierz interference coefficient,b = −2√1− (Zα)2Re[C˜S + C˜′S ]2 + |C˜S |2 + |C˜′S |2, (4)are functions of C˜S and C˜′S whereC˜S =CSCVand C˜′S =C′SCV. (5)The C˜’s will be complex if the scalar sector violates time-reversal invariance.The e-ν correlation must be inferred from the recoilmomentum of the daughter nucleus. This traditionallywas measured directly, restricting high-precision resultsto a few favorable cases such as 6He [5] and neutron decay[6]. However, if the daughter nucleus is particle unsta-ble, the daughter momentum can be determined from itsdecay products. This allows one to study energetic lightparticles rather than slow heavy ions whose atomic andeven chemical effects must be considered. Furthermorethe transformation from the rest frame of the daughter tothe lab amplifies the lepton recoil effects by a factor 2V/vwhere V is the center-of-mass velocity of the light particleand v is the daughter’s veleocity due to lepton recoil. Fi-nally, the time scale for particle decay is so short that thedelayed particle is emitted before the recoiling daughtercan slow down appreciably. Clifford et al. [7] comparedthe energies of delayed α’s detected in coincidence withβ’s emitted toward and away from the α, while Schardtand Riisager [8] studied the broadening of narrow delayedproton groups due to lepton recoil. The coincidence tech-nique allows one to measure a shift rather than a spreadwhich is favorable on statistical grounds and is less sen-sitive to the response of the charged-particle detector.1On the other hand, the extracted value of the correla-tion coefficient is very sensitive to the energy and angleof the detected β particle. We adopted the singles tech-nique because it seemed difficult to determine the beta’skinematics with sufficient precision.FIG. 1. Intrinsic shapes of the 0+ → 0+ delayed protongroup for a = +1, b = 0 (heavy curve) and a = −1, b = 0(light curve). The daughter’s 20 eV natural width is not vis-ible on this scale.The kinematics of 32Ar superallowed decay deter-mine the daughter’s velocity distribution and thereby thebroadening of the delayed proton peak. The maximumkinetic energy of the recoiling 32Cl nucleus isTmax =∆2 −m22Mi(6)where ∆ is the difference in atomic masses of the par-ent and daughter states. The accepted value of ∆ ispoorly known because of the ±50 keV uncertainty in the32Ar mass [9]. We use the isospin-multiplet mass equa-tion [10], M(T3) = c0 + c1T3 + c2T23 , to obtain an im-proved value for ∆ from the measured masses of all 5members of the A = 32, T = 2 multiplet. These masses,shown in Table I, were obtained from the known ground-state masses and excitation energies [12] of the isobars,except for 32Cl which we computed from our measuredenergy of the superallowed delayed-proton peak in 32Ardecay, ELAB = 3349.9±1.2 keV [13] and the known pro-ton and 31S masses. The isospin-multiplet mass equa-tion provides an excellent fit to the data and predictsthat ∆ = 3c2 − c1 = 6087.3 ± 2.2 keV [14], implyingTmax ≈ 638 eV and a maximum daughter velocity ofv = 2.07 × 10−4c. The 32Cl daughter state has a widthΓ ≈ 20 eV (see below) so that in one mean life thedaughter travels at most 2.1 × 10−2A˚ before emittingthe proton. The recoiling 32Cl therefore emitted the pro-ton while it was still traveling with the full velocity itreceived from lepton recoil. The intrinsic shape of thedelayed proton peak (the shape for a counter with per-fect energy resolution) is shown in Fig. 1 for the limitingcases a = +1, b = 0 and a = −1, b = 0.We performed our experiment at ISOLDE. Beams of60 keV 32Ar and 33Ar ions from the General PurposeSeparator were focused through a 4 mm diameter colli-mator and implanted in a 22.7 µg/cm2 carbon foil in-clined at 45◦ to the beam axis. Protons were detected ina pair of 9 mm × 9 mm PIN diode detectors collimatedby 7.72 mm × 7.72 mm apertures located 1.6 cm fromthe beam axis. We eliminated possible uncertainties frombeta summing effects by placing the detection apparatusinside a 3.5 T superconducting solenoid. The magneticfield prevented the betas from reaching the proton detec-tors (the highest energy betas from the 0+ → 0+ decayhad Rc = 0.53 cm), but had little effect on the protons(the superallowed proton group had Rc = 7.56 cm).The PIN diodes were maintained at −11 C by thermo-electric elements that held the diode temperatures con-stant to ±0.02 C. The signals were amplified by preampli-fiers located immediately outside the vacuum chamber.The preamplifier housings were held at +20 C by ther-moelectric devices that held the housing temperaturesconstant to ±0.01 C. Condensation of vacuum systemcontaminants on the detectors and stopper foil was min-imized by surrounding them with a copper shield cooledby a steady flow of liquid nitrogen. As an added pre-caution, the detectors were warmed to +27◦ C once eachday to drive off any condensed material. The preamplifiersignals were amplified and digitized by modules mountedin temperature-controlled crates and recorded in event-mode by a mini-computer. For each event we recordedthe detector energy signals, the absolute time, the delaytime after the arrival of a proton pulse, and the tem-peratures of the detectors, preamps, NIM crate, liquidnitrogen shroud, and the room. Our system gave excel-lent resolution; the pulser peaks for the two detectors hadfull-widths at half-maximum of 2.98 and 3.27 keV.Data were taken over a period of 12 days under severaldifferent conditions: with the stopper foil at 45◦, 135◦,225◦ and 315◦ with respect to the beam axis, and for twodifferent beam tunes. These produced 6 different spectrafor each of the 2 counters. We continually alternatedbetween ≈ 2 h long 32Ar runs and 5-15 min long 33Arruns that provided energy calibrations for the 32Ar data.The 32Ar and 33Ar beam intensities on target,TABLE I. Comparison of the measured mass excesses ofthe lowest T = 2 quintet in A = 32 to predictions of theIsobaric Multiplet Mass Equation [P (χ2, ν) = 0.71].isobar T3 Mexp (keV)a MIMME (keV)32Si +2 −24080.9 ± 2.2 −24081.9 ± 1.432P +1 −19232.88 ± 0.20b −19232.9 ± 0.232S 0 −13970.98 ± 0.41 c −13971.1 ± 0.432Cl −1 −8296.9 ± 1.2d −8296.6 ± 1.132Ar −2 −2180± 50 −2209.3 ± 3.2aunless noted otherwise, ground state masses are from Ref. [9]bEx = 5072.44 ± 0.06 keV from Ref. [12]cEx = 12045.0 ± 0.4 keV from Refs. [10,11]dfrom delayed proton energy [13] and masses of Ref. [9].2averaged over the entire run, were 94 and 3900 ions/s.FIG. 2. Fit (upper panel) and residuals (lower panel) of the0+ → 0+ delayed proton peak. This spectrum, (the sum ofdetector 2 data in reflection geometry) contains roughly 1/4 ofour data. The energy scale is 0.500 keV/channel. The pulserpeak shows the electronic resolution. The Breit-Wigner tailfrom the 20 eV daughter width is visible on the high-energyside of the peak.We computed the intrinsic proton shapes using MonteCarlo routines to generate β-decay events distributed ac-cording to Eq. 2 withEν =(Em − E)1 + (p cos θeν − E)/MiEm = ∆− Tmax . (7)The Fermi function for a screened, finite-sized nu-clear charge was interpolated from Tables II and III ofRef. [15], and Glu¨ck’s [16] order-α radiative correctionto the energy distribution of recoiling 32Cl nuclei was ap-plied. A predicted [17] 6.7×10−4 electron-capture branchwas also included. Protons were ejected isotropically inthe 32Cl frame and deflected by the magnetic field; themean energy losses of individual protons in the stopperfoil and detector dead layer (roughly 1.5 and 1.8 keV,respectively) were computed. The stopper foil thicknesswas deduced from the energy loss of 3183 keV 148Gd α’sin the foil, while the implantation profile of Ar ions in thefoil was computed with TRIM [18]. The detector deadlayer thicknesses, 23.4± 0.4 and 21.6± 0.7 µg/cm2, weremeasured by inserting into the apparatus a jig that al-lowed the 148Gd source to be moved along an arc centeredon one of the PIN detectors. The dead-layer loss variedas the secant of the angle while the energy loss in thesource was essentially constant because the α source wasalways perpendicular to the line of sight to the detector.We evaluated the intrinsic proton shape at 961 pointson a C˜S-C˜′S grid. The intrinsic shapes plus a small, flatbackground were convoluted with a proton detector re-sponse function consisting of 2 low-energy exponentialtails folded with a Gaussian. This functional form gave agood parameterization of a “first principles” calculationof the response function that included the effects of pulserresolution, the Fano factor, electronic and nuclear strag-gling in the stopper foil and detector dead layer, escapeof Si X-rays, and energy loss to phonon excitations of thedetector. We fitted our 6 pairs of delayed-proton spectraby varying the response function parameters (Gaussianwidth, tail lengths and fractional areas) to minimize χ2for each C˜S , C˜′S point. Figure 2 displays the qualityof the fits. Figure 3 shows that the extracted lineshapeagreed well with the “first-principles” calculation. Fitswere made for a series of values of Γ, the natural widthof the daughter. There was essentially no correlation be-tween Γ and C˜S and C˜′S , and we found Γ = 20± 10 eV.FIG. 3. Comparison of the detector response function ex-tracted from the data in Fig. 2 to the “first-principles” calcu-lation described in the text.Figure 4 shows constraints on C˜S and C˜′S from thiswork and from Refs. [19–23]. The annular shapes ofour constraints arise from the Fierz interference term inEq. 2. Our C˜S-C˜′S constraints may be parameterized asa˜ ≡ a/(1 + 0.1913b)= 0.9989± 0.0052(stat.)± 0.0036(syst.) 68% c.l. (8)where a and b are given in Eqs. 3, 4 with 〈m/p〉 = 0.21.Note that a˜, unlike a, does not have an upper bound of+1, so the range spanned by our experimental 2σ errorband lies entirely within the physical region.The systematic error included in Eq. 8 and Fig. 4 wasevaluated by combining in quadrature the following ef-fects. We found the dependence of a˜ on the exact val-ues of ∆ and Qp, ∂a˜/∂∆ = −1.2 × 10−3 keV−1 and∂a˜/∂Qp = −0.9 × 10−3 keV−1, by repeating the en-tire analysis with ∆ and Qp changed by ±10 keV. Theuncertainties, δ∆ = ±2.2 keV and δQp = ±1.2 keV,gave a kinematic systematic error δa˜ = ±0.0032. [24] We3checked the dependence of a˜ on the fitting regions of theproton spectra; a 28% variation in the width of the re-gion changed a˜ by less than ±0.00055. We examined thedependence of our results on the form of the detectorresponse function by reanalysing the data with a single-tail response function; by reanalyzing the data assumingthat a weak Gamow-Teller peak lay under the tail of the32Ar superallowed peak; and by simultaneously fittingthe 33Ar and 32Ar superallowed peaks using a commonresponse function. From these tests we inferred a line-shape systematic error of δa˜ = ±0.0016.FIG. 4. 95% conf. limits on C˜S and C˜′S. Upper panel:time-reversal-even couplings. The annulus is from this work.The narrow diagonal band is from b(0+ → 0+) [19]. Thebroad diagonal band shows constraints from A, B, a, andt1/2 in n decay [20]; the sausage-shaped area includes, in ad-dition, constraints from G(14O) and G(10C) [21], b(22Na) [22]and a(6He) [5]. Lower panel: time-reversal-odd couplings.The circles are from this work and correspond to C˜S and C˜′Sphases of ±90◦, +45◦ and −45◦. The shaded oval shows theconstraint with no assumptions about this phase. The diago-nal band is from R(19Ne) [23].For scalar interactions with C˜S = −C˜′S so that b = 0,we obtain a 1σ limit |C˜S |2 ≤ 3.6 × 10−3. The corre-sponding limit on the mass of scalar particles with gaugecoupling strength is MS = |C˜S |−1/2MW ≥ 4.1MW .We thank T. Van Wechel and H. Simons for help con-structing the apparatus, J.J. Kolata and F. Bechetti forlending us the superconducting magnet, D. Forkel-Wirthfor help setting up our apparatus at CERN, and B. Jen-nings and I. Bigi for useful remarks. This work was sup-ported in part by the DOE (at the University of Wash-ington) and by the NSF and the Warren Foundation (atthe University of Notre Dame).[1] P. Herzeg, in Precision Tests of the Standard ElectroweakModel, World Scientific, P. Langacker ed., 768 (1995).[2] A.I. Boothroyd, J. Markey, and P. Vogel, Phys. Rev. C,29 603 (1984).[3] J.D. Jackson, S.B. Treiman, and H.W. Wyld Jr., Nucl.Phys. 4, 206 (1957).[4] We neglect possible small leptoquark-exchange contribu-tions to CV and C′V .[5] C.H. Johnson, F. Pleasanton and T.A. Carlson, Phys.Rev. 132, 1149 (1963).[6] C. Stratova et al., Phys. Rev. D. 18, 3970 (1978).[7] E.T.H. Clifford et al., Nucl. Phys. A493, 293 (1989).[8] D. Schardt and K. Riisager, Z. Physik A 345, 265 (1993).[9] G. Audi and A.H. Wapstra, Nucl. Phys. A 595, 409(1995).[10] M.S. Antony et al., At. Data Nucl. Data Tables 33, 447(1985).[11] G. Walter, private communication (1998).[12] P.M. Endt, Nucl. Phys. A521, 1 (1990).[13] The error is dominated by the uncertainties in the ener-gies of the 33Cl daughter states fed in 33Ar decay.[14] There is no evidence for any violation of the IMME,P (χ2, ν) drops to 0.52 when a c3T33 term is added.[15] H. Behrens and J. Ja¨necke, Landolt-Bo¨rnstein, New Se-ries, Group I, Vol. 4, Numerical Tables for Beta-Decayand Electron Capture, ed. H. Schopper, Springer-Verlag,Berlin (1969).[16] F. Glu¨ck, Nucl. Phys. A628, 493 (1998).[17] N.B. Gove and M.J. Martin, Nucl. Data. At. Data Tables10, 206 (1971).[18] Written and distributed by J.F. Ziegler.[19] W.E. Ormand, B.A. Brown and B.R. Holstein, Phys.Rev. C 40, 2914 (1989).[20] Particle Data Group, Eur. Phys. J. C 3, 622 (1998).[21] A.S. Carnoy et al., Phys. Rev. C 43, 2825 (1991).[22] H. Wenninger, J. Stiewe, and H. Leutz, Nucl. Phys. A109, 561 (1968).[23] M.B. Schneider et al., Phys. Rev. Lett. 51, 1239 (1983).[24] We account for the correlation between ∆ and Qp.4

Positron-neutrino correlation in the $0^{+} \to 0^{+}$ decay of $^{32}Ar$

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Positron-Neutrino Correlation in the
                    
                      
                        
                          
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Positron-neutrino correlation in the 0^+ \to 0^+ decay of ^{32}Ar

Positron-neutrino correlation in the 0^+ \to 0^+ decay of ^{32}Ar

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