Measurement of the Spectral Shape of the beta-decay of 137Xe to the Ground State of 137Cs in EXO-200 and Comparison with Theory
S. Al Kharusi, G. Anton, I. Badhrees, P.S. Barbeau, D. Beck, V. Belov, T. Bhatta, M. Breidenbach, T. Brunner, G.F. Cao, W.R. Cen, C. Chambers, B. Cleveland, M. Coon, A. Craycraft, T. Daniels, L. Darroch, S.J. Daugherty, J. Davis, S. Delaquis, A. Der Mesrobian-Kabakian, R. DeVoe, J. Dilling, A. Dolgolenko, M.J. Dolinski, J. Echevers, W. Fairbank Jr., D. Fairbank, J. Farine, S. Feyzbakhsh, P. Fierlinger, D. Fudenberg, P. Gautam, R. Gornea, G. Gratta, C. Hall, E.V. Hansen, J. Hoessl, P. Hufschmidt, M. Hughes, A. Iverson, A. Jamil, C. Jessiman, M.J. Jewell, A. Johnson, A. Karelin, L.J. Kaufman, T. Koffas, J. Kostensalo, R. Krücken, A. Kuchenkov, K.S. Kumar, Y. Lan, A. Larson, B.G. Lenardo, D.S. Leonard, G.S. Li, S. Li, Z. Li, C. Licciardi, Y.H. Lin, R. MacLellan, T. McElroy, T. Michel, B. Mong, D.C. Moore, K. Murray, P. Nakarmi, O. Njoya, O. Nusair, A. Odian, I. Ostrovskiy, A. Piepke, A. Pocar, F. Retière, A.L. Robinson, P.C. Rowson, D. Ruddell, J. Runge, S. Schmidt, D. Sinclair, K. Skarpaas, A.K. Soma, V. Stekhanov, J. Suhonen, M. Tarka, S. Thibado, J. Todd, T. Tolba, T.I. Totev, R. Tsang, B. Veenstra, V. Veeraraghavan, P. Vogel, J.-L. Vuilleumier, M. Wagenpfeil, J. Watkins, M. Weber, L.J. Wen, U. Wichoski, et al. (8 additional authors not shown)
MMeasurement of the Spectral Shape of the β -decay of Xe to the Ground State of
Cs in EXO-200 and Comparison with Theory
S. Al Kharusi, G. Anton, I. Badhrees,
3, a
P.S. Barbeau, D. Beck, V. Belov, T. Bhatta, M. Breidenbach, T. Brunner,
1, 9
G.F. Cao, W.R. Cen, C. Chambers, B. Cleveland,
12, b
M. Coon, A. Craycraft, T. Daniels, L. Darroch, S.J. Daugherty,
15, c
J. Davis, S. Delaquis,
8, d
A. Der Mesrobian-Kabakian, R. DeVoe, J. Dilling, A. Dolgolenko, M.J. Dolinski, J. Echevers, W. Fairbank Jr., D. Fairbank, J. Farine, S. Feyzbakhsh, P. Fierlinger, D. Fudenberg,
16, e
P. Gautam, R. Gornea,
3, 9
G. Gratta, C. Hall, E.V. Hansen,
17, f
J. Hoessl, P. Hufschmidt, M. Hughes, A. Iverson, A. Jamil, C. Jessiman, M.J. Jewell, A. Johnson, A. Karelin, L.J. Kaufman,
8, g
T. Koffas, J. Kostensalo, R. Kr¨ucken, A. Kuchenkov, K.S. Kumar, Y. Lan, A. Larson, B.G. Lenardo, D.S. Leonard, G.S. Li, S. Li, Z. Li, C. Licciardi, Y.H. Lin,
17, c
R. MacLellan, T. McElroy, T. Michel, B. Mong, D.C. Moore, K. Murray, P. Nakarmi, O. Njoya, O. Nusair, A. Odian, I. Ostrovskiy,
21, h
A. Piepke, A. Pocar, F. Reti`ere, A.L. Robinson, P.C. Rowson, D. Ruddell, J. Runge, S. Schmidt, D. Sinclair,
3, 9
K. Skarpaas, A.K. Soma,
21, i
V. Stekhanov, J. Suhonen, M. Tarka, S. Thibado, J. Todd, T. Tolba,
10, j
T.I. Totev, R. Tsang, B. Veenstra, V. Veeraraghavan, P. Vogel, J.-L. Vuilleumier, M. Wagenpfeil, J. Watkins, M. Weber,
16, k
L.J. Wen, U. Wichoski, G. Wrede, S.X. Wu, Q. Xia, D.R. Yahne, L. Yang, Y.-R. Yen,
17, l
O.Ya. Zeldovich, and T. Ziegler Physics Department, McGill University, Montreal H3A 2T8, Quebec, Canada Erlangen Centre for Astroparticle Physics (ECAP),Friedrich-Alexander-University Erlangen-N¨urnberg, Erlangen 91058, Germany Physics Department, Carleton University, Ottawa, Ontario K1S 5B6, Canada Department of Physics, Duke University, and Triangle UniversitiesNuclear Laboratory (TUNL), Durham, North Carolina 27708, USA Physics Department, University of Illinois, Urbana-Champaign, Illinois 61801, USA Institute for Theoretical and Experimental Physics named by A.I. Alikhanovof National Research Centre “Kurchatov Institute”, 117218, Moscow, Russia Department of Physics, University of South Dakota, Vermillion, South Dakota 57069, USA SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA TRIUMF, Vancouver, British Columbia V6T 2A3, Canada Institute of High Energy Physics, Beijing 100049, China Physics Department, McGill University, Montreal, Quebec, Canada Department of Physics, Laurentian University, Sudbury, Ontario P3E 2C6, Canada Physics Department, Colorado State University, Fort Collins, Colorado 80523, USA Department of Physics and Physical Oceanography,University of North Carolina at Wilmington, Wilmington, NC 28403, USA Physics Department and CEEM, Indiana University, Bloomington, Indiana 47405, USA Physics Department, Stanford University, Stanford, California 94305, USA Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA Amherst Center for Fundamental Interactions and Physics Department,University of Massachusetts, Amherst, MA 01003, USA Technische Universit¨at M¨unchen, Physikdepartment and Excellence Cluster Universe, Garching 80805, Germany Physics Department, University of Maryland, College Park, Maryland 20742, USA Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA Wright Laboratory, Department of Physics, Yale University, New Haven, Connecticut 06511, USA University of Jyv¨askyl¨a, Department of Physics, P.O. Box 35 (YFL), FI-40014, Finland IBS Center for Underground Physics, Daejeon 34126, Korea Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794, USA Kellogg Lab, Caltech, Pasadena, California 91125, USA LHEP, Albert Einstein Center, University of Bern, Bern CH-3012, Switzerland Department of Physics, University of California San Diego, La Jolla, CA 92093 (Dated: May 11, 2020)We report on a comparison between the theoretically predicted and experimentally measuredspectra of the first-forbidden non-unique β -decay transition Xe(7 / − ) → Cs(7 / + ). Theexperimental data were acquired by the EXO-200 experiment during a deployment of an AmBeneutron source. The ultra-low background environment of EXO-200, together with dedicated sourcedeployment and analysis procedures, allowed for collection of a pure sample of the decays, with anestimated signal-to-background ratio of more than 99-to-1 in the energy range from 1075 to 4175keV. In addition to providing a rare and accurate measurement of the first-forbidden non-unique a r X i v : . [ nu c l - e x ] M a y β -decay shape, this work constitutes a novel test of the calculated electron spectral shapes in thecontext of the reactor antineutrino anomaly and spectral bump. Introduction.
The discrepancies between measuredand predicted antineutrino fluxes from nuclear reactorsconstitute the so-called reactor antineutrino anomaly [1,2]. In addition, an event excess (“bump”) against pre-dicted spectra between 4 and 7 MeV of antineutrinoenergy has been observed by the RENO [3], DoubleChooz [4], and Daya Bay [5] antineutrino-oscillation ex-periments. The spectral bump was apparently present,but not recognized then, in the much earlier Goesgen ex-periment [6]. Predicting the reactor antineutrino flux isdifficult due to the uncertainties related to the treatmentof the β decays of the numerous fission fragments [7, 8].One particular problem is the description of the forbid-den β -decay transitions whose spectra are translated toantineutrino spectra at energies relevant for the measure-ment of the total flux and the spectral bump [9]. It hasbeen noted that many first-forbidden β -decay transitions,like the presently discussed one, in the medium-mass A = 89 −
143 nuclei play a key role in reactor antineutrinospectra [9, 10]. Only a handful of electron spectra cor-responding to J + ↔ J − β transitions in this region hasbeen measured and with a rather poor precision [11, 12].According to [9, 10] the β spectra for the J + ↔ J − tran-sitions, relevant for solving the reactor anomaly and spec-tral bump, deviate noticeably from the allowed shape,the deviation being approximately a quadratic functionof the electron kinetic energy (see, e.g., Ref. [10], Fig-ure 3, top panel). This is the case also for the β decayof Xe (see Figure 2, lower panel), making this decayan important test case of the computed spectral shapes.In the case of
Xe there is a measurement [13] thatproposes a scheme for the decay of
Xe to the groundstate and first excited state of
Cs, but we could notfind measurements or calculations of the corresponding β -spectrum shapes. In the present work we perform the β -spectrum-shape measurement and calculation for thedecay to the ground state. Comparison with experimentconfirms that the calculated shape of the Xe decayis correct, and thus there is hope that the effects of thefirst-forbidden β decays lead to mitigation of the reactoranomaly and possible explanation of the origins of thespectral bump, as proposed by Hayen et al. [9, 10].The problem of many of the electron spectra of thefirst-forbidden β -decay transitions is connected to the un-certainty of the effective value of the weak axial coupling g A [14] and the enhancement of the axial-charge nuclearmatrix element (NME) by meson-exchange currents [15].Recently, a sustained effort has gone to clarifying thesetwo burning issues [16]. Related to this, we point outthat the effective values of g A are more of effective cor-rections to specific nuclear-theory frameworks than fun-damental corrections to the weak axial coupling [17]. For some decays the spectral shape depends on the effectivevalue of g A and, to some extent, on the mesonic enhance-ment [14–16]. The uncertainties related to these param-eters are reflected as theoretical uncertainties in the pre-dicted antineutrino spectra. Fortunately, the majorityof the shapes of electron spectra are not much affectedby the values of these quantities. In order to test theaccuracy of the theory framework used to compute theelectron spectra related to the reactor-antineutrino prob-lem one needs (a) a measured electron spectral shape ofa forbidden β -decay transition in the nuclear mass regionrelevant for the reactor antineutrino problem with (b) anon-trivial shape and (c) independent of both g A and themesonic enhancement.The three requirements are met by the first-forbidden non-unique β -decay transition Xe(7 / − ) → Cs(7 / + GS ). The condition (a) is accounted for bythe experimental spectral shape extracted in the presentwork. The condition (b) is satisfied by the complexspectral shape containing a pseudoscalar part with twoNMEs, a pseudovector part with three NMEs and a pseu-dotensor part with one NME [15, 16]. Furthermore, ourpresent calculations, based on the formalism of [18] andon its recent derivative [19], show that point (c) is alsosatisfied to a high level of precision. Theoretical description of the forbidden β shape. Forthe theoretical description of the first-forbidden β − decaywe adopt the expansion of Behrens and B¨uhring [18].NMEs up to next-to-leading order are included in thecalculations [19].The nuclear-structure calculations were done usingthe shell model code NuShellX@MSU [20] in a modelspace spanned by the proton orbitals 0 g / , 1 d / , 1 d / ,2 s / , and 0 h / and the neutron orbitals 0 h / , 1 f / ,1 f / , 2 p / , 2 p / , and 0 i / with the effective Hamil-tonian jj56pnb [21]. This interaction has previously beenused to study the mesonic-exchange effects on and g A -dependence of the electron spectra of A ≈
135 nuclei [15],as well as to predict the β shapes of the first-forbiddendecays contributing to the cumulative β spectra from nu-clear reactors [9, 10]. While Xe is not one of the ma-jor contributors itself, the neighbouring nuclei, such as , , I and , Xe, are [22]. The
Xe ground-state-to-ground-state decay to
Cs (GS decay) turnsout to be one of the spectra with negligible shape de-pendence on the adopted value of g A or the magnitudeof the mesonic enhancement effects on the axial-chargematrix element. This is the case since the involved fouraxial-vector NMEs dominantly contribute to the spec-tral shape and thus g A simply gives the overall scalingof the electron spectrum and, in turn, of the half-life.This g A dominance is clearly visible in Figure 2 wherethe g A dependent contribution (blue dots) is comparedwith the full spectral shape (blue dotted line). The shapefactor C ( E ) (ratio of the corrected spectrum to that cor-responding to an allowed decay) is plotted in the bot-tom frame of the figure. This transition is a perfect testcase for the accuracy and validity of the calculations ofthe β spectra in the context of the reactor antineutrinoanomaly [9, 10]. This is particularly important since thecalculations of Hayen et al. [9, 10] propose correctionsto the traditional Huber-Mueller model [1, 23] which ex-plain, at least partially, the anomaly and spectral bump.In contrast with the GS decay, the spectral shape ofthe Xe decay to the first excited state of
Cs (ESdecay) does depend on the value of g A and could, inprinciple, be used to constrain its value. However, theaccompanying emission of a de-excitation γ makes ac-curate measurement of the ES decays β -spectrum shapein EXO-200 challenging. Since both the motivation andanalysis approach are substantially different for the GSand ES measurements, we consider the ES decay outsidethe scope of this work and only focus on the GS decay. Experimental details and results.
The EXO-200 de-tector is a cylindrical time projection chamber (TPC).It is filled with liquid xenon (LXe), consisting of 80.6%of the isotope
Xe and 19.1% of
Xe, with the re-maining balance comprised of other isotopes. The LXeis housed in a cylindrical copper vessel of ∼
40 cm diam-eter and ∼
44 cm length. The vessel is surrounded by ∼
50 cm of HFE [24], a hydrogen-rich heat transfer fluidmaintained inside a vacuum-insulated copper cryostat.Further shielding is provided by at least 25 cm of lead inall directions. A small diameter copper tube runs fromthe outside of the lead shield through the HFE and wrapsaround the outside of the TPC vessel. It allows one toinsert miniature radioactive calibration sources and placethem close to the active volume of the detector. Energydepositions in the TPC produce ionization charge andscintillation light. The charge and light signals are re-constructed to provide energy and position of events. Ina given event, charge deposits, or clusters, that are sep-arated by ∼ β decay of Xe [29].The experimental data used in this work were collectedduring the AmBe neutron source calibration campaigncarried out in December 2018.
Xe is produced byneutron capture on
Xe and decays to
Cs with thehalf-life of 3.818 ± ∼
67% of cases [31],
Xe decays to the ground state of
Cs. In ∼
31% of cases,
Xe decays to a 5/2 + excited state of Cs,which de-excites by emission of a 455.5 keV γ -ray. Theneutrons were produced by the neutron source positionedat the mid-plane of the TPC, 3 cm outside the LXe vol-ume. The source contains ∼ µ Ci of
Am in the formof a carrier-free
AmO powder mixed with berylliummetal powder. The mixture is contained in a 1.2 mmdiameter tungsten capsule, which is in turn containedinside a 2.0 mm diameter stainless steel capsule that iswelded shut by electron-beam welding. The estimatedneutron activity of the source is ∼
90 Bq. More detailsabout the source construction and characterization canbe found in [32]. In ∼
60% of the cases [33], the neutronemission from the source is accompanied by a 4439.8 keV γ -ray. The source is positioned several centimeters out-side of the TPC during the calibrations, which leads tosome neutrons being captured in HFE by hydrogen nu-clei. The capture is followed by the emission of a 2224.6keV γ -ray. Additional γ radioactivity is expected fromneutron inelastic scattering in HFE. While advantageousfor the energy calibration, the γ -rays produced when theAmBe source is deployed close to the TPC would consti-tute a major background for the Xe β decay measure-ment. To avoid this, a special deployment procedure wasused. The deployment sequence consisted of repeated“ Xe activation —
Xe decay” cycles. During the de-cay phases, the source was retracted outside of the leadshield, ceasing the associated γ radioactivity. The lengthof the periods was chosen to maximize the number ofdetected Xe decays. Figure 1 shows the rate of re-constructed events in EXO-200 during one of the decayperiods when the source is retracted. The drop (rise) ofthe rate at the end (beginning) of the activation periodsis clearly seen. The red lines indicate the placement ofthe cuts to select the
Xe decay period. A total of 60such periods is selected during the campaign. The de-cay phase is defined as a period when the event rate isless than 1.33 Hz. The timing cuts are placed at +30(-30) seconds from each decay period’s start (end). Theintegrated livetime is 8.73 hours.
FIG. 1. Reconstructed event rate during the AmBe sourcecalibration. The vertical lines show the cuts that select
Xedecays.
The fiducial volume cuts are relaxed slightly, as com-pared to Ref. [28]. This increases the fiducial mass by ∼ Xe decays to the ground state of
Cs, onlythe β particle is emitted and detected. Electrons of O (MeV) energy are reconstructed predominantly as SSevents in the detector. On the other hand, when the de-cay proceeds to the 5/2 + excited state (ES decay), boththe β and the de-excitation γ deposit energy and are re-constructed as an MS event in most cases. Therefore, the Xe GS decay spectrum can be examined in EXO-200by looking at the energy distribution of the selected SSevents. However, several reconstruction and physics re-lated effects introduce non-negligible differences betweenthe theoretical GS spectrum and the spectrum of the re-constructed SS events. To take these effects into account,the MC of the AmBe source is first used to track the neu-trons up to the
Xe atoms on which they are captured.
Xe decays, both GS and ES, are then generated fromthe capture position distributions. The β energy is sam-pled from the theoretical β spectrum. The decay prod-ucts ( β and de-excitation γ ) are tracked, and their energydepositions are simulated and reconstructed to producethe expected SS spectrum. This spectrum, along withthe theoretical one, are shown in Figure 2. At the lowest -3 -2 -1 I n t e n s i t y ( a . l o g u . ) TheoryTheory (g A contribution only)Theory + Det. EffectsGS onlyES only0 1000 2000 3000 4000 5000 E SS (keV) C ( E ) FIG. 2. (Top frame) Theoretical GS spectrum (blue dottedline) and reconstructed MC SS spectrum (red solid line). Thetheoretical GS spectrum shape is the same for all reasonable g A and mesonic enhancements within the line width. The g A -dependent contribution to the theoretical spectrum is alsoshown as blue dots. Individual contributions of GS and ESdecays to the reconstructed spectrum are also shown as reddashed and dash-doted lines, respectively. (Bottom frame)Shape factor, C ( E ). energy one can see the expected effect of the charge recon-struction threshold, leading to the MC spectrum having alower intensity than the theoretical spectrum. While theSS spectrum is dominated by the GS decays, a residual peak at 455.5 keV is expected, due to ES decays that oc-cur outside of the sensitive volume. For such events, the β cluster of an ES decay is lost, while the de-excitation γ -ray has a chance to travel to the fiducial region andget reconstructed as a single cluster. At higher energies,the intensity of the MC SS spectrum is lower than thetheoretical spectrum, due to reconstruction related ef-fects and the production of Bremsstrahlung photons bythe β particles, which leads to some GS decays being re-constructed as MS events. Finally, the slightly higherapparent end-point in the MC spectrum is expected, dueto the finite energy resolution.The detector’s energy scale is constrained using thetotal of seven mono-energetic γ lines obtained in EXO-200 using radioactive calibration sources: 455.5 (AmBe),661.7 ( Cs), 1173.2 ( Co), 1332.5 ( Co), 2224.6(AmBe), 2614.5 (
Th), and 4439.8 keV (AmBe). Themean position of the full absorption peaks in the uncali-brated energy spectra is found using a fit by a linear com-bination of the Gaussian and error functions. The latterfunction is an ad-hoc way to account for the shoulder tothe left of the peaks, comprised of Compton scatteringevents, multi-site full absorption events with one or moresmall charge clusters missing, and other events. The cal-ibration runs collected closest in time to the AmBe cal-ibration campaign are used. The same fiducial cuts areused for the calibration events as for the
Xe dataset.The SS events are selected for all calibration lines, withthe exception of the 455.5 keV
Cs de-excitation line.Since in that case the de-excitation γ is accompanied by a β decay, the two-cluster MS events within the timing cutsare first selected. The energy distribution of the smallerof the two charge clusters is then plotted for events inwhich the larger of the two charge clusters has energy ∼ σ above 455.5 keV (560 keV). Figure 3 shows the re-sulting spectrum. It is not possible to discern contribu-
200 300 400 500 600
E (keV) C o un t s / ( k e V ) Gaus+Erf fitData
FIG. 3. Selected
Cs de-excitation γ events. The Gaus-sian+Erf fit to the uncalibrated charge energy is shown asthe red line. tions of individual clusters to the total detected scintil-lation light. So the reconstructed energy in this work isbased on charge signals only. The energy calibration ap-proach used in this work extends the constrained energyrange in both directions, as compared to previous anal-yses, at the expense of a worse energy resolution. Afterthe mean positions of all γ lines are found, they are plot-ted versus the true energies and fit by a linear function.Figure 4 shows the resulting SS data energy calibrationthat is used in this analysis. The residuals are typically E t r u e ( k e V ) p = 48.5 ± p =0.9446 ± − E fit (keV) ∆ E / E ( % ) FIG. 4. SS data energy calibration. Red line is the linear fit.Best-fit parameters are also shown. The errors are statistical. within ± ± Xe and Cu.
Xe is produced by capture of the AmBe neu-trons on
Xe, which constitutes ∼
19% of the xenontarget in EXO-200.
Xe undergoes a β decay with ahalf-life of 9.14 hours and has a Q-value of 1051 keV. Cu is produced in the copper vessel (and other con-struction elements) and undergoes a β +/EC decay witha half-life of 12.7 hours. Only a single 511 keV positronannihilation γ -ray is expected to be seen in the SS spec-trum. In ∼ Cu electron captures to anexcited state of Ni that de-excites by a 1345.8 keV γ -ray, which can also produce an SS event. The expectedSS spectra of Xe and Cu are generated by MC anal-ogously to the case of
Xe. The three spectral shapesare then fit to the calibrated charge energy spectrum ofthe selected SS events allowing the normalization of eachof the three components to float. Figure 5 shows theselected SS events and the results of the fit. The goodagreement between the best-fit and the data shapes sup-ports the expectation that Cu and
Xe are the mainactivation backgrounds.A SS low energy cut of 1075 keV is chosen to removethe
Xe and most of the Cu events. The high energycut is set to 4175 keV, based on the Q-value of
XeGS decay. Based on the fit, the residual backgroundcontribution of Cu and
Xe to the selected energyrange is 22.7(5) and 0.50(2) events, respectively. Twoknown background contributions to the AmBe datasetare two-neutrino double β and K decays, whose ratesare constrained by the EXO-200 “low background data”(LB) [28]. Taking into account the livetime and the cor-
500 1000 1500 2000 2500 3000 3500 4000 E calib SS (keV) -1 C o un t s / ( k e V ) MC all, χ /ndf = 1.11MC, XeMC,
XeMC, CuLB bkgData
FIG. 5. Calibrated SS energy spectrum of events passing theselection cuts (black points). Blue dotted, green dashed, andcyan dot-dashed lines correspond to MC spectra of
Xe,
Xe, and Cu, respectively. Thick red line corresponds tothe sum of the three best-fit components. Thin magenta linecorresponds to the LB backgrounds, described in the text.The reduced χ of the fit is shown in the legend. rection for the slightly larger fiducial volume used in thisanalysis, one expects 43 two-neutrino double β and 7.8 K events, or ∼ ∼
10% relative uncertainty. The expected LBevents are removed from the dataset by subtracting theirMC spectra, normalized to the corresponding number ofexpected events. The remaining dataset contains 4526events. For a qualitative check of the purity of the se-lected dataset, the time difference between each selectedevent and the start time of the corresponding decay pe-riod is histogrammed and fit by an exponential function(Figure 6). The best-fit half-life value, 3.81 ± Time Since Start (s) C o un t s / ( s ) T / fit =3.81 ± χ /ndf=0.9Data FIG. 6. Time distribution of selected SS events (black) withenergies between 1075 and 4175 keV. The exponential fit isshown as red solid line. in good agreement with the known half-life of
Xe of3.818 ± Xe events. The com-parison range is from 1075 to 4175 keV. The calibratedcharge energy spectrum of the selected SS data events, C o un t s / ( k e V ) Theory + Det. Effects, χ /ndf = 0.80Calibrated Data − Bkgs MC E calib SS (keV) -202 ( D - M C ) / σ p = 0.10 ± FIG. 7. (Top frame) Best fit to the selected, calibrated, background-subtracted SS data events. The data points are shown inblack. The theoretical spectrum (after passing through MC) is shown in red. (Bottom frame) Residual differences between thedata and best-fit curve, normalized by the statistical errors, are shown in black. The constant fit to the residuals is shown bydashed blue line. p with the expected residual background contributions sub-tracted, is shown in black on the top frame of the figure.It is fit with the simulated shape based on the theoreticalcalculation (red). The only parameter floating in the fitis the total normalization. The reduced χ of the fit (alsoshown) suggests a good agreement between the data andexpectation. The normalized residuals are shown on thebottom frame of the figure. All residuals are within ± σ statistical error. The residuals are fit by a constant(dashed blue line) trend line, with the best-fit parame-ter shown. The residuals show no statistically significantenergy dependence.Anything that can introduce an energy-dependent dis-crepancy between the data and MC can systematicallyaffect the comparison shown on Figure 7. Given theamount of the available statistics, we are sensitive to po-tential systematics effects on the level of a few percentor more. The data energy calibration is constrained tothe sub-percent level. The Gaussian+Erf fit model it-self may be a source of systematics when extracting thepeaks mean positions. This effect was studied by EXO-200 and is expected to introduce a ∼ ≤
1% of events and is knownto O (10%) relative uncertainty, suggesting only a frac-tion of percent residual effect. Potential imperfectionsof the MC and reconstruction can systematically affectthe comparison only if they lead to an energy-dependent difference of the SS fraction or of the overall SS spectralshape in the data and MC. Based on the latest publishedcomparison of data and MC in EXO-200 (Figure 1 inRef. [28]), the energy-dependent deviation is expected tobe small, compared to the statistical errors in Figure 7. Discussion and conclusion.
We calculate the
XeGS spectrum and find that it has no significant depen-dence on the adopted value of g A or the magnitude ofthe mesonic enhancement effects on the axial-charge ma-trix element. This makes this transition an ideal toolto validate the accuracy of the β spectra calculations inthe context of the reactor antineutrino anomaly. Weperform a precise measurement of this first forbiddennon-unique β -decay shape using the data collected dur-ing an AmBe source deployment in EXO-200. A goodagreement between the predicted and observed spectrais found. Therefore, this work provides both a rare mea-surement of the first forbidden non-unique β -decay shapeand a novel test related to the calculated electron spec-tral shapes of beta decays that contribute strongly tothe antineutrino flux from nuclear reactors. The hopeis that this test justifies the calculated spectral shapesof [9, 10] thus implying that the spectral bump andthe flux anomaly could be explained, at least partly, bythe exact spectral shapes of the abundant first-forbiddennon-unique beta decays of the fission fragments in nuclearreactors. Acknowledgments.
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