arXiv:1512.07562v2 [nucl-ex] 17 May 2016 .Lindner, M. .Bergevin, M. 14 .Camilleri, L. .Dietrich, D. ..Crespo-Anad´on,J.I. omsait` ’nri tmqee u nrisAlterna Energies aux et Atomique `a l’Energie Commissariat .Skorokhvatov, M. .Fischer, V. .Minotti, A. .Kuze, M. .Suekane, F. .Maricic, J. .Hofmann, M. .Sch¨onert,S. .Reinhold, B. ..Kalousis, L.N. .Abe, Y. Thi, .Walsh, N. ...Gonzalez, L.F.G. .Osborn, A. 7 etod netgcoe Energ´eticas, Medioambientale Investigaciones de Centro 23 29 24 UAEH NSI23 nvri´ eNne,EoedsMin des Ecole Nantes, Universit´e de CNRS/IN2P3, SUBATECH, 2 30 eateto hsc n srnm,Uiest fTenness of University Astronomy, and Physics of Department 20 eateto hsc n srnm,Uiest fAlabama of University Astronomy, and Physics of Department .Valdiviesso, G. 27 30 27 elrCne o sr n atcePyis Universit¨at Physics, Particle and Astro for Center Kepler 9 8 13 14 10, 22 ..L´opez-Casta˜no,J.M. 25 .Lachenmaier, T. ...Bezerra, T.J.C. .Carr, R. .Djurcic, Z. 9 nttt fNcerRsac fteRsinAaeyo Scie of Academy Russian the of Research Nuclear of Institute .Abrah˜ao,T. 29 12 6 .Franco, D. 29 § 4 .Nagasaka, Y. .Watanabe, H. 25 h nioFriIsiue h nvriyo hcg,Chic Chicago, of University The Institute, Fermi Enrico The 10 20, .Sukhotin, S. 32 15 eateto hsc,Ilni nttt fTcnlg,C Technology, of Institute Illinois Physics, of Department srPriuee omlge nvri´ ai Diderot, Universit´e Paris Cosmologie, et AstroParticule 29 24 28 .Martino, J. .Schoppmann, S. 1 27 eerhCne o etioSine oouUiest,S University, Tohoku Science, Neutrino for Center Research eateto hsc,Dee nvriy hldlha P Philadelphia, University, Drexel Physics, of Department nvriaeEtda eCmia-NCM,Cmia,SP, Campinas, Campinas-UNICAMP, de Estadual Universidade 33 eateto hsc,Kna tt nvriy Manhattan University, State Kansas Physics, of Department 33 19 ..Horton-Smith, G.A. 5 I.Pyiaice nttt WHAce nvriy 520 University, Aachen RWTH Institut, Physikalisches III. hskDprmn,Tcnsh Universit¨at M¨unchen, 857 Technische Department, Physik 31 § 18 eateto hsc,TkoMtooia nvriy Tok University, Metropolitan Tokyo Physics, of Department etoBaier ePsussFıia,Rod aer,RJ Janeiro, de F´ısicas, Rio Pesquisas de Brasileiro Centro eateto hsc,TkoIsiueo ehooy Toky Technology, of Institute Tokyo Physics, of Department .Palomares, C. 16 etrfrNurn hsc,Vrii eh lcsug Vi Blacksburg, Tech, Virginia Physics, Neutrino for Center ascuet nttt fTcnlg,Cmrde Massac Cambridge, Technology, of Institute Massachusetts bevtied ai,Sron ai i´,725PrsCe Paris Cit´e, 75205 Paris Sorbonne Paris, de Observatoire 22 nvriaeFdrld B,UAC at nre P 09210 Andr´e, SP, Santo UFABC, ABC, do Federal Universidade .Kamyshkov, Y. .R¨ohling,M. 7 32 eateto hsc,Ktst nvriy aaiaa 2 Sagamihara, University, Kitasato Physics, of Department .Smith, E. 8 PC nvri´ eSrsor,CR/NP,607Strasb 67037 CNRS/IN2P3, Strasbourg, Universit´e de IPHC, .Crum, K. uncpueo ih stpsi obeChooz Double in isotopes light on capture Muon .Cerrada, M. .Goodenough, L. 17 20 3 11 21 5 4 eateto hsc,Kb nvriy oe 5-51 Ja 657-8501, Kobe, University, Kobe Physics, of Department a-lnkIsiu ¨rKrpyi,617Hiebr,G Heidelberg, 69117 f¨ur Kernphysik, Max-Planck-Institut ..dsAnjos, dos J.C. iohm nttt fTcnlg,Hrsia 3-13 J 731-5193, Hiroshima, Technology, of Institute Hiroshima 3 5 nvriyo or ae or ae nin 65,USA 46556, Indiana Dame, Notre Dame, Notre of University .Vassilopoulos, N. .Franke, M. ron ainlLbrtr,Agne lios649 USA 60439, Illinois Argonne, Laboratory, National Argonne 18 8 .Almazan, H. 23 9 11 25 oubaUiest;NwYr,NwYr 02,USA 10027, York New York, New University; Columbia 20 nvriyo aiona ai,Clfri 51,USA 95616, California Davis, California, of University 26 30 18 .Sumiyoshi, T. 10 .Matsubara, T. .Navas-Nicol´as,D. .Bezrukov, L. oouGki nvriy edi 8-13 Japan 981-3193, Sendai, University, Gakuin Tohoku .Wiebusch, C. 6 30 R ucao nttt,138 ocw Russia Moscow, 123182 Institute, Kurchatov NRC ..Lane, C.E. 1 7 .Soiron, M. 7 ..Cucoanes, A.S. .Roncin, R. ..Shaevitz, M.H. ..Pepe, I.M. ..LoSecco, J.M. 7 24 .Chauveau, E. 15 29 .Kaneda, M. Dul ho Collaboration) Chooz (Double 3 .Hourlier, A. 20 .Furuta, H. 5 ..Goodman, M.C. .Dracos, M. 10 .Alt, C. 13 1 22 28 Dtd a 8 2016) 18, May (Dated: 1 28 5 4 .Lasserre, T. .Spitz, J. .Blucher, E. .Veyssiere, C. .Wurm, M. .Sun, Y. .Perasso, S. .Rybolt, B. .Mention, G. 23, 7 21 8 27 1 .Novella, P. 25 25 ∗ .Sharankova, R. .Lubsandorzhiev, B. .Appel, S. 4 ..Kaplan, D.M. .Chimenti, P. .Damon, E. 22 .Gil-Botella, I. 19 .Ishitsuka, M. 2, ie,Cnr eSca,IF,911GfsrYet,Franc Gif-sur-Yvette, 91191 IRFU, Saclay, de Centre tives, .Etenko, A. § .Stahl, A. 30, ,14 4, 6 3 24 4 enloia,CEA,200 ard Spain Madrid, 28040, Tecnol´ogicas, CIEMAT, y s .Svoboda, R. .Brugi`ere,T. 14 .Haag, N. 14 .Porta, A. †† .Sakamoto, Y. 7, 29 .Letourneau, A. .Vivier, M. .Meregaglia, A. .Yang, G. ¶ 10 ..Barriere, J.C. .Oberauer, L. 1 31 ¨ bne,706T¨ubingen, Germany T¨ubingen, 72076 12 27 ..Dawson, J.V. 27 18 .Stancu, I. e nxil,Tnese396 USA 37996, Tennessee Knoxville, ee, 7 ucloa lbm 58,USA 35487, Alabama Tuscaloosa, , ..Collin, A.P. 29 .Kawasaki, T. NSI23 CEA/IRFU, CNRS/IN2P3, .Shrestha, D. 23 .Giot, L. .Jochum, J. .Fallot, M. sd ats 40 ats France Nantes, 44307 Nantes, de es iao lios666 USA 60616, Illinois hicago, 9 13 cs ocw171,Russia 117312, Moscow nces, .Hara, T. 22 ,12 3, nslai 90,USA 19104, ennsylvania .Pronost, G. .Terao, K. 14 8Grhn,Germany Garching, 48 g,Ilni 03,USA 60637, Illinois ago, 6Ace,Germany Aachen, 56 .Lucht, S. na 8-58 Japan 980-8578, endai 26 ass656 USA 66506, Kansas , .Buck, C. uet 23,USA 02139, husetts 29-8,Brazil 22290-180, , o 9-37 Japan 192-0397, yo, .vnFeilitzsch, von F. ,1285,Japan 152-8551, o, gna201 USA 24061, rginia .Yermia, F. .Santorelli, R. e 3 France 13, dex 207,Japan 52-0373, 14 2 23 22 14 29 38-7,Brazil 13083-970, ...Stokes, L.F.F. ug France ourg, ermany .Lhuillier, D. 23 17 .Miletic, T. .G¨oger-Neff,M. 4 20 .Baussan, E. .Obolensky, M. 30 50 Brazil -580, 19 apan 15 .d Kerret, de H. 16 .Felde, J. .Haser, J. 1 .Conover, E. 20 .Jollet, C. pan 23 .Tonazzo, A. .Maeda, J. .Sibille, V. .Kemp, E. .Busenitz, J. .Reichenbacher, J. 23 n .Zimmer V. and 7 10 9, 20 14 ..Schilithz, A.C. 29 22 22 † 30 .Milincic, R. .Hellwig, D. 28, 14 ..Lm Jr, Lima H.P. ..Fernandes, S.M. 32 6 29 .Bekman, I. .Wagner, S. 4 4 .Kaether, F. .Strait, M. ..Conrad, J.M. 4 .Dhooghe, J. .Onillon, A. .Sinev, V. ‡ .Kryn, D. 2 .Gomez, H. ..Trinh H.H. .Mariani, C. .Cabrera, A. 2 29 10, 1 6, 5 1 13 4 5 20 ∗∗ § 4 5 4 9 19 33 2 e 4 2

Using the Double Chooz detector, designed to measure the neutrino mixing angle θ13, the products of µ− capture on 12C, 13C, 14N and 16O have been measured. Over a period of 489.5 days, 2.3 × 106 stopping cosmic µ− have been collected, of which 1.8 × 105 captured on carbon, nitrogen, or oxygen nuclei in the inner detector scintillator or acrylic vessels. The resulting isotopes were tagged using prompt neutron emission (when applicable), the subsequent beta decays, and, in some cases, β-delayed neutrons. The most precise measurement of the rate of 12C(µ−,ν)12B to date is reported: +0.11 × 3 −1 +0.35 6.57−0.21 10 s , or (17.35−0.59 )% of nuclear captures. By tagging excited states emitting gammas, 12 +0.14 × 3 −1 the ground state transition rate to B has been determined to be 5.68−0.23 10 s . The heretofore unobserved reactions 12C(µ−, να)8Li, 13C(µ−,νnα)8Li, and 13C(µ−,νn)12B are measured. Further, a population of βn decays following stopping muons is identified with 5.5σ significance. Statistics limit our ability to identify these decays definitively. Assuming negligible production of 8He, the reaction 13C(µ−, να)9Li is found to be present at the 2.7σ level. Limits are set on a variety of other processes.

PACS numbers: 25.30.Mr, 27.20.+n, 14.60.Pq

I. INTRODUCTION for instance electron recoil. Muon capture measurements provide input for under- A µ− that stops in a material is rapidly captured standing nuclear structure and can be used to validate into an atomic orbital and subsequently rapidly cascades models of neutrino cross sections, such as PQRPA. This down into the 1s state (referred to herein as atomic cap- is particularly true for measurements of production of ture). From this state, a muon can either decay or may the exclusive states of 12B [2]. The reaction is a close undergo nuclear capture. This process is the muon analog analogue to neutrino capture interactions such as those to the electron capture decay that proton-rich isotopes that will be observed in the event of a galactic supernova. undergo. However, muon capture is always energetically In each, about ∼ 20 MeV is available for excitations, of- favorable and therefore competes with muon decay re- ten leading to nucleon emission and a variety of excited gardless of the isotope. The large mass of the muon also states. Another similar situation occurs in the baryon- makes available a wide variety of final states. In addi- number violating process of proton or bound-neutron de- tion to converting a proton to a neutron, nucleons can cay to invisible products, as is being studied by several be ejected from the nucleus [1]. large underground detectors. While not currently a com- 12 − 12 Measurements of the probabilities of these various petitive technique, the rate of C(µ ,ν) Bg.s. has also states are interesting for reactor neutrino experiments, been used as input for measurement of gP [3]. for example, because they form backgrounds to the in- The structure of this paper is as follows. In Sec. II, the verse beta decay reaction. In particular, production detector is described, including its isotopic composition. of isotopes that undergo beta-delayed neutron emission In Sec. III, the rate of stopping muons in a clean sample (henceforth called βn isotopes) forms a nearly irreducible of events (the “high-purity sample”) is found. This rate background, since the inverse beta decay signal is a is used in Sec. IV to find the probabilities of forming 12B positron and a neutron. Production of ordinary beta- and 13B. These probabilities are then used in Sec. V to unstable isotopes is less troublesome for reactor neu- find the stopping muon rate in a less clean, but three trino experiments, but as these isotopes often have Qβ times larger, sample of stopping muons (the “loose sam- values far in excess of natural radioactivity, they will ple”). Total nuclear and atomic capture rates for each contribute to the high-energy accidental spectrum of relevant isotope, along with their systematic errors, are delayed-coincidence searches. In addition, it could be tabulated here. This larger sample is used to analyze relevant for experiments whose signal is a single event, production of isotopes in the following sections. Analysis of all the rest of the isotopes follows: βn emit- ters are presented in Sec. VI, the 12Be decay chain in Sec. VII, and a variety of simple beta decays in Sec. VIII. ∗ Now at ELI-NP, “Horia Hulubei” National Institute of Physics Section IX shows exclusive measurements of 12B states. and Nuclear Engineering, 077125 Bucharest-Magurele, Romania Finally, Sec. X concludes. † Now at Department of Physics, University of Maryland, College Park, Maryland 20742, USA. ‡ Now at Department of Physics, Kobe University, Kobe, 658-8501, Japan. § Now at Department of Physics & Astronomy, University of II. THE DETECTOR Hawaii at Manoa, Honolulu, Hawaii 96822, USA. ¶ Now at Instituto de F´ısica Corpuscular, IFIC (CSIC/UV), 46980 The Double Chooz experiment consists of two nearly Paterna, Spain. ∗∗ Corresponding author. E-mail address: [email protected] identical detectors, the near and far detectors, placed (M. Strait). 400m and 1km, respectively, from a commercial nuclear †† Now at Institut f¨ur Physik and Excellence Cluster PRISMA, Jo- reactor. It has been described in detail elsewhere [4]. It hannes Gutenberg-Universit¨at Mainz, 55128 Mainz, Germany. consists of four concentric liquid zones, passive shielding 3 and an outer veto of plastic scintillator. The innermost 5. Capture of neutrons from nuclear de-excitation: three zones form one optical volume as follows: 10–100 µs after µ capture

• The neutrino target is a cylinder with height 2.5 m 6. β or βn decay of daughter nucleus: 10 ms–10 s after and diameter 2.3 m filled with gadolinium-loaded µ capture liquid scintillator. The gadolinium allows for effi- 7. Capture of neutron from βn decay: 10–100 µs after cient and nearly background-free detection of neu- βn decay trons because of its large thermal cross section and the 8MeV of gammas released from each capture, Signals 1, 5, 6 and 7 are easily observable in Double which rise well above the background from natural Chooz. In particular, neutrons (5 and 7) can be detected radioactivity. by the 2.22 MeV gamma resulting from capture on hy- drogen in either the neutrino target or gamma catcher, • The gamma catcher is a cylindrical layer with thick- or by the 8 MeV of gammas resulting from capture on ness 0.6 m filled with liquid scintillator without gadolinium in the neutrino target. The efficiency for ob- gadolinium. Its purpose is to provide an interac- serving these neutrons is acceptable, but lower than the tion region for gammas produced in the neutrino neutron efficiency of the Double Chooz neutrino analysis target. because the trigger is not fully efficient following large • The buffer is a 1.1 m layer of non-scintillating min- signals such as muons. eral oil surrounding the neutrino target and gamma Signal 4 with gammas is observable with some com- catcher. In it are mounted 390 10” PMTs. The plications due to muon-induced deadtime and baseline oil shields the scintillator from PMT glass radioac- shifts. Signal 2 is not observable because it is always tivity as well as externally produced gammas and prompt and completely masked by the muon track’s light. neutrons. It would be easily observable in a segmented detector, however, at least for high Z targets (for instance, gadolin- ium gives muonic x-rays at 4.7 MeV and 1.8 MeV, and The neutrino target is separated from the gamma about 1MeV of softer x-rays and Auger electrons). Sig- catcher by a clear acrylic vessel with thickness of 8 mm, nals 3 and 4 with charged particles are not visible because and the gamma catcher from the buffer by an acrylic the scintillation is highly quenched. vessel of thickness 12 mm. The neutrino target, gamma catcher and buffer are collectively called the inner detec- In Double Chooz, therefore, the coincidence can be up to 5-fold, but as it turns out, no reactions using all 5 tor. signals are practical to observe. Examples do exist for The inner detector is contained in a steel vessel, outside 1+6 (track+β, such as 12B produced by 12C, Sec. IV), of which is a 0.5 m thick layer of liquid scintillator called 1+5+6 (...with a neutron, such as 12B produced by the inner veto, in which 78 8” PMTs are mounted. The 13C, same section), 1+6+7 (track+βn, such as 9Li pro- inner veto is, in turn, surrounded by 15 cm of passive duced by 13C, see Sec. VI), 1+5+6+7 (...with a neutron, steel shielding. Above the steel shield, the outer veto, such as 17N produced by 18O, same section), or 1+4+6 consisting of several large-area plastic scintillator panels, (track+gamma+β, excited states of 12B, see Sec. IX). provides additional muon tagging and tracking. The far detector is located under a hill with 300 meters water equivalent overburden. The muon rate through A. Candidate Isotopes the inner veto is 40 Hz, of which about 0.3% stop in the neutrino target or gamma catcher. Only data from the The most common isotope in Double Chooz is 12C, but far detector is included in this analysis. The far detector 13 14 16 17 18 has been running since 2011. The first 489.5 days of C, N, O, O, and O are also present in relevant quantities. While there is also hydrogen in the detec- livetime are used in this analysis. − Muon capture can be observed with, in principle, up tor, µ never undergoes nuclear captures on it. In the to a seven-fold coincidence: case that the muon captures atomically on hydrogen, it is always quickly picked off by a heavier element [1]. 1. Muon track Some previous data exists for partial capture rates in 12C, 14N and 16O, as summarized in Ref. [1]. Some newer 2. Muonic x-rays and Auger electrons from the atomic results on nitrogen and oxygen are also available [5, 6]. 13 cascade: ≪ 1 ns after stop For C, no previous measurements of partial capture rates are available. 3. Capture nuclear recoil: O(1 µs) after the atomic Tables I and II display all isotopes that could possibly cascade be observed in Double Chooz from muon capture on any stable isotope of carbon, nitrogen, or oxygen. This is 4. γ/charged particles from nuclear de-excitation: the same as listing all possible muon-capture products of usually ≪ 1 ns after capture, but > 1 µs in some 18O, i.e., anything that can be made by removing zero cases or more nucleons from 18N. In Table I, isotopes analyzed 4 in this paper are shown non-italicized. Stable isotopes minor loss in visible energy, with the exception of those are shown as long dashes (—) and those that decay too in the gamma catcher vessel that escape into the buffer. slowly as dots (•). Isotopes that undergo strong decays The neutrino target scintillator has an additional 21 kg are not shown. Isotopes that can only be formed from of oxygen, and the gamma catcher scintillator has 3 kg. 17O or 18O are italicized. Because of the rarity of these After deriving the rate of nuclear captures on carbon two parent isotopes, their daughters are not measured, in Sec. IV, these figures will be used to derive an esti- but some are taken into account when measuring other mate for the number of nuclear captures on oxygen. One isotopes. major difficulty arises. While the nuclear capture prob- ability given a µ− bound to an oxygen nucleus is well- measured, the rate of atomic capture is uncertain. As TABLE I. Beta-decaying isotopes that can be produced by discussed in [1], there is no good rule for what happens muon capture in Double Chooz. The lower left box contains those that can be produced from 12C. in mixed targets. A large systematic error is taken for this uncertainty in Sec. V. 12N • — — 16N 17N 18N Nitrogen is only present in the scintillators, with 4.8 kg 9C • • — — • 15C 16C 17C in the neutrino target and 2.8 kg in the gamma catcher. 8B —— 12B 13B 14B 15B A similar difficulty with regard to the atomic capture • — • 11Be 12Be 14Be probability exists with nitrogen as with oxygen. Given 14 — — 8Li 9Li 11Li the small total amount of nitrogen, only N is important, 15 6He 8He the contribution of N being completely negligible. Muons may also capture on gadolinium in the neu- trino target scintillator, or the various components of steel in the calibration system and phototubes. How- ever, despite the higher probabilities of nuclear capture B. About Carbon when µ− become bound to these atoms, 96.3% in the case of gadolinium [10], the total amounts available are The neutrino target and gamma catcher scintillators sufficiently small that these elements can be ignored both and acrylic vessels contain 24.0 t of carbon. From EA- as possible opportunities for measurement and as sources IRMS measurements, the molar 13C fractions of the of background for the measurements presented here. Double Chooz scintillators are known to be 1.0925(1)% for the neutrino target and 1.0906(1)% for the gamma − catcher. The atomic capture rates for different isotopes III. RATE OF STOPPING µ of an element are identical. The nuclear capture rate on 13C is a few percent lower than that of 12C [1]. Because The analyses below determine the number of decay the individual relative errors are 0.01%, these values can events for various isotopes. To translate these counts be treated as exact for our purposes. Even the difference to probabilities, one needs to know the number of nu- in 13C fractions in the two scintillators is only 0.17% rel- clear µ− captures. This number is obtained by counting ative. The most precise measurement reported in this reconstructed stopping muons and using a Monte Carlo paper has a statistical error over 1% relative, so the neu- simulation to get the µ−/µ+ ratio, giving the number of trino target/gamma catcher difference can be neglected stopping µ−. Using previous experimental data, this can and a mass-weighted average value of 1.0919% used in- be translated into the number of nuclear µ− captures. stead, again treated as exact. Overall, it is expected that Double Chooz has no capability to distinguish between (1.01 ± 0.06)% of the nuclear captures on carbon are on µ+ and µ− tracks. From studies using the MUSIC [11] 13C. Monte Carlo simulation along with charge ratio data from MINOS [12, 13] and L3+C [14], it is estimated that (44.1±0.3)% of stopping muons are µ−, which gives C. About Oxygen and Nitrogen a 0.7% normalization error for all measurements herein. Results from MUSIC were cross-checked using a custom Both the gamma catcher and neutrino target scintil- fast Monte Carlo simulation incorporating the Gaisser lators contain nitrogen and oxygen due to their PPO model [15], as modified by Guan et al [16]. The error is (C15H11NO) component. The neutrino target scintilla- dominated by the systematic error from L3+C, with only tor additionally has oxygen in the gadolinium complex a small contribution resulting from the modeling of our (GdO6C33H57) and in tetrahydrofuran (C4H8O) [8, 9]. overburden. The acrylic (C5H8O2) vessels also contribute oxygen. Muons that stop in the inner detector scintillator can The vast majority of the oxygen is in the acrylic ves- be identified by selecting events with a large energy depo- sels. The neutrino target vessel, including supports and sition in the inner detector and energy in the inner veto stiffeners, contributes 138 kg of oxygen, while the gamma consistent with a single muon crossing. By reconstruct- catcher vessel contributes 260 kg. Since the acrylic is ing candidates under both stopping and through-going thin, most decays in it should be observable with only a hypotheses and selecting based on the relative goodness- 5

TABLE II. Decay characteristics [7] for all detectable isotopes that could be produced, in principle, from muon capture in Double Chooz, and the most likely reaction(s) producing them. Reactions are marked as “exotic” if more than one charged particle or more than two neutrons are emitted, and “obs.” if they have been observed prior to this work.

Isotope Decay mode Half-life (ms) Qβ (MeV) Qβn Reaction Comment 6He β− 801 3.505 12C(µ−, νnpα)6He Exotic 8He β−: 16% βn 119.1 10.664 8.631 13C(µ−, νpα)8He Exotic 8Li β−α 839.9 16.004 12C(µ−, να)8Li 13C(µ−, νnα)8Li 9Li β−: 50.8% βn 178.3 13.606 11.942 13C(µ−, να)9Li 11Li β−: 83% βn 8.75 20.551 20.049 13C(µ−, ν2p)11Li Exotic 11Be β− 13 810 11.509 12C(µ−, νp)11Be 12Be β− 21.49 11.708 13C(µ−, νp)12Be 14Be β−: 81% βn 4.35 16.29 15.32 18O(µ−, νn3p)14Be Exotic 8B β+α 770 16.958 12C(µ−, ν4n)8B Exotic 12B β− 20.20 13.369 12C(µ−, ν)12B Obs. 13C(µ−, νn)12B 13B β−: 0.29% βn 17.33 13.437 8.491 13C(µ−, ν)13B 14B β− 12.5 20.644 16O(µ−, ν2p)14B Exotic 15B β−: 93.6% βn 9.93 19.085 17.867 18O(µ−, νn2p)15B Exotic 9C β+pα 126.5 15.473 14N(µ−, ν5n)9C Exotic 15C β− 2449 9.772 16O(µ−, νp)15C Exotic 16C β−: 99% βn 747 8.010 5.521 18O(µ−, νnp)16C 17C β−: 32% βn 193 13.161 7.276 18O(µ−, νp)17C 12N β+ 11.000 16.316 16O(µ−, ν4n)12N 16N β− 7130 10.421 16O(µ−, ν)16N Obs. 17N β−: 95.1% βn 4173 8.679 4.536 18O(µ−, νn)17N 18N β− 620 13.896 18O(µ−, ν)18N

of-fit, an 80% pure sample of muons with stopping points It was found that (99.72 ± 0.19)% of muons passing in the neutrino target or gamma catcher can be obtained. these cuts were stopping muons. This was determined The remaining 20% are primarily muons that stop in the by testing the uniformity of the probability of a Michel buffer and through-going muons that pass through in- decay following a stopping muon candidate across the efficient regions of the inner veto. Because of Double selected spatial region. It was cross-checked, at lower Chooz’s underground location, the level of contamination precision, by verifying that the total number of observed by stopping pions is negligible. The muon reconstruc- Michel decays over 10 MeV was consistent with the se- tion algorithm has been described in detail in Ref [17]. lected stopping muon count. Efficiencies for this study The position resolution for the stopping point is typically were evaluated using the Michel spectra for µ− bound to 150mm in each of x, y, and z. carbon [18] and free µ+ [19]. A second cross-check veri- fied the spatial uniformity of the probability of observing In order to select a high-purity sample of stopping a 12B decay after a stopping muon candidate. muons, a series of further selection cuts is used. In par- ticular, candidate muons must have reconstructed stop- To test the rate of reconstruction failures directly, a ping points far from the bottom and sides of the gamma sample of through-going muon events from our data set catcher since many muons reconstructed to stop in these was modified to remove inner veto hits at the endpoint. regions are in fact through-going. The stopping position This causes them to resemble muons that stop in the must have z > −1.175m and r < 1.05m, where (0, 0, 0) buffer, allowing us to test the rate at which such muons is the center of the neutrino target. Further, the en- reconstruct with end points far from the edge. No such ergy deposition in the inner veto must be within a tight reconstructions were found, and a limit was set that less range consistent with the reconstructed crossing, and the than 0.03% of the selected sample consists of such mis- reduced χ2 of the muon track fit must be less than 2.0. reconstructions. Because our technique of hit removal Finally, stopping muon candidates are rejected if another is only an approximation for the real background, this muon event precedes them by less than 0.5 ms. This en- study is treated as a cross-check for numerical purposes, sures that any neutrons produced can be assigned to the but gives us confidence that the purity quoted above is correct muon. conservative. 6

In this high purity sample, there are 1628874 recon- 12 13 structed stopping muons. Of the µ−, (99.8 ± 0.1)% be- TABLE III. Results for B and B production from carbon, come bound in carbon atoms. The uncertainty on this expressed as a probability per atomic capture (top), per nu- clear capture (middle) and as a transition rate (bottom). In number derives from the uncertainty on the probability each case, the total error is given, and then each component − of a muon becoming attached to non-carbon atoms, as N − µ − of the error is shown. µ gives the error due to count- described in Sec. IIC. From the purity and µ fractions ing, P(cap) is the error due to knowledge of the total nuclear 5 − above, this gives (7.149 ± 0.054) × 10 µ that are avail- capture rate, and τµ− is the error due to the knowledge of the able to undergo nuclear capture on carbon. Given total bound µ− lifetime. Limits are given at 90% CL. nuclear capture probabilities of (7.69±0.09)% and (7.3± 12 13 Probability per atomic capture (%) 0.4)% for C and C [1], respectively, and 489.5 days 12 of livetime, the nuclear capture rates in the high purity Reaction Prob., total error Stat Nµ− B eff. . . 12 12 →12 +0 022 +0 016 ± ± sample are 111.1 ± 0.6/day for C and 1.16 ± 0.06/day C B 1.322−0.042 −0.040 0.010 0.010 13 12 for 13C. C→ Bn 3.75 ± 0.36 ±0.36 ±0.03 ±0.03 13C→13B < 2.8

IV. 12B/13B ANALYSIS Probability per nuclear capture (%) 12 Reaction Prob., total error Stat Nµ− B eff. P(cap) 12 12 →12 +0.35 +0.21 ± ± ± Previous experiments have measured B production C B 17.35−0.59 −0.52 0.13 0.13 0.21 by stopping muons in carbon, although none have done so 13C→12Bn 51.6 ± 5.6 ±5.0 ±0.4 ±0.4 ±2.6 using a method that can separate production by 12C and 13C→13B < 40 13 C [1, 20]. Given its short half-life and high Qβ value of 12 (see Table II), B is readily observable. This applies to Capture rate (×103s−1) 13 12 B as well, but is quite difficult to distinguish from B 12 Reaction Rate, total error Stat Nµ− B eff. τµ− given its very similar half-life and beta spectrum. 12 →12 +0.11 +0.08 ± ± ± C B 6.57−0.21 −0.20 0.05 0.05 0.01 13C→12Bn 18.4 ± 1.8 ±1.8 ±0.1 ±0.1 ±0.1 13C→13B < 14 A. Selection

Beta decay candidates must occur at least 1ms after a stopping muon without a Michel electron. The efficiency tures. In the zero neutron case, the signal is either 12 − 12 13 − 13 for observing Michel decays is about 78%, as determined C(µ ,ν) B or C(µ ,ν) B. In the one neutron case, 13 − 12 by comparing the number found in the high-purity sam- the signal is C(µ ,νn) B. The two neutron case exists ple of stopping muons to the number expected given the to account for this reaction when an additional accidental muon charge ratio and inclusive capture probability. The neutron-like event is selected, which has a probability of −4 stopping muon must be followed by at least 100s of con- 1.1×10 . The neutron efficiency during the data taking tinuous data-taking. period analyzed here is a function of the preceding muon An event is selected as a beta decay if it is not light energy and has a value, averaged over the neutrino target noise (spontaneous emission of light from PMTs, de- and gamma catcher, of (57 ± 1)%. scribed in [4]) and is between 4 and 15 MeV. The energy An extended unbinned maximum likelihood [28] fit us- cut has an efficiency of (85.0 ± 0.7)%, as found from a ing the event timing is done simultaneously for these low-background subset of 12B events. In evaluating this three reactions. The fit takes into account neutron ef- efficiency, the portion of the 12B spectrum below 0.5 MeV ficiencies on an event-by-event basis, with nuisance pa- was filled with a beta spectrum [21–27] Monte Carlo sim- rameters for production of 8Li (half-life (839.9±0.9)ms), ulation, taking into account the detector response. In 8Li+n, 9Li (half-life (178.3 ± 0.4) ms), 9Li+n, 16N (half- addition, it must not occur within 0.5 ms after any sub- life (7.13 ± 0.02)s) and accidental coincidences. The sequent muon, to avoid selecting neutron captures as beta lifetimes of each isotope are allowed to float with pull decays. terms constraining them within published errors. The The overall selection efficiency, including inefficiency total probability of isotope production from 13C is con- due to light noise removal, the 12B energy cut, Michel strained to be at most 100% with a pull term taking into electron selection, subsequent muon veto and the require- account the error on the total nuclear capture rate on ment of continuous data-taking, is (81.0 ± 0.6)%. No po- 13C. The neutron efficiency is included as a fit parameter sition cut is made for the beta decay in order to avoid and allowed to float within its errors. incurring additional error due to the efficiency of such a Selected events and the fits are shown in Fig. 1. The cut. While this is advantageous for the measurement of results of the fit for each reaction follow. For each, three 12B, a position cut will be used in the following sections numbers are given: (1) the probability per atomic cap- for all other isotope searches to reduce background. ture, which has the least dependence on external mea- This sample of events is divided into those in which surements, (2) the capture rate, which relies on previous the muon is followed by zero, one, or two neutron cap- measurements of the bound µ− lifetime, (2028 ± 2)ns for 7

12C→12B V. TOTAL NUCLEAR CAPTURE RATES 103 0 neutron 1 neutrons For all remaining reactions, a looser selection is used 102 2 neutrons for stopping muons to increase the statistics for processes

ms ms 13 C→12Bn less common than 12B production. This selection re- laxes the above-described requirements on stopping po- 10 sition, track fit quality and inner veto energy. Stopping

Events/10 muon candidates are accepted if the stopping point is 1 13C→ not within 35 mm of the bottom or sides of the gamma 12Bn,"n" catcher and if the fit reduced χ2 is less than 10. The 10−1 constraints on acceptable inner veto energy are also loos- 100 200 300 400 500 ened. Time since stopping muon (ms) To determine the number of true stopping µ− in this expanded sample, the ratio of 12B-like events found in the two samples is used. The high-purity sample has FIG. 1. 12B production with and without a neutron, inter- 7882 ± 95, while 17 580 ± 150 additional events are found − − preted as 13C(µ ,ν)12B (filled circles), 13C(µ , νn)12B (open in the expanded sample. This gives (2.309 ± 0.032) × 106 circles). Neutron efficiency and accidental neutron-like events atomic captures on carbon in the new sample. Some are accounted for, including those occurring along with a real impurity and a larger normalization error are therefore neutron (open squares; “n” denotes an accidental neutron- traded for 3.2 times the statistics. like event). The solid red curves show the fit results, while 12 13 the dashed red lines give the 12B components thereof. The two samples have very similar C/ C ratios, as described in Sec. II B, however the new sample contains substantially more oxygen by including the neutrino tar- get vessel and supports. There is therefore a concern that 12 13 the simple ratio above may be incorrect due to presence C and (2037 ± 8)ns for C [1], and (3) the probability 12 16 − 12 per nuclear capture, which depends on the total nuclear of B from the reaction O(µ , να) B. Data on this capture probability. The total nuclear capture probabil- reaction appears to be limited to a single emulsion ex- ity has been determined using the bound µ− lifetime, so periment [30], but even under moderately pessimistic as- the external uncertainties on the capture rate and nuclear sumptions, this is enough to argue that it has a negligible capture probability have the same origin. However, since effect. determining the nuclear capture probability involves sub- The following rates for the expanded sample are found using the total number of atomic captures for carbon tracting two similar numbers, P = (τfree − τbound)/τfree, the fractional uncertainty is much larger. above and the known total nuclear capture probability: Results are given in Table III. All sources of errors • 12C handled in the fit, such as the neutron efficiency and ex- – ternal lifetime measurements, are considered statistical. 4664 ± 65 atomic captures/day Note the asymmetric errors for 12C(µ−,ν)12B. These are – 358.8 ± 6.5 nuclear captures/day due to the possibility of a large contribution from 13B. 13 Since the best fit for 13B is zero, this source of error is • C one-sided. – 51.5 ± 0.71 atomic captures/day The most recent previous measurement of any of these – 3.75 ± 0.19 nuclear captures/day processes comes from Ref. [20], in which the probabil- ity per atomic capture for 12C→12B is given as (1.55 ± The error on the 12C nuclear capture rate is shared 0.06)%. This was converted by Ref. [29] to a rate of equally between the 12B-like event statistics discussed (7.05±0.27)×103 s−1 and subsequently quoted by Ref. [1] above and the probability of nuclear capture following as a probability per nuclear capture of (18.6±0.7)%. Two atomic capture. The error on 13C results mainly from corrections to these figure are needed. From the begin- the probability of nuclear capture. ning, the contributions from 13C are neglected, which Rates for other isotopes are estimated using the chemi- requires a downward correction. Second, the rate re- cal composition of the detector. These are given as ranges sults from an erroneous division of the atomic capture to emphasize the large uncertainties surrounding proba- probability by the free muon lifetime, rather than the bility of atomic capture in chemical compounds. Based bound lifetime. This requires an upward correction. Our on data presented in Ref. [1], it is conservatively assumed best estimates of the correct figures for comparison are that oxygen (nitrogen) overcaptures by a factor of 1–2 (1.51 ± 0.07)% for the probability per atomic capture, (1–1.5) as compared to its number density. The proba- (19.6 ± 0.8)% per nuclear capture, and (7.44 ± 0.35) × bility within these ranges will be treated as uniform: 103 s−1 for the rate. In all cases, our figures are about 2.5σ lower. • 0.2–0.3 14N nuclear captures/day 8

16 12 103 B 14 Signal Background 12 Background 102 10 8

10 Events/bin 6 Events/50mm 4 1 2 0 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 µ-12B distance (m) ∆r3 (m3)

FIG. 2. Distance between selected 12B events and preceding FIG. 3. The distance-cubed distribution of βn events less stopped muon (black), as compared to a background sam- than 0.4 s after a stopping muon with all other cuts applied. ple (red). The efficiency for a distance cut is the fraction of The dashed line is the ∆r cut. background-subtracted 12B within the cut.

16 lowing the muon and the case of selecting one neutron fol- • 6–13 O nuclear captures/day lowing the muon. The flat background is formed from ac- • 1–2 17O nuclear captures for the entire data set cidental coincidences between stopping muon candidates and βn-like events. It is due almost entirely to reac- • 5–12 18O nuclear captures for the entire data set. tor neutrino interactions. As at least one reactor of the Chooz power plant was active for 98% of this data set’s livetime, this background is unavoidable. The efficiency 9 VI. βn ISOTOPES of this selection for Li βn decays in the neutrino target with the neutron capturing on gadolinium is (82.0±0.5)% The Double Chooz detector is optimized for the detec- and for decays in the gamma catcher with the neutron + capturing on hydrogen is (62.7 ± 0.4)%. tion ofν ¯e via the inverse beta decay reaction, p(¯νe,e )n. The resulting positron gives a prompt signal and the sub- In the case of no neutron requirement, the time dis- sequent capture of the neutron on either gadolinium or tribution is fit using the unbinned maximum likelihood hydrogen gives a delayed coincidence. A major back- method [28] under the hypothesis that the excess over ground to this process is production of 9Li by cosmic a flat background consists of a combination of sev- muons, as its βn decay produces a signal that is nearly eral βn isotopes (half-lives given in parentheses): 11Li 13 8 9 indistinguishable from the inverse beta decay signal. For (8.75 ms), B (17.33 ms), He (119.1 ms), Li (178.3 ms), this analysis, the existing inverse beta decay selection 16C (747 ms), and 17N (4.183 s). The fit is done in three is used to select βn decays in the neutrino target and bins of reactor power to take advantage of the lower back- gamma catcher, both for events with captures on gadolin- ground rates during zero- and one-reactor periods. Some ium [4] and hydrogen [31]. potentially-present βn isotopes were excluded from the 14 15 12 An excess over background of βn events is found near fit. First, Be, B and Be were excluded because their stopping muons both in time and space. Events for which half-lives of 4.35 ms, 9.93 ms and 22 ms are close to those 11 13 the reconstructed distance from the muon stopping point of Li and B, and, as will be shown in Sec. VIA, there 17 to the β decay is less than 300mm are selected for the is no evidence of an O(10ms) component. Second, C fit described below. The efficiency of this cut is esti- was excluded because its half-life of 193 ms is very close 9 18 − 17 mated using the sample of 12B events (see Sec. IV A) to Li’s and it can only be produced by O(µ ,νp) C. and is found to be (92.0 ± 0.5)% in the neutrino target With a βn branching ratio of 32%, it is expected to con- and (74.9 ± 0.5)% in the gamma catcher (see Fig. 2). tribute much less than 1 event for any reasonable esti- − 18 Fifteen βn-like events are selected within 300 mm and mate of the (µ ,νp) probability. Third, N is excluded 16 400 ms of stopping muons. The spatial distribution for because its half-life of 620 ms is very close to C’s and these events is shown in Fig. 3. The close correlation in with a βn branching ratio of only 7%, the expected num- space demonstrates that the isotopes are being produced ber of events is less than one regardless of the probability 18 − 18 at the stopping point, rather than along the muon track. of O(µ ,ν) N. This also excludes the possibility that they are created With all six isotopes free in the fit, there is a 5.5σ by correlated through-going muons. preference for a βn signal over the background-only hy- The time distributions are shown in Fig. 4 for the case pothesis. The fit is unable to constrain the probabili- in which no requirement is put on neutron detection fol- ties of producing the isotopes with half-lives longer than 9

16 (a) 14 Data 1 68%, 90% CL 12 Fit with 1σ error Neutrons ignored 0.8 10 1 neutron 8 0.6 He probability 8 Events/0.2s 6 0.4 3

4 10 0.2 2 0 0 0 0.5 1 1.5 2 2.5 3 50 100 0 0.1 0.2 0.3 0.4 0.5 Time since stopping muon (s) 103 9Li probability 16 (b) 14 Data, 1 neutron FIG. 5. 90% and 68% contours for 9Li and 8He with no neu- 12 Fit with 1σ error tron requirement (violet) and requiring a neutron (blue), with probabilities given per natC capture. 10 8

Events/s nat 6 a muon capture in C is found to be (2.4 ± 0.9(stat) ± 0.04(syst)) × 10−4. The systematic error is dominated 4 by the uncertainty on the number of µ− captures. If no 2 constraint is put on 8He, only limits can be set on it and 9 9 8 −4 0 Li. The Li limit with He unconstrained is < 4 × 10 0 0.5 1 1.5 2 2.5 3 50 100 at 90% CL. For 8He it is < 7 × 10−4 at 90% CL. Time since stopping muon (s) If 9Li were produced via 12C(µ−,νn2p)9Li, most events

nat − 9 would have an observable neutron capture between the FIG. 4. Observation of C(µ ,νX) Li. (a) With no require- stopping muon and the β decay. Because only a minor- ment for a neutron following the muon. (b) Requiring exactly ity of stopping muon candidates satisfy this demand, re- one neutron. The fit results for 9Li plus correlated (16C, 17N) quiring observation of this neutron reduces the neutrino and accidental (¯νe) backgrounds are shown. Note the change of horizontal scale at 3 s. background considerably. Efficiency for observing these neutrons is reduced by deadtime following muons dur- ing the data period used in this paper; it is 57% for the 9Li’s due to the amount of accidental background. With neutrino target and 87% for the gamma catcher. all isotopes free to take any value in the fit, significant In fact, few of the events survive the neutron require- degeneracy exists between these and the shorter lived ment, as shown in Fig. 4. The remaining events give an isotopes. In order to be able to measure the 9Li and overall significance of βn production of 3.4σ and are com- 18 − 17 8He probabilities, the contributions from 16C and 17N patible with the expected rate of O(µ ,νn) N. The 9 8 are therefore given pull terms constraining their proba- fitted amount of Li+ He in the two samples is incom- 12 − 9 bilities to (5 ± 5)% and (50 ± 25)%, respectively, based patible with the hypothesis of C(µ ,νn2p) Li at the 13 − 9 on previous measurements of similar reactions in other 2.7σ level, indicating that the reaction C(µ , να) Li 9 isotopes [1, 5]. This done, the significance of 9Li and 8He most likely is responsible for the Li produced by stop- specifically being present is 2.7σ. As shown in Fig. 5, ping muons. Under this interpretation, and assuming no 8 13 there is little power to distinguish these two isotopes from He production, the probability for production from C each other. is (2.4 ± 0.9(stat) ± 0.05(syst))%. As shown in Fig. 6 the beta spectrum of selected βn events is compatible with that of 9Li plus the reactor 11 13 neutrino background. While the statistics do not allow A. Li and B a detailed fit, the event at 9.47 MeV provides further evidence against the hypothesis that neutrinos or other The above analysis also constrains 11Li and 13B, which backgrounds are the only events present, since only a would appear as early βn events given their half lives very small fraction of reactor neutrinos reach this energy, of 8.75 ms and 17.33 ms, respectively. Both would be and the rate of other neutrino backgrounds is small com- produced from 13C without neutrons. The constraint on pared to the neutrino rate. It is also incompatible with 13B is independent of that found in Sec. IV, since in that all events being 8He, 16C, 17C, or 17N (see βn endpoint fit the β mode was used. in Table I). The efficiency for selecting 11Li is reduced to 92.7% Assuming no 8He, the probability of forming 9Li from compared to 9Li due to events lost in the 1 ms muon 10

8 are very similar in energy and lifetime. The first decay (12Be→12B, half-life 21.49 ms, β endpoint 11.7 MeV) is 7 Data 12 IBD bkgd estimate selected with a similar procedure as used to find B in 6 9Li Sec. IV. The decay is required to occur 1–100ms after the 12 5 IBD+9Li stopping muon (92.9% efficiency, using the Be lifetime), IBD-only within 400 mm of its stopping point (91.6% efficiency, 4 as judged by the sample of 12B decays, as in Sec. VI),

Events/MeV 3 and have energy 3–12MeV (89 ± 2% efficiency, based on 2 Monte Carlo simulation). The overall selection efficiency for the 12Be decay is (75 ± 2)%. 1 If a 12Be candidate is found, the selection is then re- 0 12 0 2 4 6 8 10 12 peated to search for the B decay. The distance cut is Prompt energy (MeV) applied relative to the 12Be decay candidate, since the position reconstruction for point-like events has higher resolution than that for muons. The 12B decay is re- FIG. 6. Prompt energy for 9Li candidates with ∆t < 0.5 s. quired to occur 1–150ms after the 12Be decay (96.0% An IBD background estimate from offtime samples is shown efficiency), within 400 mm (97% efficiency), and have en- in dashed red. MC for 9Li is shown in dashed blue, normalized ergy 3–15MeV (92.5 ± 0.7% efficiency). The 12Be and so that the sum (solid black) matches the data. In dashed red 12B decays are not allowed to occur within 1ms of each is shown the IBD-only spectrum normalized to the data. The other to avoid selection of inverse beta decay events or highest energy event has 9.47 MeV. 12B produced by neutron spallation. The overall selec- tion efficiency for the 12B is (85 ± 1)%. The selection efficiency for the decay chain is (63 ± 2)%. 10 No events are selected. An upper limit is set of Data, no neutrons < 0.20% per 13C capture at 90% CL. 8 Fit with 1σ error

6 VIII. β ISOTOPES

8 Events/0.05s 4 A. Li

2 For 8Li, for which the signal is a single beta decay (half- life 839.9 ms, β endpoint ∼13MeV), the same analysis as 0 0 0.1 0.2 0.3 0.4 0.5 was used to measure 12B in Sec. IV is used, but with Time since stopping muon (s) modifications to reduce background. The 8Li decay is required to have an energy of 5–14MeV and be within 400 mm of the stopping muon. Events are selected with 11 13 FIG. 7. Search for Li and the βn mode of B. The dashed and without neutrons following the muon. Events with line shows the best fit, which finds no significant amount of a neutron are interpreted as 13C(µ−,νnα)8Li and those 11Li or 13B. without as 12C(µ−, να)8Li. Since the 8Li lifetime is fairly close to the 9Li lifetime, 11 inverse beta decay candidates are excluded from the sam- veto. The fraction of Li that undergoes βn decay is 9 13 ple to reduce contamination from Li. The remaining 83%. The efficiency for selecting B is likewise 96.1% 9 relative to 9Li. Its βn branching fraction is only 0.29%. 49.2% of Li that undergo plain β decay are not affected by this cut. The small amount of remaining 9Li is con- The procedure described in the previous section is re- strained with pull terms derived from the βn analysis. peated, but requiring no neutrons. The fit finds no ev- To suppress background caused by muon-induced idence for either isotope (see Fig. 7). Because of the 12C(n, p)12B, a likelihood classifier is used that takes as low probability of 13B-βn, this fit adds no significant in- input the distance between a candidate decay and the formation to the result of the 12B/13B fit described in most recent through-going muon and the number of neu- previous sections. The 11Li probability, allowing the 13B tron captures following that muon [4]. This classifier re- contribution to float freely, is < 0.7% at 90% CL. moves 50% of the accidental background and has a signal efficiency of 90.6%. The selected events and fit results are shown in Fig. 8. 12 VII. DECAY CHAIN: Be If the 8Li half-life is allowed to float without a pull term in the zero (one) neutron sample alone, the result is 12 +120 +260 The isotope Be is a special case because it decays 870−100 ms (750−270 ms), as compared to the accepted via a 2-step chain to 12C via 12B. The two beta decays value of 839.9 ms. 11

such as 12C(µ−,νn3He)8Li or 12C(µ−,νndp)8Li occur at 250 (a) Data, 0 neutrons any significant rate. 200 Fit with 1σ error s s B. Isotopes Produced with Many Neutrons 150 The isotopes 8B, 12N and 9C must be produced via 100 8 Events/0.5 12 Li B 16 the emission of 4 or more neutrons by the parent nu- N cleus following muon capture, which allows for a nearly 50 background-free search. First, 12C(µ−,ν4n)8B is consid- ered. The resulting 8B has a half-life of 770 ms and a β+ 0 2 4 6 8 10 12 14 endpoint of ∼14MeV (it decays to a broad resonance of Time since stopping muon (s) 8Be), providing up to 15 MeV of visible energy. The aver- age efficiency for observing all four neutrons is (48±2)%. (b) 25 Candidate 8B events are selected with 4–18MeV, which Data, 1 neutron has (97 ± 1)% efficiency due to the positron annihilation 20 Fit with 1σ error following the β+ decay. Candidates are required to be s s within 400 mm of the stopping muon. These energy and 15 position cuts are shared with the other isotopes in this section. The overall efficiency is (40±2)%. No events are −5

Events/0.5 10 selected, and a limit of < 3.2 × 10 per nuclear capture on 12C at 90% CL is set. 5 Next, 16O(µ−,ν4n)12N is examined. With a β+ end- point of 17.3 MeV and half-life of only 11 ms, we restrict 0 the search to 1–100ms and can allow events with either 2 4 6 8 10 12 14 Time since stopping muon (s) 3 or 4 observed neutrons without admitting significant background. As 12N would be produced primarily in the 35 (c) acrylic, and the neutron efficiency is a function of posi- 8 30 Li data tion, this efficiency is reevaluated and found to be 70% Monte Carlo for seeing at least 3 out of 4 neutrons. The overall selec- 25 tion efficiency is 54%. No events are selected. A limit is MeV

−4 16 20 set of < 8×10 per capture on O at 90% CL. The sys- tematic error on the number of oxygen captures is taken 15 into account in this limit using the method described in

Events/0.5 10 Ref. [32] taking the prior to be flat in the range quoted in Sec. V. 5 Finally, we search for 9C. Possible production mech- anisms include 16O(µ−,νp6n)9C, 16O(µ−,νd5n)9C, and 0 4 6 8 10 12 14 16 18 20 14N(µ−,ν5n)9C. The half-life of 9C is 127 ms and it has Decay energy (MeV) a β+ endpoint of 15.5MeV. Events are selected between 1ms and 1s if at least four neutrons are observed after the muon. In the case of oxygen, it is conservatively as- 8 12 8 16 FIG. 8. Li search. (a) Joint fit for B, Li, N and acciden- sumed that the true number of neutrons is five. Given tals when no neutrons follow the muon. (b) Same, with one this assumption, the neutron efficiency is 64% for an over- neutron. (c) Energy of events in the zero-neutron case with all efficiency of 53%. With no signal and no background, a tighter cut of ∆r < 200 mm when 0.3 s < ∆t< 2 s (points). −4 The solid line shows Monte Carlo normalized to the data. a limit of < 9×10 at 90% CL is set. In the case of nitro- gen, the neutron efficiency is 63% and overall efficiency is 55%. A limit is set of < 3.6% per nuclear capture on 14 The probability of 12C(µ−, να)8Li per nuclear cap- N at 90% CL. ture is found to be (0.64 ± 0.04(stat) ± 0.02(syst))%, where the systematic error is dominated by the uncer- 15 11 tainty on the 8Li energy cut efficiency. The probability C. Long-lived Isotopes: C & Be of 13C(µ−, ναn)8Li per nuclear capture is found to be +1.1 15 16 11 (5.1−1.0(stat) ± 0.3(syst))%, where the systematic error The isotopes C, N and Be are those with the is dominated by the uncertainty on the fraction of muons longest half-lives included in this analysis, being 2.449, that undergo nuclear capture on 13C. It should be noted 7.13 and 13.81 s, respectively. Since the fraction of cap- that since Double Chooz is nearly blind to heavy charged tures on 16O that produce 16N is already known to be particles, these probabilities are not correct if reactions (11 ± 1)% [1], it is treated as a background for the other 12

pull term is used for 16N, constraining it to the ex- (a) 140 pected number of events within errors. No significant Data 11 15 amount of the other isotopes is found. Limits are set of 120 Fit without Be, C < 0.20% for 12C(µ−,νp)11Be at 90% CL and < 9% for 11 15 s s Fit with Be, C 16O(µ−,νp)15C at 90% CL. 100 Events/4 80 D. 6He

60 8Li The half-life of 6He is very close to 8Li’s (801 and 40 840 ms, respectively), but it has a much lower β end- 10 20 30 40 50 60 70 80 90 100 point of 3.51 MeV. When fitting for 8Li above, any possi- Time since stopping muon (s) ble contribution from 6He is removed by the energy cut. 6 (b) To search for He, however, it is necessary to fit the spec- 0.4 trum, setting this analysis apart from all others reported Best fit on in this paper. 6 0.3 68% CL To search for a correlation between low energy He Be (%)

11 90% CL decays and their parent muons, a complex fit is needed to reduce the accidental background. Most of this back- 0.2 ground results from gamma decays outside the gamma catcher, such as in the PMTs and surrounding rock, and 0.1 so drops dramatically as one moves towards the center Probability of of the neutrino target. Therefore, a binned fit is done in energy and position. There are five spatial bins, the first 0 0 2 4 6 8 10 12 14 16 four of which have approximately equal volume: Probability of 15C (%) 1. r < 740 mm and |z| < 740mm (2.546m3), where r is horizontal distance from the center of the neu- FIG. 9. (a) Search for 11Be and 15C. The solid (dashed) line trino target and z is the vertical distance. shows the best fit without (with) 11Be or 15C. The lower curve shows the contribution of 8Li; all contribution from 12B is to 2. r < 933 mm and |z| < 933 mm, excluding the in- the left of the plot area due to its short half-life. (b) Statistics- nermost volume (2.557 m3) only confidence regions for 15C and 11Be. Blue (tan) shows 68% (90%) CL. 3. r < 1068 mm and |z| < 1068 mm, excluding the innermost two volumes (2.551 m3) isotopes. It and 15C can be produced by oxygen in the 4. r> 1068mm or |z| > 1068 mm and inside the neu- acrylic, while 11Be is produced from carbon, primarily in trino target (2.759 m3) the scintillator. Accidental background limits our ability to observe 5. In the gamma catcher (22.74 m3) long-lived isotopes. For this search, a very tight spatial cut is made, restricting the decay candidate to be within Each spatial bin is binned in energy with 0.125 MeV 200 mm of the muon. Events are vetoed if any neutrons bins in the range 0.375–15MeV. The following selection are observed. The candidate must be at least 1ms after is used: The time since the stopping muon must be at the most recent muon anywhere in the detector and at least 0.3s and not more than 1.602s (two 6He half-lives). least 0.1 ms after the previous trigger. The 12B likeli- The lower bound reduces the background from correlated hood (see Sec. VIIIA) is applied. The decay energy is 12B to 1.1 events for the whole data set. The decay must restricted to 4–12MeV. The efficiencies are 33% for 11Be, be within 200 mm of the muon stopping point, at least 27% for 15C and 27% for 16N. 0.1 ms since the last trigger, at least 1 ms since the last A joint fit for 12B, 8Li, 15C, 16N, and 11Be is performed. muon, and must not have a high likelihood of being 12B With all isotopes freely floating, the fit favors the pres- produced by a through-going muon. In four separate ence of some combination of 15C, 16N and 11Be, as com- analyses, the muon must be followed by exactly 0, 1, 2, pared to none, at 6.4σ (see Fig. 9). The fit prefers to ex- or 3 neutrons. 16 +1.3 2 6 plain nearly all of the excess as N, finding 7.2−3.4 × 10 The He efficiency after these cuts ranges from 25% for 16N events, corrected for efficiencies, compared to an ex- the zero-neutron case to 10% for the three-neutron case. pectation of (3.0–7.0)×102 given the amount of oxygen in The fit is done with 16 free parameters: the detector and the known 16N production probability. To produce the final results for 11Be and 15C, a (1) The amount of 6He. 13

104 (a) (a) Data 10 Data Best fit Best fit 103 All bkgd All bkgd Accidental bkgd Accidental bkgd 1

102 Events/MeV Events/MeV 10−1

10 10−2 200 2 4 6 8 10 12 2 4 6 8 10 12 5 100

0 0

−100 Signal - bkgd Signal - bkgd −5 −200 2 4 6 8 10 12 2 4 6 8 10 12 Energy (MeV) Energy (MeV)

103 (b) (b) Data 10 Data Best fit Best fit 102 All bkgd All bkgd Accidental bkgd Accidental bkgd 1

10 Events/MeV Events/MeV 10−1

1 10−2

60 5

40 0 20 Signal - bkgd Signal - bkgd 0 −5 2 4 6 8 10 12 2 4 6 8 10 12 Energy (MeV) Energy (MeV)

FIG. 10. (a) Fit for 6He with zero neutrons. (b) Same, for FIG. 11. (a) Fit for 6He with two neutrons. (b) Same, for one neutron. This is a display binning that combines the four three neutrons. The conventions are the same as in Fig. 10. neutrino target regions. The accidental background is shown in solid red. Stacked on this is the correlated background (8Li and 16N) in solid blue. The best fit including 6He is shown in dotted red. 14

TABLE IV. Results for 6He search with various neutron re- 103 Accept quirements. Data 14B MC, arb norm Nn signif. limit value 102 0 0.5σ < 0.43% — +0.14 ± 1 2.7σ < 0.47% (0.33−0.13 (stat) 0.02(syst))% 2 0.5σ < 7 × 10−4 — 10 3 0.2σ < 8 × 10−4 — Events/0.5MeV

1 5 10 15 20 25 (5) The accidental background normalization in each Energy (MeV) region. This background is measured using an off- time window. The normalization is constrained by a pull term to be within the statistical errors of the FIG. 12. Energy cut for 14B search, showing no events in the off-time sample. signal region. The data below the cut is primarily 12B.

(5) The amount of 8Li in each region, which is the dom- 12 inant background at the 6He endpoint for the inner IX. EXCLUSIVE STATES OF B regions. When 12B is formed in an excited state, it is possible (5) The amount of 16N in each region. This is al- to observe gammas from its de-excitation. This allows lowed to float freely in each region since its 6.1 MeV measurements both of the rate of transition to excited gamma means that the number reconstructed in states and, by subtraction, of the ground state. Because each region is not simply the fraction produced Double Chooz has 4π coverage and good gamma contain- there. The inclusion of 16N is not very impor- ment, each state can be identified unambiguously, despite tant, but accounts for the 6–7 MeV peak seen in the “unbelievably capricious” [1] arrangement of bound the plots and avoids slightly overestimating the 8Li levels, giving nearly degenerate individual gamma ener- background in the signal region. gies, that has plagued earlier measurements. The states of 12B are well known, with three relevant bound levels at 951keV, 1674keV and 2621keV, each The results are shown in Figs. 10 and 11 and Table IV. of which has previously been shown to be populated by There are no clear signals, but the 1 neutron case does muon capture on 12C. As will be shown, our data sug- have an excess. Without claiming to have discovered this gests that some unbound levels are also populated at a process, we note that 12C(µ−,νpα)7He would give this measurable rate, including 3759 keV. signal since 7He immediately decays via neutron emission to 6He. In contrast, the 0, 2, and 3 neutron final states would require less favorable combinations of charged par- A. Selection ticle emission. In order to only use events for which the trigger has been shown to be fully efficient and the event energy reli- 14 E. B able, only stopping muons depositing less than 215 MeV in the inner detector are used, this being (38.6±0.4)% of With its 12.5 ms half-life and extremely high Q value stopping muons. Also due to the behavior of the trigger, of 20.6 MeV, 14B can be identified with very little back- the times of the events are limited as follows: ground by looking for early events above the 12B β end- point. Events are therefore selected if the candidate de- 1. When studying 953keV and 1674keV levels, the cay has 15–22MeV, occurs between 1ms and 62.5ms af- capture must be 4 µs ≤ t< 5 µs after the muon. ter the stopping muon, and within 400 mm of the stop- 2. For 2621keV and 3759keV, 3 µs ≤ t< 5 µs. ping point. The energy cut efficiency is evaluated us- ing beta branch probabilities found at TUNL [33] and is 3. To search for higher levels: 2 µs ≤ t< 5 µs. found to be 39%. The overall efficiency is 31%. No events are observed with no background (see Fig. 12), giving a Using the bound muon lifetime, these timing require- limit of < 0.16% at 90% CL for 16O(µ−,ν2p)14B, includ- ments have efficiencies of 5.5%, 14.3% and 28.6%, respec- ing a systematic error on the number of oxygen captures. tively. See Table V for a summary of isotope production re- To reduce background from other processes, notably sults. 12C(µ−,νn)11B∗, it is necessary to require observation of 15

possibility is that these originate from the 6600 keV level TABLE V. All measurements of isotope production probabil- of 12B, but as this assignment seems less clear, we simply ities per nuclear muon capture in this work. All limits are set at 90% CL and include systematic errors. Protons and note that it appears that other states are populated to alphas are shown as products for illustration; they are not some extent. Similarly, the five events between 10 MeV observed. The reaction product “X” indicates several possi- and 25 MeV are significantly over the background of 0.15 ble unobserved additional products. The 9Li results assume events. no 8He, and the 13C(µ−, να)9Li result assumes no contribu- tion from 12C. Reaction Probability/capture B. Fit 12C(µ−, ν0nX)6He < 0.43% 12C(µ−, ν1nX)6He < 0.47% Figure 13 shows the fits used to extract the number of 12C(µ−, ν2nX)6He < 7 × 10−4 events at each level. The fit for selection 1 is used to find 12C(µ−, ν3nX)6He < 8 × 10−4 the number of 953 keV and 1674 keV events, while that 12C(µ−, ν4n)8B < 3.2 × 10−5 for selection 2 is used to find the number of 2621 keV and 3759keV events. The fit for selection 3 is used only to 12C(µ−, να)8Li (0.64 ± 0.04(stat) ± 0.02(syst))% demonstrate the level of consistency of the higher energy 12C(µ−, νp)11Be < 0.20% data with expectations. The fit includes terms for each 12C(µ−, ν)12B (17.35+0.21 (stat) ± 0.27(syst))% −0.52 of the following, which will be explained in detail in the natC(µ−, νX)8He < 7 × 10−4 following sections: natC(µ−, νX)9Li (2.4 ± 0.9(stat) ± 0.04(syst)) × 10−4 12 12 ∗ 12 13 − 8 +1.1 ± • The signal: gammas from C→ B → Bg.s.γ C(µ , νnα) Li (5.1−1.0(stat) 0.3(syst))% 13C(µ−, να)9Li (2.4 ± 0.9(stat) ± 0.05(syst))% 13 − 11 • Accidental background from the sequence (1) stop- C(µ , ν2p) Li < 0.7% 12 13 − 12 ping muon track (2) muon decay (3) accidental B- C(µ , νp) Be < 0.20% like event. Event (2) is selected as the gamma, giv- 13 − 12 ± ± C(µ , νn) B (51.6 5.0(stat) 2.6(syst))% ing a Michel spectrum. 13C(µ−, ν)13B < 40% 14N(µ−, ν5n)9C < 3.6% • Accidental background from the sequence (1) stop- ping muon track — the muon creates 12B in the 16O(µ−, ν2p)14B < 0.16% 16 − 9 −4 ground state (2) accidental gamma-like event (3) O(µ , νp6n) C < 9 × 10 12 16 − 15 B decay. This gives an accidental spectrum O(µ , νp) C < 9% mostly at low energy from detector radioactivity. 16O(µ−, ν4n)12N < 8 × 10−4 • Correlated background from 13C→8Li∗.

• Correlated background from 13C→12B∗+n, where the 12B beta decay as well as the gammas. These events the neutron is lost. are selected in a similar way as in Sec. IV, with the ad- ditional requirements that the decay be between 2–60 ms 13 12 • Correlated background from C→ Bg.s.+n, in after the stopping muon and reconstruct within 400 mm which the neutron captures early and is selected of the muon endpoint. By requiring the beta decay to oc- as the gamma. cur 2 ms after the muon stop, we avoid selecting neutron captures as 12B. • Background from through-going muons producing Given these requirements, the overall efficiency is 12B and several neutrons via spallation. 1.09% for selection 1, 4.14% for selection 2 and 6.8% for selection 3, with 1.5% relative error on each, with the Following the sections on each background, additional requirements on muon energy and gamma timing being systematics are discussed. the main drivers. Selected events are shown in Fig. 13. The 2621keV and 952 keV levels are clearly visible. The 1674 keV level 1. Accidentals is not so clear, but fortunately is already known to be present. The accidental spectrum was derived by repeating the There are also four events in selection 2 between selection with the timing window for 12B beta decays 3500 keV and 4000 keV, which may be due to the shifted to be a long time after the muon. Many win- 3759 keV level. This level is known to de-excite via dows were used to give a high-statistics determination of gamma emission some fraction of the time [34]. It is the spectrum. The accidentals characterized in this way therefore included in the fits below. Further, in se- include both the case of an uncorrelated gamma (up to lection 3 there are six events between 5800keV and ∼3 MeV) with a real 12B decay, and the case of a Michel 7400keV, which also rises well above background. One electron with an uncorrelated 12B candidate. 16

Selection 1 Selection 1 9 8 10 7 1 6 5 10−1 4 10−2 Events/0.1MeV 3 Events/0.1MeV

2 − 10 3 1 0 10−4 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0.7 1 2 3 4 5 6 7 8 9 10 γ energy (MeV) γ energy (MeV)

22 Selection 2 Selection 2 Selected events 20 Full signal fit 10 18 Signal peaks 16 Accidental bkgd 1 14 Accidental bkgd fit 8 Corr. bkgd: Li −1 12 8 10 10 Li fit Corr. bkgd: 12B+n −2 8 12B+n fit 10 Events/0.1MeV Events/0.1MeV 6 Neutron bkgd − 4 10 3 2 0 10−4 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0.7 1 2 3 4 5 6 7 8 9 10 γ energy (MeV) γ energy (MeV) Selection 3 Selection 3 7 102 6 10 5 6600keV? 4 1

3 10−1

Events/0.5MeV 2 Events/0.5MeV 10−2 1 − 10 3 0 5 10 15 20 25 0.7 1 2 3 4 5 6 7 8 910 20 γ energy (MeV) γ energy (MeV)

FIG. 13. 12Bγ spectra for each selection, shown on a linear scale on the left and a log scale on the right. Selected events and the overall fit are shown in black with filled circles and a thick solid line, the signal components of the fit with a dashed black line, accidental background (section IX B 1) in gray with crosses and a dot-dashed line, correlated background from non-12B isotopes assumed to be all 8Li (section IX B 2) in blue with squares and a triple-dot-dashed line, and from early neutron captures following 13C(µ−,νn)12B selected as gammas (section IX B 5) with a green dashed line. The data and fit for 13C(µ−,νn)12B∗ (section IX B 3) is shown in orange with open circles and a thin solid line and is scaled to the level at which it acts as a background to 12C(µ−,ν)12B∗. The fit line includes the spallation background to 13C(µ−,νn)12B itself (section IX B 4), visible at the Gd-n energy, which does not affect 12C(µ−,ν)12B.

2. Correlated Background: 8Li with about the same efficiency as 12B if they fall into the 2–60 ms selection window. However, the much longer half-life of 8Li puts only a small fraction in this window. From Sec. VIII A, it is known that 8Li is produced in Because 8Li is produced with an alpha, the visible energy significant quantities. It has one bound level at 981 keV. is the sum of that from the alpha and gamma. Given our No previous results are available on the rate of transition measurements of scintillator quenching, and assuming a to particular states. Beta decays of 8Li will be selected mean alpha energy of 4.5 MeV [30, figure 5b], the total 17

− − 1+: Ground state 2+: 953 keV 2 : 1674 keV 1 : 2621 keV Theory Fukui 1983/’87 Hayes 2000 Krmpotic 2005 Samana 2015 Experiment Maier 1964 Miller 1972 Roesch 1981 Giffon 1981 This work 5 6 7 8 0.5 1.0 0.5 1.0 0.5 1.0 1.5 2.0 Rate (103 s −1) Rate (103 s −1) Rate (103 s −1) Rate (103 s −1)

FIG. 14. Comparison of results for each bound state of 12B to theory (from top to bottom: [1, 35, 36], [37], [2], [38]) and previous measurements ([20], [39], [29], [40]). Krmpoti´c[2] presents three parameterizations of PQRPA; all are displayed here. Each of the more recent experiments depends on Maier [20] for the total rate, but here is shown updated using the Double Chooz total rate. Maier’s result has itself been corrected here to account for their 13C fraction and to correct an error in their calculations. Giffon [40] is reanalyzed to remove the erroneous assumption that the 953 keV level is negligible. One experiment [41] has been excluded due to having made the same assumption and there being insufficient information to reanalyze. visible energy expected is 1.23 MeV. 3. Correlated Background: 13C→12B+n

The contribution from 8Li(981) is determined by se- No previous results are available for the reaction lecting events as in Sec. IX A, but with a beta decay 13C(µ−,νn)12B, so there is no constraint on the exclusive window of 0.3–4.2 s after the muon. The significance of rates to each 12B state in this process. In the case of this the presence of these gammas is 2σ. Limits are obtained, analysis, the neutron efficiency is high, (85.8±1.0)%, and and are shown in Table VIII. The central value, scaled the probability of selecting an event as a neutron when to the number expected in the 12B time window, is input no true neutron is present is low, 1.1×10−4, which means into the 12B fit and the errors used as a pull term. the 12C and 13C variants can be largely separated. Events with and without neutrons are therefore both selected and a simultaneous fit is performed with both Other isotopes were considered for this treatment. No samples, with 13C and 12C processes on equal footing. significant background to the three bound 12B levels The fit includes the neutron efficiency as a parameter, from 13B is expected, since 13B’s first excited state is which is constrained by a 1% pull term. The fit results for at 3483 keV. It is possible that the four events tenta- 13C(µ−,νn)12B are shown in Table VII. Because there tively attributed to 12B(3759) are instead 13B(3483); the are so few events, none of the lines is confidently ob- energies are more compatible with the former, but not served. However, upper limits can be set. No unitarity enough information is available to confidently distinguish condition is applied (i.e. the fit allows the levels to add the possibilities. up to more than 100% of the 12B+n production), making the limits conservative. Other known products of muon capture are disfavored Assuming no unaccounted-for background, the total because their long lifetimes and/or low production rates fraction of 12B produced from 13C in an excited state +34 will reduce their contribution to negligible levels. For is (78−21(stat) ± 8(syst))%. This is much higher than instance, only 0.6% of 16N beta decays will be within the probability for 12B produced from 12C to be in an the selected time window. The bound levels of 16N’s excited state, but the production mechanism is different are all below 400 keV. It has unbound levels at 3353 keV, so they cannot be compared directly. In a naive shell 3523keV, and 3963keV, but even if these accounted for model, 13C(µ−,νn)12B involves removing a proton from 100% of 16N production, the background contribution an inner shell 2/3 of the time, whereas in 12C(µ−,ν)12B, would be well under one event, particularly since they no nucleons are removed. are known to de-excite primary by neutron emission.

There is one bound level in 9Li, at 2691keV, but be- 4. Background: Spallation cause the production rate is so low, even if it was pro- duced in this state 100% of the time, we would only ex- The following sequence of events can also contribute pect to select about 0.3 events. Other isotopes yield even a background at the H-n and Gd-n energies and would lower background rates regardless of what assumptions appear in the 13C(µ−,νn)12B sample: (1) through-going are made. muon, selected as a stopping muon, that produces three 18

TABLE VI. Transition rates to each 12B level measured in the reactions 12C(µ−,ν)12B(∗). For 3759 keV, this is the probability of reaching the level and de-exciting via gamma emission; it is assumed that no other gamma lines contribute.

Daughter Rate (103 s−1) Per 12B β decay (%) Significance 12 +0.13 ± B(g.s.) 5.68−0.22 (stat) 0.06(syst) +0.14 −0.23(total) 12 +0.09 ± +1.3 +0.2 B*(953) 0.31−0.07 (stat) 0.01(syst) 4.8−1.1(stat)−0.1(syst) 6.2σ +0.09 +1.3 −0.07(total) −1.1(total) 12 +0.04 ± +0.7 +0.05 B*(1674) 0.06−0.03 (stat) 0.003(syst) 0.9−0.5(stat)−0.04(syst) 1.6σ +0.04 +0.7 −0.03(total) −0.5(total) 12 +0.06 ± +0.9 +0.2 B*(2621) 0.47−0.05 (stat) 0.01(syst) 7.1−0.8(stat)−0.1(syst) 15.3σ +0.06 +0.9 −0.05(total) −0.8(total) 12 +0.015 ± +0.23 ± B*(3759) 0.026−0.011 (stat) 0.001(syst) 0.39−0.17(stat) 0.01(syst) 2.8σ +0.015 +0.23 −0.011(total) −0.17(total)

TABLE VII. Transition rates for each 12B level measured in the reactions 13C(µ−,νn)12B∗. The limits are taken as the primary results. They result from a Bayesian analysis that takes a flat prior from 0–100%. Because it is assumed that any or all of the events are background, none of the levels are imposed as constraints on the probabilities of other levels.

Daughter Rate (103 s−1) Per 12B β decay (%) Significance 12 +5 ± +29 ± B*(953)+n 8−4(stat) 0.2(syst) 46−21(stat) 4(syst) 3.0σ < 15 at 90% CL < 80. at 90% CL 12 +4 ± +22 ± B*(1674)+n 5−3(stat) 0.1(syst) 25−14(stat) 2(syst) 1.6σ < 9.9 at 90% CL < 54 at 90% CL 12 +1.1 ± +6 ± B*(2621)+n 0.7−0.6(stat) 0.02(syst) 4−3(stat) 0.3(syst) 1.2σ < 2.2 at 90% CL < 12 at 90% CL 12 +1.1 ± +6 ± B*(3759)+n 0.8−0.6(stat) 0.02(syst) 4−3(stat) 0.4(syst) 1.8σ < 2.2 at 90% CL < 12 at 90% CL

or more neutrons through spallation; one makes 12B 5. Correlated Background: 13C(µ−,νn)12B neutrons through the (n, p) reaction (2) another neutron captures selected as gammas on hydrogen or gadolinium and is selected as a gamma (3) a third neutron capture is correctly selected as such If the neutron from 13C(µ−,νn)12B captures within (4) the 12B beta decays. the gamma time window, the event will be selected as Lacking an estimate for the rate of this sequence, it is 12C(µ−,ν)12B with a gamma energy of 2225keV. Using taken into account by including free parameters in the the measured rate of this reaction from Sec. IV and the fit that control contribution at the H-n and Gd-n ener- probabilities of capture within the gamma timing win- gies in the 12B+n sample. There does seem to be Gd-n dow, about 1.2 H-n events and 0.7 Gd-n events are ex- present, primarily visible in selection 3 (with one event pected for selection 1, 2.4+1.3 for selection 2, and 3.5+1.7 in selection 2), but the fit finds no H-n component in any for selection 3. These rates are included in the fit as fixed selection. The uncertainty on this is propagated through amounts. They are not allowed to vary in the fit because the fit. any 12B levels below 10 MeV that are not included in Since this sequence is therefore observed to be rare, the fit will spuriously pull the neutron rate up. Instead, and spallation typically produces many neutrons, the a systematic error is assigned after the fact, as shown corresponding sequence without event (3), the third below. neutron capture, which would instead contaminate the As a cross-check on the rate of H-n events contami- 12C(µ−,ν)12B sample, is assumed to be negligible, par- nating the 2621 keV line, the timing distribution of these ticularly because it is much more likely for a single neu- gamma candidates was fit for a combination of the bound tron to be captured during the longer neutron selection µ− lifetime and the neutron capture lifetime. No evi- time window than the gamma time window. dence of a neutron timing component was found, with 19

TABLE VIII. Rate for the exclusive reaction 12C(µ−, να)8Li∗(981). The methodology is the same as in table VII.

Daughter Rate (103 s−1) Per 8Li β decay (%) 8Li*(981) 0.10 ± 0.05(stat) ± 0.002(syst) 40 ± 20(stat) ± 3(syst) < 0.16 at 90% CL < 67% at 90% CL

a limit from timing alone of less than 25% neutron con- These results are compared to previous experimental tamination at 90% CL. and theoretical work in Fig. 14. Note particularly the comparison of these results to the PQRPA model, which is also used to generate neutrino cross sections. For in- C. Results and Systematics stance, for their parameterization III (the bottom points shown for Krmpoti´c2005) the ground state prediction is Numerical results are shown in Tables VI, VII 4σ high of our measurement (experimental errors only), and VIII. These include the rate for ground state the 953 keV level is 2σ low, the 1674 keV level is 2σ high, 12C(µ−,ν)12B, which is found by subtracting the excited and the 2621 level in good agreement. state rates from the total rate. To cover the possibility that the 3759 keV measurement is spurious, its contribu- tion is allowed to vary from zero to the stated value in X. SUMMARY this calculation. Likewise, to cover the possibility that higher energy states also cascade down to the ground Using the Double Chooz neutrino detector, the proba- state, an error is added that covers the possibility that bilities of final states of muon capture on carbon, nitrogen all the events from 5–30MeV in Fig. 13 are such events. and oxygen have been measured. One set of reactions, Both of these effects are small compared to the statistical 12C(µ−,ν)12B(∗), has been observed before; more precise error. results are reported here. Other reactions have been ob- In the tables, all sources of error handled directly in served for the first time, and limits on several more have the fit are considered to be statistical. The additional been set. systematic errors are as follows: The near detector is now also taking data. Because it

12 has an overburden of 120 meters water equivalent, it re- • For results stated as a fraction of B produc- ceives several times the flux of muons as compared to the tion, many systematic errors cancel, leaving an ef- far detector. This flux is also softer, giving a higher frac- ficiency error of 1.1%, primarily due to the muon tion of stopping muons. This provides an excellent data energy cut. The statistical error on the total rate set for future analysis of relatively short-lived isotopes. of 12C(µ−,ν)12B found in Sec. IV applies, giving +3.0 The RENO [42] and Daya Bay [43] detectors have sim- an additional systematic of −1.2% relative. ilar capabilities as Double Chooz and could also perform • For results stated as a transition rate, the entire these measurements. Similarly, a possibility to increase 1.5% efficiency error from Sec. IXA applies, as does world data on muon capture in oxygen comes from Super- the error on the number of atomic captures on 12C, Kamiokande, which has collected a large sample of stop- 1.4% (see Sec. V), plus a very small 0.1% error from ping muons in water [44], but has thus far treated them the µ− lifetime in 12C. only as a background to spallation studies. The observed rate of βn decays shows that stopping • An additional overall systematic on each level is as- muons do not form a significant background to θ13 mea- signed for uncertainty in the energy reconstruction surements at any of the current facilities. Since the ratio following a muon. The relative uncertainties in the of stopping to through-going muons rises as the amount event counts from this effect are 0.5% for 953keV, of overburden decreases, it is possibly a relevant back- 2.8% for 1674keV, 0.2% for 2621keV and 1.7% for ground for inverse beta decay detectors with very small 3597 keV. overburdens, such as those investigating the reactor neu- trino anomaly [45]. • To account for uncertainties in the number of H-n captures assumed in Sec. IXB5, a further system- atic error is assigned to the two adjacent levels. XI. ACKNOWLEDGMENTS This is evaluated to be 1% relative for 2621 keV and 3% relative for 1674 keV. We thank the French electricity company EDF; the All systematics combined are much smaller than the European fund FEDER; the R´egion de Champagne Ar- statistical error, which for the most precise level is 12% denne; the D´epartement des Ardennes; and the Com- relative. munaut´ede Communes Ardenne Rives de Meuse. We 20 acknowledge the support of the CEA, CNRS/IN2P3, the Forschungsgemeinschaft DFG, the Transregional Collab- computer centre CCIN2P3, and LabEx UnivEarthS in orative Research Center TR27, the excellence cluster France (ANR-11-IDEX-0005-02); the Ministry of Educa- “Origin and Structure of the Universe”, and the Maier- tion, Culture, Sports, Science and Technology of Japan Leibnitz-Laboratorium Garching in Germany; the Rus- (MEXT) and the Japan Society for the Promotion of sian Academy of Science, the Kurchatov Institute and Science (JSPS); the Department of Energy and the Na- RFBR (the Russian Foundation for Basic Research); the tional Science Foundation of the United States; U.S. Brazilian Ministry of Science, Technology and Innova- Department of Energy Award DE-NA0000979 through tion (MCTI), the Financiadora de Estudos e Projetos the Nuclear Science and Security Consortium; the Min- (FINEP), the Conselho Nacional de Desenvolvimento isterio de Econom´ıa y Competitividad (MINECO) of Cient´ıfico e Tecnol´ogico (CNPq), the S˜ao Paulo Research Spain; the Max Planck Gesellschaft, and the Deutsche Foundation (FAPESP), and the Brazilian Network for High Energy Physics (RENAFAE) in Brazil.

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