Co1nments on the Super-Kamiokande Project

Co1nments on the Super-Kamiokande Project

(Next Generation Underground Facility at KAMIOKA)

T. Ki tmnura

Resea.1·ch Institute of Science and Technology, J(inki Unive1·sity, lfiga.sh-Osa.ka:, 577

T. Nakatsuka

JVa.goya. W01nen University, Shioji, Nagoya., 467 (H.eceived Nove1nber 15, 1989)

Abstract

After proposing Grand Unification Theory, many experiments for the search of nu- cleon decay events and the search of GUT monopoles have been done in the whole world. At. the present stage, however, there a.re no nucleon decay events and no GUT monopoles up to the upper limits of the present technical level of detectors. It should be necessa.ry to have some new developments of detectors for the second- generation experiments, not simply enla.rgement of the present detectors. As a next genera- tion underground experiment, a large water (::erenkov detector with a total mass of 32,000 tons is proposed at Kamioka., called SUPER KAMIOKANDE. The physics po- tential of Super Ka.mioka.nde lies in the detection of phenomena predicted by grand unified theories and neutrino astronomy, part.icula.rly the search for nucleon deca.y, and the detection of ⁸B solar neutrinos via. electron-neutrino electron scattering. The authors comment on ba.ckground events in the search for nucleon decay in all decay modes measured by the Ka.miokande I and -II detectors, and by reason of circular statistical tests, on the angular distributions oflow energy electrons produced by solar electron-neutrinos as observed in 1\a.mioka.nde II. On the basis of these discussions about the i-i1easured experimental result.s of the Kamioka.nde I and -II detectors, we present some critical comments on the detection capability and physics potential of the proposed experiment.

Key Words: Nuclear decays; neutrino interactions (cosr111ic rays); solar neutrinos;

cerenkov detector.

1 Introduction

In the 1970's, after witnessing the brilliant. success of the unification of electromagnetic and weak in- teractions, it has been believed that. t.he strong, weak, electromagnetic interactions a.re different aspects of a single universal interaction (Grand Unified Theory, GUT) and thus the GUT predicts the nucleon decay and the GUT monopole. Many experiments, however, do not find nucleon decay

with a. life time a.t the level of several x 10³² years for a. decay mode of the proton (p---+ e+1r⁰⁾ and a GUT monopole flux around

w-

¹³ cm-² s-¹ sr-¹ for

f3 <

10-³.

It is in the present stage that we should make the experiments for the next generation of non- accelerator particle physics by using some new developed techniques. As a. next generation un- derground facility a.t K amioka., a large water Cerenkov detedor with total mass of 32,000 tons

- 93-

Table 1: Comp<nison of par<unctcrs between I<amiobnc!e I and Super-ICunioka.nde (taken from the Super-1\amiokande proposal)

Parameters Ta11k

Totill m<'lss

Fiducial llJCl . .;;s N um h c r of P l\1 Ts

% photose11sit.ive coverage photoelectron yield/Mev Resolution for EM shower Anti-counter byer

PMT time resolution 01. I p ho t.oelec t. ron

fJ+ ---+ e + decay ckt.cdion eff.

Accuracy in vertex dctenninotion(n)

rvr /S

scp0.rat.ion(bl

7r / fl SCJMrat.ion

ej

¹ separation

(a) for lOOMev/c electrons (IJ) 1\1; 7r or Jl , S:r,c nr 1r0

(c) under detailed study

I\AMIOKANDE I 16m h x Him (p

.3,0001.

8801.

1,000 20%

.1.8

0.0·1/

.JB (

^{E in Cev)}

depth > lm

t' ~

· J. I TIS

70%

I..) Ill

yes only for noll-o\·erlappi ng nngs

110

II o_

-- 04 -

SUPER 1\AMIOI<ANDE 40m h x .18m rjJ

~~2,0001.

22,0001.

11,000

110%

.5.8

0.03/

VE (

^{E in Gcv)}

depth > 2m lns

> 9S%

10un

yes 11 p to C'-J 80% over] a ppi 11 g

rings( c)

partly yes for p > 400

. rvrev /c

p<Ht.ly yes(r)

is proposed, called Super-Kamiokande

(1·

^2). It is an order of magnitude extension of the present.

Kamiokande detector with total mass of 3.000 tons and fiducial volume of 880 tons

e·

^{4). The}

proposed 22,000 ton fiducial volume is 25 times larger tha.n that of Kamiokande. Table 1 shows the comparison between Kamiokande 1 and Super- Kamiokande, cited from the proposal. The physics potential of Super- Ka.miokande lies in the ca.pa- bility to detect phenomena predicted by grand unified theories, in neutrino astronomy, specially in the next generation nucleon decay experiment with a life time sensitivity of

>

10^{33 rv} 10³⁴ years for all conceivable decay modes, and a detection of ⁸ B solar neutrinos by neutrino-electron scatter- ing, vee- --+ vee-. The present authors have some critical comments concerning the actual detection possibilities of the proposed project.

2 Comments on the Search for Nucleon Decay Phe- nomena·

Before constructing detectors for the nucleon de- cay search, we had discussed about ad vantages and disadvantages concerning water Cerenkov de- tectors and fine-grained tracking calorimeters.

The strength of detectors based on the track- ing calorimeter technique is their excellent. spa.- t.ia.l resolution ( 0' rv 1 em) in comparison to wa.- t.er Cerenkov detect.or·s ( (]' ^rv 1 m), their power to resolve mult.iprong events, and their capability to detect non-relativistic secondaries. The water Cerenkov detector is superior in the determination of the direction of incidence for charged particles, and it has the advantage of a low detection thresh- old for light particles (e.g. electrons) down to rv 10 MeV, an energy, to which tracking calorimeters are blind. For detectors of moderate size ( ^rv 1000 tons) the costs for both detector techniques are comparable. However, for tracking calorimeters the costs rise linearly with the detector volume, whereas water Cerenkov counters with huge vol- umes can be built with decreasing costs per ton.

In the early days of experiments searching for nucleon decay essentially three detectors were run- ning: The IMB experiment (USA) incorporated a water Cerenkov detector of 8000 tons total mass and a fiducia.l volume of 3300 tons (";). The

Kamiokande experiment (JAPAN) used the same technique (total mass: 3000 tons; fiducial volume:

880 tons) while a little later the Frejus-experiment

(6

) (French/German Collaboration) used a fine- grained tracking calorimeter (total mass: 1000 tons of iron) to sea.rch for nucleon decay. Other smaller detectors are omitted in the present dis- cussions. Reference to them can be taken from the literature e).

The search for nucleon decay was motivated by predictions for the nucleon lifetime on the basis of grand unified theories of the order of 10²⁹±¹ years.

The most frequent decay mode anticipated for the proton (p--+ e+1r⁰) should be easy to detect in wa- ter Cerenkov counters. Actually, one of the most important results of water Cerenkov counters was to establish a litfetime limit for this decay mode of r

>

3·10³² yr (90% C.L.) essentially ruling out the simplest grand unified theory. At the beginning of these experiments the situation was not so clear, because of difficulties to estimate the background for the e+ 1r⁰-final states coming from neutrino in- teractions in wa.ter Cerenkov counters. But the Frejus experiment also did not find events for the p --+ e+ 1r0 decay mode and this increased the con- fidence in the lower limit. of the proton_ lifetime es- tablished by the 1MB and Kamioka experiments.

Table 2 shows a comparison between the re- sults obtained iby water Cerenkov counters and by tracking calorimeter type detectors, as cited from the Super-Kamiokande proposal C). From this ta- ble one can rea.d that 1MB and Kamiokande have observed 7, respectively 4 ca.hdiclate events (Nn).

Assuming that these candidates are real, their as- sociated possible decay modes are listed in table 3a .for 1MB (⁸) and table 3b for Kamiokande

C).

The tables also summarize limits on partial life- times r/B x 10³¹ yr (90% C.L.) and expected background rates which are mainly caused by at- mospheric neutrinos.

The 1MB detector uses photomultiplier tubes (PMT) of 5 inch diameter, while the Ka.miokande experiment incorporates 20 inch diameter PMT's.

Since the PMT diameter in the 1MB experiment is smaller than that of Kamiokande and the vol- ume of the 1MB water tank is larger than that. of Kamiokande, the percentage photosensitive cover- age of the total PMT with respect to the surface area of the wa.ter tanks is only 1.2 % for IMB in contrast to 20 % for Kamiokande. Accordingly,

- 95-

Table 2: Experimental results from nucleon decay experiments as of April 1987

KGF NUSEX FRE.JUS IMB K A Ivll 0 I< A N IJ t<;

Began operation 1980 1982 198¹1 1 ~)82 1981

Tota.l mass ( t.) 140 150 900 8,000 1,000

Fiducial mass ( t) 60 130 ^GOO 3,.100 880

Source of nucleons Fe Fe Fe H20 ^H2⁰

Integral sensitivity (a) (kt.yr) 0.38 0.36 0.88 4.·1 1.92

Number of (b) contC~ined events 30 17 83 ;J.)8 211

Number of CCindida.te events (ND) 3 3 l ^l(t:) ·1

Expected number of events 11 8.4 1.2 sams ^i\S 2.G

from z; -interactions ( p, ) f\bove

(a) lkt·yr corresponds to 2.8 x 10³² proton· yr

+

3.2 x 10³² neutron· yr for iron, and to 3 .. 1 x 10³² proton· yr

+

2.7 x 10³² neutron· yr for W<lter, respectively.

(b)" contained" means that Cl.n event occms within a fiducial volume and no particles exit out of the det.ector. The event rates ( event.sjkt.yr) vary among the experiments mC~inly due to differences in trigger and selection conditions.

(c) This number is consistent wit.h bitckground expectation.

the I<C~.miobncle group claims that. the ntnnber of fake events produced by atmospheric neutrinos in their detector should be less compared to t.he Uv1B ex peri men t..

Table .1 shows again the candidate events from TMB (7) and Kamiokande ('1) and their tentative assignment. t.o possible decay modes. To check whether Karniokande actually hits a better back- ground rejection, one must. determine the num- ber of candidate events (which are assumed to be background) per kilot.ron · year (the product. of observation time a.nd 1~nass of water). BecC~use the lifetimes for IMB and Kamiokande nre 1.1 kt yr and 1.92 kt yr, respectively, the number of can- didate events for 1MB is 1.59 pPI kt yr and 2.08 per kt. yr for Kamiokande, which is in contrC~st.

to the claim of the I<amiokancle group. The rea- son, why IMB is slight.ly better t.ha.n Kamiokande ma.y be attributed to the fad that IMB can mea- sure the arrival times of t.he Cerenkov light to each P MT while K amiokande hns not such a measure- ment (Kamiokande 1I has, however, also adopted this technique). Without. the meC~surement of ar- rival times of the Cerenkov light the Clccuracy to determine the vertex of candidates is 0.8 - 1.5 m in Kamiokande compared to 0 .. 5 - 1.0 m for lM B based on the information of arrival time mea- surements in addition to analogous light. registra- tion. So, the smaller percentage PMT-coverage by 1MB is more than compensa.t.ed by the measure-

ment. of a.rriva.l times of the Cerenkov light. ca.using 1\a.mioka.nde, in fact., to pick up more background events.

From table J, we see thnt. Kamiokande found one candidate event. for a decay mode of J7 --t fl.+

1l

(candidate A). This candidC~te is not. considf'red genuine, although the expected neutrino back- ground is

<

O.CH ~ Similarily, IMB observed 4 candidntes for p-+ fl+w0 (see t.able 1). Again, this is not. considered as proton decay, in spite of the low estimated background of 1.3

±

0.3

±

O.G. The reason for this reluctance becomes clear after in- specting table 1, which shows how difficult it. is t.o estimate the neutrino-background rates reliably.

Table 4 summarizes the results of three different.

background estimates for different. decay modes

C'·

^9). Two rows are contributed by two diflcrcnt subgroups in the IMB collaboration and one is the result of simulations based on the Gargamelle bub- ble chamber data. There is agreement in the gen- eral trend, but there are also deviations. ln view of this difficult.y one can understand that JMB hes- itates to interpret the 1 cC~ndidates for p -+ fl+w0 as genuine events in spite of the estimated back- ground rate of 1.3 ± 0.3

±

O.G. It is likely tha.l the accuracy of background estimates in 1\a.miokandc is plagued by the same problems. Otherwise it is hard to understand why one observed event for fJ+

rl

is considered to be in agreement with a background estimate of less than 0.04 events.

- (.)6-

Table 3: Recent. results from the Il'vJB nucleon decay experiment. (taken from ref. 5)

The Kamiokande results (at April 1987). Limit.s on partial lifetimes {90% C.L.) r/B · 10³¹ yr for X candidate events and expected background.

Detection efficiency, candida.te events a.nd

expected neutrino backgrounds for e+ X modes 1MB result ( rv 4.4K ton · year) ( 1987, April)( 1.92Kt · year) cited from ref. 5

Ca.ndi- Expected r/B No. of Expected r /B dates v-B.G. x 10³¹yr candidates v-B.G. x 10³¹ yr

e+?ro

<

0.02 15. 0 0.6±0.2±0.1 31.

e+17o h'Y)

<

0.02 9.3 0 0.6±0.2±0.1 19.6

{3 ?ro) 0.0.5

e+w⁰ ( ?r+?r-7ro) B 0.9 3.9 0 1.0±0.3±0.2 2.6

(rro'Y) 0.0.5 2.6

e+ Po 0.9 6.2 0

e+ f{o (27ro) 0.05 10. 0 1.8±0.3±0.4 7.5

(rr+ ?r-)

<

0.1

e+ f{*o B 0.9 2.4

fl+ ?ro 0.05 12. 0 0.5±0.2±0.1 27.

p.+ 170 h'Y) ^A

<

0.02 3.8 1 1 . .5±0.3±0.1 3.4

( 3 rro) 0.02

p+ ]{0 {27ro) 0.02 .5.6 3 2.5±0.4±0.5 1.8

(rr+ ?r-) D 0.3

fl+ Po 0.7 .5.6 0 0 .. 5±0.2±0.2 4.7

e+Jr- 0.1 7.0 0 1.6±0.3±0.4 10.

e+p- 0.7 3.4 2 4.1±0 . .5±.0.7 1.8

f.J+ 7r-

<

0.1 .5.6 0 0 . .5±0.2±0.1 6.3

p+p-

c

^{0.9 1.0 1} 1.1±0.3±0.1 1.1

fl+WO 4 1.3±0.3±0.6 1.3

'Tfl+ 0 0.5±0.2±0.1 38.

?ro fl+ 0 0.5±0.2±0.1 27.

re+ 0 0.6±0.2±0.1 46.

p-p+ 1 1.1±0.3±0.1 0.7

e-17+ 0 1.6±0.3±0.4 6.5

p-?r+ 0 0.5±0.2±0.1 4.9

e-p+ 2 4.1±0.5±0.5 4.2

- 97-

Table 4: Comparison of estimated u -simulation bilckground by three different methods (t.aken fro111 rd. 9). The systematic uncertainties are about.-t-30% for the UCI ano Ul'vf estimates a.nd -SO%/+ 100% for the GGM estima.te.

I! Simulation Candidates Background Estimates

Mode Observed UCI UM GGM

Calc.

--

J7 ^{--t r:+ro} 0

Jl ^{-~ r+ lfo} 0

Jl ^{--t c+/\'o} 5

0

Jl ^--t c+17° 0

.s

ll ^{- - t} + ()

e p 7

J) ^{--} (' ()}

()

Jl ^{---} / 1+1° .)}

Jl ^--t fl+ ;ro 2

7) --t f/+ }\ () 4

.'3

J) --t f/+1/) 3

4 Jl

-·

^{fl+ flo ·1}

Jl ^{- t I'+ ct:0} G

2

Jl ^{--} /I I\.+} 6

J I ^---4 l/f7+ G

Jl ^{- - t ]! I\.·+ 7}

p ^{--t e+c+e-} 0

p ^--t ,,+ ,,+ fl-- 1

n ^{- - } p + -;r} 8

7J. --t _f -_7f +

s

It

)) --t (+[!- 9

n ^{--t ('-(!+} B

n. ^--t _fl + -

7f 8

17. --t fl-Jf+ 7

17. ^--t fl+ 1'- G

n ^{--t 1'-1'+} 7

n ^{- t J!')} 73

n ^{--t J! iTO} 73

11. ^{- - t I!} J\·O 3

n ^--t l/1)0 7 n ^{--t II flo J.S}

n ^{--t JILt'()}

.s

77 --t J! I\-·o 8

Ca.! c.

.28 .28 4.2

.28 .28 :1.0 6.7 5.0 .28 1.9

.9

·1.S 1 . ~)

1.9 4.2 LS 5.5 1.1 '1.7

·1.7 6.2

.28 .I 8.6

3.1 :).6 3.9 5.6 7.2 G.2 4.6 4.9 60.

GO.

.s.o

S.9 9.7

. ).0

o .. s

7.1

Calc.

.33

.::n

3.6 .3.3 .31 3.:3

6.8 ItA

.:n

3.1 2.2 G.l

3.4 3.¹1

4.7 6. J

.5.8 2.3

8.1 :3.9 7.9 .33 .T3 8.2

3.9

3.0 J.8 6.7 8.J 6. ,, 1.2 4.5 62.

6 2.

11.4 6.3 7.'1

·1. ^~) 0.9 7.8

·1.

0.7

0.7 /1.

7.

.S.

0.7

.t).

:3.

:),

.s.

.s.

6.

I.

.s.

5.

G.

0.7 0.9 8.

1.

.).

2.

S.

8.

7.

!S.

.5.

5G.

.SG.

.S . 0.7 8.

Even for the decay mode e+Jr⁰, which is favorable to search for with water Cerenkov counters, there seems to be some ambiguity. Gaisser ct. al. eo) have estimated the background to this mode to be O.OG events per kt. yr in water Cerenkov counters.

for the integral lifetime of 1MB ('1.4 kt. yr) this corresponds t.o 0.26 neutrino induced background events. This must be compared to the larger hrtck- ground level of 0.6 ± 0.2 ± 0.1 (Trt.ble 1) estimated by ll'vTB. Their value includes also systematic er- rors in the me<~."nrcment. and estimation. On the other hand Kamiokande quotes only < 0.02 hrtck- grouncl events for this decay cha.nnd (Table :)), corresponding t.o < 0.0·1(1 events per '1.4 kt yr, which is at least. a factor of .S smaller than Caisscr's estimate and an order of magnitude smaller than the v<~luc given hy !MH. ft. is very dist.mhing that.

t.he different estimates on neutrino-induced L<lck- ground differ by so much, where I\arniokandc ap- pears t.o be on the optimistic low side <~nd l r-.1 B on the high side.

The observed H'stdts for the i/"Y deca.Y chan- nels are displa.yed in t.a.hle 5 (¹·8

,0·¹¹ ). lt is h;nd to conceive t.h;~J nndcon decay can be estahlishul in the light of the present. accuracy of 1/-backgrnund estimates. Before searching for nucleon decay in extremely large Cerenkov detectors it. must. be dcnwnst.rat.ed t.hat. the 11-hackgronnd c<~n he cal- ndat.ed in a. more rf'liilblc way and that it. c<~n he significa.ntly J'('ducerl by improvements in f'Xpcri- mentill techni(jne. A well-known a.nd low h;lck- ground rate is ;) key-point. in searching for such r;ue phenomena ..

i\d.ually there <trf' a.lready irnprovcnwnt.s: The initial I<a1niokande l detector hilcl no t.illling fnr the observed Cercn kov· light. The rncsf'nt

T\~miokamle ll experiment ma.kes usc of PMT- t.iming, and it ha.s ildcled an a.nticoincidcncc layer which, howcv0r, reduces the fiducial volume from 8RO t.o G80 t.ons. I<amiokande ll is now operating and t.he observed data arc included in the tilhles 1 and .5. But. they contribute only a small pa.rt.

of t.he total event sample. These improvements allow t.o reconstruct t.he vertex of events t.o a.n ac- curacy of 0.7 m, compar('d t.o ] .. 5 m previously.

This r0sult h<~s been obtained with Monte Cil.rlo sitnulat.ions. An improved vf'rtcx reconstruction will, of course, redun: the background level. More- ovf'r, the percentage photosensitive coverage (20

%

in T<a.miokancle) will become ,10

%

in Super-

n ^{- - t} C+C-1-'⁰

s

^{.S.O G.O 5.}

11.

-- CJ8 -- n ^{--t fJ+ 1'-I/o} 14 7.3 16.8

Kamiokande by increasing the number of 20 inch PMT's. Also t.he time resolution at the one pho- toelectron level will be reduced from the present value of 5. 7 ns to 3 ns, thanks to the efforts of Hammamatsu Co. (The 1MB experiment uses PMT's with a resolution of 5 ns and a. jitter of less than 2 ns ). With these experimental improve- ments, Super-Kamiokande will be able to recon- struct vertices to an accuracy of 0.3 m resulting in a substantial reduction of background events compared to I<amiokande II. Even in the light of these improvements we feel, that at the present stage the best suited detector to search for nu- cleon decay is a. fine-grained tracking calorimeter type detector such as the Frejus detector (^6). The

· costs for a. larger tracking calorimeter, however, become considerable. Such a detector could re- construct the vertex to an accuracy of less tha.n 5 mm compared to 300 mm (Super-Kamioka.nde).

There is no way to achieve such a high a.ccura.cy in Super-Ka.miokande.

The latest results of Kamioka.nde II were re- ported at t.he Ninth Workshop on Grand Unifi- cation in 1988

(1

^2). As can be seen from Ta- ble 6, the observation of Ka.mioka.nde II consti- tutes about half of the total event sample. A comparison of experimental parameters between Kamioka.nde I a.nd -II is shown in table 6. There- sults for e+(f.l+)X a.nd DX decay modes are sum- ma.rized in table 7 a and 7b. They were taken from the Kamioka.nde paper contributed to the work- shop. Originally, improvements on the detector and the event analysis were expected to reduce the vertex reconstruction from the previous value of 1.5 m to an accuracy of 0,7 m in Kamiokande I. However, table 6 indicates that only an im- provement. to 1,0 m in Kamiokande I and 0,2 m in Kamiokande II for the e+ ^1r0 decay mode have been achieved. An improved vertex recon- struction should, of course, reduce the background level. The results shown in table 7 are based on the data. t.a.ken from July 1983 to November 1985 by Ka.mioka.nde I a.nd from November 1985 until November 1987 by Kamiokande II, corresponding to a total of 2.48 kt years. Kamioka.nde II (1.18 kt year) ha.s observed no candidates for e+(p+)x decay modes (see table 7a). It ha.s seen 5 indepen- dent candidates (excluding the decay p -+ D1r+) in the i/X decay mode, however (see ta.ble 7b). The background expectation for charged lepl.on final

states was 3.65 events plus anything less than 0,23 and for the final states with neutrinos 5.6S events plus anything < 0, 07.

On the other hand, the Frejus collaboration pre- sented their data on nucleon decay for an inte- grated fiducial sensitivity of 1.4 kt year (up to April 198S) based on the fine-grained tracking calorimeter at the same meeting. Their results are shown in table Sa for the e+(f.l+)x decay mode and table Sb for D X decays (1³). Table Sb shows 7 observed candidate events for n -+ DX to be compared to 9.1 expected background events. For the evaluation of this background, a. Monte Carlo sample corresponding to a minimum of 10 kt years of data has been used. For the modes with a charged lepton in the final state (table Sa, 3 can- didate events observed) the background evalua- tion has not been completed yet, but, they con- clude: O.S events are expected in the decay mode p -+ e+

rl,

whille 2 are observed, and 0.9 events are expected for p -+ J.-l+

rl,

while 1 is observed.

For the other final states considered, the back- ground varies between 0.1 and 1 event, and no events are observed. Thus, the total number of background events for the charged lepton decay modes is close to 3 events. So the observed Fre- jus candidate events a.re well accounted for by the expected background. This is also true for the Ka.miokande II events with neutrinos in the final state (table 7b), but for the e+(J.-t+)x decay mode there is a difference between observation (zero) and expectation

>

3.65 in Ka.miokande II (table 7a). This discrepancy can, of course, be related to ambiguities in the background estimation, es- pecially iffor iudividual decay channels only frac- tions of one event are expected. It can also be considered as a hint that the Monte Carlo simula- tion does not describe the detector in every detail.

It should also be mentioned that Kamioka.nde II

(14) has observed a low flux of muon neutrinos of energy

>

0.2 GeV in comparison to expectation

(Nob$erved/Nexpected

=

^0.57

±

0.07), while the event rate due to electron neutrinos agreed with expec- tation

e

^5). In contrast to this, the Frejus

e

⁶⁾

and NUSEX groups (1⁷⁾ find agreement for both the electron-neutrino and muon-neutrino flux with predictions based on atmospheric neutrino pro- duction. Table 6 claims an improvement of vertex reconstruction from 1 min Kamioka.nde I down to 0,2 min Kamioka.nde II for the e+ ^1r0 decay mode.

- 99-

Table 5: Experimental result.s of Kamiokande and IMB for the DX nucleon decay channel. vskip lex

Kamioka result for vX deary modes IMB result 1MB result

(cited from ref. [4]) (cited from ref. [7]) (cited from ref. [5])

T /B Unsub-

Number X 10³¹ yr Candi- trac!Pd Number r/B

of Expected (90%C.L.) dates IJ B.G. Limit on of Expected x10³¹yr

Mode selected IJ B.G. NO B.G. B.G. observed 1) R candi- v R.G.

events subtraction estimate ± 30% x 10³¹ yr dates 90% C.L.

90% C.L.

fnr+ 17 1.5.5 0.1 1.5

Dp+ 4 1.0 1.1 1.5 6. ·1.7 0.8 1.1±0.3±0.1 1.3

f;J(+ (lt+v) 4 3.2 1.0 7.4 6. 4.7 1.0

( 7r+7fO) 0.4

i/ J(•+ ( 71'+ J(O( 71'+ 71'-)) 2 0.3 7. 6.2 1.0

( rr+ go( 7ro7ro)) 2 1..3 1.1 1.4

(n°K+(fL+v)) 0.4

ilrrO 1.0 4.2 5.4 73. 60. 0.6

ilrl (n) ^{0.1 5.8 5.8 7. 5.q 2.5 3} 2.1±0.•1±0.5 1.6

( ITOIT011'0) 0.3

f)'J)O (IT+7f-rro) 2 2.1 2.9 1.1 5. .5.0 1.2 2 1.3±0.3±0.3 0.6

( ')'7ro) <0.1

i!po 2 2.1 0 . .5 0.8 15. 9.7 0.2

jj [(0 ( 71'+ Tr-) 0.9 .5.4 5.4 3 . .5.0 L'i

(;ro;r) 0.7

i/ [\··O (rro J<.:o ( ;r+ "-)) 2 1.6 8. 7.1 0 . .5

( 7ro J(o( 7fo7ro)) _{0.1 0.9 1.2}

(7r-K+(p+v)) 0.1

100 --

Table 6: Some paramet.ees for Kam.ioka.nde-I and-JI

Period Luminosity Fiducial Volume Trigger threshold Vertex resolution(e+JT⁰⁾ p decay detection efficiency (cosmic ray f.1)

a) Soon enlarged to 1040t.

K-1

J ul.1983-Nov.1985 1.30 kt.yr

880t 30MeV

100cm 68±3%

I<-11 Nov.l985- 1.18kt .. yr (Nov.1987)

780ta) 7.6MeV

20cm 80.0±1.1%

RUN 1378

EVT 460

In spite of t.his substantial improvement of a factor 5, the estimated background for the e+(lt+)x de- cay mode (3.65+

<

0.26 events per 1.18 kt year in Ka.m.ioka.nde I) has remained about. the same per kt year a.nd has decreased only by a factor of 1. 7 for the DX-deca.y modes (from 15.9 +

<

0.1 per 1.92 kt year in KI to 5.68 +

<

0.07 per 1.18 kt year in KII). Accordingly, it is rather dificult. to accept the difference be.t.ween observation (zero) and expectation

>

3.65 for the e+(p+)X decay mode in Kamioka.nde II which is seen from Ta- ble 7a. The fiducial volume of Super Kamiokande

V I E w · · - - · - - - , .

is over 25 times larger than that of Kamiokande II. Extrapolating from the present techniques of Kamiokande II one would expect.

>

77 events of type e+(p+)x and

>

120 events of type DX in Super Kamiokancle per year of running time. An una.mbigous event identification for the e+ 1r0 de- cay mode ( expect.ed background

<

0.25 events per year in Super- K amiokandc) in the presence of such a. high background from other sources appears ex- tremely difficult.. At the present stage it remains questionable whether the Super I<a.m.ioka.nde de- tector can reduce the background ra.tes for a.ll de- cay modes by one order of magnitude or more.

In spite of their accurate vertex reconstruct.ion, the Frejus experiment also has reported one se- rious proton decay candidate in 0.67 kt yr run- ning time (see. Fig. 1)

e

^8). The event could be interpreted either as p ~ e+ /(~ ~ e+?Trr or a rare three prong neutrino-electron interaction.

In the present statistics the neutrino-background for this candidate estimated from a Monte Carlo simulation appears to be less than 0.25 events.

The event display (Fig. 1) shows tw·o differ-

2

~'/..·' A

,(

B ... ·- .

~

..

,

~

2. B

VIEW t----·---1

1 ~3

..

·.

x··~

.. A B

... ·

.

-

^·.

Figure 1: Candidate event of the Frejus experi- ment.

e

⁸⁾

-101-

Table 7a: Experimentol resuHs of Kamiokande I and I I for f+X decay modes_l2l

Modes K-1 I\-I I BG for TjB r/B

1.3kt·yr l.l8kt·yr I<- I I BG Subtraction

e ;ro < 0.01 19.x 1031 yr 19.x 1031 yr

C7)0

hr) < 0.01 11. X 1011 ll.x 1

o·'

¹

(3 7ro) < 0.01

(:'(1) (3 7r) B OA 4 .. 5 X 1031 _5.8 X 1031

(r7ro) < 0.01

f J•:o (;r+Jr-) 0.()7 12. X 1031 12.x

to'

¹

(2 7ro) < 0.01

c,,o 0.9 7.8 X 10''1 7.8 X 1031

e f(*o (1 7ro) < 0.01 2.9 X 1031 4.2 X I 031

(;r+;r-;ro) R OA

( Jr-fl+ 11) 0.1

1'7ro < 0.01 15.x 1

o'

¹ 15.x 1031

fl1) hr) ^A < 0.01 4.6 ^{X 10:11} 4.6 ^X 1 o:>¹

( Jrro) < 0.01

/i.J(O (7r'+-7r-) _D 0.07 6.8 ^X 1031 8.0 ^X 1031

( 2 rr⁰) 0.01

f ^t.p() 0 .. 5 G.8 ^X 10 11 ^{6.8 X} I 0¹¹

e;r < 0.07 8.2 ^X 1 o-'1 8.2 ^X 1031

ep 0.8 4.5 X 1031 •1.5 X 1031

I I 7f < 0.07 6.6 ^X 1031 6.6 X 1031

pp

c

0.4 1.2 ^X 1031 1.5 X 1031

- 102 --

Table 7b: Experimentol results of Kamioka.nde I and-11 for ii.)( decay modes.¹²⁾

Modes K-1 K-11 BG for r/B r/B

1.3kt.·yr 1.18kt·yr K-11 BG Subtraction

V?r+ 10 7 9.6 0.6 x 10³¹yr 2.0 x 10³¹yr

llp+ 4 0.1 1.6 ^X 10³¹ 2.0 ^X 10³¹

vf{+ (J.t v) 4 3 2.0 3.'9 X 10³¹ 6.4 ^X 10³¹

( ?r+ ?ro) 0.07

v [{•0 (7r07r07r+) _{2 0.2 1.'2} X 10³¹ 1.8 X 10³¹

(7r+ •Jr+ ?!"-) ₂ 0.2

( ?roJ.l+ v) 0.1

v1r⁰ 1 1.1 5.1 ^X 10³¹ 6.8 ^X 10³¹

V1] ('y-y) 0.1 7.1 ^X 10³¹ 7.1 X 10³¹

(37ro) 0.2

vw (r?ro)

<

0.07 3.:3 ^X 10³¹ 5.4 ^X 10³¹

(3 7r) 2 0.2

vpo 2 0.7 O.G X 10³¹ 0.9 ^X 10³¹

v/{ 0 (27ro) 0.3 6.1 ^X 10³¹ 6.1 ^X 10³¹

(?r+?r-) _0.07

IJ 1\-*o (3?ro) 0.07 J.() X 10³¹ 1.7 X 10³¹

(7r+?r-7ro) _{2 0.2}

( ?r-j.J.//) 1 0.07

-103-

Table Sa: i':xpcrilllcnt.s rcsultal of ihc Frejns eppcriment for e-+ X decay nwdcs.¹ll

Decay mode Final state ^t mode Data ^{r/B (10l1y).}

----~--~---

p-+ e+ 7ro

rr

^{31. 0 S.l}

P-+ ^{e+ [\' 0 7!0710} lG. 0 2.G

+ - 71 1f

!'-+ e+11 Tl ^{22. 0 :).8}

7ro 7ro 71o

P-+ e+ Po ^{iT+ iT-} 10. 2 0.8

p -+ fl+ iTO

rr

^{26. 0 ·i .}

.s

p-+ p+[(o iT+'lf- 20. 0 3.¹1

vo _\L

P-+ f¹+ P^{0 1f +} 11 ^- 21. 2.5

n-+ ^{e+ 71-} iT 16. 0 3.1

n -+ e+p- 'iT ^- 71 ⁰ 20. 0 3. ~) /),-+ + -

I' iT iT 12. 0 2.:3

n -+ fl.+ p- ^{71- 7r()} 9. 0 1.8

P-• ^{r+e-c+ 70. 0 12.}

p -+ l'+ fl-fl+ GO. 0 1 ().

T<tble Sb: l·~xpcriment.fll results of the Frcjus expcrimeni for i/X decay Jnodcs.l'll

Decay mode n -+ 1iiT⁰

n ---> D {(⁰

n -+ i!p⁰ n ----> f.lcu

P-+i/71+

p-+ [)[(+

p-+ ilp+

p -+ /l [(*+

Final state

rr

iTO iTO iT+ JT-

''

^{iTO 710 710}

7T + JT- JT+ 71- 710 7Tol

7ro /(~(71+ JT-)

7ro ](~ ( 71 o JTo) 7T ](+ (p-+ /1)

71+

fl+l/

7T + 7To

iT+ 7ro 71+ ](~(71o 7To)

7r+ I(~( JT+ 1r-)

JTO {((fl.+ lJ)

iT0l\'(JT + 1r⁰) t

10 /15 9 16 31 13 9 32

12 r15 18 16 12 22 15 36 9 15 .31

]() 10

lG I :3 11

12

16 12 15 ll

Bk 1.2 J.;) 0 .. ) 0.3 0.6 2.1

().:)

0.·1 J 0.6

1.2

};!

l.O

0.8 0.9 0.8

O.G

0.1 0.6

Datil

0 1

()

0

·'1

()

I 0 0

()

1 l 1 0 0 0 0 0 0

T /8( 10¹¹

Y)_

1.3 l.S 2.9

0.9 1.7 2.2

1.0 1.5

The detection efficiency r' ohtilined for each final state takes into account t.hc effects of the reinter;Ktion of the decay products inside the iron nucleus. These t arc weighted according to the known bcilnching ra.tios of the meson decay in order to ohtain the efficiency t mode for t.hP nucleon decay modes. The partial lower lifetime limits given in the last column of table are background subtracted 0nd comrmtecl at. 90% C.L.

-- 104 -

ent vertices (A and B) only 9 em apart, which could never have been resolved by Kamiokande or IMB and not even by Super-I(a.miokande. In fad, Kamiokancle and IMB have never claimed to have found double vertex events with close separation. Very recently, however, the Sudan group (USA) obtained a similar event in neutrino- background Monte Carlo simulations for their fine- grained tracking calorimeter type detector called Sudan II. Sudan II has a good spatia.l resolution for track points ( 4 x 3 x 2 mm rms) in an effective volume of a.bout 3000 tons (1⁹).

From the above arguments it is clear that the basic problem in experiments searching for nu- cleon decay is the reduction of neutrino back- ground. It. does not make sense to build second- generation experiments which are just an exten- sion of existing detectors. Accordingly, the 1MB group ha.s no plans to enlarge the present wa- ter Cerenkov detector, and the Frejus Collabo- raJ.ion has closed down their 1000 ton tracking calorimeter. The major objective of the delayed 3000 ton Sudan II detector appears to be a search for extra.t.errestric high energy muon point sources ra.ther t.ha.n a sea.rch for nucleon deca.y.

New detectors, which are under development, must have excellent spatial resolution for the mea- surement of tracks and reconstruction of vertices, and they must be able to identify particles. For example, t.he ICARUS project (It.a.lian/USA Col- laboration) (2°) will use a 6.5 kt liquid argon time projection chamber in· a 0.5 Tesla. magnetic field.

The expected position resolution is 2 mm, and it has a threshold energy of 5 MeV

e

^{1 ). Super-}

Kamioka.nde plans for a. volume ⁷ times larger as ICARUS, but the key point for the next genera- tion of nucleon deca.y experiments is not only the larger effective volume but also the capability of a precise evaluation of background rates, and the ability to identify particles.

3 Comments on the Detec- tion of Solar Neutrinos

Super- Kamiokande plans to detect. solar ⁸ B neu- trinos (⁸ B --+ 8 Be*

+

e+

+

ve) via. elastic neu- trino electron scattering (z;ee- ^--+ vee-) in water.

The energy spectra. of sola.r neutrinos predicted by the standard solar model (SSM) are shown in

Fig. 2, cited from Bahcall and Ulrich (2^3). The first detection of solar neutrinos was performed with the ³⁷ Cl radiochemical experiment by Davis et al. Davis has operated a 600 tons C2Cl4 detec- tor for two decades since 1968 in the Homestake Gold Mine, located 1180 m underground in USA.

Solar neutrinos have been detected at a.n average va.lue of (2.07 ::!: 0.25) Solar Neutrino Units (SNU)

(22

), which is a.bout 1/3 ^f",./ 1/4 compared to the predicted rate of 7.9 x (I

±

0.3) SNU calcula.ted by Ba.hcall et a!.

(2

³⁾ on the basis of the SSM for the ³⁷Cl experiment. (1 SNU = 10⁶ve/crn²s)).

The discrepancy between the calculation and ob- servation is known as the solar neutrino puzzle.

Ka.miokande II

(2

⁴) has also searched for ⁸B so- lar neutrinos. As a preliminary result they derive a.n upper limit flux of 3.1 · 10⁶ve/cm²s (90% C.L.) based on 220 days of detector life time. This has t.o be compared to a value of (5.8±2.0)·10⁶IJe/cm²s (effective 30' error) expected for the detection of

8B neutrinos in their water Cerenkov counter. The energy threshold for the detection of electrons from vee- scattering was 9.6 MeV. The upper flux limit is derived from the angular distribution of selected electrons. At energies in excess of ^f",./ 10 MeV the z;ee- -scattering is peaked i~to the for- ward direction, so that one should observe a corre- lation of the scattered electrons with the direction

to the sun (see Fig. 3).

For the ⁸B solar neutrino experiment in a water Cerenkov detector there are many back- ground sources: radioactivity of the water and surrounding rock (Bismuth 214, spontaneous fis- sion of Uranium, etc.); background induced by cosmic rays, and antineutrinos from nuclear reac- tors. Electrons induced from background sources have isotropic angular distributions. After suit- able background reduction the Kamiokancle group claims a signal to background ratio of S/N = 0.07 (for Ee

>

9 - 10 MeV, see table 6). Accord- ingly, the vee- -scattering events have to be ex- tracted from the large isotropic background (see.

fig. 3). The flux upper limit of 3.1 · 10⁶ve/cm² s (90

%

C.L.) was derived with a maximum likeli- hood method on the basis of the observed angular distribution of electrons taking the effect of multi- ple Coulomb scattering of electrons in water into account. In this method the exactness of the used angular distribution of electrons clue to multiple Coulomb scattering in water is most important..

-105-

10 12'

10 II

:>

1d

<D

2

7 ³

'-' 10

<D

"' '

"' 10

E '-'

1d ^nF~--

--

X ::::J l.J_ 1d

10 ⁴

1d 1d 10 I

0.1 10

Neutrino energy in MeV

Figure 2: The solar neutrino energy spect.rum predicted hy the st.fl..nda.rd solar model. ('') Fig. ¹l shows a comp;Hison for the angular de-

pendence of multiple scattering of electrons in wa- ter. belwcen the calculated results of N akat.sukrt et al. e·s) (thick solid line with Mott. formula

<tnd thin solid line with Gaussian formula) and those of 1\arniokande II ( dash-dot.t.ed line). l"or electron energies below 20 MeV the scattering an- gles calculated h.v f( amioka.nde are smaller than those of Nakrtt.suka. et. al e~). The calculation of I\;uniokandc is based on the EGS 4 code

e

^6),

which 11ses the Moliere· approximflt.ion for elcci.ron sca.t.t.ering (the scattering nucleus is approximated as a point charge). In this rt.pproxirna.t.ion t.he fre- quencies of single large angle sc<tttering events a.re increilsed with respect. i.o the real Cilse, and the root mean square scattering ctngle will diverge for low energies. In order to nvoid the divergence, the EGS code conl.flins a weighted funct.ion which be- comes zero at. a. scattering a.ngle of rr, independent of t.he energies of incident. electrons. This corre- sponds to an c!Tect.ive cut.-off angle of Bc,.t -::::

trr.

Instead, it. wnnld he reason<1.hle to use n cut-off for a scattering nngle of (}mwr: -:::: ,\jd (d: nuclear ra- dius, ,\ - wavelength of t.he electron (A = h/p)).

'The EGS cut. converted to energy (Ajd :::::::; ~rr) leads t.o 20 -- :JO MeV. 1\ccnrdingly, if the elec- tron encrg.Y I·~ is larger than Dcut = 20-30 MeV,

eCU( > ^e71lflT holds, leading to an OVerestimation

of the scattering a.nglc, (sec Fig. '1). ·On the

other hand, if the electron energy is sma.llcr t.l1<Ul

Cut, ,\jd might exceed rr, which is unphysical.

To avoid this, EGS introduces a cut.-off angle of

(}n.t = ~rr, thus underestimating large a.ngle scat- terings at. low electron energies. This is clearly seen in Fig. ~ (The I< amiokande II resu lt.s beyond 20 MeV (dashed line) have been calcula.i.ed hy ^11s.

For the ⁸B neutrino observation t.hey are of no relevance). i\lso shown in Fig. '1 arc the 12 in- dividual events (black circles) of the l\amiobnde I I observation (²⁷) of the SllJWrnova SN 19SI !\. for comparison. The angles of electrons are me;tsured wit.h respect to the direction of SN 1'JR7.1\. The errors shown correspond to Ia Gaussian errors.

The corresponding R events of the l M R observa- tion (2⁸) are shown by the full circles. The solid li nc of N akat.suka ct a!. gives a. hett.er reprcsen- t.ct!ion of t.he measmed scattering angles than the 1\allliokande II prnamctri?;at.ion. Since the scat.- (('ring angle distribution is use<! to derive ;111 ilp-

pcr limit. for t.hc solar ncl!trino flux, this upper limit. must. he increased, if the improved multiple Coulomb scattering calculation by N akat.su ka ct al. is taken.

The 1\rnnioka group has continued t.o observe solar neutrinos with the I<amiokande l f detector.

Very reccut.ly they h;we published a mcilsured so- lar neutrino flux for /~'~ 2;> ~L) MeV corresponding

~· 106 --

Table 9: Results (P-values) of circular statistics tests applied to the measured angular distributions cos Bsun for various run periods

Total Live Electron Rayleigh Zn-test Watson V -test Chi-sq Li & Ma

event time energy Zn

u2

_n

u x2 s

no. days Mev

bins no.

feed om 6 7

39

856 220 > 9.6 P=0.016 P(4)= 0.213 2.623 3.5.84 1 . .58.5 0.108 0.061 a<0.005 a<0.005 a=0.615

P(6)=

0.160

1021 330 ~ 9.3 P=0.065 P(4)= 0.159 2.336 44.64 3 . .539 2.683

0.170 a<0.10 a<0.01 a=0.247 P(6)=

0.320

1239 450 ~ 9.3 P=0.305 P(1)= 0.0813 1.50.3 35.80 2.110 1.281

0.598 a>0.10 a<0.10 a=0.617 P(6)=

0.731

.368 220 ~10.4 P=0.471 P(4)= 0.0587 1.145 33.45 1. 7 4.5 0.625

0.720 a>>0.1 a>0.1 a=0.721 P(6)=

0.600

623 382 >10.2 P=0.240 P(4)= 0.124 1.689 53.53 4.088 2.861

0.209 a>0.1 a<0.05 a=0.061 P(6)=

0.217

723 4.50 ~ 10.1 P=O . .S77 P(4)= 0.072 1.019 48 . .56 3.463 2.619 0.500 a>>0.1 a>0.1 a=0.140

P(6)=- 0.374

1282 288 ~ 7.5 P=0.0085 P(4)= 0.278 3.058 54.10 3 . .543 2.499

0.037 a<O.Ol a<0.005 a=0.055 P(6)=

0.057 Ohya observation for

UHE 1-ray flux from Cyg X-3

2 bins 4 bins 1770 ^rv .3yrs > 100 P=0.0069 P(4)= 0.319 3.083 59.11 3.7.59 3.962

Tev 0.00088 a<0.005 a<O.OO.S a=0.002 P(6)=

0.0036 -107-

~ 60~~~~~~~--~~~~~~~~

?i

^{(b) Ee ~} 10. 1M e V

0 0 lD

\: 40

z

i:IJ

~20~++~~~~~~~~~~~~~

.z w

> _w

o~~~~~~~~~~~~~--~~

-1 -0.5 0 0.5

COS ( 8 sun)

Preliminary'

1

oo.--...

-~--,.-~--__,...,.

_____

-r-...--_;,.__,

en >- 80

~ 60

Ee;?:7.5MeV

S.S.M. ·---.

o~~~~~~~~~~~--~~~~~~

-1 .o -0.5 o.o 0.5 1 .o

COS ( () sun)

Figure 3: Distribution in cos Bsun, where Bsun is the angle between the trajectry of a.n electron and the direction of the sun at a given time. The data. in the 680-ton fiducial region a.re based on 450 days in the time period January 1097 through May 1988, (a) with Ee ~ 9.3 MeV and (b) with Ee ~ 10.1 MeV, respectively. The solid histgram near cos esun = 1 is the prediction from the stan- dard solar model. The dotted histgram is the best.

fitted value. Cited from ref. 29. (c) Same figure as above, for the improved da.ta. with Ee ~ 7.5 MeV in 288 days run since June 1988. Cited from ref.

34.

to a fraction

0.46

±

0.13

±

0.08

of the flux predicted by the sta.ndard solar model (The first error is statistical, the second system- atic). This result is based on an event sample of 450 clays lifetime in the period between Jan- ua.ry 1987 and May 1988

(2

^9). The corresponding cos Bsun distribution (Bsun is the angle between t.he observed electron and the direction of the sun) is shown in their paper for Ee ~ 9.3 MeV and for Ee ~ 10.1 MeV.

To check whether their neutrino signal is statis- tically significant one can proceed along two dif- ferent lines. Firstly, one can simulate solar neu- trino events in the detector and overlay them with a uniform background distribution. The hatched histogram in figure 3 shows the expected ⁸ B solar neutrino signa.! on the basis of the standard solar model on top of such a uniform ba.ckground. Then one ca.n fit the observed angular distribution with two components: one coming from background, the other from the neutrino source. Such a fit gives a certain number of "observed" solar neutri- nos resulting in a flux fraction as given above.

Secondly one can just take the observed angu- lar distribution and check with statistical tests whether the measured result is compatible with a uniform distribution or not. For this purpose we use the published data for 450 days

(2

⁹) and the previously given data for time periods of 220 days

(2

^4), 330 clays and 382 da.ys eo) to compare how strongly the cos esun distributions contradict a uniform distribution, which one would expect for background events only (null hypothesis of ran- domness).

To do this, we apply the following sta.tistics tests

e

¹⁾ to the data: Rayleigh test, Z11-test, 11-test (modified Rayleigh test), Watson's U~- test,

x

^2-

test, a.nd I< uiper's test. The Rayleigh test is per- haps the most familiar circula.r statistical test. It is based on the resultant length of randomly ori- ented unit vectors in two dimensions. The Z11-test is the Rayleigh test with n-harmonic folding. De Jaeger et al.

(3

²⁾ have tried to determine the op- timum test with the largest discriminating power.

According to their analysis, vVatson's test is best for duty cycles larger than 10

%,

while the

x

²-test is superior for duty cycles less than 10 %. The input for the statistical analysis are the angular -108-

--Present calculation, Gaussian formula

, Mott formula - - - a calcalculation by EGS code

~Obs. values of Kamiokande 1--0--iObs. values of IIviB

0\~---~---~---~--~

0 10 20 30

Electron Energy [Mev]

Figure 4: Comparison for the rms angular dependence of multiple scattering of electrons in water between the calculated results of N a.katsuka et al

e

⁵⁾ (thick solid line with Mott. formula. and thin solid line with Ga.ussia.n formula.) and those of Ka.m.iokande II (dash-dotted line). See in the text for black and open circles.

-109-