Limits on Active to Sterile Neutrino Oscillations from Disappearance Searches
in the MINOS, Daya Bay, and Bugey-3 Experiments
P. Adamson,1,‡ F. P. An,2,† I. Anghel,3,4,‡ A. Aurisano,5,‡ A. B. Balantekin,6,† H. R. Band,7,† G. Barr,8,‡M. Bishai,9,†,‡ A. Blake,10,11,‡S. Blyth,12,13,†G. J. Bock,1,‡D. Bogert,1,‡D. Cao,14,†G. F. Cao,15,†J. Cao,15,†S. V. Cao,16,‡T. J. Carroll,16,‡
C. M. Castromonte,17,‡ W. R. Cen,15,†Y. L. Chan,18,† J. F. Chang,15,† L. C. Chang,19,†Y. Chang,13,† H. S. Chen,15,† Q. Y. Chen,20,†R. Chen,21,‡S. M. Chen,22,† Y. Chen,23,† Y. X. Chen,24,† J. Cheng,20,† J.-H. Cheng,19,† Y. P. Cheng,15,† Z. K. Cheng,25,† J. J. Cherwinka,6,† S. Childress,1,‡ M. C. Chu,18,† A. Chukanov,26,† J. A. B. Coelho,27,‡L. Corwin,28,‡
D. Cronin-Hennessy,29,‡J. P. Cummings,30,† J. de Arcos,31,† S. De Rijck,16,‡ Z. Y. Deng,15,†A. V. Devan,32,‡ N. E. Devenish,33,‡ X. F. Ding,15,† Y. Y. Ding,15,† M. V. Diwan,9,†,‡ M. Dolgareva,26,† J. Dove,34,† D. A. Dwyer,35,† W. R. Edwards,35,†C. O. Escobar,36,‡ J. J. Evans,21,‡ E. Falk,33,‡ G. J. Feldman,37,‡ W. Flanagan,16,‡ M. V. Frohne,38,*,‡
M. Gabrielyan,29,‡ H. R. Gallagher,27,‡ S. Germani,39,‡ R. Gill,9,†R. A. Gomes,17,‡ M. Gonchar,26,† G. H. Gong,22,† H. Gong,22,†M. C. Goodman,4,‡ P. Gouffon,40,‡ N. Graf,41,‡ R. Gran,42,‡ M. Grassi,15,† K. Grzelak,43,‡ W. Q. Gu,44,† M. Y. Guan,15,† L. Guo,22,† R. P. Guo,15,† X. H. Guo,45,† Z. Guo,22,† A. Habig,42,‡ R. W. Hackenburg,9,† S. R. Hahn,1,‡ R. Han,24,†S. Hans,9,§,†J. Hartnell,33,‡R. Hatcher,1,‡M. He,15,†K. M. Heeger,7,†Y. K. Heng,15,†A. Higuera,46,†A. Holin,39,‡
Y. K. Hor,47,† Y. B. Hsiung,12,† B. Z. Hu,12,† T. Hu,15,† W. Hu,15,† E. C. Huang,34,† H. X. Huang,48,† J. Huang,16,‡ X. T. Huang,20,†P. Huber,47,†W. Huo,49,†G. Hussain,22,†J. Hylen,1,‡G. M. Irwin,50,‡Z. Isvan,9,‡D. E. Jaffe,9,†P. Jaffke,47,† C. James,1,‡K. L. Jen,19,†D. Jensen,1,‡S. Jetter,15,†X. L. Ji,15,†X. P. Ji,51,22,†J. B. Jiao,20,†R. A. Johnson,5,†J. K. de Jong,8,‡ J. Joshi,9,†T. Kafka,27,‡L. Kang,52,† S. M. S. Kasahara,29,‡ S. H. Kettell,9,†S. Kohn,53,†G. Koizumi,1,‡M. Kordosky,32,‡ M. Kramer,35,53,†A. Kreymer,1,‡K. K. Kwan,18,†M. W. Kwok,18,†T. Kwok,54,†K. Lang,16,‡T. J. Langford,7,†K. Lau,46,† L. Lebanowski,22,†J. Lee,35,†J. H. C. Lee,54,†R. T. Lei,52,†R. Leitner,55,†J. K. C. Leung,54,†C. Li,20,†D. J. Li,49,†F. Li,15,† G. S. Li,44,†Q. J. Li,15,†S. Li,52,†S. C. Li,54,47,†W. D. Li,15,†X. N. Li,15,†Y. F. Li,15,†Z. B. Li,25,†H. Liang,49,†C. J. Lin,35,† G. L. Lin,19,†S. Lin,52,† S. K. Lin,46,† Y.-C. Lin,12,† J. J. Ling,25,9,†,‡ J. M. Link,47,† P. J. Litchfield,29,56,‡L. Littenberg,9,† B. R. Littlejohn,31,†D. W. Liu,46,†J. C. Liu,15,†J. L. Liu,44,†C. W. Loh,14,†C. Lu,57,†H. Q. Lu,15,†J. S. Lu,15,†P. Lucas,1,‡
K. B. Luk,53,35,† Z. Lv,58,† Q. M. Ma,15,† X. B. Ma,24,† X. Y. Ma,15,† Y. Q. Ma,15,† Y. Malyshkin,59,†W. A. Mann,27,‡ M. L. Marshak,29,‡D. A. Martinez Caicedo,31,†N. Mayer,27,‡K. T. McDonald,57,†C. McGivern,41,‡R. D. McKeown,60,32,† M. M. Medeiros,17,‡ R. Mehdiyev,16,‡ J. R. Meier,29,‡ M. D. Messier,28,‡W. H. Miller,29,‡ S. R. Mishra,61,‡ I. Mitchell,46,†
M. Mooney,9,† C. D. Moore,1,‡L. Mualem,60,‡J. Musser,28,‡ Y. Nakajima,35,† D. Naples,41,‡ J. Napolitano,62,† D. Naumov,26,† E. Naumova,26,† J. K. Nelson,32,‡ H. B. Newman,60,‡ H. Y. Ngai,54,† R. J. Nichol,39,‡Z. Ning,15,† J. A. Nowak,29,‡ J. O’Connor,39,‡J. P. Ochoa-Ricoux,59,† A. Olshevskiy,26,†M. Orchanian,60,‡R. B. Pahlka,1,‡ J. Paley,4,‡
H.-R. Pan,12,† J. Park,47,† R. B. Patterson,60,‡ S. Patton,35,† G. Pawloski,29,‡ V. Pec,55,† J. C. Peng,34,† A. Perch,39,‡ M. M. Pfützner,39,‡ D. D. Phan,16,‡S. Phan-Budd,4,‡L. Pinsky,46,†R. K. Plunkett,1,‡N. Poonthottathil,1,‡ C. S. J. Pun,54,†
F. Z. Qi,15,† M. Qi,14,† X. Qian,9,† X. Qiu,50,‡ A. Radovic,32,‡ N. Raper,63,† B. Rebel,1,‡ J. Ren,48,† C. Rosenfeld,61,‡ R. Rosero,9,† B. Roskovec,55,†X. C. Ruan,48,† H. A. Rubin,31,‡ P. Sail,16,‡ M. C. Sanchez,3,4,‡J. Schneps,27,‡ A. Schreckenberger,16,‡P. Schreiner,4,‡ R. Sharma,1,‡ S. Moed Sher,1,‡ A. Sousa,5,‡ H. Steiner,53,35,† G. X. Sun,15,† J. L. Sun,64,†N. Tagg,65,‡R. L. Talaga,4,‡W. Tang,9,†D. Taychenachev,26,†J. Thomas,39,‡M. A. Thomson,10,‡X. Tian,61,‡
A. Timmons,21,‡ J. Todd,5,‡ S. C. Tognini,17,‡ R. Toner,37,‡ D. Torretta,1,‡ K. Treskov,26,† K. V. Tsang,35,†C. E. Tull,35,† G. Tzanakos,66,*,‡ J. Urheim,28,‡ P. Vahle,32,‡ N. Viaux,59,† B. Viren,9,†,‡ V. Vorobel,55,† C. H. Wang,13,†M. Wang,20,† N. Y. Wang,45,†R. G. Wang,15,†W. Wang,32,25,†X. Wang,67,†Y. F. Wang,15,†Z. Wang,15,†Z. M. Wang,15,†R. C. Webb,68,‡ A. Weber,8,56,‡H. Y. Wei,22,†L. J. Wen,15,†K. Whisnant,3,†C. White,31,†,‡L. Whitehead,46,†,‡L. H. Whitehead,39,‡T. Wise,6,†
S. G. Wojcicki,50,‡ H. L. H. Wong,53,35,† S. C. F. Wong,25,† E. Worcester,9,† C.-H. Wu,19,† Q. Wu,20,† W. J. Wu,15,† D. M. Xia,69,† J. K. Xia,15,† Z. Z. Xing,15,† J. L. Xu,15,†J. Y. Xu,18,†Y. Xu,25,†T. Xue,22,† C. G. Yang,15,† H. Yang,14,†
L. Yang,52,† M. S. Yang,15,†M. T. Yang,20,† M. Ye,15,† Z. Ye,46,† M. Yeh,9,† B. L. Young,3,†Z. Y. Yu,15,†S. Zeng,15,† L. Zhan,15,†C. Zhang,9,†H. H. Zhang,25,†J. W. Zhang,15,†Q. M. Zhang,58,†X. T. Zhang,15,†Y. M. Zhang,25,†Y. X. Zhang,64,†
Z. J. Zhang,52,† Z. P. Zhang,49,† Z. Y. Zhang,15,† J. Zhao,15,†Q. W. Zhao,15,† Y. B. Zhao,15,† W. L. Zhong,15,† L. Zhou,15,†N. Zhou,49,† H. L. Zhuang,15,†and J. H. Zou15,†
†(Daya Bay Collaboration) ‡(MINOS Collaboration)
1Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 2
Institute of Modern Physics, East China University of Science and Technology, Shanghai
3Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 USA 4
Argonne National Laboratory, Argonne, Illinois 60439, USA
5Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA 6
Physics Department, University of Wisconsin, Madison, Wisconsin 53706, USA
7Department of Physics, Yale University, New Haven, Connecticut 06520, USA 8
Subdepartment of Particle Physics, University of Oxford, Oxford OX1 3RH, United Kingdom
9Brookhaven National Laboratory, Upton, New York 11973, USA 10
Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
11Lancaster University, Lancaster, LA1 4YB, United Kingdom 12
Department of Physics, National Taiwan University, Taipei
13National United University, Miao-Li 14
Nanjing University, Nanjing
15Institute for High Energy Physics, Protvino, Moscow Region RU-140284, Russia 16
Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
17Instituto de Física, Universidade Federal de Goiás, 74690-900, Goiânia, GO, Brazil 18
Chinese University of Hong Kong, Hong Kong
19Institute of Physics, National Chiao-Tung University, Hsinchu 20
Shandong University, Jinan
21School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom 22
Department of Engineering Physics, Tsinghua University, Beijing
23Shenzhen University, Shenzhen 24
North China Electric Power University, Beijing
25Sun Yat-Sen (Zhongshan) University, Guangzhou 26
Joint Institute for Nuclear Research, Dubna, Moscow Region
27Physics Department, Tufts University, Medford, Massachusetts 02155, USA 28
Indiana University, Bloomington, Indiana 47405, USA
29University of Minnesota, Minneapolis, Minnesota 55455, USA 30
Siena College, Loudonville, New York 12211, USA
31Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616, USA 32
Department of Physics, College of William & Mary, Williamsburg, Virginia 23187, USA
33Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom 34
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
35Lawrence Berkeley National Laboratory, Berkeley, California, 94720 USA 36
Universidade Estadual de Campinas, IFGW, CP 6165, 13083-970, Campinas, SP, Brazil
37Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 38
Holy Cross College, Notre Dame, Indiana 46556, USA
39Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom 40
Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP, Brazil
41Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA 42
Department of Physics, University of Minnesota Duluth, Duluth, Minnesota 55812, USA
43Department of Physics, University of Warsaw, PL-02-093 Warsaw, Poland 44
Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai Laboratory for Particle Physics and Cosmology, Shanghai
45
Beijing Normal University, Beijing
46Department of Physics, University of Houston, Houston, Texas 77204, USA 47
Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
48China Institute of Atomic Energy, Beijing 49
University of Science and Technology of China, Hefei
50Department of Physics, Stanford University, Stanford, California 94305, USA 51
School of Physics, Nankai University, Tianjin
52Dongguan University of Technology, Dongguan 53
Department of Physics, University of California, Berkeley, California 94720, USA
54Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 55
Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
56Rutherford Appleton Laboratory, Science and Technology Facilities Council, Didcot, OX11 0QX, United Kingdom 57
Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA
58Xi’an Jiaotong University, Xi’an 59
60Lauritsen Laboratory, California Institute of Technology, Pasadena, California 91125, USA 61
Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA
62Department of Physics, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122, USA 63
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
64China General Nuclear Power Group 65
Otterbein University, Westerville, Ohio 43081, USA
66Department of Physics, University of Athens, GR-15771 Athens, Greece 67
College of Electronic Science and Engineering, National University of Defense Technology, Changsha
68Physics Department, Texas A&M University, College Station, Texas 77843, USA 69
Chongqing University, Chongqing (Received 6 July 2016; published 7 October 2016)
Searches for a light sterile neutrino have been performed independently by the MINOS and the Daya Bay experiments using the muon (anti)neutrino and electron antineutrino disappearance channels, respectively. In this Letter, results from both experiments are combined with those from the Bugey-3 reactor neutrino experiment to constrain oscillations into light sterile neutrinos. The three experiments are sensitive to complementary regions of parameter space, enabling the combined analysis to probe regions allowed by the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE experiments in a minimally extended four-neutrino flavor framework. Stringent limits on sin22θμeare set over 6 orders of magnitude in the sterile mass-squared splittingΔm241. The sterile-neutrino mixing phase space allowed by the LSND and MiniBooNE experiments is excluded forΔm241< 0.8 eV2 at95% CLs.
DOI:10.1103/PhysRevLett.117.151801
The discovery of neutrino flavor oscillations [1,2]
marked a crucial milestone in the history of particle physics. It indicates neutrinos undergo mixing between flavor and mass eigenstates and hence carry nonzero mass. It also represents the first evidence of physics beyond the standard model of particle physics. Since then, neutrino oscillations have been confirmed and precisely measured with data from natural (atmospheric and solar) and man-made (reactor and accelerator) neutrino sources.
The majority of neutrino oscillation data available can be well described by a three-flavor neutrino model [3–5] in agreement with precision electroweak measurements from collider experiments [6,7]. A few experimental results, however, including those from the Liquid Scintillator Neutrino Detector (LSND)[8]and MiniBooNE[9] experi-ments, cannot be explained by three-neutrino mixing. Both experiments observed an electron antineutrino excess in a muon antineutrino beam over short baselines, suggesting mixing with a new neutrino state with mass-squared splitting Δm241≫ jΔm232j, where Δm2ji≡ m2j− m2i, and mi is the mass of the ith mass eigenstate. Precision
electroweak measurements exclude standard couplings of this additional neutrino state for masses up to half the Z-boson mass, so that states beyond the known three active states are referred to as sterile. New light neutrino states would open a new sector in particle physics; thus, con-firming or refuting these results is at the forefront of neutrino physics research.
Mixing between one or more light sterile neutrinos and the active neutrino flavors would have discernible effects on neutrino oscillation measurements. Oscillations from muon to electron (anti)neutrinos driven by a sterile neutrino
require electron and muon neutrino flavors to couple to the additional neutrino mass eigenstates. Consequently, oscil-lations between active and sterile states will also neces-sarily result in the disappearance of muon (anti)neutrinos, as well as of electron (anti)neutrinos[10,11], independently of the sterile neutrino model considered[12,13].
In this Letter, we report results from a joint analysis developed in parallel to the independent sterile neutrino searches from the Daya Bay[14]and the MINOS experi-ments [15]. In this analysis, the measurement of muon (anti)neutrino disappearance by the MINOS experiment is combined with electron antineutrino disappearance mea-surements from the Daya Bay and Bugey-3 experiments
[16] using the signal confidence level (CLs) method
[17,18]. The combined results are analyzed in light of
the muon (anti)neutrino to electron (anti)neutrino appear-ance indications from the LSND[8] and MiniBooNE[9]
experiments. The independent MINOS, Daya Bay, and Bugey-3 results are all obtained from disappearance mea-surements and therefore are insensitive to CP-violating effects due to mixing between the three active flavors. Under the assumption of CPT invariance, the combined results shown constrain both neutrino and antineutrino appearance.
The results reported here required several novel improve-ments developed independently from the Daya Bay–only
[14] and MINOS-only [15] analyses, specifically, a full reanalysis of the MINOS data to search for sterile neutrino mixing, based on the CLsmethod, a CLs-based analysis of the Bugey-3 results taking into account new reactor flux calculations and the Daya Bay experiment’s reactor flux measurement, the combination of the Daya Bay results
with the Bugey-3 results taking into account correlated systematics between the experiments, and, finally, the combination of the Daya Bay + Bugey-3 and MINOS results to place stringent constraints on electron neutrino and antineutrino appearance driven by sterile neutrino oscillations.
We adopt a minimal extension of the three-flavor neutrino model by including one sterile flavor and one additional mass eigenstate. This 3 þ 1 sterile neutrino scenario is referred to as the four-flavor model in the text. In this model, the muon to electron neutrino appearance probability Pνμ→νeðL=EÞ as a function of the propagation length L, divided by the neutrino energy E, can be expressed using a 4 × 4 unitary mixing matrix U by
Pνμ→νeðL=EÞ ¼ X i UliUl0ie−iðm2i=2EÞL 2: ð1Þ In the region where Δm241≫ jΔm232j and for short baselines (ðΔm232L=4EÞ ∼ 0), Eq.(1)can be simplified to
Pνμ→νeðL=EÞ ≈ 4jUe4j2jUμ4j2sin2
Δm2 41L 4E ≈ P¯νμ→¯νe: ð2Þ
A nonzero amplitude for the appearance probability, 4jUe4j2jUμ4j2, is a possible explanation for the MiniBooNE
and LSND results. The matrix element jUe4j2 can be constrained with measurements of electron antineutrino disappearance, as in the Daya Bay[14]and Bugey-3 [16]
experiments. Likewise, jUμ4j2 can be constrained with measurements of muon neutrino and antineutrino disap-pearance, as in the MINOS [15] experiment. For these experiments, the general four-neutrino survival probabil-itiesP¯νe→¯νeðL=EÞ and Pð−Þ
ν μ→ð−Þν μðL=EÞ are P¯νe→¯νeðL=EÞ ¼ 1 − 4 X k>j jUekj2jUejj2sin2Δm 2 kjL 4E ; ð3Þ Pð−Þ ν μ→ð−Þν μðL=EÞ ¼ 1 − 4 X k>j jUμkj2jUμjj2sin2Δm 2 kjL 4E : ð4Þ The mixing matrix augmented with one sterile state can be parametrized by U ¼ R34R24R14R23R13R12 [19], where Rij is the rotational matrix for the mixing angle θij, yielding
jUe4j2¼ sin2θ14;
jUμ4j2¼ sin2θ24cos2θ14;
4jUe4j2jUμ4j2¼ sin22θ14sin2θ24≡ sin22θμe: ð5Þ
Searches for sterile neutrinos are carried out by using the reconstructed energy spectra to look for evidence of oscillations driven by the sterile mass-squared difference Δm2
41. For small values of Δm241, corresponding to slow
oscillations, the energy-dependent shape of the oscillation probability could be measured in the reconstructed energy spectra. For large values corresponding to rapid oscilla-tions, an overall reduction in neutrino flux would be seen. The CLs method [17,18] is a two-hypothesis test that compares the three-flavor (null) hypothesis (labeled3ν) to an alternate four-flavor hypothesis (labeled 4ν). To deter-mine if the four-flavor hypothesis can be excluded, we construct the test statisticΔχ2¼ χ24ν− χ23ν, whereχ24νis the χ2value resulting from a fit to a four-flavor hypothesis, and
χ2
3νis theχ2value from a fit to the three-flavor hypothesis.
TheΔχ2 value observed with data,Δχ2obs, is compared to theΔχ2distributions expected if the three-flavor hypothesis is true, or the four-flavor hypothesis is true. To quantify this, we construct
CLb¼ PðΔχ2≥ Δχ2obsj3νÞ; CLsþb¼ PðΔχ2≥ Δχ2obsj4νÞ;
CLs¼CLsþb
CLb ð6Þ
over a grid of (sin22θ14,Δm241) points for the Daya Bayþ Bugey-3 experiments and a grid of (sin2θ24,Δm241) for the MINOS experiment. CLb measures consistency with the three-flavor hypothesis, and CLsþbmeasures the agreement with the four-flavor hypothesis. The alternate hypothesis is excluded at the α confidence level if CLs≤ 1 − α. The construction of CLs ensures that even if CLsþb is small, indicating disagreement with the four-flavor hypothesis, this hypothesis can only be excluded when CLb is large, indicating consistency with the three-flavor hypothesis. Thus, the CLsconstruction ensures the four-flavor hypoth-esis can only be excluded if the experiment is sensitive to it. Calculating CLb and CLsþb can be done in two ways. The first method is the Gaussian CLsmethod[20], which uses two GaussianΔχ2distributions. The first distribution is obtained by fitting toy Monte Carlo (MC) data assuming the three-flavor hypothesis is true, thus labeled as Δχ23ν. The second distribution is obtained by assuming the four-flavor hypothesis is true (Δχ24ν). The mean of each distribution is obtained from a fit to the Asimov data set, an infinite statistics sample where the relevant param-eters are set to best-fit values for each hypothesis[21]. The Gaussian width for the Asimov data set is derived analyti-cally. In the second method, the distributions of Δχ2 are approximated by MC simulations of pseudoexperiments.
The Gaussian method is used to obtain the Daya Bay and Bugey-3 combined results, while the second method is used to obtain the MINOS results.
The MINOS experiment[22]operates two functionally equivalent detectors separated by 734 km. The detectors sample the NuMI neutrino beam[23], which yields events with an energy spectrum that peaks at about 3 GeV. Both detectors are magnetized steel and scintillator calorimeters, with the 1 kton Near Detector (ND) situated 1 km down-stream of the NuMI production target, and the 5.4 kton Far Detector (FD) located at the Soudan Underground Laboratory[22]. The analysis reported here uses data from an exposure of 10.56 × 1020 protons on target, for which the neutrino beam composition is 91.8%νμ, 6.9% ¯νμ, and 1.3% (νeþ¯νe).
To look for sterile neutrino mixing, the MINOS experi-ment uses the reconstructed energy spectra in the ND and FD of both charged-current (CC) and neutral-current (NC) neutrino interactions. The sterile mixing signature differs depending on the range of Δm241 values considered. For Δm2
41 ∈ ð0.005; 0.05Þ eV2, the muon neutrino CC
spec-trum in the FD would display deviations from three-flavor oscillations. For rapid oscillations driven by Δm2
41 ∈ ð0.05; 0.5Þ eV2, the combination of finite detector
energy resolution and rapid oscillations at the FD location would result in an apparent event rate depletion between the ND and FD. For larger sterile neutrino masses, correspond-ing to Δm241> 0.5 eV2, oscillations into sterile neutrinos would distort the ND CC energy spectrum. Additional sensitivity is obtained by analyzing the reconstructed energy spectrum for NC candidates. The NC cross sections and interaction topologies are identical for all three active neutrino flavors, rendering the NC spectrum insensitive to standard oscillations, but mixing with a sterile neutrino state would deplete the NC energy spectrum at the FD, as the sterile neutrino would not interact in the detector. For large sterile neutrino masses, such a depletion would also be measurable at the ND.
The simulated FD-to-ND ratios of the reconstructed energy spectra forνμCC and NC selected events, including four-flavor oscillations for both the ND and FD, are fit to the equivalent FD-to-ND ratios obtained from data [15]. Current and previous results of the MINOS sterile neutrino searches, along with further analysis details, are described in Refs.[15,24–26]. The MINOS experiment employs the Feldman-Cousins ordering principle [27] in obtaining exclusion limits in the four-flavor parameter space. However, this approach requires a computationally imprac-tical joint fit to be consistent, since it requires minimizing χ2overΔm2
41, a shared parameter between the MINOS and
Daya Bayþ Bugey-3 experiments. Thus, the CLs method described above is used.
While the MINOS experiment does not have any sensitivity to sin2θ14, there is a small sensitivity to sin2θ34 due to the inclusion of the NC channel. During
the fit, sin2θ34is allowed to vary freely in addition toΔm232 and sin2θ23, while sin2θ24 and Δm241 are held fixed to define the particular four-flavor hypothesis that is being tested. Since the constraint on sin2θ34 is relatively weak, the distribution ofΔχ2 deviates from the normal distribu-tion and the Gaussian CLs method cannot be used. The Δχ2
3ν and Δχ24ν distributions are constructed by fitting
pseudoexperiments.
In the three-flavor case, pseudoexperiments are simu-lated using the same parameters listed in Ref. [15], i.e., sin2θ12 ¼ 0.307, Δm221¼ 7.54 × 10−5 eV2 based on a global fit to neutrino data[28], and sin2θ13¼ 0.022, based on a weighted average of results from reactor experiments
[29–31]. For the atmospheric oscillation parameters, equal numbers of pseudoexperiments are simulated in the upper and lower octant (sin2θ23¼ 0.61 and sin2θ23¼ 0.41, respectively), with jΔm232j ¼ 2.37 × 10−3 eV2, based on the most recent MINOS results[32]. The uncertainties on solar oscillation parameters have negligible effect on the analysis, so fixed values are used. In the four-flavor case, jΔm2
32j, sin2θ23, and sin2θ34are taken from fits to data at
each (sin2θ24,Δm241) grid point. In both the three- and four-flavor cases, half of the pseudoexperiments are generated in each mass hierarchy. A comparison of MINOS exclusion contours obtained using the Feldman-Cousins procedure
[15]with those obtained using the CLsmethod is shown in Fig.1. Note that ifΔm241¼ 2Δm312 orΔm241≪ Δm231and sin2θ23 ¼ sin2θ34¼ 1, θ24 can take on the role normally played by θ23. In these cases, the four-flavor model is degenerate with the three-flavor model, leading to regions of parameter space that cannot be excluded.
The Daya Bay experiment measures electron antineu-trinos via inverse β decay (IBD): ¯νeþ p → eþþ n.
24 θ 2 sin 3 − 10 10−2 10−1 1 ) 2 (eV 41 2 mΔ 4 − 10 3 − 10 2 − 10 1 − 10 1 10 2 10 ) Exclusion s CL MINOS 90% C.L. ( Feldman-Cousins Method Method s CL
FIG. 1. Comparison of the MINOS 90% CL contour using the Feldman-Cousins method[15]and the CLs method. The region to the right of the curve is excluded at the 90% CL (CLs).
The antineutrinos are produced by six reactor cores and detected in eight identical Gd-doped liquid-scintillator antineutrino detector (ADs) [33] in three underground experimental halls (EHs). The flux-averaged baselines for EH1, EH2, and EH3 are 520, 570, and 1590 m, respectively. The target mass in each of the two near EHs is 40 tons, and that in the far EH is 80 tons. Details of the IBD event selection, background estimates, and assess-ment of systematic uncertainties can be found in Refs.[29,34]. By searching for distortions in the ¯νeenergy spectra, the experiment is sensitive to sin22θ14 for a mass-squared splitting Δm241∈ ð0.0003; 0.2Þ eV2. For Δm2
41 > 0.2 eV2, spectral distortions cannot be resolved
by the detector. Instead, the measured antineutrino flux can be compared with the predicted flux to constrain the sterile neutrino parameter space. Recently, the Daya Bay Collaboration published its measurement of the overall antineutrino flux[35]. The result is consistent with previous measurements at short baselines, which prefer 5% lower values than the latest calculations [36,37], a deficit com-monly referred to as the reactor antineutrino anomaly[38]. However, the reactor spectrum measurement from the Daya Bay Collaboration[35](and from the RENO Collaboration
[30]and the Double Chooz Collaboration[31]) shows clear discrepancies with the latest calculations, which indicates an underestimation of their uncertainties. The uncertainties on the antineutrino flux models for this analysis are increased to 5% from the original 2% as suggested by Refs. [39,40]. The Daya Bay Collaboration has recently updated the sterile neutrino search result in Ref.[14]with limits on sin22θ14 improved by about a factor of 2 with respect to previous results [41]. This data set is used in producing the combined results presented here.
Two independent sterile neutrino search analyses are conducted by the Daya Bay Collaboration. The first analysis uses the predicted ¯νe spectrum to generate the predicted prompt spectrum for each antineutrino detector simultaneously, taking into account detector effects such as energy resolution, nonlinearity, detector efficiency, and oscillation parameters described in Ref. [29]. A log-like-lihood function is constructed with nuisance parameters to include the detector-related uncertainties and a covariance matrix to incorporate the uncertainties on reactor neutrino flux prediction. The Gaussian CLs method is used to calculate the excluded region. The second analysis uses the observed spectra at the near sites to predict the far site spectra to further reduce the dependency on reactor antineutrino flux models. Both analyses yield consistent results [14].
The Bugey-3 experiment was performed in the early 1990s and its main goal was to search for neutrino oscillations using reactor antineutrinos. In this experiment, two 6Li-doped liquid scintillator detectors measured ¯νe generated from two reactors at three different baselines (15, 40, and 95 m)[16]. The Bugey-3 experiment detected IBD
interactions with the recoil neutron capturing on
6Liðn þ6Li→4Heþ3Hþ 4.8 MeVÞ. Probing shorter
baselines than the Daya Bay experiment, the Bugey-3 experiment is sensitive to regions of parameter space with largerΔm241 values.
The original Bugey-3 results obtained using the raster scan technique are first reproduced employing a χ2 defi-nition used in the original Bugey-3 analysis[16]:
χ2¼X3 i
XNi
j
f½Aaiþ bðEj− 1.0ÞRprei;j − Robsi;jg2
σ2 i;j þX3 i ðai− 1Þ2 σ2 ai þðA − 1Þ2 σ2 A þ b 2 σ2 b; ð7Þ where A is the overall normalization, ai is the relative detection efficiency,b is an empirical factor to include the uncertainties of the energy scale,i represents the data from three baselines, and j sums over the Ni bins at each baseline. The values ofσaiandσbare set at0.014 MeV−1 and0.020 MeV−1, respectively, according to the reported values in Ref.[16]. Theσi;jare the statistical uncertainties. The uncertainty on the overall normalizationσAis set to 5% to be consistent with the constraint employed in the Daya Bay analysis[14]. The ratio of the observed spectrum to the predicted unoscillated spectrum is denoted byRobs
i;j, while
Rpre
i;j is the predicted ratio of the spectrum including
oscillations to the one without oscillations. To predict the energy spectra, the average fission fractions are used
[42], and the energy resolution is set to 5% at 4.2 MeV[16]
with a functional form similar to the Daya Bay 14 θ 2 2 sin 3 − 10 10−2 10−1 1 ) 2 (eV 41 2 mΔ 4 − 10 3 − 10 2 − 10 1 − 10 1 10 2 10 s
Daya Bay/Bugey-3 (reproduced) 90% CL Bugey-3 original RS 90% C.L.
s
Bugey-3 reproduced 90% CL
s
Daya Bay 90% CL
FIG. 2. Excluded regions for the original Bugey-3 raster scan (RS) result[16], for the reproduced Bugey-3 result with adjusted fluxes, for the Daya Bay result[14], and for the combined Daya Bay and reproduced Bugey-3 results. The region to the right of the curve is excluded at the90% CLs.
experiment’s. The predicted energy spectra are validated against the published Bugey-3 spectra [16].
In the Bugey-3 experiment, the change in the oscillation probability over the baselines of the detectors and the reactors is studied with MC simulations assuming that antineutrinos are uniformly generated in the reactor cores and uniformly measured in the detectors, and approximated by treating the baselines as normal distributions. To achieve the combination with the Daya Bay experiment, two changes are made in the reproduced Bugey-3 analysis: the change in the cross section of the IBD process due to the updated neutron decay time [6] is applied, and the anti-neutrino flux is adjusted from the ILLþ Vogel model
[43,44] to that of Huber [36] and Mueller [37], for
consistency with the prediction used by the Daya Bay experiment. These adjustments change the reproduced contour with respect to the original Bugey-3 one, in particular by reducing the sensitivity to regions with Δm2
41 > 3 eV2, with less noticeable effects for smaller
Δm2
41 values. The reproduced Bugey-3 limit on the sterile
neutrino mixing, and the limit obtained by combining the Bugey-3 with the Daya Bay results through a χ2fit, with common overall normalization and oscillation parameters, are shown in Fig.2.
Individually, the MINOS and Bugey-3 experiments are both sensitive to regions of parameter space allowed by the
LSND measurement through constraints on θ24 and θ14, shown in Figs. 1 and 2, respectively. We illustrate this sensitivity in Fig. 3, which displays a comparison of the energy spectra for the Bugey-3 and MINOS data to four-flavor (4ν) predictions produced at the LSND best-fit point[8]as an example. For the Bugey-3 experiment, aΔχ2 value of 48.2 is found between the data and the four-flavor prediction. Taking equal priors between these two models, the posterior likelihood for3ν vs 4ν is 1 vs 3.4 × 10−11in the Bayesian framework. For the MINOS experiment, a Δχ2value of 38.0 is obtained between data and prediction.
The posterior likelihood for3ν vs 4ν is 1 vs 5.6 × 10−9. In our combined analysis, we obtain Δχ2obs as well as Δχ2
3νandΔχ24νdistributions for each (sin22θ14,Δm241) grid
point of the Daya Bay and Bugey-3 combination, and for each (sin2θ24,Δm241) grid point from the MINOS experi-ment. We then combine pairs of grid points from the MINOS and the Daya Bay and Bugey-3 results at fixed values ofΔm241to obtain constraints on electron neutrino or antineutrino appearance due to oscillations into sterile neutrinos. Since the systematic uncertainties of accelerator and reactor experiments are largely uncorrelated, for each (sin22θ14, sin2θ24,Δm241) grid point, a combined Δχ2obs is constructed from the sum of the corresponding MINOS and Daya Bayþ Bugey-3 Δχ2obs values. Similarly, the com-bined Δχ23ν and Δχ24ν distributions are constructed by adding random samples drawn from the corresponding MINOS and Daya Bayþ Bugey-3 distributions. Finally,
Positron Energy (MeV)
1 2 3 4 5 6 Ratio to Three Flavor 0.8 1 1.2 1.4 1.6 Bugey-3 Data LSND Prediction
CC Reconstructed Energy (GeV)
0 10 20 30 40 Ratio to Three Flavor 0.5 1 1.5 2
MINOS CC-selected Data LSND Prediction
FIG. 3. The top panel shows the ratio of the Bugey-3 15 m IBD data to a three-neutrino prediction, while the bottom panel shows the ratio of the MINOS FD-to-ND ratio data for CC events to a three-neutrino prediction. The red lines represent the four-flavor predictions at (Δm241¼ 1.2 eV2, sin22θμe¼ 0.003). The shaded band displays the sizes of the systematic uncertainties. A value of sin22θ14¼ 0.11 is used for the Bugey-3 prediction so that when multiplied by the MINOS90% CLslimit on sin2θ24, it matches sin22θμe¼ 0.003. A Δχ2value of 48.2 is found between the data and this 4ν prediction. Similarly, a value of sin2θ24¼ 0.12 is combined with the Bugey-390% CLslimit onθ14to produce the MINOS four-flavor prediction, resulting inΔχ2¼ 38.0 between the data and the prediction.
2 | 4 μ U | 2 | e4 U = 4| e μ θ 2 2 sin 6 − 10 10−5 10−4 10−3 10−2 10−1 1 ) 2 (eV 41 2 mΔ 4 − 10 3 − 10 2 − 10 1 − 10 1 10 2 10 90% C.L. Allowed LSND MiniBooNE mode) ν MiniBooNE ( ) Excluded s CL 90% C.L. ( NOMAD KARMEN2
MINOS and Daya Bay/Bugey-3
FIG. 4. MINOS and Daya Bayþ Bugey-3 combined 90% CLs limit on sin22θμe compared to the LSND and MiniBooNE 90% CL allowed regions. Regions of parameter space to the right of the red contour are excluded. The regions excluded at 90% CL by the KARMEN2 Collaboration [45] and the NOMAD Collaboration[46]are also shown. We note that the excursion to small mixing in the exclusion contour at around Δm2
the CLsvalue at every (sin22θ14, sin2θ24) point is calculated using Eq.(6), while theΔm241value is fixed. While CLsis single valued at every (sin22θ14, sin2θ24) point for a given value ofΔm241, it is multivalued as a function of sin22θμe [cf. Eq.(5)]. To obtain a single-valued function, we make the conservative choice of selecting the largest CLs value for any given sin22θμe. The 90% CLs exclusion contour resulting from this procedure is shown in Fig.4. Under the assumption ofCPT conservation, the combined constraints are equally valid in constraining electron neutrino or antineutrino appearance. The combined results of the Daya Bayþ Bugey-3 and MINOS experiments constrain sin22θμe< [3.0 ×10−4(90% CLs),4.5 × 10−4(95% CLs)] for Δm241¼ 1.2 eV2.
In conclusion, we have combined constraints on sin22θ14 derived from a search for electron antineutrino disappearance at the Daya Bay and Bugey-3 reactor experiments with constraints on sin2θ24 derived from a search for muon (anti)neutrino disappearance in the NuMI beam at the MINOS experiment. Assuming a four-flavor model of active-sterile oscillations, we constrain sin22θμe, the parameter controlling electron (anti)neutrino appear-ance at short-baseline experiments, over 6 orders of magnitude in Δm241. We set the strongest constraint to date and exclude the sterile neutrino mixing phase space allowed by the LSND and MiniBooNE experiments for Δm2
41 < 0.8 eV2 at a 95% CLs. Our results are in good
agreement with results from global fits (see Refs.[13,47]
and references therein) at specific parameter choices; however, they differ in detail over the range of parameter space. The results explicitly show the strong tension between null results from disappearance searches and appearance-based indications for the existence of light sterile neutrinos.
The MINOS experiment is supported by the U.S. Department of Energy, the United Kingdom Science and Technology Facilities Council, the U.S. National Science Foundation, the State and University of Minnesota, and Brazil’s FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior). We are grateful to the Minnesota Department of Natural Resources and the personnel of the Soudan Laboratory and Fermilab. We thank the Texas Advanced Computing Center at The University of Texas at Austin for the provision of computing resources. The Daya Bay experiment is supported in part by the Ministry of Science and Technology of China, the U.S. Department of Energy, the Chinese Academy of Sciences, the CAS Center for Excellence in Particle Physics, the National Natural Science Foundation of China, the Guangdong provincial government, the Shenzhen municipal govern-ment, the China General Nuclear Power Group, the
Research Grants Council of the Hong Kong Special Administrative Region of China, the Ministry of Education in Taiwan, the U.S. National Science Foundation, the Ministry of Education, Youth and Sports of the Czech Republic, the Joint Institute of Nuclear Research in Dubna, Russia, the NSFC-RFBR joint research program, and the National Commission for Scientific and Technological Research of Chile. We acknowledge Yellow River Engineering Consulting Co., Ltd. and China Railway 15th Bureau Group Co., Ltd. for building the underground laboratory. We are grateful for the ongoing cooperation from the China Guangdong Nuclear Power Group and China Light & Power Company.
Note added.—Recently, a paper appeared by the IceCube Collaboration that sets limits using sterile-driven disap-pearance of muon neutrinos [48]. The results place strong constraints on sin22θ24 for Δm241∈ ð0.1; 10Þ eV2. Further, a paper that reanalyses the same IceCube data in a model including nonstandard neutrino interactions also appeared[49].
*Deceased. §
Present address: Department of Chemistry and Chemical Technology, Bronx Community College, Bronx, New York 10453, USA.
[1] Y. Fukuda et al. (Super-Kamiokande Collaboration),Phys. Rev. Lett. 81, 1562 (1998).
[2] Q. R. Ahmad et al. (SNO Collaboration),Phys. Rev. Lett. 87, 071301 (2001).
[3] B. Pontecorvo, Sov. Phys. JETP 6, 429 (1957). [4] B. Pontecorvo, Sov. Phys. JETP 26, 984 (1968).
[5] Z. Maki, M. Nakagawa, and S. Sakata,Prog. Theor. Phys. 28, 870 (1962).
[6] K. Olive et al. (Particle Data Group), Chin. Phys. C 38, 090001 (2014).
[7] S. Schael (ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration, OPAL Collaboration, SLD Collaboration, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group),Phys. Rep. 427, 257 (2006).
[8] A. Aguilar et al. (LSND Collaboration),Phys. Rev. D 64, 112007 (2001).
[9] A. Aguilar-Arevalo et al. (MiniBooNE Collaboration),
Phys. Rev. Lett. 110, 161801 (2013).
[10] N. Okada and O. Yasuda,Int. J. Mod. Phys. A 12, 3669 (1997).
[11] S. M. Bilenky, C. Giunti, and W. Grimus,Eur. Phys. J. C 1, 247 (1998).
[12] C. Giunti and E. M. Zavanin, Mod. Phys. Lett. A 31, 1650003 (2016).
[13] J. Kopp, P. A. N. Machado, M. Maltoni, and T. Schwetz,
J. High Energy Phys. 05 (2013) 050.
[14] F. P. An et al. (Daya Bay Collaboration), following Letter,
Phys. Rev. Lett. 117, 151802 (2016).
[15] P. Adamson et al. (MINOS Collaboration), this issue,Phys. Rev. Lett. 117, 151803 (2016).
[16] B. Achkar et al.,Nucl. Phys. B434, 503 (1995). [17] A. L. Read,J. Phys. G 28, 2693 (2002).
[18] T. Junk,Nucl. Instrum. Methods Phys. Res., Sect. A 434, 435 (1999).
[19] H. Harari and M. Leurer, Phys. Lett. B 181, 123 (1986).
[20] X. Qian, A. Tan, J. J. Ling, Y. Nakajima, and C. Zhang,
Nucl. Instrum. Methods Phys. Res., Sect. A 827, 63 (2016).
[21] G. Cowan, K. Cranmer, E. Gross, and O. Vitells,Eur. Phys. J. C 71, 1 (2011);73, 2501(E) (2013).
[22] D. G. Michael et al. (MINOS Collaboration),Nucl. Instrum. Methods Phys. Res., Sect. A 596, 190 (2008).
[23] P. Adamson et al. (MINOS Collaboration),Nucl. Instrum. Methods Phys. Res., Sect. A 806, 279 (2016).
[24] P. Adamson et al. (MINOS Collaboration),Phys. Rev. Lett. 107, 011802 (2011).
[25] P. Adamson et al. (MINOS Collaboration),Phys. Rev. D 81, 052004 (2010).
[26] P. Adamson et al. (MINOS Collaboration),Phys. Rev. Lett. 101, 221804 (2008).
[27] G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873 (1998).
[28] G. L. Fogli, E. Lisi, A. Marrone, D. Montanino, A. Palazzo, and A. M. Rotunno, Phys. Rev. D 86, 013012 (2012).
[29] F. P. An et al.,Phys. Rev. Lett. 115, 111802 (2015). [30] J. H. Choi et al. (RENO Collaboration), Phys. Rev. Lett.
116, 211801 (2016).
[31] Y. Abe et al. (Double Chooz Collaboration),J. High Energy Phys. 10 (2014) 086; 02 (2015) 74.
[32] P. Adamson et al. (MINOS Collaboration),Phys. Rev. Lett. 112, 191801 (2014).
[33] F. P. An et al. (Daya Bay Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 811, 133 (2016).
[34] F. An et al. (Daya Bay Collaboration),Phys. Rev. Lett. 112, 061801 (2014).
[35] F. P. An et al. (Daya Bay Collaboration),Phys. Rev. Lett. 116, 061801 (2016).
[36] P. Huber,Phys. Rev. C 84, 024617 (2011);85, 029901(E) (2012).
[37] T. A. Mueller, D. Lhuillier, M. Fallot, A. Letourneau, S. Cormon, M. Fechner, L. Giot, T. Lasserre, J. Martino, G. Mention, A. Porta, and F. Yermia,Phys. Rev. C 83, 054615 (2011).
[38] G. Mention, M. Fechner, T. Lasserre, T. A. Mueller, D. Lhuillier, M. Cribier, and A. Letourneau,Phys. Rev. D 83, 073006 (2011).
[39] A. C. Hayes, J. L. Friar, G. T. Garvey, G. Jungman, and G. Jonkmans,Phys. Rev. Lett. 112, 202501 (2014).
[40] P. Vogel,arXiv:1603.08990.
[41] F. An et al.,Phys. Rev. Lett. 113, 141802 (2014). [42] Y. Declais et al.,Phys. Lett. B 338, 383 (1994).
[43] K. Schreckenbach, G. Colvin, W. Gelletly, and F. Von Feilitzsch,Phys. Lett. B 160, 325 (1985).
[44] P. Vogel,Phys. Rev. D 29, 1918 (1984).
[45] B. Armbruster et al. (KARMEN Collaboration),Phys. Rev. D 65, 112001 (2002).
[46] P. Astier et al. (NOMAD Collaboration),Phys. Lett. B 570, 19 (2003).
[47] S. Gariazzo, C. Giunti, M. Laveder, Y. F. Li, and E. M. Zavanin,J. Phys. G 43, 033001 (2016).
[48] M. G. Aartsen et al. (IceCube Collaboration), Phys. Rev. Lett. 117, 071801 (2016).
[49] J. Liao and D. Marfatia, Phys. Rev. Lett. 117, 071802 (2016).
![FIG. 1. Comparison of the MINOS 90% CL contour using the Feldman-Cousins method [15] and the CL s method](https://thumb-ap.123doks.com/thumbv2/9libinfo/7663947.140678/5.918.507.801.70.364/comparison-minos-contour-using-feldman-cousins-method-method.webp)
![FIG. 2. Excluded regions for the original Bugey-3 raster scan (RS) result [16] , for the reproduced Bugey-3 result with adjusted fluxes, for the Daya Bay result [14] , and for the combined Daya Bay and reproduced Bugey-3 results](https://thumb-ap.123doks.com/thumbv2/9libinfo/7663947.140678/6.918.508.801.70.346/excluded-regions-original-reproduced-adjusted-combined-reproduced-results.webp)
