Recent re-Evaluation of Reactor n Flux D. Lhuillier – CEA Saclay Based on: Phys. Let. B218,365 (1989)+ refs therein A. A. Hahn, K. Schreckenbach, W. Gellently, F. von Feilitzsch, G. Colvin, B. Krusche Phys. Rev. C83,054615 (2011) T.A. Mueller, D. Lhuiller, M.Fallot, A. Letourneau, S. Cormon, M. Fechner, L. Giot, T. Lasserre, J. Martino, G. Mention, A. Porta, F. Yermia Phys. Rev. C84, 024617(2011) P. Huber D. Lhuillier SNAC2011 - Blacksburg

Reactor Anomaly Phys. Rev. D83, 073006, 2011 Reactor + Gallium G. Mention, M. Fechner, T. Lasserre, M. Cribier, Th. Mueller D. Lhuillier, A. Letourneau Reactor + Gallium Average = 0.943 ± 0.023 (c2=19.6/19) D. Lhuillier SNAC2011 - Blacksburg

n spectrum emitted by a reactor The prediction of reactor ν spectrum is the dominant source of systematic error for single detector reactor neutrino experiments Thermal power, δPth <1% Fraction of fissions from isotope k, δak=few % E released per fissions of isotope k, δEk≈0.3% ν spectrum per fission This work ! Reactor data Nuclear databases Reactor evolution codes D. Lhuillier SNAC2011 - Blacksburg

n spectrum emitted by a reactor = S all fission products D. Lhuillier SNAC2011 - Blacksburg

The guts of Sk(E) Sum of all fission products’ activities Sum of all β-branches of each fission product Theory of β-decay D. Lhuillier SNAC2011 - Blacksburg

Corrections to Fermi Theory See P. Vogel’s talk Correction Physics Size Error Gn Real&virtual g emmision by charged fermion lines Small L0 Coulomb field from finite size nucleus ~% MeV-1 CW* Weak interaction inside a finite size nucleus S Screening of nuclear charge by atomic electrons dWM Weak magnetism Assumed 0.5% MeV-1, could be large 100% relative error (?) *: not implemented before P. Huber’s work D. Lhuillier SNAC2011 - Blacksburg

Corrections to Fermi Theory Example with Z=46, A=117, E0=10 MeV, Effect on fission spectra results from the sum over quasi continuous end-point distribution P. Huber D. Lhuillier SNAC2011 - Blacksburg

Complementary approaches Integral measurements of e- spectra Nuclear Data Sum of all fission products’ activities fission product inventory (t) U & Pu fission rates (t) Reference e-spectrum for each isotope to be converted to n spectrum Sum of all β-branches of each fission product Build total spectrum from sum of β-branches Complete β-decays schemes (ENSDF) β-strength (Greenwood et al.) Total β spectrum per nucleus (Rudstam et al.) Masses (Qb) Nuclear models … Theory of β-decay Corrected Fermi theory ab-inito Mixed Effective D. Lhuillier SNAC2011 - Blacksburg

The ILL electron Data “Anchor point” See K. Schreckenbach’s talk Total electron spectra from the b-decays of 235U, 239Pu and 241Pu fission products. Target foil (235U, 239Pu, 241Pu) in thermal n flux High resolution spectrometer ILL research reactor (Grenoble, France) e- Accurate e- measurements @ ILL in Grenoble (1980-89): High resolution magn. Spectrometer Calibration by extensive use of reference internal conversion electron lines Normalization syst 1.8% Unique reference to be met by any other measurement or calculation D. Lhuillier SNAC2011 - Blacksburg

Normalization of ILL e- data Dominant error of e- data Correlated across all energy bins of all isotopes Relies on well known/checked n-g cross sections (conversion lines). 207Pb(n, g)208Pb 115In(n, g)116mIn 113Cd(n,g)114Cd D. Lhuillier SNAC2011 - Blacksburg

e- n conversion Fission product level b-branch level Exact conversion requires complete knowledge from fission yield down to b-transition between parent ground (or isomeric)-state and daughter states b-branch level Fission product level Lot of relevant quantities: Z, A, End-points, Jp, nuclear matrix elements, branching ratios, fission yields, life time… but scarce data as E0 increases D. Lhuillier SNAC2011 - Blacksburg

Conversion of reference e- spectra 1- Fit total e- spectrum with a sum of 30 effective b branches determined by iterative method (instead of ~10,000+ real branches) 2- Convert each effective e- branches to ν branches 3- Sum all converted ν branches to get total ν spectrum K. Schreckenbach et al., Phys. Lett. 99B, 251 (1981). D. Lhuillier SNAC2011 - Blacksburg

ILL n spectra Emitted Interacting Reference spectra over the last 25 years D. Lhuillier SNAC2011 - Blacksburg

Stack of quadratic sum of 235U errors: ILL n spectra Stack of quadratic sum of 235U errors: Conversion error from envelop of numerical studies Correction to Fermi theory in the effective branches: What Z? : Mean fit on nuclear data Z=f(E0) - Effective Coulomb + Weak magn. Correction: Can we do better ? D. Lhuillier SNAC2011 - Blacksburg

Ab initio Approach BESTIOLE code: build up database of ~ 800 nuclei and 10000 b-branches MURE evolution code: inventory of fission products All data from ENSDF (b-branches) and JEFF (fission yields) databases + Complementary measurements of fission products spectra to tag and replace pandemonium candidates Unmeasured nuclei described by gross-theory (JENDL database) + our own model based on ENSDF mean fits. Residues w.r.t. reference ILL e- data  95+/-5% of the spectrum reproduced but still not meeting required precision D. Lhuillier SNAC2011 - Blacksburg

Ab initio Approach Stack of quadratic sum of 238U errors First propagation of all ENSDF quoted errors + correlations. Demonstrate that uncertainty on shape factors has ≤1.5% impact on total spectrum. Total error dominated by (rough) estimate of syst of nuclear databases in the 10-20% range. D. Lhuillier SNAC2011 - Blacksburg

Relative change of n spectrum w.r.t. infinite irradiation time Ab-initio approach RELATIVE off equilibrium effect Relative change of n spectrum w.r.t. infinite irradiation time ILL reference data are photos of b emission after 12-36h irradiation time. Long-lived isotopes contribute to a significant fraction of the low energy part of the n spectrum and keep accumulating over several weeks.  Sizeable correction to ILL data in the low E range. ILL conditions D. Lhuillier SNAC2011 - Blacksburg

238U reference spectrum No measurement of total b-spectrum available yet – requires fast n flux Updated prediction using the ab-initio approach ~10% above previous calculations, with uncertainties in the 10-20% range. Deviation from Vogel’s spectrum, Phys. Rev. C24, 1543 (1981) D. Lhuillier SNAC2011 - Blacksburg

238U reference spectrum Upcoming results from 238U irradiation in fast neutron flux of FRMII reactor – Munchen. New conversion procedure to be applied on e- data. See K. Schreckenbach’s talk D. Lhuillier SNAC2011 - Blacksburg

New Mixed Approach Ratio of Prediction/ Reference ILL data Th. Mueller et al, Phys. Rev. C83,054615 (2011) Ratio of Prediction/ Reference ILL data ILL electron data anchor point Fit of residual: five effective branches are fitted to the remaining 10%  Suppresses error of full ab initio approach “true” distribution of all known β-branches describes >90% of ILL e- data  reduces sensitivity to virtual branches approximations Corrections to Fermi theory applied on all b-branches D. Lhuillier SNAC2011 - Blacksburg

New Mixed Approach +3% normalization shift with respect to old ν spectrum Residuals to ILL e- Residuals to ILL n Similar result for all isotopes NB: this +3% shift is above the IBD threshold, the total integral of emitted spectrum remains unchanged (1 e- and 1 nu emitted per decay) D. Lhuillier SNAC2011 - Blacksburg

Consistency Check Define “true” e- and n spectra from reduced set of well-known branches from ENSDF nuclei data base. “Perfect knowledge” of both e and n spectra. Apply exact same OLD conversion procedure to true e- spectrum. Compare the converted n spectrum to the true one. Converted spectrum 3% below true ν spectrum  ILL analysis leads to a 3% bias w.r.t. the true ν spectrum D. Lhuillier SNAC2011 - Blacksburg

Origin of the 3% shift E <4 MeV Effective linear correction of ILL data replaced by correction at b-branch level: and Effective correction “à la ILL” New conversion at branch level Correct a bias. Assume 100% syst error. Still the correction at branch level neglects all effects of nuclear structure. Uncertainty could be larger than 100%? D. Lhuillier SNAC2011 - Blacksburg

Origin of the 3% shift E >4 MeV Mean fit of nuclear charge doesn’t reflect accurately enough the true Z distribution D. Lhuillier SNAC2011 - Blacksburg

Correlation matrix of the 4 isotopes Error Budget Stack of quadratic sum of 235U errors Correlation matrix of the 4 isotopes D. Lhuillier SNAC2011 - Blacksburg

What we learned Mixed approach: Revisit conversion procedure: ILL conversion procedure have 2 independent biases (~1.5% each in total detected rate): - Low energy: correction to Fermi theory should be applied at branch level. - High energy: mean Z fit is not accurate enough. Combination of all “well known” nuclear data can provide a good proxy for neutrino spectra (~90% of experimental spectrum described) Revisit conversion procedure: Apply all above Complementary approach, minimizing the use of nuclear data  P. Huber, Phys. Rev. C84, 024617(2011) D. Lhuillier SNAC2011 - Blacksburg

Conversion with virtual branches Bias Spectrum conversion problem is mathematically ill-posed Total spectra built from JEFF (fission yields) and ENSDF (b-spectra) nuclear databases already known to be a good proxy for real reference spectra.  Allow complete numerical studies to determine the size of potential bias for given number of branch and binning. D. Lhuillier SNAC2011 - Blacksburg

Conversion with virtual branches Statistical uncertainty Fluctuate b-spectrum by the variance of the actual data  Determine the envelope of converted spectra. D. Lhuillier SNAC2011 - Blacksburg

Mean nuclear charge Demonstrate that proper weighting by fission yield and branching ratio when fitting the mean nuclear charge cures the conversion bias at high energy. Quite robust with respect to approx of poorly known nuclei. D. Lhuillier SNAC2011 - Blacksburg

Well Established deviation from ILL spectra New conv. New conv. with simple b-shape Mixed-approach ILL inversion Confirms global increase of predicted spectrum Fixes remaining oscillations of mixed-approach prediction Extra deviation at high energy from more complete correction to Fermi theory (weak interaction in the finite volume of the parent nucleus). D. Lhuillier SNAC2011 - Blacksburg

Weak Magnetism , assume 100% error Experimental slope in good agreement for transitions with low ft values Contribution of large ft’s in fission neutrino spectra? D. Lhuillier SNAC2011 - Blacksburg

Weak Magnetism Preliminary Preliminary Relative contribution Preliminary Preliminary High log(ft) values have a sizeable contribution to fission n spectra across all E range (reflects the large contribution of forbidden decays) No obvious argument can reject a substantially larger dWM contribution or error Better constraint from analysis of experimental reactor spectra? D. Lhuillier SNAC2011 - Blacksburg

Experimental Constraints on global slope factor Rovno 175 000 evts Compare shape distortion of dWM with available experimental shape information Rovno data, courtesy V. Sinev Bugey 3, Chooz, … data to be added Upcoming data from Reno, Daya Bay and Double Chooz near detectors. Relative errors Uncertainty on E scale ? D. Lhuillier SNAC2011 - Blacksburg

Experimental Constraints on global slope factor This test: assume predicted and Rovno spectra in perfect agreement and compare the error envelope with the distortion induced by an increasing dWM correction Position of this crossing point might depend on the conversion procedure (Mixed approach used here) A 4 times larger dWM would compensate the 3% flux increase. Preliminary  Existing+upcoming data might be able to provide constraint at the “reactor anomaly level”. D. Lhuillier SNAC2011 - Blacksburg

<Residue> in [2-8] MeV <Flux ratio> in [2-8] MeV Conclusions Normalization ILL electron data are high quality data Common systematic error to all converted n spectra +3% bias of conversion to anti-n spectra: ~1.5% from better nuclear charge distribution ~1.5% from implementation of corrections at the branch level Current error on total detected rate ~ 2% But unsolved issues from weak magnetism correction Emitted <Residue> in [2-8] MeV Detected <Flux ratio> in [2-8] MeV 235U +3.0% +2.5% 239Pu +3.5% +3.1% 241Pu +4.3% +3.7% 238U +6.2% +7.8% D. Lhuillier SNAC2011 - Blacksburg

Conclusions Shape  Compile data: Improved shape correction and control of conversion error from P. Huber’s recent work. Large weak magnetism correction would show up in reactor data as a slope.  Compile data: Existing (upcoming) spectral data collected at reactors might bring stringent enough constraint on the shape to clarify the situation. Expected new 238U reference data from FRMII. Bugey-4 measurement provides an accurate absolute anchor point as well as upcoming near detector data (DC, Reno, Daya Bay)  No impact on q13 search. D. Lhuillier SNAC2011 - Blacksburg

Outlook Reactor anomaly: About half of the effect is independent on new spectra normalization: Mean value of all measurements was already below Off-eq effects, neutron life-time are well established corrections. Anomaly analysis should be updated using new P. Huber’s results and experimental shape constraints. See T. Schwetz’s talk D. Lhuillier SNAC2011 - Blacksburg

Backup Sides D. Lhuillier SNAC2011 - Blacksburg

Pandemonium Measurements of b-decay scheme based on b-g coincidence    Z N A Z-1N’ det drops fast with E + difficult analysis of continuum Under (over)-estimation of the low (high) E part of the spectrum - Missed g are attributed to GS transition.  New measurements using total Absorption Gamma Spectrometers (only sensitive to the total energy of the g decay chain) D. Lhuillier SNAC2011 - Blacksburg

Bugey D. Lhuillier SNAC2011 - Blacksburg

Error Budget 235U 239Pu 241Pu D. Lhuillier SNAC2011 - Blacksburg

Error Budget Phys. Rev. C84, 024617(2011) D. Lhuillier SNAC2011 - Blacksburg

4th neutrino hypothesis Combine all rate measurements, no spectral-shape information Fit to anti-ne disappearance hypothesis allowed Absence of oscillations disfavored at 98.6% C.L. excluded area D. Lhuillier BLV2011 - Gatlinburg

1981 ILL measurement Reactor at ILL with almost pure 235U, 8.76 m away from compact core Reanalysis in 1995 by part of the collaboration to account for overestimation of flux at ILL reactor by 10%... Affects the rate only Large errors, but a striking oscillation pattern is seen by eye ? 1981 D. Lhuillier BLV2011 - Gatlinburg

Combined Rate+Shape contours Including original Bugey-3 & ILL Energy Spectra constraints D. Lhuillier BLV2011 - Gatlinburg

Reactor Rate+Shape + Ga + (MB) The no-oscillation hypothesis is disfavored at 99.8% CL D. Lhuillier BLV2011 - Gatlinburg

Unique potential to detect new oscillations A 144Ce Source Experiment M. Cribier et al., arXiv:1107.2335, submitted to PRL. Activity : 50.0 kCi (1.85 PBq) Mass: 15.7 g (1.4 kg all Ce isotopes) Heat released: 373 W Unique potential to detect new oscillations D. Lhuillier BLV2011 - Gatlinburg