EUHOEEAN OHGAIHZATIOll FOil .NUCI.J:.~AH EES.EAHCH

A 1ITI1,.,n7 rrrh1::ir;1 "";:i'("T." m1 :i:._1;:t T11-'P"..'f-" m..,-·ol~ r)Tji 1.TP 1; VY 7·n1.)m1-...i-,_-r(:1 Tl, .... rrrrr--, -rrO --.,";.'"" .1 . .. _ .. J."i .JH ..l...i. . .i0 .i.... ..L .-r..Lt. L . ..l..I ..:.. \).1..d1J.r>.J.. .. L J.'J. \... -L J.U.;.1~H. .. u.2J..:...1-Ul~:...J .L.U :.L.fl5 AL 0....:..v.H.l

-------"""""""""" ____ .......,._, _____ ,,, ___ ~-..-ko .. ,.,.---~-.,.-... ~-~-----·--

range 0.400 < E !J.T(

C .,Ji. Ra.nrrn.

0~4~)0 Ge\r tb.e st~~uct111""e of t11e mv.oD.-pior:

in two bubble chwnber experimonta. Near 0.429 GeV there are t~e

aJ:apl.i ttldG of the atzvcturos in

to the decay of an • The fl JI

tte Ll distribution3 from t~cso f'1:

experiments is greater than that obs0rved by Bisi ct al. Ttis

discrepancy is un~ikcly to bo due to statistical errors, if it is a

physical effect j_t would indtcate that the selcct:Lon of the decay

c or1::f igtlra t :i~o11 irLf llL011c cs tl10 1/I clir; t:ci b:_tt =~~.011 ar1d tb. eI~ef or·e ~~·;.e.:t µn

the K~ decay j_;_; anisotropic with rN1pcct to ti:"w :ur~e of fl:i.gh"t.

(Geneva - 20 I:.Iay 1 971 )

- 1 -

According to the usual understanding of the K~ decay the muon-pion

invariant mass distribution (r.1 ) from the mode : Ko~~ ( µnv) µn ( 1) µ;i

should be smooth. A previous analysis of observations from the

CEH.U 1.1 m3 heavy liquid bubble chamber (HLBC) and from the

Brookhaven 1411 hydrogen bubble chamber (HBC) indicates that this

does not seem to be the case. Similar fluctuations in the M mass

distributions have been found in the ranee

(L <... LI < H), at the same value of T;I as µn -~m

muon-pion invariant mass distribution f·rom

µn 0.422 <'.'. M .<( 0.437 GeV

µn an enhancement in the

high energy neutrino

interactions. This result is unlikely to be due to a statistical

coincidence ; the fluctuations have properties which are compatible

with the formation of a short lived neutral heavy lepton (I.I''' ) which o * - * - + µn . decays into a muon and pion : KL-711 + v ; 11 :--7- µ + n • The

µn µn following report describes a new test of this hypothesis in data

which have been made available to me,very kindly, from spark

chamber (sc) obnervations ( 2) of the charged particles from K~ decays.

Principles of this analysis

Experimental studies of the Dalitz plot of the K0 _ ems show . µ.'.> that the muon momentum distribution is most populated at the low

momentum botmdary of the plot. This feature or the distribution is

associated with the nature of the interaction between the muon and the

neutrino in the :r.I ems the probability distribution of the muon µn

tends to be maximum in the direction parallel to the neutrino and

minimum in the antiparallel direction.

:&'or any given value of M the least probable conf'iguration of .0 µn;

the Kµ 3 ems is that for which the muon momentum:is highest ; this is

also the configuration in which the muon momentum is antiparallel to

the neutrino and pion and, in general, greater than either of them.

The most probable configuration of the K0 ., ems is that for which the . µ.:>

pion momentum ir> highest, i.e. antiparallel to the neutrino and muon

and greater than either of them.

- 2 -

In the ems of a particle which decays isotropically the probability

distribution of decay products is, by definition, uniform in solid

angle. Therefore from geometry 7 for any given direction, the

greatest population density of any decay product will be found

transverse to that direction. In particular, in the Kµ0 _ ems with )

respect to the K~ line of flight the greatest population density

of muons is in the transverse direction : components of momenta in this

direction are invariant in their transformation into the laboratory.

Thus it follows that decays with p'.11µ > pTre in the laboratory

are less frequent than decays v1j_ th Pm < Pm • These transverse J..µ 1: n

momenta are represented in Fig. 1 ; the decays for which Pm > Pm :.i.µ '.l n;

are characterised by configuration 1 , those for which Pm < p,,, are l µ J..re

characterised by coruiguration 2. We shall designate that part of

the l.:I distribution for which pT ) Pm as (I.I ) 1 and the other µre µ :i.:n µn part as (I.I )2 • We note also that the neutrino momentum (p ) in

t ,, Ko 11n. (- .2 I ,2 )/2'' d th t I v . rt I ile •7 ems is ::.:i.,.,. - ,. l,;K an a· Pm = PT + PT == P SJ.n p ; µ:; J\. µJ.4. 0 :.i.: µ re v

¢ is the angle between p v and the. KL line of ~1.:i,ght : _6 is the angle

between the muon and the neutrino directions j_n the M ems. µre

Suppose now that as the result of the formation of an r,:* the µn

distribution of 6 changed from that in the usual K07 decay. If it

µ.:> became more symmetrical, for example, this would cause an increase

in the population of muons antiparallel to the neutri.no direction

in the M ems, hence more decays with PT ) pT in the laboratory µn * µ n

and therefore an en.fiancement at J;J in (IiI )1 • An effect would also . µn µn

be produced at M;i< in (I.1 ) r, however (M ) 1 is norm.ally a less µn µn 2 µn

populated distribution than (1,1 ) 2 , therefore the effect in (1.: ) 2 would µn µre be likely to have a lower statistical significance than that in (M ) 1 •

µn We shall study the (l\1 ) 1 and (M ) 2 distribut~ons from the SC

µn µn observations in the neighbourhood of L < :r.I Z H.

µn

(M ) 1 and (IJ ) 2 in the total SC data µre . tm

In order to avoid the b.nematical selection due to the

experimental systems for particle identifj_cation we shall not, at

- 3 -

this stage, use any information on track assignment. l"or the

calculation of (M )1 the track with the higher transverse momentum µ n;

in each pair is assigned as a muon, for (M ) 2 the other is assigned µn

as a muon : the fundamental observations are the direction of the 0

K1 beam and the vector momenta of the pair of tracks from the decay

vertex.

In addition to

of decay of the K~. the K~3 these track pairs contain other modes Of t 1 th TTO }TO ;rO l, ~1ese e l'• '7, .\. 3 and i• , wi~e11 assig.aed as

G.) 1t S

muon-pion combinations, produce backgrounds in the ltl spectrum of µTC

the K03 • Only a part of the contribution from the decay K0 -:'!>- (n + 1i-)

µ s is line-like ; this is located in the range 0.480 <: Mµn < 0.486 GeV,

the rest is a continuum. The track. pairs from K~3 ~ ( n: + n: - n °) give

a continuum in M with a sharp upper limit at 0.346 GcV ; the

decay K~3 -7 (env)rcgives a continuum. throughout the whole range.

We define n1 as the ratio of the observed PTµ to the maximum

possible for the calculated M and configuration 1, R2 is the µn

corresponding ratio for configuration 2. Histograms of (I,l ) 1 fron µn

32250 track-pairs, for various ranges in R1 are shown in }'ig. 2 for

O. 380 ~ M < 0 .4 70 GeV. No detailed shape is lmovm for the phase µn

space expected for the experimental distributions, however in this

region, according to the usual concepts, it should alvmys be a smooth

curve. Therefore, as a reference for the measurement of fluctuations,

the least squares fitted polynomial mean, of order < 20 and whi.ch

gives the lowest value of X2 for the range 0.370 < .iJ < 0.480 GeV, µJt is shown dotted for each histogram.

The lower three histograms are for high values of R1 , they

represent those decays in which Pm is near the maximum possible for J.µ (1)

configuration 1. From the previous analysis it is expected tha"'.;

the decay of the r.r* will cause an enhancement in the range L to H ; µre

there are indications of' such an effect but the observed worst fits

of any five consecutive bins have probabilities of rv 10 % of being

due to statistical fluctuations •. The (Mµn) 2 hiotogram for R2 <. 1 .o, shown in Fig. 3, is statistically smooth between J~ and H ; the dis­

tribution of the fluctuations has a qualitative reoe:rablance with (lJ )1 • . µn

- 4 -

~I.'hc result of adding the bistosram of (l,I ) , :for o. 8 ,(_ R .(_ 1 .O µn I 1

(Fig. 2) and the (Mµn) 2 histogram is also shown in Pig. 3, together

with that obtained in the previous analysis by adding the spect·a

from both possible muon-pion assignments of all trac1;;: paj_rs in the

HL.BC and HBC. (We shal1 designate the combined data from the HLBC

and Imc, by J3C). Al though these SC ancl BC histograms are obtaj_ned

from different expcrimeirts by d:i.fi:'erent analyses, both contain i.1 o µn

spectra from the KJ. decay and tt.eref·ore they should be co1Telated • • J

Their correlation has b-::;en measured by calculating the coefficient

of correlation (x 2), used prcviousl;y. :Figure 3 (d) shovm the various

values of X 2 obta:Lned by comparing the 20 bins of the SC histogrm:i

between 0.400 <.. I.lµn z 0,450 GeV wj:th tl1e 20 com.:;ecutive bins of the

BC histogram '!lhich commence in the range of :t 5 bins about 0. 400 GcV

this range is larger than the conceivable nasc errors i.n the nean

ma~rn scales. Por the direct superpcsj.tj_on of the tvro set;:> of 20 bins

X 2 ,..,, 14 .6, foT 19 degrees of freedom. If two such hi;.;togra::c.s

represent the i.3an10 phys:Lcal distribu.tion a value higher t::1an 1.;.6

would be expected in 75 % of such tests. Thus these distributions

have a hj_gh corr·::;lation. '.rhe highest correlatj_on ir> obt2,j_ned if t:Ce

range of 20 bins from tho SC histogram is superposed on the BC 0

histogram with a displaceEwnt of one bin to -the right : X'- = 11.6

(probability 90 50). All other supe:rposi tions yfold hj_eher vall~es o:::

x 2 , i.e. they show lower degrees of correlation.

This pre1i1;1inary examination of the comb:i.ned (l'J ) 1 and (l.: ) 2 µir µn -histosrams thus shows that in the range 0.400 to 0.450 GeV there is

a structure which is hiehly correlated w:Lth that of the BC histcg:rr::.m

and located v1ithin one bin (0.0025 GeV) of it ; there is also an

enhancement of low sta ti;Jtj_cal significance between r, and H. The

reductj_on of the correlatj_on between the SC and I:C histocrans

relative displacements greater than one bin shows that a higi.1 mass

resolution ancl a stable mean mass scale are important for the st'-.<dy

of this structure.

- 5 -

Calibration of the mass scale

Both the K0 and K0 decays are useful references for calibration s n3 of the mass scale. A histogram of Mmt in the region of MKt for the

first 16292 events on the SC data tape is shown in Fig. 4 a. The

enhancement in the bin between 0.493<. M < 0.503 GeV is compatible 1t1t

with that expected from the K~---:,. K~ decay mode. The enhancer:J.ent due

to this decay mode is less significant in the remaining data, shown

in Fig. 4 b. A comparison of the Mnn distribution

(11K - Mn:o) for the same data sets indicates that

more sharply defined in Fig. 5a than in Fig. 5b.

in the region of

the Tro d . ~'n 3 e ge is

These observations indicate that the calibra·tion o:f the mean

mass scales in the experimental data is satisfactory ; they suggest

that the mass resolution in the data from the first part of the data

tape is higher than in the remainder.

-* More detailed tests for the h µn

In an attempt to obtain an Mµn spectrum with the highest possible

resolution, the analysis illustrated in Figs. 2 and 3 has been

repeated on the same sample of data from which Pigs. 4 a and 5 a were

obtained. For the rest of this report we shall refer only to these

data from the SC, they are about half the total sample.

The (hl ) 1 histograms are shown in Fig. 6 ; they are conpatible . µn

with Fig. 2 in that there is an enhancenent between L and H which is

larger in the data with high values of n1 • For the histogram with

0.75 < n1 <. 1.0 the worst fit to the mean of any five consecutive

bins is between L and H and has a probability o.f O. 7 ?b of being due

to statj_stical fluctuations. A histogram of (Mµn;) 2 for R2 z 1. 0 is

shown in Fig. 7, there is a similarity with (IJ µn;) 1 between L and H.

The addition of the histograms of (!:I ) 1 for 0. 75 L.. n1 z 1 .o µ n: '

and the (1•Iµ 11) 2 hiGtogram is also shown : independently of the choice

of 3, 5 or 7 consecutive b:i..ns, the worst fit is between L and H.

- 6 -

This result corresponds with that first observed over the total

range in III in a different type of analysis of the K03 decay in

~ µ the HLBC (see Fig. 2, ref. 1). In the SC histogram. the probability

of the worst fit of five consecutive bins being due to statistical

fluctuations is 4.2 x 10-3 ; the corresponding worst fit for the

HL:BC histogram is 0.7 x 10-3 • The probability that these worst fits

should be due to statistical fluctuations at the same place, between

L and H, in both histograms is < 1 o-5 ; if we take account of the

similar effect in the HBC the overall probability of the results

being due to a statistical :fluctuation is < 1 o-7 •

As is also shown in Fig. 7 the SC histogram is correlated with

the total histogram from the BC, referred to in Fig· 3. For direct 2 superposition of the 20 bins between 0.400 and 0.450 GeV, X = 25.0

(probability 16 %) the highest correlation : x2 = 16.4

(probability 63 ~;) i.s obtained if, as with the total data, the SC

histogram is displaced one bin to the right relative to the 3C

histogram.

The results oi' tests as to whether the origin of tl~e effect

between L and H is really in the K0~ contribution to (11 ) 1 are µ) µn

shown in l!'ig. 8. Histogram (a) is that from Fig. 6 for 0.75<'..R1 ..(_1.0.

Histogram (b) is that part of (a) for which PT< pv + 0.020 GeV/c,

where p v

is calculated :for each value of M : this criterion

selects the values of PT µn

for the K~3 decay, assuming that the

maximum errors are 0.020 GeV/c. There is little difference betvreen

(a) and (b) which shows that the analysis by which (a) was obtained

already imposed a s1Jnilar selection in Pm• That part of (b) wnich l

satisfies the criterion that the muon detector in the apparatus

registered a muon in the track-pair, is shown i.n (c). The stopping

power of this detector is such that it does not register muons with

p ~ 1 GeV/c. µ

In order to assess whether (c) represents the same physical

distribution as (a) the coefficients of correlation between (a),

(b) and (a), (c) have been calculated as before for the ranges

- 7 -

0.400 to 0 .450 GeV. Ylhen (a) a.11d (b) are superposed directly a r,

high correlation : Xe: = 2. t1 (probability 100 /~) is found. Such a

result is expected a priori, sh1ce (a) and (b) are almost the Da.ne

data. A high corre1ation : x2 = 9.6 (probabj_lity 96 ~~) is also

obtained for the comparison of (a) and (c) ~ here, because of the

la:q;e difference of their data contents there was no a prior:!.

reason to expect it. These tests are compatible with tho effects

under study originati.ng from the K~3 decay. ~:'hey also demonntrate

again that the structure in the spectrum is sucb that a relative

displacenent of one bin greatly affects the decree of correlation.

These studies of the data from the SC confirm the hypothesis

that there is a physical effect between L and H which is due to a

change in the anc;u1ar distribution in the K~ decay. The greater .u enhancement in (1'1 ) than in (11 _) 2 and the fact that the enlmnce-

·-~L11 1 111• _ ment in (Bµ n) 1 j_s greater for hj_gh values of E1 are consequences to

JI< be expected from the decay o:f an k : thus we are led to the same µn

conclusion as that drawn from the previov.s exper:i.ments in t110 HIJ3C

and HBC, but by a dj_fferent r.1ethod of analysis and using dii:"ferent

data.

Comparison with the previous method of analysis

In the 3C analysis

the track-pai.r from the

( 1 ) ') is l 1

0 KL decay,

defined c~s the higher L1Gr:Jent'..illl in

p refers to the other. Except for 2

very lov: values of lI , the change in ant;ular di str:i. but ion due to the ;y; µii

decay of a11 1 1' would produce ~ "'"µn a greater enhancement j_n the IJ fLTC

distribution fron events with Pµ = p1 tho.n from those for v1h:i.ch

Pn == p 1 • In principle such an analysis requires no knowledce of the

K~ direction.

The J3C histogram of 11 for µn

is shown in Fig. 9. ~:hese

data come from rJ 1 500 rc0 ~ decays µ)

in the HLBC and .-v 1 )000 track--1)0.irs

containing v 3400

of the background

HTIC, all the data

v 0 decays in the IIBC. In order to suppress ·'-µ3 due to K~ interactions and regenerations in

,_, ( 1 ) . ;-were f.lelected so that p1 /p2 <. ::> and

GOJllC

- 8 -

PT<. 0.100 GeV/c ; the former criterion loses 'V 15 % of the K~3 decays ; for perfect measurements the latter criterion only affects

0 the Kµ3 spectrum for Mµn z 0.385 GeV. The histogram obtained from

the same selection of the 16292 track-pairs from the SC is also

shown for comparison : the actual number of K~3 decays in these

data is not known precisely, it is probably about 5500.

Also shown in Fig~ 9 are the usual X..2 and x2 variations ; they

indicate that the SC and 13C histograms are sim:i.lar, their

distributions are essentially equivalent to those obtained from

the SC in terms o:f PTµ and pT 11 • In the region L to H the enhance­

mentsreinforce by addition, as can be seen in the histogram of the

total of the SC and BC data.

The results from the 13C and the SC have also been compared with

those (3 ) from which Bisi et al. concluded that there was no

evidence --* Those authors have obtained histograms of the for an lJ • µ1~

neutrino kinetic energy (T ) in the Ko ems in steps of 0.2 in cos e v µ3 for events in which the ffiUO!l was identified ; e is shown in our

Fig. 1 . The observable range of Mµn is restricted because of their

particular experimental technique. Their data I, which came from

the operation of the experiment in the mode with higher mass

resolution, have been reconstructed for this comparison by reading

the bin heights in the histograms of their Figs. 4a and 4b.

Histograms from these reconstructed data for cos e .C:... 0 and

cos 9 > 0 are shown in Fig. 10. In the absence of ~ an IJ µn

these

histOGI'a:ns would be expected to be statistically smootn, as would also

be the ratio of their corresponding bins. As can be seen from the

X.2 distributions ·the worst fit of any five consecutive bins is in

the range L to II for the histogram for cos 8 <"o ; it has a

probability .( 1 o-3 o:f being due to a statistical fluctuation. The

largest discontinuity in the ratio of corresponding bins is about

7 standard errors and is located at 0.425 GeV. Such a magnitude of

discontinuity is unlikely to be due to sta·tistical fluctuations

it suggests that the histograms for cos e .c:_ 0 and cos e > 0 are not

smoot.i1ly correlated., as they should be if there were no I.I~ • µn

- 9 -

The values of x. 2 for all corresponding sets of fivo consecutive

bins is f;hown in Pig. 1 ·i ; it is evident that the rnaxitTLun value

of x2 , and thorefore the lowest correlation, occui~s in the :cange

JJ to H. The probability t:J.at this value of x 2 could be caused by

statistical fluctuations is entirely negligible : neither can j_t

be acco1mted for by tne possible errors in the reading oi~ the

original histograms from which these data were reconstructed.

Thus in the range r, to H the hh1togra111s o:f Bisi et al. show,

with great statistical significance, a change in the distribution

of t1 in the IJ ems. '.foj_s :Ls the same type of effect r1hich we have f!1t

associated with the h;ypcthesis of an I,I~ in the HltBC, HBC and SC p:rr

e:A."})eriments. However, if we compare the re1ative amplitude o:f the

fluctuations in their i.Ipn sp8ctra with thos;.'°' observed in the othc:c

e:x:perimenta it appear8 as if in this respect the results of l3isi

et al. are incompatible with the otherG.

On a possible experimental i.nfluence on the di.stributions

The combined sta tisb_cal signif:i.cance of the erfrmncen:ent in

the range JJ to H in tlw !.: µn spectra from the HI.BC, H3C and SC

experimentr:J, together with their detaj_led co2·relations, r..akes

untenable anv hypothesi:::J triat the effects aDc.ribed to tlle d" are ~ µn

due to statistical fluctuations. Any hypothesis that the i.mex~0ectedly

small ru;ipli tude of the str1J.cture, in tho results of 23isi. et al., is

due to stat:i.stical fluctuations :i.s also untenable, because of the

hieh statistics of their data.

It is evident that this discrepancy in the a;l:})litudes could

be due to errors in one or ;;:wre of the expcr:Lm.ents, or in t:he ncthods

of analysis. However, v1e have not found such errors, therefore y;e

cannot reject the pocrnibility that the obscrvat:i.ons from all fm.::.r

experiment::; are correct. If this were true, then the reasons for

the discrepancy i11 the procedlu--e by \v11:Lch t:he =-~ µn; distributions were obtained.

- 10 -

The experiment of Bisi et al. was designed primarily to

study the charged two-body deca;;lsf1·om the K~ bea...in and therefore

to select decay configurati.ons with pT rv O. TheDe arc configuratj_ons

in which tht" neutrino direction in the K 0 _ deca'y" is a1on0,.,. the line µ) '

0 of :flight of the KL. As we have discussed already, because they

accept all decay confj_gurations without selection, the HLl3C, HBC

and SC yield },I spectra from the K0 ~ in which the neutrino µn µ)

d · +. · · - 1 l _,_ 1 t J h 1 · f fl · "!, J o-_"· t:rie r- 0 J.rec vlOll lo arge .y vransversa. 0 GL e . UlC 0 . lgll li I -- l~L.

A test of the posDibili ty that this difference j.n the predominant

decay orientc•.tion is the cause of the discrepancy in ampl:i.tudcs is

s11ov1n in pj_c. 12. The U})}Jer histogram is fr~om botl1 mu~on-pio11

assignments o:f the SC data (pµ :::: p 1 and pn = p1 ), with the only

selection that 0 .8 < p1/pv < 1 .1 ; pv is calculated fox- each

value of III • The lower histogram is the same type of spectrum for µn

0 < pT/pv < 0.8, If

the data is divided

-~ the direction of p is

v into two approximately

isotropic in the Ko~ µJ

equal parts about

cn1s

1-\/.P ::: 0.8. Ho track pa:i.r contributes the same J,I value to both .1. V r µll:

histograms. In the )'.:_L distribution for all sets of 3 consecutive

bins of the upper hj_stogra:m the effect due to u* can be recognised ~ µn;

it has a probability of ~4 x 10-J of being due to a statistical

fluctuation. There is no immediately recognioable effect in the

histograra :for lower values of pT/pv. :S'r.om the x2 var:i_ations it

can be seen that the histograms are correlated ; essentially it is

the enhancement due to IJ* which :is reduced in the lower histograr:1. µn

This test is therefore coopatible with the hypothesis that the

' -'' t' ' 0 . . t . aecay 0£ ne ~ 2 is aniso ropic 0 µJ v

vvi th respect to the line of flight

o:f the K11 and the r.1;n

J:"u:cther tests are obviously necessary ; if the hypothes:Ls of

an anisotropic decay is really true it vrould contribute to the

explanation of the discrepancy between the expcrj..ment of l3isi et

and the others. It would also contribute an explanat:i.on to the

t dl , · , J · t 1 a+ "1·,·_,.¥ at '111· g .. '11 y::\l• 1 Po~ of p /•) , uncxpec ·e y n1g11 amp _J_ --,_w_e v -- --- ~-- - 1

tire. (1) rt µ mentioned in the prevj_ous analysis

", CJ,._J_. '

- 11 -

Conclusion

Tl · " c- i .. r* f 0 4 29 11s searcn ior an l'" o mass N • _ ~m

GeV originated in a

study of the kinematics of the interactions of neutrinos in the

}ITJ3C. The L1 µ distribution from those events with secondaries wr1icb. n:

include pions has a group of values compatible with the decay of a

short lived heavy lepton with a mass in the range L < I.I < H. p.n

The I.I spectra from the K~ decay in both the HJ:...,130 and the µn ~

HBC show a structure in the range Ii to H which is compatible Hi.th

the changes in ant;ular distribution which could come from the decey

of an 11* • A mean mass : J,1* = 0 .429 GeV was obtained fro.:n the µn µ1t

combination of the mass values of the enhancements between L and. H

and the neutrj_no results. '.I'he systematic errors in the mean 1J mass µ n:

scales in these K~ experimenta are L_ 0.0025 GeV.

These previous reoul ts are confi,rmed by this analysis o:f data

f'rom the SC experiment on the K~ decay. '1.1here is an enhancement

betvmen L and H : f'urthermore, for at least the range

0.400 < H ~ 0.450 GeV, the correlation of the li1 spectra fror:i ~~ ' ~

the BC and SC are such that they can be considered to represent

the same physical distribution. The statistical significance of

the enhancements and the detailed correlatj_ons exclude any

reasonable possibility that all these effects are due to statistj_cal

fluctuations •

. None of thj.s reproducible structure is expected accord:'._ng to

the usual concepts of the decay of ., I··'o ~ne ~L" While the h:,rpothcsis of

tl .p _,_ . d ' :f t' ~ r¥ 10 .i:orma-.ion an aecay o · ne i11 µre

accom1ts for the effects betwee::.

L and H; it scer:ls un1L1-\:ely that it can account for an appreciable

part o:f the structUl'e outs}.de of that range. Some, but not all, could

be due to the existence of hea>"Y leptons with other masf.les.

It is clear that the discrepar,cy between the ampli tuG.e of tr_e

effects in the U spectra from the expori~ent by Bisi et al. a~d µn .

theoe other experiments cannot be expl:.:dncd iri terms of s·~atistical

fluctuations. In fact, as was seen in Fig. 11, there is an obvious

- 12 -

correlation between the distribution in U of the structures in µ1L

all the experirnentf:3. We mlwt conclude therefore that either there

arc ei-rors in the observations or in the analyses, or else the

difference in experimental procedure j_n:Cluences the M spectra. 1111.

A knmvn fundamental difference j_n teclmique bet\veen the Bisi ct

al. experiment and the others j_s the selection o:t' the decay

configuratj_on of the K~ with respect to the line of flic)1t. If

this r::election is confirmed as the cause of the discrepanc;y', then

the K~ must have an anisot:r-opy with respect to its line of flight

and to the decay of the r.1* • p.n:

These conclasions imply the need for further highly precise

experimental studies of the K~ decay.

- 13 -

Acknowledgements

The present analysis has been made possible by my colleague

P. G. Innocenti. Not only d:id he obtain and translate the magnetic

tape from the f)C experiment but he also gave me the con.tinua1

expert advice and help necessary for the understanding o:f the

obscrv2.tions. I am profoundly grateful to him and his other

colleagues from that experiment for thetr aid and encourager:wnt

in this search for heavy leptons.

I have greatly appreciated discussions with R. Johnston

and hj.s colleagues at LRL and TI. Mozley and his colleagues at

SLAC on their different experiments on the K~ decay.

It is a pleasure to acknowledge the continued collaboration

of Mrs. H. Cabel wi.th the data analysis for these studies.

- 14 -

References

1) C.A. Ramm - On the possible existence of heavy leptons,

Nature 227, 13 2~5 ( 1 970) •

') ) ,_ C.Y. Chien, B. Cox, L. Ettlinger, L. Resva .. nis, R.A. Zdanis,

E. Dally, P. Innocenti, E. Seppi, C.D. 13uclw .. nan, JJ.J. Drickey,

I!'.D. Hudnj_ci:, P.I!'. Shephard, D.H. Stork, H.K. Ticho -

A mea::nu-cmcnt o:r the form factors for the decay K~ -7 n µ v.

Physics Letters 33 B, 627 ( 1970).

3) V. JJisi, I.:L Cullen, :P. Darriulat, c. Grosco, ILI. :Perrera,

E. Hadermacher,

Search for (n !l)

(Aprn 1970).

c. Rubbia, D. Shambroom, A. Staude aLd K. Tittcl -+ -

• jr ...,,. + 1 c-,--,..--,,-,T _,., --,.-..,.. ..,.. ·· re<;onance in J\.1 --:;. n p v aecay. '".ru.. JJ •. ::h .L

4) C .A. Ramm ~· On a search in spark char:J.1.Jer data for the pos~:;j_ble

existence of !:"1ee.vy lcptonG. CBHN liPA 69-G, Add. 2 (April 1970).

- 15 -

Figure Captions

li'jg.

:B'ig. 2

Fig. 3

J!'ig. 4

Fig. 5

Fig. 6

}!'ig. 7

Kinematics of the K0 ., decay. µ)

HirJtograins o:f the (M ) 1 spectra from the 32250 track-pairs ~li(

of the SC data. The pointG indicate the leaGt sq~;_ares

f j_ t t e d me unB •

Comparison of 1.1 distributions from the K1°J. µ.rt

a) Histogram of (I.lµn) 2 for n. 2 . < 1 .O from the SC.

b) The addHion of the hirstogram for 0 .8 .(. R1 < 1 .O from

lri· u 2 •.-;·' t>1 ( ~ ;' b~ ~ML- t.1,. e

c) The total M distribution from the HLBC and lGC µn.

obtained fron a different type of analysis.

d) 2 Values of X for various superpositions of the range

0.400 ~ Mµx ~0.450 GeV of (b) on (c).

IIistogr<:.ms of ltI near I,IKLo for selections in Pm. xn ~

a) Results from the first 16292 trac~-pairs on the data tape.

b) Results fro1:i the remainder of the data.

Histogrm.:J.s of H near r· •. o - I:I 0 for se1ections i.n PT· J,.~ J.. ~d .. K .... rm J~ 1t

a) Hesults fr on the same data as Fig. 4 a.

b) Results from the same data a.s Fig. 4 b.

Histograms of the (l .. ~µ1) 1 spectra from the data o:f Fig. 4 a.

Combination of the l.Tµn spectra from the data of lci.g. ,t a.

a) Hif;tocram of (1:µn) 2 for H2 < 1 .0.

b) The addition of the hL~togram for 0. 75 < n1 < 1.0 fro.o

:E'ig. 6 v:ith (a).

c) Va1ues of X.2 for all sets of ) ~ 5 and 7 consecutive bins.

d) Values o:t' X 2 for variou:J superpositions of the ranc;e

0.400 L.... I,~ <. 0.450 GeV of (b) on the total BC ~m

distribution (c) in Fig. 3.

E'iG. 8

:Pig. 9

Fig. 11

- 16 -

,0 The effect of teats for hµ 3 decays.

a) Hic;togram of (LI ), for 0.75< n1 <1.0 from J!'ig. 6. µn I

b) Hefrn.lt of the selectj_on p'.l~ < pv + 0.020 GeV/c.

c) Hecult of requiring a muon indication in the data of (b).

d) Yalu.es 2 of X for various superpositions of the range

0 • 4 0 0 < 1·\rn L_ 0 • 4 5 0 Ge V of ( b ) on (a ) •

e) Values of x2 for various superpositions of the range

0.11,00 <.I.I < 0.450 GeV of (c) oi1 (a). µn

Resultr:; obtainecl by the previous method o:f analysis.

a) liistogram of .... µ1t

from the BC

b) H:i.:;togra1n from tho same analysir:i as (a) for the SC data.

c)

d)

e)

The addition

VB~l lJ..e tJ of • \! 2 )...

Ve .. 1ucs of x_2

of (a)

for all

for all

a11d (b) . sets Of 5 cmrnecuti ve b:ins of (a) . sets of 5 co11aecut:Lve ' . of (b) OlllS .

f) Values of x 2 for various sapeTpor;:Ltions of the range

0.400 < IJ <0.450 o:t' (b) on (a). µn

Analysis of the data reconstructed from the report of

:Bisi et. al., (see text).

a) HiDtogram in m for cos e < o. .l.

v

b) iii st o gr·c1rrr 1.11 r;l for cos El > o. -"-v

c) ~~l1e ratio of correspond inc bi11c :Ln (b) to (a)•

d) Va.1LlGS o:f x2 for all sets o.f> .t. 5 consecutive bi11s in

e) Values of x._2 for all sets of 5 consecutive bins j.n

Comparison of statistical significances in all sets of

five consecutive bins.

(a).

(b).

a) Of ·/v2 Values ~ from the results of the present analysis

of the JC data in (b) o~ • 7.

l"ig. 12

- 17 -

b) Values of X2 from the analysis with p~1 = p1 of the

combination of the BC and SC data uhow:n in (c) of

c) Values of x 2 for the correlation bet·,veen al1

corresponding ;3ets of 5 conr:3ecutive bins in (a) and

(b) of }?lg. 10.

Llµn distributions from the SC, selected in Pn/P • l. v

a)

b)

c)

d)

e)

The I.Iµ1t histogram for bo·ch· p µ = p1 and I\, == :P 1

0. 8 Z.... pT/i\. < 1 • 1 •

As for (a) but 0 < pT/pv / 0.8. '--.

Values o·"' .L x_2 for all sets of 3 COrlSCCU.ti ile

Va1ues of 12 /'-. for all set:-J of 3 co11sectlti ve

') O..r...-. -.:r c_

..LA for variou.s superposit.j.or:,s of' Vcilues

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