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0

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4 June 1965

Analysis of 358T T* Decays

T. uetter, B. Taylor, 1. L. Koller P. Stamew, and J. Or&

Dqwtmeat of Physics, Stevens Institute of Technology, Hoboken, le Jersey

DDC

SJUN 2 2 1965

IDD.RA E

Submitted to Thbe lqb-olea:L Review, Jue 1965

SIT-PI&8 (6/65)

ANALYSIS 0F 3581 ir* DECAYS

T. Kuetter, S. Taylor, E. L. Koller, P. Sterner, ad J. Graiuman

Department of Physics, Stevens Institute of Technology,Hobokien, Now Jersey

Abstract

An analreis of 3587 T* -$ w w+I+ decay events Is presented.

These events were found in an area scaning of an emulsion stack of

600 va Wlord G5 emulsion pellicles exposed to a 300 16eV/c separated

K* beims at the Devatran of the Lawrence Radiation Laboratory. The

pion energy spectra are compared to the predictions of linear matrix

element theory, the pion pole model, and the s-vwe resonance msodel,

and to the existing spectra of the secondsrIe from n, T , T', and e2

oResearch supported in pert by grats from the National Scence Fundationand by am "uimsnt loam contract with the U. S. Office of Naval MeeearcheThis pops: Is based on a thesis submitted (by T. I.) in partial talfil~asntof the requirements for the ft. Do degree In Physics at Stevens Instituteor !eohmolg.

+ Supported by a National Aeronautics and Bpace, Administration Traneeship.

Stuitted to The Physical Review, June 1965

2

1. ITRODUCtION

In the recent literature, considerable interest has been shn In the

three pice decay modes of the K and Yi mesons, and their connection with low

energ pion-pion interactions. Early da on the r decay mode of the K

meson (K w" + V+ ,+)1.2 shoved systematic deviations in the plan spectra

from that determined by the phase space alone. The deviation is mswh that

the unlike plon has a higher probability of being emitted vith hlgh energy.

Subsequent measurements of T" decay3 , spectra confirmed the effect. Attempts

to explain the pla asymntries by final state pica-plo Interections,54

using the scattering length approximation and neglecting p-vw and higher

partial vwe effects, led to the requirements that the s-wave pin-plan

scattering lengths in the TO and T2 states be s -1. ad 2 N -0.31 6

oever, experiments utilising other means of measuring these parmeters,810

and theoretical eonsideratios,11,22 led to the requIrments that a , A

with a2 small and positive. Other attempts to explain the final state pica

asymetries included the hypothesis of a Ke intermediate state,13 ad

inclusion of p-vave pion-plo final state Interaction, both withl1 and

without 1 ' "Intrinsic" structure in the veek interaetions.

The w enerig distribution in ' ( W * w+ .go 0o) decaos vas see

to have a related deviation from phase space 1 " , predcted by Venbrg.21

Simlarly, the 10 energ speetrun divided by pbsee space (the redused wo

energy speotrtm) in e * To 4 w + w" vas found to be a doeresaig fumetioe

of the 1e energ,22 in agreement vith theoretical preditioms. 2 3 Similarities

to the Man decay spectra vere ls noticed in the Dlits plots of10,1* 24,-26

+ w + - decoys. The present theoretical models which could

explain the similar final state spectra in all these decays ae (a) the pica

3

pole mod1, 9 and (b) an -vave w-w resonance, 3 0 '31 a eI in

Moser' s eticle. 32

Analyses of about 2300 't" 3.4 and 900 T+ 1,2,3 3 decays hav, been

reported. The present vork roughly doubles this sample vith the addition

of 3587T* decay events.3 The secondary spectra from these w decays are

compared vith the existing decay spectra for i, t' k and n. *comparison'2

of the data vith the predictions of the theories (a) and (b) above Is made.

II * XPERZIIN!AL HWOCIMMR

A. Zxpoour* and Scannin

An 84. pallicle stack of 6 In x 8 In x 600 ma Ilford 05 swulsion vas

exposed to a 300 1eV/c separated k* beau at the Boetrom or the JLwgnce

Radiation Laboratory of the University of Califarnia. 35 The bern kas

com to rest wear the center of emch plate, In an aweea % 1.5 =n x Itn.

In oder that the scanning time required to find a kaca decor event be

fairly short, It vas desired that the density of stopping kaas, be relatively

high. Therefo the stack was inseted in the berns after cOl cas stae of

separation, and a background of azcimately 10 berni jpics for each stopping

K* vas present. These pions were, of minimum iomistioa, and traversed. the

e=tire stack. The density of keon ending In the stopping region of the

exposed stack vas M* 2xzC K 's/rn. The individual pe=0248e Vwr aligne4

for manning and track ftolloing by the method outlined in Ref 36.

The stack was systematically area scanned for K -meson endings with

multiple secomdaries * 7 3359 three-secondary events, each with two or three

of the secondaries having poeater than 1.5 times Mmm icaimatica were

separated from the total sanning: emple. Three events with a minimm-

icaiSsin econdary are Imcomslstent with the I deoy mode, and were ezeluded.

one of these events was shams to be an example ot the deeor mode

Kk (K * + w- * + v), and has been previously repostd h

other two L.vests are also consistent with this deco mode, but are not

sufficiently complete to allow clear Identification. The redmann Gseple

of 3356 "t-like* events, together with 9? events from the Columbia stash C

and 9) events from the Colubia stack D 39 were included in the detailed

analysis described below. Six obvious decays in flight were excluded. In

addition, seventy-one previously analysed events from the Columbia stacks

A and B hoare included In the total sample.

B. Determination of Secondary Energies

The measurement of the pica energies for each event was carried oat

as follows:

(a) The plane angles between the secondaries (the angles between the

projections of the pla tracks an the plane of the emulion) f obac event

were measured, using a six inch protractor mounted on one of the microscope

eyepiece tubes. The estiated errors for these measurements are + 20,

Including distortion effects. The tangents of the dip angles betwee the

plane of the eulon and the secondaries were measurd by usin the fine

&-motion of the microscope and a calibrated eyepiece grid. Errors In the

2-measurements ar e estimated to be of the order of ome micron. The us--

certainty of the emulsion shrinkage factor Is of the order of 10%. Secondary

tracks were followed, recording any scatters of 0, 20 or greater, until the

W- as Identified., secondaries are Identified by their charatreitic

wa decays; v~ secondaries are absorbed In the emuls nulei, giving

ris to staes with sero or mote Ionizing promgs. Events for' whisk the 9

could not be identified are discussed below.

(b) te point-to-point ranges, Including scatter points, were usd to

find the energies for those plans which bad been folloved. to an ending. An

aver"*e emudlon thickns, measured before exposure, yes used for each stack.

The range-energy charts of Darkas and Young are used throughout this work.h

The energies calculated directly froma a range are expected to be good to ".3%.

Usming these energies and the measured angles, each event veasanalyzed an the

13N 1620 of the Stevens Computer Center to find the missing pion energies.

Since the events are overdetermined, the ro-value was csalculated as a check,

as was the quantity.

where the fil w5me the secondary three-mmenta, # Is an Indication of the

coplanarity of the event, and Is an invariant under labeling of the tracks.

A limit of 5 36eV was placed on the deviation of the calculated Q-value ro

the accepted Q-value, 75.11 1 0.*11. 3eV, 42and the coplanarity measure was

required to differ from sero by no more than 0.075.

(a) Any event falling outside the above limits was returned to the

scanne for rameasurement. It the two measuroments agreed within statistics

an additional track van followed, and the event was returned to pat (b) of the

schedule. It all tracks had been followed, the event was examined for poesible

reintexpretatiams, such as secondary scatters near the K ending, inelastic

scattering of the secondary, decay of the secondary in flight, or alternate 6ecay

mode. Seven of the events In the lower tail of the distribution were shows to be

incoosistent with the i decay mode, and were Identified as examples of the- + * 4.3

radiative:i decay mods, W + V + I * Y.At the close of the analysis 51 events remained outside the 5-34eV Q-value

limt. This would correspond to a standard deviation for the Q-valve distri-

buation fr all events of A* 2.2 NOe, If the distribution were Oassin. TMe

&*a Q-value for 65 events for which It was necessary to follow all three

tracks was 71..? 14V; the standard deviation of their Q-ValUe distribution

was 1.7 MaO.

There were 35 "i~ncoplete" events for which the v- could not be

Identified, due to interactions IS flight of the secondaries or secondary

tracks leaving the stack. Each of those events had one en+ erg measured

by range, and were subjected to the sme Q-value and "coplanarity" tests

iescribed. above. The energies vera renorinalized by preserving the ratio of

the energies of the unidentified traks as calculated from the space angles

of the event, and requiring the sum of the three energies to be the accepted

Q-value. Por seventeen of these events, the difference between the two

unidentified pica energies vas less than. 9.6 14eV. hsme seventeens events

are Included in the distributions, using the man of the tvo "missing

energies far the unidentified v and v-. Thu no energy is shifted by 3ore

than 4.8 NeO (the data are divided for analysis into 4.8 NoV pzatps; sa"

below). The resinin 18 eveonts are excluded fram the distributions.

The pica enemrgies used In the distributians- for events having two

follared tracks are the two measured energies end the difference between the

know. Q-vmlus and the sum of the measured energies. Plan energies for' events

for which onea or three tracks were followed veze remaiUsed to the known

Q-valus by maltiplying the rav pica energies by the ratio or the know.

Q-valus to the calculated Q-value far the event

C. The Data

Or 3W0 stopplogv Tecays, 3587 events are Included In the floal Vice

distribstioms * A eummery or the different obase" or events In the tta

omple Is preented In Table I. uistoprams of the v- enerff distribution,

ad the distribtion T1L - Ta, where TjL is the kinetice enw of te ameenergetis i* and 'ta iSaewatma eeg, wre sowon Lu Wg. 1 aud a.

8

Since 0mly 18 events of a total sample of 3605 stopping v decays re

excluded, the sample Is quite free of geometricel bias. One possible some

of scanning bias, despite the distinctive sppearanc of stopping i decays in

oulsion, Is the possibility of the saner missing an event vith a very short

secondary pil. The other two tracks are then very nearly colinear, and may

be mistaken for a coincidental crossover track. Iach event recorded a a

stopping kaon vith heavy secondary and a crossover track vas reexamined.

About five of these vere found to be v decays.

Another possible bias Is msidentification of secondary ohre. Steep v

tracks vith forward decays may be mistaken for v" tracks vhich end in sero-

prong strs, said w" tracks either with a scatter 1 600 p from the eand, or

ending In a ane-prong star vith the pong " 600 long, may be mistakenly

Identified as v -* decas. All secondary treks vith eneg le than 12

Ne vw careftlly reexamined in connetion vith snother experimnt, 1706

tracks in total. Among these, 6 v vere fiond to be misdentified as a-,

ad T v" wee alsidentifled as v This omrises; a rate of misidetiftatio

of 0.S0. Resalculation of the spe tram including the nev valus amsed

negligible oanections.

It was foand that excluding the events in the few plates newrest the

top sd bottao of the stask did not Ohmage the dsps.s of cmteminatim of

the sample with "ioamplete" sweta. The stack was lar Sao"& so tha

seconday tracks sould not leave the stak from the sides.

9

111. T1BAZGW OF rZFI 4ITAL DATA

lbe final state kinematics in K or n + 3w decays is eoepletely

described by two independent varlabLes, for ezample the Lorents Invariant

variables (83 -8 ) and (11 - 02), where

8, - 1 - PI) 2 a (M _-.t)2 _ m,

and

380- 8 1 + 82 *a3 a 1 (m-Qa2-

Po and 3 are the fou-mmentum and mus of the decaying particle, ?I, a,

and T, are the four-mcment, mass, and kinetic eeury of the Ith plen

respective y, and Q is the am of the pion kinetic energies. 83 refers

to the unlike plea i t and T' dea s, and to the go In go W+ *w-

ad q * go + v+ + w- decays. Pea convouience, the variables

Y , -3(83 - e S ad I me - 43 (81 - S2 ) / JMIwe ntroduce. t

!he differential decay probability may be written

"(1.y)ua a IN(x.r)1 2 c(j,) *(x,T)dXdy

ihere (X.) In the invariat 1haso space for the de y, CC(ZX) Is a

footer to isolute ial te Coem b effects, and (XI,) Is the matwiz

ele*on feo te dese. Mw fater C(X,!) nlied, In Ws veak Is that

gives %W Datts, ! " whieh iA the sen-relativistle lmit redsee to that

eals2At 1W as..T

10

T!he Y-depende -3 of the decias to exmiaed by plotting

N; (Y) K-aY

vs. Y, where NI(Y) is the number of events in the interval AYi, 0o t Is

the total number of events, and C6I (T) is the oorreepomdlng "Coulmb

acorrected" " ets Invariant phase space. Then NI (Y) / n" Cs (T)

s proportion l to IN(xT)12 aTeae over &y and the oozzeepmding

valmes of X. These data wie presented In Fig. 3. The data ae

normlised such that the veighted sne ordinate Is 1.0. SularJ7, te

I-dependence of the distribution to exmined b plo ttin Ng 1() / 1t

c#1 (x) vs. X. These data are preeented in Fig. k.

_________

11

IT, OWIIAIMI WM'IIII1

A. Linew Mabriz meunt Theory

It has been proposed that the matrix elm at i K * 3w dayeoqa w be

expmne a power series In I anad.a Due to the Doee atistles ao the

final state plan, the expansln Mu outain may even Powers of I.

Negletlg bLaer orer te in the ezpansion,

NJX Tlx (xJr)l 2 . i. 'I

Aner j Asv v' -, or K; and a. Is the ebargud plans mime. If the flail state

pie ae In a pure Tol st"Ot, the relatimehip %v, - b lo"OM I' M

this Is smaistemt wit the AT a IA2 v.3, bft Gins .t r.3. out lzt~tu'ee

of a a 3/A In the deq InatetlumI, oioe the Me state is esesile

WON& eithe a 0 In wr 3/9 t34 has bees ohm that the we smar

spetru in 11 * I 3./1 ' *wP $IeI. I s idestle alu uit the e sptrom

iv' 6ourw . It a t rule is qeralve. 'o Id It MUMS tmha a -a,u=er te a a In rle. "yer, this Is a week $ tet th rule, sift OW

mabomiem. vUb leads to the m M final statbe hr bfth the dehswA

inwal eeq wll oatisfy Vhe suditios em the sloes.

A uiste" least stree fit af th fumblom I , T to the me m.Li

ree , m Pewi doat xf tve s amt ezp perl t give. a Vo m eIt 0.11o 0.0.

the X, v.amn is. 5. to a 2 a oeilt o-..K f a4 Is r damepem

at j m Alhouo te 2 almIs e hir , U eIsoreal doeto

12

a quadratio term in the exp wea, since the deviations of the ee

points rm the linear fit are "soattered" rather than systematic. See

nsi. 3.

The X-dependence of the events is vell fitted by a sero slope straigbt

line, with a X2 value of 12.5. The X2 probability for 9 degrees of ftredo

is % 20%. Although there seems to be csm sustiom of "shape" to th data,

there Ls no statistically significant evide e ftar hIgher order terms in the

I-depemdeme of the matrix element. See Fig. 4.

The resulte of this experiment are in agreemet vith those of othebr

eoeImes n I + 1,2 and ,r. 3,b Table II ootaina the values of eI fod

by othe ezeietrs lu ith values of s,.,s0 , and a afrom.

various SXPerimeto.

Combinng the valu, of a for the present experiment vith that obtained

by mithe at. al.,h a T 0.12 t 0.02, in an anaals at a empilston of

3M0 t* daWy events, the combined value %t a 0.115 ± 0.015 is obtained.

Kisi at. al. 2 0 have fitted the reduced v+ oner spectru ft. ink 1'

dec events with a linar sqaed matrix s lement, using M error aelysie

similar to that used in the present vork, a have obtained s, -0.0 + 0.0.

Uing the value

!V' = -3.5 + 0.6

scapered to the predicted ratio of -2. Ue lT52 v' events, aaled aena

et. l. 19 ee tted with a linearmtrix element, rather then linear r oeded

sptrm. owwwvor, their value for u, is consistent with the value otad

bys 211 t. .

13

Luers et. al. 2 2 have fitted the reduced w° energy spectrum for

83 e v v witha alinear function and obtain a -O.32 .O.T.

Using the combined aT value and their value

-2.8 + 0.7

as compared to the predicted ratio -2.

All of the X * 3w reduced spectra re well fitted by linear functios.

The ratio ago / ac is In agreement with the predictions of linear matrix

element theory, a final Toi state, and the AT a 1/2 rule. However, this is

ouly weak test of the rule. The ratio of a., / sT i about 2. standard

deviations ro that predicted by the theory, and further dat are needed to

clarify this situation. However, it is felt that the data on K 4 3w spectra,

viewed as a whole, are consistent with linear matrix element theory, a pure

Tl final state, and the AT a 1/2 rule.

B. The Pion Pole Model

Barton and Rosen2 T have considered a model in which the decays

S0,o + 1,+ + - and K & 3, both proeed predmiatly through a me-pio

intermediate state, the pin pole model." Than the decay emplituids for the

a and the various K mods ae Just different Isotopic projections of the sae

Ta ftmetion, apart from a constant factor depending on the mechanism wbheby

the single pia state is reached. The matrix element is expended in the

Invariant variables, and neglecting quadratic and higher order terms, the

relationship a., e, holds, at least insofar as the K - n mss difference

can be neglected In the structure of the Interactions. Since the predictions

for the ratios of the a's in the various K * 3w states are identical with

those given under section A above, the relationship a a -2 T holds under the

plan pole model. However, since the saew predictions follow for a:W model in

which the K and n have the seme Tel final state, this Is a weak test for the

pion pole model.

Combining the value for an quoted by Crawford et. al. on the basis of

109 q decays and that of Foster et. al. with 27k n decays (see Table 11),

the obined value a ns-0.25 t 0.025 is obtained. Using this value for an o

togethr with the cnbined aI obtained above

aq a -2.2 # 0.35

as empared with the predicted ratio -2. The ratio a, / aT is in good

agreement vith the predictions of the plan pole model.

C. 8-rave Diplca Resonance

several utore '2 5 5 have found evidence for the existence of a v-w

resonance at an energy of about kO0 HeY. ecnsistent with the signment of the

qumntae nubers T.mJO. Dd ad Singer have formlated a model based an

the existence of such a zee" *e, the, Or in order to explain the apparent

enhanement of the three pia decay mode in the msean. These authrs have

extended th model to include both i "o 3v and K + 39 deca"s 0 As In the pion

pole andel, the final state pions must be in a pare T-1 state, which Is con-

ststest with the AT o 1/2 rule, but 4oes not rule out AT o 3/2.

1,

The theory predicts that the reduced w" spectrum in W + + W "

decay is given by

where

haM-3, -2A-T 3

A a t(M _ %)2 _ 23/ MOr

Bar rr / 2H

Nere ar and rr are the parameters of the theory, the mass and full width of

the resonance.

The functLon F(T3 ) for various values of the parameters was compared to

the normalized experimental data in a lO-dyvIslo test. 7(T3 ) was normallsed

such that the mean ordinate vms 1.0, and since the function in nearly linear

for the range of parameters under consideration, the Integral@ over the divisions

wer approximated by the ordinate of the function at the midpoint of the division.

Since F(T 3 ) Is a slowly varying function of the resonance parameters, tbewe Is

a large range of mr and rr for which a reasonable fit is obtained. A contour

plot of constant x2 for the parameters r and rr is shown in Fig. 5. The

ctours X2 a 20 and 23 are shown; these correspond roughly to one amd two

standard deviations from atniwm X 2 , respectively. The miimum X2 value i

16.1, with a X2 probability crrespodin to T degrees o tf*"=eeor% 3%.The best fit values of the parameters are approximately ar a 30 NOV. rr a 90 NOV.

The data, fitted vith the optimua parameter spectrum, are shown in FU. 6. in

addition, spectra 4or other selected valuies of the parameters are shown. They

alU fit the data as vell as the linear function

As ca be "see from Fis. 5 and 6 9 the Piseseut data eant detenuins

the resOSno04 s rmtera with aOW degree of certitude.* Obber ezpr ,immters

bane fitted this theory to' a nd it des. Kaboss at. a., 19with 1792:'

~9 n d fauw337 4 NsV9 tuaBT*29Rv, OrwfOrd at.&l.2 5 find

N a 39Bt 9 WTr. m881l5 NOT anthe bassofl109 q deqs anld

Poster at. &L 26 with 271i n dewa eoents find rwO +2*V

117 a 1T25 MeY. Bach of these pairs of parmeters ovelap the "afloed"

reonm an Fig. 5. S1U1 at. al. 2 hav "reanted a oou plot of arsad Y

their plot ad Pig. 5 have the emis geral shap wa rage of the paa'mr.

A similar theory has bee= fomnUated by mitsa sad hTyn Mw redused

'spetrsIn TdeyIs given IW

PC 3 ).

** +2yiN

r* 2~ 2 2)1/2

Zn the above sWprseim and -I we the total smug an fUl widft of the

rescomm.

V(23) for Hitra and Eq's theory is fitted to the daa of the pesent

eSpeIumM In the same wmu as that of Drom wan Singe' above. A eastew

plot of 00ssmX2 for the parmeters Is sbon In Pig. T. Me beet fit

IT

parameters are approximately ar a 335 MV nd r r 65 V; the mlainum X2

value isl 5.8, corresponding to a X2 probabilitY of - 3% vith T dree of

freodom. The data, fitted vith the best value prameter spectrum is

presented in VIg. 8. The spectra for two other vaues e alAso sha; as

in the other resonane model the fit Is reasonable for all three viwues.

8everal authors have found other experimental evidnce for a resonance

with parameters near the region required in the resonme models. 8nis

et. 41. 51 have found evidence for the eistence of a resonance vith YwO or I

and ar w 395 1o Ne, r. = 5o ± 20 O in aaanalis of w" - p collsmms.

However, Alff et. asi, have found no evidence ftor a resonance In this region

In the product of W - p oollis ons. Kirs et. al.52 have shorn the existence

ot a pek LIn the TO d-pan state In the processw " p * + + w" * n, but

the peak changes position with the Incident pian eNm g. BU et. al.3

have also food avidsen for a peak ner 380 NOY in the Invarieant w-w mess

squared ft this reaction. Del l'bbro et. A.54 find that the di-pls

efft ctive mass spetim In the redmtiony + p--+ + w- * p am be eaaed

by the in0lsien of n s-wve reseiee with the parMerOr U 39 2 4 J*VI,

rr 139 13 NV. Bwas eat. 61.5 have found in - p colisios a 3.05

standard deviatis departwe from phase space In the w - ,effctive mas

spectrum whh could be explained by a resomane with ar % M NOy T, r1'k, so Ny.

The present data are ressonab= veil fitted bw the resomeN odels,

and the rens of resensne parameters found In this experloet for the Br.,.

a"d Singer model re osistent vth those foad in other ezperimts an I

ad T', as cited above. Mile the resomanee parameters proposed by lmLas

et. 03.5 could not e=plain T decay with the present models, the other ex-

perimntal2* detected resoamose quoted above, wee, vithin statisties,

to the present "ta.

18

V. NOeaRY

Ci1Parisons betwen the various K -* 3w desay spectra wre recaol

coosisteft with a linear spectru, a Tel final stt. and the &! a 1/g r.3..

NBwever, this ts a weak test of the rule. The ratio a /sT Is about 9,5

standard deviations way frcm the predicted vaue, ad should be Inv tgated

further. noe gcwpaison of 4 spectra with K .. 31 deway spectra is consistent

with the 4 having a Pw~dc1inatly Tel final sate 9 sod with the predictions

of the pla pole model.

!he resomance models fit the dat Of the present eacerUsnft VINSCOMa3Y

well, and the range of resonanc paimeters determined ane ecasistat, with

those f..ad by other 1 epsimmnteru In ' Ad q~ dee. Umver, the prest

data can be ressca3y well fitted by a larg ran"s of parmetess I ish

reecmmoe models.

Since both the pica pole model al the rescuae bypobeuis have Obuilt-

In" Tel final, states and consistency with the AT a 1/ rideq the rato at

the linea teaNO in en e3WMICS Of the mtri e0200=t IS tVe vaiN K * 36

sa i . 3w final states Is fixed. Oas9u 3 so 14eg as the expemwatel

data as the 6*Ma speatra, can be well fitted by a liner foiatica, the caL

available Intermati.. will be cs the vaUdltr of the Tel final state NAd

001m8istemey with the AN 0 in2 rule. in fact, ftvww"' mas swuma equiest3

* that the limew mtrix elmt sqaed is ftqiaabe wiLth a ressuft 9-9 phse

in the !.O shammel with you"Us the reewme paometes as these seed

* ~in the am "a Klnew theory. 1h& -us,. to the paestift .t the validitv of

-w w the Obheu af th models wALL have t wait go=i the MOW mawe t

1n the espiNSiem beegin statistl2 sipifiaaat.

29

We wish to thack the staff @f the Lawrence Radiation Labworo,

Uivesty of California, far inakiaS the exposure possible, We gp'atUl2

eAknowledge the invauable help~ ot D. NMa, 0. Yaplin, and 0. Womvbnwo

eivied act the great bulk or the soamuin. Vs also thank Je Fletm,

L. Frank, 0. fnpsfulia, P. Jaum, J. Lemesew, R. 1esmo, A* Rakouski,

amd R. Silbewlitt for help with sWannfiin and compting.

20

1.. N. U3o-Csollu, A. Dmttl, V . D. .Shel. B. uetal, K. Nor"n,fm 0. VeIraiNwo OCaSmto 6 b(9

2. S. Naloun B. latall, M. 0'0oan.11, J. !1.4g, and 1. C. Varshogya,Nuovo Clamnto LO,. T63 (1958).

3. N. Pnvr-LUaaal D. 2. Millers J. J. Nurr. A. He ofoaud3, maR. D. !rlPP, luavo Clumuto 99 108" (1961)

b. L. T. Ma1th, D. J7. Promi, and D. 1. Stark, Posits Tatte s Nkio (19b2).

5. DB114 B. fbams &M W. 0. lolladsy, Ph".. Rev. laq IM3u (39,9).

6. N. N. lbwl &MA S. 3. Teluma, bP". Rev. MJj 115 (2960).

T. R. 1. $Mapr &Mu 1. C. Val, bPs*. RNw. "J1 , 1ii29 (3960).

8. ftm Ngt.. Tramng, Ph". Rev. Letters 69 308 (W961).

9. Howard.J. Schaltaer, 1P". Rev. M1, 1059 (1962).

10. J. Kira, J. SBhwinits,, wA R. D. b1ipp, 1Ps. 3.,. A~, 763 (3962).

U1. Sign 3. Desal, 1Ps. 3wv. Taotters 69 b9T (196).

12. D. 1. amsdAm and J7. W. Na~t, 1Phs. Rm ev, tters is T08 (3961).

13. Riasmdda and 70yasuddl, 199. Rev- lafttr.9 40s (3961).

lit. 0. Berto and C. Earerw, 1Ps. My. Letters 9~ E(3963), =A 1bps. 3tw.Latters j, 3533 (3962).

15. Nil.. A. Baqi 36g and Paul C. DeC.11.., bPs. low. Latters 1, W (W962).

16. B. Ijwbknmd, 3. L. Koller, and B. 2*plas Whys. Rev. Tattes !k. bi(960), mA Ph". Rev. Latter. . br53 (3960).

1?. J. K. ~1AK. R.Hason J. IHoeftergN. Sdbert, endP. K. Adtyaq

18. 0. 01..m.11L D. Nmcti, 0. *amaeia, A. Qnrn1-gmudel11 V. Posebel,amA.J. f1tv, Physles Letter. It Wh (1963).

39. 0. 3. Masn A. Esa, .. No V. M. powel. am 3. DaM, Ph". UT.

20. 31*1, SDowe o~ete, Delaro-rbbee Posrer, OmmU,111 Mesowasslat iauao Vigo"$ mA Vermk, 3w. c~mu ,YS (196).

21

21. Steven VW9brg Phys. Rev, Letters 4 9 87 (1960) end 1h3B. byw. Letters!, 5Z (1960).

22. D. lImr, 1. S. Klttra, W. J. Villa, and B. S. YTto, Ibiso Rev.

Mfl iBW6 (i96)).23. Re 7. SuuWI end K. C. Wall, Nuovo ClUentO IT. 938 (1960).

As. Do Dery, Do Co11eys and Jo. ebhu2ts, Pays. Rev. Letters 10.9 li (963)9MAn referen there. This Is a ocaplistiom of the data of severalexperiments.

25. Ire so Cruvtord, .r, R. A. Oreueman L. J. Llcqd, L. 3. Prlce, sad 1. C.levier. 5be Rev. Letters 11, 5a1 1963)9 a Pbva. Rew. Letters ~

26. N. rester, M. Peters, 1. Hertmag, Be Matse.,, Do Seeder He Goods He Nlee,F. Leefler, ad B. mnolvua, Pays. bym. 1&,o 9652 (39&5).

2?. 0. Dartomnd S. P. Rosen$, Phy. Rev. aLetters 1, 414 (og62.

26. Minsa A. & D4 ~, Ibys. byw. Letters j 6? (1962).

29. 1. c. Well, Pas. fev. Letters P., 120 (1962).

30. Iawl K. Brown and Paul Singer Ibys. Rev. M. 381 (29a).

31. A. 1. 1ltra ad Shuhba Rai, Ph"s. NOT. L, RIM1 (19a).

32.- C1Me Kasser, Ph". Rev. W* 355 (1963).

33. In &Altlmm,! ToIelO# asa, G. GO3haber sd S. 0O3.dmbe OU 3.1s. Ibis.ome. 6, 09(961) hav pwested a fewi~aw repo t M -T &"w0,uiqe.

341. See!.T Ruetter , 3. L. Kller, S1 !q8 r P WW . 8t k am n d :. Gr, gn.1A. Ibys. Sm.. , 23 WOO11 for a WO1SIaar reO t. Ohe 0 Ust 10119 eeae.

35. 0. Oolhbaber et &I a urmwe Rmdatl~m Laboubmoy Repu't =-43 310)ua~lshed.

.96. ,oTww 0. kiwIs, 1. aver, P. Rowmel, ma i. lie, my. St. z~ew.

.138. Z. L. Kle S.!1 S m! etter, MA P. atms' zs ev.ltues

39. S. !q a0. lewls, .7. ar,7J. lie, ma P. Damels. Rev 3w3" 6O 4

'100 7 jo u' Q S. Go rls, m S. Be or TW PY. Rev. Jj,113 25)

Us1 3urhas mwa 1mg, U.G.R.L. lopms WM-05T Moe.,2led

22

42. The Q-vauo for the v and an3 other partiale date are taken from RooeelBgrbaro-Gtelr, Barka", Bastion, Kia, and Roea, Rev. Mod. Phys. ~977 (9614).

43. p. temr,! ToNetter, B. L. Koller, So Taylor* ad J. Oramsa, Pb. loe=, B1440 (1965) and 3. L. Koller, S. Taylor, T. hotter, and P. temor,

Phys. Rev. _W,. 1381 (1963).

144. S. Taylor, Z. L. Koller, T. hoetter, P. Stamer, ad Js Orsa~n, Phys. Rev.Letters 114, T145 (2965).

45. In the case of T decay, the variables X and Y are Identical with the Dalitsvariables x - /5 (T-T) / 2Q and T (3T3-Q) / Q. See for ezemple, I. 3.Dalits, Phil. - ag.-W 06 35

46. R. 1. Dalits, Proc. Phys. S1oc. A69, 527 (1956); see footnote ca Page 537.

47. Earle L. Lamo, Ph"s. Rev. M, 458 (3957).-

48. G. Barton, C. Kacoer, and S. P. Bosem, Ph"s. Rev. Mg 783 (U963).

49. smith at .1, Ref. 4, have Included a quadratic tere In the expmoam; thesiror In the coeffilent of the quadratic term, Is as large as the co-efficient Itself.

50. 1cr further Information on the polo model see, tlor 8~o S.wls, a. a"".S. Chibas and A. Vakasa. Physics Letters 2,39(963). 1. Owlse ad S. 11.0,Physics Latters 6. 238 13963), Riasuddin ad A. Zimaim Ph". am Nov.31211 (9"1) S.8 Oneda, .g . o im and L. N. Wopln, Imovo Ciamtoli r~TV, ~

51. .So sc, A. Bachman, R. loss To Kalogeropouloee and V. Mpkard, Phs.Rev. Latter. 1, 139 (3962).

52. J. Kings J. Schvarts, and R. D. Tripp, Pap. Rev.w. 2141 (U963).

53. 1. N. Ulsir, 0. Comfrto, C. Robbie, 0. To'elli, and 3. Zavattlai, PhysiesLettes" -4. 79 (9a1).

514. 3. DelUabbm, N. o BePrtis 93. James, 0. Nrini, A. Mae.m 0. todni,9 andL. Van, 1Ps. Rev. Letters P_9 6714 (9614).

55. y, Barn", V. Fowler, K. Wa, D. Radojele, N. Wbters, A. Bammin, P. Saunoland 3.I* LoseBll. An. 1Pso. Soc. ps9 65 (3965).

96. 1mbFI N. Drew. and Pod 0 Sigr Phys. Mev. Letters ~ 146 WO9UM).

ff. 0. Alff, P.Do VAW, D. Co011W, I.SelfaOMM To mbrg P.fAM#M Do er 11 V Jo 81111%8J. Steiabaerer,. van, a. DMU er P. Murner ai 3. Nine, Ph"* ov.Letter 1* 32, 325 (3960).

R8 . Premed, N6mo, Clamato 1.68M (1965).

*i0IjIs'

' °4

j!l

I'I i i

Toble n. 8wmsW of published values ot the pazmeter a for the limear

mtrix elment theory in J, T's X; end n decoys. The unlike plan remod

spetra (the w° In n and 11 deae) re fitted vith either the function

IN12 a I + a N I I & (l. + I a y)1, dee ,d by L end 8 re ,gpetivly% St

in colum 3. if the A! n 1/2 rule Is valid In K * 3w decaqs md the decay.

K * 3w a q 3w have the mm Tel final state, the reltimuiMpe 2 t -sT ,

- a should hald.

09 -C a 2 0 .1420030722 L 0.11 t0.09

358T: e L 0.11. * 0.02

l3AT " 3 L 0.15 * 0.02,IsS I".,x o.,, to. o&

831; 22 L -0.32 t 0.08

18T r'+ 20 L -0.40 t 0.0?a -0.36 t 0.09

1T92 V' 19 8 -0.32 a 0.03

109 2 5 a -o.26 0.o4

2' q 26 8 -o.94 t 0.03

% W00 ot these eveate fe ftm not. 1

25

nowUU CAM=K8

Fluae 1. Iistorm of the v emew distributian for 358T -' deqi.

MW Umber of events in saoh division is iolested.

Fiaws 2. Histog r f the distribution - , b and s2 sr the

positive picn eneries, for 3"8 s* deoeq. e mmber of events In eah

"ivisioa Is Indieated.

Flgrae 3. Depeadanhe of the matrix element sured cmn like picn me .

Me solid Use In the fitted cure IN12 a I* uvj , w , . a o.U,.2.

Figure 4. Depeodene of the mata.lz elet eqtsared on, ltke pian eerw.

Mhe old line Is the mer-slope fitted cuve.

Fla"S. Contou Plot of content xfor the mass, sr. and full AMdt r.,

ot the resonanee In the ran end 8Ig model fo v dew. loit A eemems

to the beet fit prmte, * 16.1; the points A, 3, end 0 nosmmd to

curves A,I v ed C IFamm 6. Me lines X2 a 0ad 2a23RN-Irogh to cue ed tMwo stard de'vaw from m 2 the,,m ooUo O

"alloved" re for the pmeter.

Figure 6. Inu Gepedmes of th reded eme"M spee tru tu the aw

end 6a1er model for deed o (rvs A is for the beat fit permstes,

r. 3ao v aom c a go No. C tuvis urt Moprmete va. a WO No and

r ro Mrb!W C is V % a hTS a.

mreepud to poits A, 3, emd C cm Pip"5.

26

Figure T. cOmtour plot of oCmstmnt X tr the tota' Maerv, art W faul

Vidth, 9 lr$ of the reioinmcs 14 the Mitre "Am ROY uOd4l fort T 640. Point A

correspands to the best fit permewte, X2 0 15.8; tes points A, 50 a 0oiespand to ourves A, B, and C in iur 8. no. Xr. X2 0 20 am X2 23

correspond roughly to am and two standard deviatioms tram gisp X2 r@PUpeVWY.

the "shoved range for the P~rezitee.

Figur 8. lera dependence of the redced-y wa rg pectrm for the Mitre

a&M Sq moel fW T decay. Curve A Is ftr the beft fit Memter. ar a 335 Noy

anda *65ueev. Curve Dis for the permtwgr a *ho0 lby d a n N~OT.,

auveC Is for m *bT5 ev smA? .10 NOV. CarveeA, 39ad Ceaepondto

point. A, B, mad C as Figgre T.

0

0

fOD

CD

0 00W) N

I______ H1e~n

0

W

N 0

(0N

0

8 0 8 c 0

SJ.N3A3 :10 &3evWN

q ~ ,...a. - ta.n...,..0asn .~e.inac.

lZOb)6

C,

N

0

-~>-~

Li

--~o---

6I

~If I -0--

___________ ~ ~

- - - 0

I

I

0

NN

o w

00

cLL

00

-0

0 In 19)

V WW)'

(APW

-_______ 0-(0

41(\jC,

A I L

-~ -IIn

V) - &

t ~1 - Vt