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New limits on nucleon decays into invisible channels with the BOREXINO Counting Test Facility
H.O. Back a, M. Balata b, A. de Bari c, T. Beau d, A. de Bellefon d, G. Bellini , e , J. Benziger f , S. Bonetti e, C. Buck g, B. Caccianiga e, L. Cadonati f , F. Calaprice f , G. Cecchet c, M. Chen h, A. Di Credico З, b , O. Dadoun d,2, D. D'Angelo З, i , V.Yu. Denisov r, A. Derbin j,1, , M. Deutsch k,5, F. Elisei , A. Etenko m, F. von Feilitzsch i, R. Fernholz f , R. Ford 2, f , D. Franco e, B. Freudiger З, g,2 , C. Galbiati З, f , F. Gatti n, S. Gazzana З, b , M.G. Giammarchi e, D. Giugni e, M. Goeger-Neff i, A. Goretti З, b , C. Grieb i, C. Hagner a, G. Heusser g , A. Ianni З, b , A.M. Ianni З, f , H. de Kerret d, J. Kiko g, T. Kirsten g, V. Kobychev b,3, G. Korga e,4, G. Korschinek i, Y. Kozlov m, D. Kryn d, M. Laubenstein , b , E. Litvinovich m, C. Lendvai З, i,2, P. Lombardi З, e , I. Machulin m, S. Malvezzi e, J. Maneira h, I. Manno o, D. Manuzio n, G. Manuzio n, F. Masetti , A. Martemianov m,5, U. Mazzucato , K. McCarty f , E. Meroni e, L. Miramonti e, M.E. Monzani e, P. Musico n, L. NiedermeierЗ, i,2 , L. Oberauer i, M. Obolensky d, F. Ortica , M. Pallavicini З, n , L. Papp e,4, L. Perasso e, A. Pocar f , O.A. Ponkratenko r, R.S. Raghavan p, G. Ranucci , e , A. Razeto b, A. Sabelnikov e, C. Salvo2, n , R. Scardaoni e, D. Schimizzi f , S. Schoenert g , H. Simgen g, T. Shutt f , M. Skorokhvatov m, O. Smirnov j,, A. Sonnenschein f , A. Sotnikov j, S. Sukhotin m, V. Tarasenkov m, R. Tartaglia b, G. Testera n, V.I. Tretyak r, , D. Vignaud d, R.B. Vogelaar a, V. Vyrodov m, M. Wo jcik q, O. Zaimidoroga j, Yu.G. Zdesenko r, G. Zuzel q
a

arXiv:hep-ex/0302002 v2 25 Mar 2003

Virginia Polytechnique Institute and State Univercity Blacksburg, VA 24061-0435, Virginia, USA

Preprint submitted to Elsevier Science

25 March 2003

b c

L.N.G.S. SS 17 bis Km 18+910, I-67010 Assergi(AQ), Italy

Dipartimento di Fisica Nucleare e Teorica Universita` di Pavia, Via A. Bassi, 6 I-27100, Pavia, Italy
d

Laboratoire de Physique Corpusculaire et Cosmologie, 11 place Marcelin Berthelot 75231 Paris Cedex 05, France

e

Dipartimento di Fisica Universita di Milano, Via Celoria, 16 I-20133 Milano, ` Italy

f

Dept. of Physics, Princeton University, Jadwin Hal l, Washington Rd, Princeton NJ 08544-0708, USA
g

Max-Planck-Institut fuer Kernphysik, Postfach 103 980 D-69029, Heidelberg, Germany

h

Dept. of Physics, Queen's University Stirling Hal l, Kingston, Ontario K7L 3N6, Canada
i

Technische Universitaet Muenchen, James Franck Strasse, E15 D-85747, Garching, Germany
j

Joint Institute for Nuclear Research, 141980 Dubna, Russia

k

Dept. of Physics Massachusetts Institute of Technology, Cambridge, MA 02139, USA Dipartimento di Chimica Universita di Perugia, Via Elce di Sotto, 8 I-06123, ` Perugia, Italy
m n

RRC Kurchatov Institute, Kurchatov Sq.1, 123182 Moscow, Russia

Dipartimento di Fisica Universita and I.N.F.N. Genova, Via Dodecaneso, 33 ` I-16146 Genova, Italy
o p

KFKI-RMKI, Konkoly Thege ut 29-33 H-1121 Budapest, Hungary

Bel l Laboratories, Lucent Technologies, Murray Hil l, NJ 07974-2070, USA

q

M. Smoluchowski Institute of Physics, Jagel lonian University, PL-30059 Krakow, Poland
r

Institute for Nuclear Research, MSP 03680, Kiev, Ukraine

Abstract The results of background measurements with the second version of the BOREXINO Counting Test Facility (CTF-I I), installed in the Gran Sasso Underground Lab oratory, were used to obtain limits on the instability of nucleons, b ounded in nuclei, for decays into invisible channels (inv ): disapp earance, decays to neutrinos, etc. The approach consisted of a search for decays of unstable nuclides resulting from N and N N decays of parent 12 C, 13 C and 16 O nuclei in the liquid scintillator and the water shield of the CTF. Due to the extremely low background and the large mass (4.2 ton) of the CTF detector, the most stringent (or comp etitive) up-to-date exp erimental b ounds have b een established: (n inv ) > 1.8 З 1025 y, (p inv ) > 1.1 З 1026 y, (nn inv ) > 4.9 З 1025 y and (pp inv ) > 5.0 З 1025

2

y, all at 90% C.L. Key words: proton decay, baryon numb er conservation, scintillation detector PACS: 11.30, 11.30.F, 12.60, 29.40.M

1

Introduction

The baryon (B ) and lepton (L) numbers are considered to be conserved in the Standard Mo del (SM) 6 . However, no symmetry principle underlies these laws, such as, e.g. gauge invariance, which guarantees conservation of the electric charge. Many extensions of the SM include B and L violating interactions, predicting the decay of protons and neutrons bounded in nuclei. Various decay mechanisms with B =1, 2 and (B -L)=0, 2 have been discussed in the literature intensively [2,3]. A novel baryon number violating pro cess, in which two neutrons in a nucleus disappear, emitting a bulk ma joron nn , was proposed recently [4]; the expected mean lifetime was estimated to be 1032-39 y. Additional possibilities for the nucleon (N ) decays are related to theories which describe our world as a brane inside higher-dimensional space [5,6]. Particles, initially confined to the brane, may escape to extra dimensions, thus disappearing for the normal observer; the characteristic proton mean lifetime was calculated to be (p)=9.2З1034 y [7]. Observation of the disappearance of
Corresp onding author. St. Petersburg Nucl. Phys. Inst., 188350 Gatchina, Russia. E-mail: derbin@mail.pnpi.spb.ru Corresp onding author. Joint Inst. for Nucl. Research, 141980 Dubna, Russia. E-mail: smirnov@lngs.infn.it Corresp onding author. Institute for Nuclear Research, MSP 03680, Kiev, Ukraine. E-mail: tretyak@lngs.infn.it 1 On leave of absence from St. Petersburg Nuclear Physics Inst. - Gatchina, Russia 2 Marie Curie fellowship at LNGS 3 On leave of absence from Institute for Nuclear Research, MSP 03680, Kiev, Ukraine 4 On leave of absence from KFKI-RMKI, Konkoly Thege ut 29-33 H-1121 Budap est, Hungary 5 Deceased Sp okesman Pro ject manager 2 Op erational manager GLIMOS З Task manager 6 It should b e noted that nonp erturbative effects at high energies can lead to the B and L violation even in the SM [1].

3

e- , N , N N would be a manifestation of the existence of such extra dimensions [6]. No evidence for nucleon instability has been found to date. Experimental searches [8] with the IMB, FrДjus, (Super)Kamiokande and other detectors e have been devoted mainly to nucleon decays into strongly or electromagnetically interacting particles, where lower limits on the nucleon mean lifetime of 1030-33 y were obtained [9]. At the same time, for mo des where N or N N pairs disappear or they decay to some weakly interacting particles (neutrinos, ma jorons, etc.), the experimental bounds are a few orders of magnitude lower. Different metho ds were applied to set limits for such decays 7 (see table 1 for summary): (1) Using the limit on the branching ratio of spontaneous fission of 232 Th under the assumption that p or n decay in 232 Th will destroy the nucleus [10]. The bound on the mean lifetime obtained in this way can be considered independent of the a p or n decay mo de, since the 232 Th nucleus can be destroyed either by strong or electromagnetic interactions of daughter particles with the nucleus or, in the case of N disappearance, by subsequent nuclear deexcitation pro cess; (2) Search for a free n created after p decay or disappearance in the deuterium nucleus (d=pn) in a liquid scintillator enriched in deuterium [11] or in a volume of D2 O [12,16,17]; (3) Geo chemical [13] or radio chemical [14] search for daughter nuclides which have appeared after N decays in the mother nuclei (valid for decays into invisible channels); (4) Search for prompt quanta emitted by a nucleus in a de-excitation pro cess after N decays within the inner nuclear shell [18] (valid for invisible channels); (5) Considering the Earth as a target with nucleons which decay by emitting electron or muon neutrinos; the e , Е can be detected by a large underground detector [19,20] (valid for decay into neutrinos with specific flavors); (6) Search for bremsstrahlung quanta emitted due to a sudden disappearance of the neutron magnetic moment [21] (limits depend on the number of emitted neutrinos); (7) Study of radioactive decay of daughters (time-resolved from prompt pro dWe are using the following classification of decay channels: decay to invisible channel (inv ) means disapp earance or decay to weakly interacting particles (one or few neutrinos of any flavors, ma jorons, etc.). Channel to any thing, mentioned b elow, includes also decays to inv .
7

4

Table 1 Lower limits on the mean lifetime for decay of nucleons, b ounded in nuclei, into invisible channels established in various approaches (see footnote 7 for channels classification). N or N N decay limit, y Year, reference and short explanation and C.L. p any thing 1.2З1023 1958 [10] limit on 232 Th sp ontaneous fission 23 3.0З10 1970 [11] search for free n in liquid scintillator enriched in deuterium (d n+?) 4.0З1023 95% 2001 [12] free n in D2 O volume inv 7.4З1024 1977 [13] geochem. search for 130 Te...129 Xe 26 1.1З10 1978 [14] radiochem. search for 39 K...37 Ar 1.9З1024 90% 2000 [15] search for 128 I decay in 129 Xe detector 1028 2002 [16] free n in D2 O volume 28 90% 3.5З10 2003 [17] free n in D2 O volume 26 90% 1.1З10 2003 [ a ] search for 12 B decay in the CTF detector 23 n any thing 1.8З10 1958 [10] limit on 232 Th sp ontaneous fission inv 8.6З1024 1977 [13] geochem. search for 130 Te...129 Xe 26 1.1З10 1978 [14] radiochem. search for 39 K...37 Ar 4.9З1026 90% 1993 [18] search for with E =19-50 MeV emitted in 15 O deexcitation in Kamiokande detector 1.8З1025 90% 2003 [ a ] search for 11 C decay in the CTF Е Е Е 5.0З1026 90% 1979 [19] massive liquid scint. detector fired by Е in result of n decays in the whole Earth b,c 1.2З1026 90% 1991 [20] FrДjus iron detector fired by Е c e e e e 3.0З1025 90% 1991 [20] FrДjus iron detector fired by e d e i i i 2.3З1027 90% 1997 [21] search for bremsstr. with E >100 MeV emitted due to sudden disapp. of n magn. moment (from Kamiokande data) e 27 90% i i i i i 1.7З10 1997 [21] the same approach e n n Е Е 6.0З1024 90% 1991 [20] FrДjus iron detector fired by Е f e e e 1.2З1025 90% 1991 [20] FrДjus iron detector fired by e g e 25 90% inv 1.2З10 2000 [15] search for 127 Xe decay in 129 Xe detector 4.2З1025 90% 2002 [22] radiochem. search for 39 K...37 Ar h 4.9З1025 90% 2003 [ a ] search for 10 C and 14 O decay in the CTF pp inv 5.5З1023 90% 2000 [15] search for 127 Te decay in 129 Xe detector 5.0З1025 90% 2003 [ a ] search for 11 Be decay in the CTF detector pn inv 2.1З1025 90% 2002 [22] radiochem. search for 39 K...37 Ar h a This work b The result of [19] was reestimated in [20] to b e more than one order of magnitude lower c The limit is also valid for p decay ЕЕЕ d The limit is also valid for p decay eee e i = e, Е, f The limit is also valid for pn and pp decays into ЕЕ g The limit is also valid for pn and pp decays into ee h On the base of the data of ref. [14]

5

ucts), created as a result of N or N N decays of the mother nuclei, incorporated into a low-background detector (valid for decay into invisible channels). This metho d was first exploited by the DAMA group with a liquid Xe detector [15]. In the present paper we use the same approach to search for N and N N instability with the Counting Test Facility, a 4.2 ton prototype of the multiton BOREXINO detector for low energy solar neutrino spectroscopy [23]. The preliminary results were presented in [24].

2

Experimental set-up and measurements

2.1 Technical information about CTF and BOREXINO

BOREXINO, a real-time 300 ton detector for low-energy neutrino spectroscopy, is nearing completion in the Gran Sasso Underground Laboratory (see [23] and refs. therein). The main goal of the detector is the measurement of the 7 Be solar neutrino flux via - e scattering in an ultra-pure liquid scintillator, while several other basic questions in astro- and particle physics will also be addressed. The Counting Test Facility (CTF), installed in the Gran Sasso Underground Laboratory, is a prototype of the BOREXINO detector. Detailed reports on the CTF results have been published [23,25,26], and only the main characteristics of the set-up are outlined here. The CTF consists of an external cylindrical water tank ( 11з10 m; 1000 t of water) serving as passive shielding for 4.2 m3 of liquid scintillator (LS) contained in an inner spherical vessel of 2.0 m. High purity water with a radio-purity of 10-14 g/g (U, Th), 10-12 g/g (K) and <2 ЕBq/l for 222 Rn is used for the shielding. The LS was purified to the level of 10-16 g/g in U/Th contamination. We analyze here the data following the upgrade of the CTF (CTF-II). The liquid scintillator used at this stage was a phenylxylylethane (PXE, C16 H18 ) with p-diphenylbenzene (para-terphenyl) as a primary wavelength shifter at a concentration of 2 g/l along with a secondary wavelength shifter 1,4-bis-(2methylstyrol)-benzene (bis-MSB) at 50 mg/l. The density of the scintillator is 0.996 kg/l. The scintillator principal de-excitation time is less than 5 ns which provides a go o d position reconstruction. In the CTF-II an additional nylon screen between the scintillator vessel and PMTs (against radon penetration) and a muon veto system were installed. 6

The scintillation light is collected with 100 phototubes (PMT) fixed to a 7 m diameter support structure inside the water tank. The PMTs are fitted with light concentrators which provide a total of 21% optical coverage. The number of photo electrons measured experimentally is 3.54 per PMT for 1 MeV electrons at the detector's center. For each event the charge and timing of hit PMTs are recorded. Each channel is supported by an auxiliary channel, the so-called second group of electronics, used to record all events coming within a time window of 8.2 ms after the trigger, which allows tagging of fast time-correlated events with a decrease of the overall dead time of the detector. For longer delays, the computer clo ck is used providing the accuracy of 0.1 s. Event parameters measured in the CTF include the total charge collected by the PMTs during 0-500 ns, used to determine an event's energy; the charge in the "tail" of the pulse (48-548 ns) which is used for pulse shape discrimination; PMT timing, used to reconstruct the event's position; and the time elapsed between sequential events, used to tag time-correlated events.

2.2 Detector calibration

The energy of an event in the CTF detector is defined using the total collected charge from all PMT's. In a simple approach the energy is supposed to be linear with respect to the total collected charge. The co efficient linking the event energy and the total collected charge is called light yield (or photo electron yield). The light yield for electrons can be considered linear with respect to its energy only for energies above 1 MeV. At low energies the phenomenon of "ionization quenching" violates the linear dependence of the light yield versus energy [27]. The deviations from the linear law can be taken into account by the ionization deficit function f (kB , E ), where kB is an empirical Birks' constant. For the calculations of the ionitazion quenching effect for PXE scintillator we used the KB program from the CPC library [28]. The "ionization quenching" effect leads to a shift in the position of the full energy peak for gammas on the energy scale calibrated using electrons. In fact, the position of the 1461 keV 40 K gamma in the CTF-II data corresponds to 1360 keV of energy deposited for an electron. The detector energy and spatial resolution were studied with radioactive sources placed at different positions inside the active volume of the CTF. A typical spatial 1 resolution is 10 cm at 1 MeV. The studies showed also that the total charge response of the CTF detector can be approximated by a Gaussian. For energies E 1 MeV (which are of interest here), the relative resolution can be expressed as E /E = 3.8 З 10-3 /E + 2.3 З 10-3 (E is in MeV) [29] for events uniformly distributed over the detector's volume. 7

The energy dependence on the collected charge becomes non-linear for the energies E 4.5 MeV in the first group of electronics because of the saturation of the ADCs used. In this region we are using only the fact of observing or notobserving candidate events, hence the mentioned nonlinearity do esn't influence the result of the analysis. Further details on the energy and spatial resolutions of the detector and ionization quenching for electrons, quanta and particles can be found in [29,30].

2.3 Muon veto The upgrade of the CTF was equipped with a carefully designed muon veto system. It consists of 2 rings of 8 PMTs each, installed at the bottom of the tank. The radii of the rings are 2.4 and 4.8 m. Muon veto PMTs are lo oking upward and have no light concentrators. The muon veto system was optimized in order to have a negligible probability of registering the scintillation events in the so-called "neutrino energy window" (250-800 keV). The behaviour of the muon veto at the higher energies has been specially studied for the present work. Experimental measurements with a radioactive source (chain of 226 Ra) [31] gave, for the probability (E ) of identification of an event with energy E in the LS by the muon veto, the value of (1Б0.2)% in the 1.8-2.0 MeV region (see fig. 3 later). The energy dependence of (E ) was also calculated by a ray-tracing Monte Carlo metho d accounting for specific features of the light propagation in the CTF which are detailed in [26]. The calculated function was adjusted to repro duce correctly the experimental measurements with the 226 Ra source.

2.4 Data selection As it will be shown below, the candidate events, relevant for our studies, have to satisfy the following criteria: (1) the event should o ccur in the active volume of the detector and must not be accompanied by the muon veto tag; (2) it should be single (not followed by a time-correlated event); (3) its pulse shape must correspond to that of events caused by or particles. The selection and treatment of data (spatial cuts, analysis of an event's pulse shape to distinguish between electrons and particles, suppression of external background by the muon veto system, etc.) is similar to that in ref. [30]. The experimental energy spectra in CTF-II, accumulated during 29.1 days of measurements, are shown in fig. 1. The spectrum without any cuts (spectrum 8

1) is presented on the top. The second spectrum is obtained by applying the muon cut, which suppressed the background rate by up to two orders of magnitude, depending on the energy region.

1000

10000

100

1

Counts / (36 keV x 29 d )

1000
10 400 600 800 1000 1200 1400 1600

100

2

3
10

4
1 0 1000 2000 3000 4000 5000 6000

Energy, keV

Fig. 1. Background energy sp ectra of the 4.2 ton BOREXINO CTF-I I detector measured during 29.1 days. From top to b ottom: (1) sp ectrum without any cuts; (2) with muon veto; (3) only events inside the radius R100 cm with additional / discrimination applied to eliminate any contribution from particles; (4) pairs of correlated events (with time interval t8.2 ms b etween signals) are removed. In the inset, the simulated resp onse function for external 40 K gammas is shown together with the exp erimental data.

On the next stage of the data selection we applied a cut on the reconstructed radius. In the energy region 1-2 MeV we used R 100 cm cut aiming to remove the surface background events (mainly due to the 40 K decays outside the inner vessel) and leave the events uniformly distributed over the detector volume. The efficiency of the cut has been studied with MC simulation and lays in the range of R = 0.76 - 0.80 in the energy region 1-2 MeV. Additional / discrimination [25] was applied to eliminate contribution from particles (spectrum 3 in fig. 1). 9

The time-correlated events (that o ccurred in the time window t<8.2 ms) were also removed (spectrum 4). The peak at 1.46 MeV, present in all spectra, is due to 40 K decays outside the scintillator, mainly in the ropes supporting the nylon sphere. The peak-like structure at 6.2 MeV is caused by saturation of the electronics by high-energy events. The lower spectrum of fig. 1 presents all the candidate scintillation events in the search for the decay of radioactive nuclides created in the active volume of the CTF after the nucleon disappearance in parent nuclei.

3

Data analysis and results

3.1 Theoretical considerations The decay characteristics of the daughter nuclides, resulting from N and N N decays in parent nuclei - 12 C, 13 C and 16 O - contained in the sensitive volume of the CTF liquid scintillator or in the water shield, are listed in table 2.
Table 2 Initial nuclei B = 1, 2 an Initial nucleus
12 6

in the Counting Test Facility, their abundance [32], processes with d characteristics of daughter nuclides [33]. De- Daughter nucleus, half-life, modes of decay and energy release cay n p nn pn pp n p nn pn pp n p nn pn pp
11 6 11 5 10 6 10 5 10 4 12 6 12 5 11 6 11 5 11 4 15 8 15 7 14 8 14 7 14 6

C =98.93%

C B C B Be C B C B Be O N O N C

T1/2 =20.38 m stable T1/2 =19.2 s stable T1/2 =1.6З106 y stable T1/2 =20.4 ms T1/2 =20.38 m stable T1/2 =13.8 s T1/2 =122 s stable T1/2 =70.60 s stable T1/2 =5730 y

+

(99.76%), EC(0.24%); Q=1.982 MeV

+ ; Q=3.651 MeV - ; Q=0.556 MeV

13 6

C =1.07%

- ; Q=13.370 MeV + (99.76%), EC(0.24%); Q=1.982 MeV - ; Q=11.508 MeV
+

16 8

O =99.757%

(99.89%), EC(0.11%); Q=2.754 MeV

+ ; Q=5.145 MeV - ; Q=0.156 MeV

After the disappearance of one or two nucleons in the parent nuclide, one or 10

two holes appear in the nuclear shells; these holes will be filled in a subsequent nuclear de-excitation pro cess, unless the nucleons reside on the outermost shells. If the initial excitation energy, Eexc , is higher than the binding energy SN of the least bound nucleon (N is p or n), the nucleus will be de-excited by particle emission (p, n, , d, etc.); otherwise (Eexc < SN ) a quantum will be emitted. In the following, we will take into consideration the N and N N decays from the last filled single-particle levels, when only quanta could be emitted. Thus the daughter nucleus is exactly known. We also neglect by the prompt signal from gamma quanta emitted in initial deexcitation pro cess (in particular, because of generally big half lives of daughter nuclei, and uncertainty in the number of emitted 's, their energies, and rejection of high energy events by the muon veto), and search only for subsequent radioactive decay of created nuclei. The number of nucleons or nucleon pairs participating in the pro cess can be calculated following refs. [13,15]. For example, after the decay of a neutron b with binding energy En (A, Z ), the excitation energy of the (A - 1, Z ) daughter b nucleus will be Eexc = En (A, Z ) - Sn (A, Z ). The condition to emit only quanta in the deexcitation pro cess, Eexc < SN (A - 1, Z ), gives this restriction b on the neutron binding energy: En (A, Z ) < Sn (A, Z ) + SN (A - 1, Z ). Similar equations can be written for p, pp, pn and nn decays (see ref. [15]). The values of the separation energies SN and SN N were taken from ref. [34]. For singleb particle energies of nucleons Ep,n on nuclear shells we used the continuum shell mo del calculations [35] for 12 C and 13 C, and the Hartree-Fo ck calculations with the Skyrme's interaction [36] for 16 O.

3.2 Simulation of the response functions

The expected response functions of the CTF detector and related efficiencies for the decay of unstable daughter nuclei were simulated with the EGS4 package [37]. The number of initial electrons and quanta emitted in the decay of the nucleus and their energies were generated according to the decay schemes [33]. The events were supposed to be uniformly distributed in the whole volume of the liquid scintillator (and in a water layer close to the LS). The energy and spatial resolution of the detector [29], light quenching factors for electrons and gammas [28], Е veto and triggering efficiency were taken into account in the simulations. The calculated responses for the decay of 11 C and 10 C in the liquid scintillator (created after n and nn disappearance in 12 C, respectively) and 14 O in the water shield (nn decay in 16 O) are shown in fig. 2. In the last case only the water layer of 1 m thickness closest to the liquid scintillator was taken into consideration. Contributions from layers further out are negligible. The CTF background was simulated as well in order to check the understand11

Fig. 2. Energy distribution of the CTF-I I installation collected during 29.1 d with all cuts. The exp ected resp onse functions of the detector are also shown for 11 C (3.4 З 103 decays in the liquid scintillator; corresp onding mean lifetime for the n decay is n = 1.8 З 1025 y), 10 C (6.8 З 102 decays; nn = 4.4 З 1025 y), and 14 O (1.4 З 104 decays in 1 m thick water layer closest to the sphere with liquid scintillator; nn = 5.7 З 1024 y).

ing of the detector. The simulated 40 K 1.46 MeV gamma peak together with experimental data is shown in the inset of fig. 1. The shift in the position of the full absorption peak is due to the ionization quenching effect (see section 2.2). One can see the go o d agreement between the experimental and simulated 40 K peak position and resolution.

3.3 Limits on probabilities of the N and N N disappearance The experimental data (see fig. 2, where the spectrum with all cuts is shown in detail) gives no strong evidence of the expected N and N N decay response functions, thus allowing only bounds to be set on the pro cesses being searched for. In the present study, in order to extract the limits on the relevant mean lifetimes, we assumed conservatively that al l events in the CTF experimental spectrum in the corresponding energy range E are due to nucleon decays. 12

The mean lifetime limit was estimated using the formula l
im

=

E

З Nn

uc l

З Nobj З t/Sl

im

= Nn

uc l

З Nobj З t/Dlim ,

(1 )

where E is the detection efficiency in the E energy window calculated in the full simulation of the relevant pro cess, taking into account the radial cut efficiency R , and probability of identification by muon veto ; Nnucl the number of parent nuclei; Nobj the number of ob jects (n, p or N N pairs) inside the parent nucleus whose decay will give the specific daughter nucleus; t the time of measurements; Slim the number of events (in the E window) due to a particular effect which can be excluded with a given confidence level on the basis of experimental data; and Dlim = Slim /E the corresponding number of decays in the liquid scintillator/water. The parameters in (1) were defined in the following way. The mass of scintillator was defined measuring the buoyancy with a precision of 5%. The total time of the data taking is 29.1 days and takes into account the dead time of the electronics of 3%. The measurements were performed in runs of about 24 hours. The internal source of 40 K was used to check the energy calibration stability. The position of the 40 K peak was defined for every run with statistical accuracy of 20 keV. No systematical shift in energy scale with a time has been found. The same is valid for the energy resolution, which is directly connected to the energy scale. In addition, all the response functions for the searched decays are wider than detector's resolution, hence the result is insensitive to the observed energy scale uncertainties. The probability of detecting scintillation events by the muon veto = 1 Б 0.2% has been defined from the experimental data for the energy E = 1.9 MeV. This value is in agreement with the MC simulation. For (1.9 MeV) = 1.2% the changes in the integral efficiency 1 - (E ) is negligible in the case of n and nn decays, for the p and pp decays the E will decrease by 7%. 3.3.1 n and nn disappearance For the nn decay, there are four neutrons on the outermost 1p3/2 level of 12 C which gives the number of nn pairs Nobj = 2. The disappearance of the nn pair from this level will result in a 10 C nucleus in the ground state. Taking into account the statistical uncertainty in the number of experimental events in the 2.0-3.0 MeV energy window (276Б17), we calculate Slim = 297 at 90% C.L. Accounting for the asso ciated efficiency E = 0.44, the limiting value for 10 C decays is Dlim = 6.8 З 102 . With the values of Nnucl = 1.9 З 1029 for 12 C nuclei and t = 29.1 d, we obtain lim (nn,12 C) = 4.4 З 10 13
25

y with 90% C.L.

For the 16 O nucleus we will account for only one nn pair on the outermost 1p1/2 orbit (nn decay in deeper levels will result the 16 O nucleus being to o excited). With the number of 16 O nuclei (in a 1 m thick water layer) Nnucl = 9.8 З 1029 , Nobj = 1 and Dlim = 1.4 З 104 for the energy region 2.2-2.6 MeV, the result is lim (nn,16 O) = 5.7 З 10
12 24

y with 90% C.L.

With the assumption that the mean lifetime of the nn pair is the same in C and 16 O nuclei, and that nn decays in both of them contribute to the experimental spectrum simultaneously, one can obtain a slightly more stringent limit for nn decay: lim (nn inv ) = 4.9 З 10
25

y with 90% C.L.

For n decay in 12 C we used a similar approach, just demanding that the simulated response function for 11 C decay should be equal to the experimental spectrum in the energy region of 1.0-1.1 MeV (fig. 2). In this way the value Dlim = 3.4 З 103 was determined for the full number of 11 C decay events. Together with Nobj = 4 (four neutrons on the 1p3/2 level), it gives the following limit: lim (n,12 C) = 1.8 З 10
25

y with 90% C.L.

3.3.2 p and pp disappearance As for the p and pp decays into invisible channels, the p disappearance in 13 C will result in 12 B nuclei, the - decaying with high energy release Q=13.370 MeV. The pp decays in 13 C will pro duce 11 Be nuclei, also the - decaying with Q=11.508 MeV (with probability of decay to the ground state of 57%). To estimate the lim for p and pp instabilities, we use the fact that no candidate scintillation events were observed in the CTF spectrum with energies higher than 4.5 MeV (fig. 2). High energy release in the liquid scintillator can activate the muon veto of the CTF, resulting in rejection of the event. We take into account such a suppression of high energy tails in decays of 12 B and 11 Be using the probability (E ) for identification of an event with energy E in the LS by the muon veto (fig. 3). The beta spectra of 12 B and 11 Be without and with suppression by the muon veto are also shown in fig. 3. The part of the 12 B beta spectrum with E 4.5 MeV reduced by a factor of 1 - (E ) gives an integrated efficiency E = 0.39. With zero observed events (and with the assumption of zero expected background), the limiting value for the number of events is Slim = 2.44 with 90% C.L. in accordance with the Feldman-Cousins pro cedure [38] recommended by the Particle Data Group [9]. Thus we arrive at the value Dlim = 6.2 for 12 B 14

decay. Together with Nnucl = 2.1 З 1027 for parent of Nobj = 4 for protons in 1p3/2 orbit, we obtain lim (p,13 C) = 1.1 З 10
26

13

C nuclei and the number

y with 90% C.L.

Fig. 3. Probability of identification of an event with energy E in the scintillator by the muon veto (1). The sp ectra of 12 B without (2) and with (3) suppression by the muon veto are also shown in arbitrary units. For signals with E < 3 MeV (10 C, 11 C and 14 O decays), Е veto does not have a big effect on the overall efficiency. In the inset the exp erimental data taken with the radon source are presented. The tagged events of 214 Bi-214 Po at the energy E =1.9 MeV are 'seen' by the muon veto system with an efficiency of = 0.01.

In a similar way, for the pp decay in 13 C with the value Nobj = 2 for the number of pp pairs and E = 0.36, the mean lifetime limit is lim (pp,13 C) = 5.0 З 10
25

y with 90% C.L.

All mean lifetime limits obtained here together with the numbers of parent nuclei, Nobj and the numbers of decay events are summarized in table 3. 15

Table 3 Mean lifetime limits, lim , (at 90% C.L.) for N and N N decays in the CTF. Nnucl is the numb er of parent nuclei; Nobj the numb er of ob jects (n, p and N N pairs) p er parent nucleus; Dlim the excluded numb er of decay events. Decay p n nn pp
a 13 6 12 6 12 6 16 8 13 6 2 C15 B 11 C C 6 0 C16 C 14 O O 8 1 C14 Be

N

nuc l

N

obj

Dl

im

lim

,y

2.1З1027 1.9З1029 1.9З1029 9.8З1029 2.1З1027

a

4 4 2 1 2

6.2 3.4 З 103 6.8 З 102 1.4 З 104 6.7

1.1 1.8 4.4 5.7 5.0

З З З З З

1026 1025 1025 1024 1025

In 1 m thick layer of water closest to the CTF liquid scintillator

4

Conclusions Counting Test Facility - the r mass of 4.2 ton and the low decays into invisible channels etc.) have been set:
26

Using the unique features of the BOREXINO extremely low background, the large scintillato energy threshold - new limits on N and N N (disappearance, decays to neutrinos, ma jorons, (n inv ) > 1.8 З 10
25

y, (p inv ) > 1.1 З 10

y,
25

(nn inv ) > 4.9 З 10

25

y and (pp inv ) > 5.0 З 10

y with 90% C.L.

Comparing these values with the data of table 1, one can see that the established limits for nn and pp decays are the best up-to-date limits set by any metho d, including radio chemical and geo chemical experiments. These limits are obtained in a very conservative assumption that all events in the corrresponding energy region are due to the nucleon decays. The data from the full scale Borexino detector will improve the presented limits by at least two orders of magnitude.

16

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