WEAK INTERACTIONS�

Carlo Rubbia� CERN�

Geneva, Switzerland�

and�

Harvard University� Cambridge, Massachusetts�

1. Introduction

Because of obvious limitations in the available time, a number of contributions to the con­

ference cannot find space within the present report. They are discussed in the excellent reports

on the Parallel Sessions and therefore they shall not be repeated here.

The report has been subdivided as follows:

II. Some Basic Properties of the KO_i{0 system:

1 . The K lifetimeS

2. The K -K mass differenceL S

III. CP Violation in Neutral K Decays

1 . Introduction + - + ­

2. The ratio KL - " " IK S - " "

3. The ratio K - "O"O/K _ ,,0,,0L S

4. The phase of TJ+_

5. The phase of TJ 00

6. The charge asymmetry in K - "Lv

7. The KS - 3" ° , "+" -" ° L

8. The decays TJ - 3", """

9. Overall fit to KO decays; CP or CPT violation?

10. Direct proof of CP or CPT violation in KO decays

IV. Neutral Currents and Other Forbidden Processes

1. Introduction

2. K+ - VVVIJo. K+ - VV1r

+ + + ­3. K -1T e e + - + ­

4. KL -" " e e

5. The K - ...... puzzleL

6. KS - ......

II. Some Basic Properties of the KO _i{0 System

n.i The K LifetimeS 1

Two contributions to this conference , 2 have revived interest in the ,!uantity, until now

considered as well known. The number is of considerable importance because of its connection

to very many basic parameters of KO decay and of CP violation.

-157­

1II.i.1 The first contribution is a bubble-chamber experiment of an international collaboration at

CERN. The process studied is

The whole process which involves only charged particles in the final state is a 7c fit. The decay OK _ 1T+1T- is a 3c fit. Approximately 50,000 events have been observed in the Z-m Hz bubble

chamber, sufficiently large to contain very generously the whole process. The main features of

the experiment are

1. A good understanding of the K - 1Tlv, K - 1T1T'{ contributions

Z. Only 10 events out of 50,000 could have had a mistaken production origin

3.� The geometry of the chamber is extremely well known « 0.01 cm/1 m)� O�

4. The momentum of the K can be determined separately from the production and from the

decay kinematics. The agreement between the two values is excellent.

5. Results are independent of cuts on momentum intervals, dip angle, decay length and

(pr-oper-i.ttme of decay. 10

The result (Fig. 1) gives the raw lifetime: T = 0.8866X10- sec. After CP effects areS10

accounted for, the value rises to 0.8932X10- sec. Another small correction for interactions in -10

the hydrogen of the chamber leads to the final value T = (0.8958±O.0045) x10 sec. The errorS

is only statistical (X 2 =6Z for 50 degrees of freedom; confidence level = 0.15). The authors claim

to be unaware of comparable systematic errors.

This result is considerably larger (3.7%, i. e. -5 standard deviations) than the world's

average of previous experimental results (Table 11.1), which represent as a whole a sample of KS

decays of the same order as the new experiment. The newer result is pr-obably better protected

against systematic errors.

Table II.1. Recent T Determinations.S

Number Value Reference Technique of Events (10 -10 sec) Comments

Krisch, 66 3 Hz - BCH 5000 0.8430 ±0.0130

4Donald, 68 Hz - BCH 19994 0.8560

±0.0080

2�

J,.",."."5� . ±0.005Hill, 68 D - BCH 20000 0.8720 New. revised ±0.0090 value (old was

0.865)

1Skjeggestad, 72 HZ - BCH 50000 0.8958

±0.0045 this conference 7 ~~~"~'j

Steffen, 72 Z Proportional 10 0.8990 Contribution to 0.897X10-1O (Preliminary) Chambers ±0.0050 thrs co~ference'±0.0033

errors inflated x7; fit to c>m,

TS ' "'+-' '\­

-158­

n.L2 Confirmation of the increased value for T has been given by the contribution to this con­S ference of the CERN- Heidelberg group. 2 The experiment (so called "vacuum regeneration") is a

study of the time-dependent interference from an initial, incoherent mixture of KO and KO states

produced by high energy protons in a beryllium target. The time dependence (Figs. 2 and 3) of

the 11"+11' - decays from the proper time t from the target is

The first term within the brackets has the characteristic decay of the short-lived component. + ­the second one is related to K - "" decays. and the third is a K -K interference term in the

L L S " +" - decay channel. The interference, which precesses with a frequency related to the K -K

L S mass difference zxm is expected to have an initial relative phase "'+_ =Arg ("+-' and an amplitude

(dilution facto e).

where S(PK)' S(PK) are the production yields of KO, KO at momentum PK in the conditions of the

experiment. This is a consequence of CPT invariance in the KO -KO system

An important quantity is the detection efficiency € (t, PK)' which in the experiment is calculated

by Monte Carlo methods. The effects of the variation of the detection efficiency are evident if one

compares Fig. 2 and Fig. 3.

The data, which cover the time interval 6 < t < 16 x 10-10 sec, are fitted, keeping as free

parameters T ' 1,,+_1, A(p), zxm, <p+_. The/=650. for 530 degrees of freedom. has a modestS 3).confidence level (-2 x 10­

The results* are

-10 T = (0.8990 ±0.005) x 10 secS

1,,+_1 = (2.35 ±0.07) x 10-3.

Because of the insufficiency of the fit, authors have increased the actual errors from the fit as

much as seven times.

In order to exhibit more directly the effects on the K lifetime of the other parameters, the s -10

authors have performed a fit to additional data with PK > 12.5 GeV Ic and 2.5 < t < 5 x 10 sec.

*Authors are not yet prepared to quote values for the other parameters of the fit. i. e .• Am, <p+_.

-159 ­

The parameters 111+_1 , A{p), Am, .p+_ can be treated as a small perturbation, and they are kept

fixed. The result is

. -10 T = (0.896 ",,0.01) X 10 secS

in excellent agreement with the fit to the main data set.

I1.1.3 It can be seen from Fig. 4 that, although the early results6-12

on TS

are compatible with

these new results, the apparently precise results of Refs. 3, 4, and 5 cannot be forced to agree

on a purely statistical basis and one has somehow to choose between possible alternatives.

Obviously more experimental work is required. Still, the bubble chamber work of Skjeggestad 1

et al. is very complete and in my own opinion convinciug. The experiment of the CERN-Heidelberg

group may appear somehow less obvious to interpret, because of the need to unravel the effect of

the several parameters on the fit, and because of the greater contributions of the CP-violating

effects. However, a rate change of 3"/. for each lifetime is very large, when referred to the number

of lifetimes over which the observations takes place, the high statistical accuracy and the high

detection efficiency of the multiwire proportional chambers.

The increased value of the K lifetime has considerable effect on several related quantities.S

In particular the CP-violation parameters and the value of the K -K mass difference are appre­L S

ciably affected (see Section III). A more subtle effect of the variation of the K -lifetime may beS

present in several classes of experiments, especially with electronic techniques, when it has been

tacitly assumed in estimating detection efficiencies, etc. Examples of this type are the Ll.I e 1/2

tests for K - 2" decays and perhaps some of the more precise tests of Ll.Q =AS rule in KS 13.

I1.2 The K -K Mass DifferenceL S

The recent demand for more precise values of the mass difference Am has given a con­13-15

siderable impulse to new experimental investigations. Three experiments have been recently

reported, each one quoting errors of the order of 1%of Ll.m. Experiments make use of more or 16 19

less perfected schemes all derived from the classic "gap" method introduced by Fitch and Okun

several years ago. Since the accuracy of the mass difference now approaches that of the lifetime,

experimenters quote their results in absolute units of sec -1 rather than in the dimensionless

quantity Ll.mT as had been customary before. The effects of the variation in the lifetime areS'

somewhat reduced and in one case, even completely absent.

II.Z.1 The "gap" method [Fig. 5(al] consists in the observation of the number of K-"+" - decays

behind the second of two regenerators as a function of their separation, 1. When 1 is increased,

the coherently regenerated 1T+".- rate decreases faster than the rate expected only from the decay

over the distance I, because of the precession of the relative phases between the two regenerated

amplitudes, determined by Ll.m. Although in principle one could fit the 1 dependence for Am and

T simultaneously, the value of TS

was injected as an external (known) parameter and the dependenceS

of the result on T is specified. Increasing the lifetime increases the value of .6.m, since a fasterS precession is necessary in order to compensate in first approximation for the slower decrease due

to decays. The new lifetime increases the quoted results (0.542 ±0.006) x 1010 sec -113 and 1(0.535 ±0.006) X 1010 Sec -1 14 to (0.552 ",,0.006) X 1010 sec and (0.547 ±o. 006) x 1010 sec­

respectively, which is as much as a two-standard deviation move.

-160­

15 11.2.2 The "zero-cross" method has been introduced in order to overcome some of the systematic

effects associated with the "gap" method, i. e. , :

1. monitoring from one position to the other,

2. dependence on the K lifetime andS

3. correction due to CP violation.

Data are taken in the fixed regenerator configuration of Fig. 5(b). The zero cross condition

is achieved when the sum of the counts recorded in tracks 1 and 3 where only regenerator 1 and 2,

respectively, are active is equal to the counts recorded in the middle track where both regenerators

are acting. * This condition is possible when the precession due to L>m rotates the relative phase between

regenerators 1 and 2 of 90', making the interference term zero. The condition is independent of

contribution from CP violation and lifetimes. Also, there is no monitoring since data are taken

in one configuration. The finite momentom spread of the recorded events is used to cover a

reasonable interval of proper times of flight between the two blocks and hence to locate precisely

the zero cross time.

10 The result reported is (0.542 ± 0.006) x 10 sec-1.

11.2.3 The original agreement between the "gap" and "zero cross" measurements was extremely

good as long as the older value of the K lifetime (T ; 0.862 x 10 -10 sec) was retained. The newS S10

value (T ; 0.900 x 10- sec) introduces a very considerable (more than two standard deviations)S

relative shift (see Table n.2). It makes the agreement between results somewhat marginal, since

the "zero cross" method suggests a smaller value for L>m. Furthermore, zsm from the gap

method, injected in the vacuum regeneration experiments, gives a phase q, +_; Arg ('1+) two

standard deviations away from the "superweak" value (see Section III.). This deviation is in turn

difficult to accept, at least as long as the results of ,,,,-scattering phase shifts and the more recent

determinations of are combined within the Wu-Yang triangle scheme.1'100/'1+_1

Table 11.2. K -K Mass DifferenceL S

Value for Revised value for� Reference Method T ; 0.862 T ; 0.900 Remarks�S S�

15�Cullen Zero Cross 0.542 0.542 no dependence on T " S±O.006 ±O.006 monitor,

CP violation 13

Aaronson Gap Method 0.542 0.552 New Average±O.006 ±O.006 14 0.549

Carnegie Gap Method 0.535 0.547 } ±O.0042±O.006 ±O.006

World's Average 0.5400 0.5470 ±O.0035 ±O.0035

l for 3 degrees 0.72 1.39 of freedom

-10 10 -1 All units are 10 sec or 10 sec

*Nuclear absorption effects are corrected by suitable complementary blocks upstream enough as to eliminate regeneration effects.

-161­

III. CP Violation in Neutral K Decays

III. i� Introduction

Eight years after the discovery of the CP violation, the field is far from settled, although

the general tendency of the results is to converge slowly but decisively towards a super-weak CP

violation and CPT conservation.

The main recent advances are of instrumental nature. They rely mainly on�

L the improved detection of the K _ ,,°,,0 channel and�L

2. the advent of multiwire proportional chambers in the charged particle spectrometers.

+ - + ...III.2.i� The ratio R(KL - " " )/R(KS - rr rr )

A new, surprising value for 1'1+_' + ­A(KL -",,)

'1+_ = +_ A(KS-"" )

came from the CERN-Heidelberg group2 in a report to this conference.

3.1'1 I = (2.35 ±0.07) x iO­+­3,The value is larger than the world's average (i.96±0.03) x iO- by about 6 standard devia­

18 tions. The WOrld's average has been the resultant of the convergence of investigations by several

groups at different times and of many laboratories. (Fig. 6.) The CERN-Heidelberg result comes

from a fit to the vacuum regeneration data discussed in Section II.L2 and it is directly related to

the increased value of the K lifetime. This can be elucidated as follows:S

L If the old value T£=0.865 x iO-ro sec is imposed on the CERN-Heidelberg data, then

1'1+_' = 2.iO x 10-3, but l rises to 1200 (for SiO dellrees of freedom)!� 9�2. If the Chicago experimenti on vacuum regeneration is fitted with the new value TS =

0.900 X iOiO sec, the result. 1'1 I = (2.30 ±0.08) x ro-3, is reproduced. 20 Agreement with the +­

world's average value for 111+_' fS is found for the old value of T S. On the other hand the statistics

of this experiment are not enough to make a significant impact onto the value of T ' S 21-26 O

III.2.2 All former determinations of 1'1+-' have been performed in a long lived K beam, i.e., + -� + - ° the number of K - 11' 11' is compared to other known charged decays, usually K - 1TfJ.V, Trlv, 11' 11' 1T •

L The algorithm is as follows:

+ ­R(K -" ,,) R(K -charged)L L R(K -s charged) x R(K -all) x

L L

3•If indeed 1'1 1= 2.35 x iO- R has to be increased by as much as 44%. It is almost in­

+­evitable to concentrate search for possible deviations on the first term of the above expression,�

since

L The ratio R(K - charged)/R(K - all) is dominated by the decay K _ ,,0,,0,,0 which isL L L�

(21.4±0.7)% of all decays, well known and verified by AI=i/2 rule.�

2. The ratio R(K all)/R(K all) = TS/TL is measured to better than a few percent, noL - S ­

matter whose values are accepted.

-162­

+- 00 +- +­3. Finally the ratio R(KS -all)/R(KS -" " ) = R(KS -" " )+R(KS -" " )/R(K -" " )S

has been measured with high precision by experiments probing the III = 1/2 rule in K - "" decay.S

Is it conceivable that all six experiments on the ratio R(K -,,+,,-)/R(K -charged) could L L

have missed the correct result by as much as 40-50%? * At first sight, it looks extremely im­

probable. The experiments do not present very specific difficulties. K -"+" - events are usuallyL

detected almost free of backgrounds and coherently regenerated K -"+" - are a very convenientS

calibration tool. Three-body decays are used for normalization. They are detected at the same

time and the relative efficiencies are calculated by Monte Carlo methods. Several distributions

are available in order to verify the agreement between calculations and experimental data.

lII.2.3 The disagreement between the older and new experimental results on 111+_' may be

1. of instrumental nature (i. e; , wrong experimental results) or

2. it might be due to some yet unsuspected, physical phenomenon.

In fact the determination of 111+_1 by vacuum regeneration is conceivably an experiment independent

of the previous determinations of 111+_' from R(K -"+" -)/RIK all charged).L

­L

Consistency between the two sets of measurements rests on our understanding of the phe­

nomenon in terms of standard formalism. Finally, it is important to stress again that almost the

whole discrepancy rests on the value of the K lifetime being - 3% larger than the older world'sS

average.

lII.2.4 The value of 111+_1 has been utilized by several experiments on coherent transmission

regeneration. There are two classes of experiments: 1) regeneration by complex nuclei, and

2) regeneration by hydrogen. The proposed change of 111+_1 may modify the interpretation of the

results, since what is measured is P/I1+_, where P is the complex regeneration amplitude, pro­

portional to the difference between the forward elastic scattering amplitude s for Ko and KO

on the

target: P - i [f( 0) - f( 0) J • The optical theorem and charge independence can be exploited to

connect the imaginary part of [f( 0) - f( 0) 1 to the difference of the cross sections

4" - -0 0 - +- k Im [f(0) -flO) 1 = a(K p) -a(K p) = o IK n) -a(K n) , (1)

Assuming 1)+_ known (modulus and phase), a test can be performed with the help of expression

(1). Note that the resulting expression is linear in 111 I. The test of regeneration from hydrogen28 +­

is not sufficiently precise to separate the 111+_1 alternatives. 29

The work on complex nuclei is more accurate. The result clearly favors the alternative

111 I = 2.20 x 10 -3. An increased value of 111 I settles a long-standing discrepancy between+- +­the scattering and the regeneration phase.

. 0 0 0 0III.3 The Batio R(KL -" tr )/R(KS -" " )

0 0Two recent experiments have been reported on the decay rate for the proce 8S K _". 'If .

L They represent substantial progress over the former work. Both experiments actually determine

Othe ratio 111 which is most relevant to the analysis of the K system and they are free of00/11+_1, normaltzatton problems.

*In a report pres:3'ted to the Conference the CERN -Heidelberg group has given the result 111+_1 = (2.37,o0.1)X10 fromanewmeasurementoftheratioR(K -,,+,,-)/R(K -Trlv), confirming 27 the instrumental nature of the discrepancy. However, sinceTn.en this restih has been withdrawn.

-163­

The results are

1.00 z 0.06 Holder et al, 30

1.03 z 0.07 Banner et al. 3t

1.01S z 0.046 Average

and are largely independent of T and 11)+_1 .S18 0 0 .

Former measurements of R(K -2" )/R(K - 3" ) have gwenL L

o R(KL -2,,) = (0.439 zO.098) x 10-3

oR(K� -3" )L

from which one can evaluate

3.11)001 = (2.20±0.Z4S) x 10­

The error is too large to be affected by the changes of the value of 111+_1 •

lll.4� The Phase of 1)+_

The quantity ~+_ =Arg (1)+) is only slightly affected by T The vacuum regeneration experi­S'

ment is mostly affected by the change of 6m (L e .• the value is increased). This is evidenced in

Fig. 7 where the prediction ~ +_ =tan-1 (26mTS) is also shown.

nr.s Phase of 1)00

A new value of ~OO - ~+_ [~OO = Arg (1)00) 1 has been reported. 32 The difference between

the two phases•. which is a relevant parameter in the phenomenological analysis, is determined by O Ocomparing the time dependence of the K _ "+,,- and K - ,,0,,0 after the same regenerator. In

this way a relative phase is determined, independently of the regeneration phase. Unfortunately

the error in the result is still quite substantial

~OO-~+- = (Oz17)" Darriulat et al, 32

An older measurement has-given

~OO = (43 z 19)" Chollet et al•• Wolff et al, 33

Using the old world average of ~+_ = (43 z 3)" 18 (because of the large errors on ~OO' slight

changes in ~ +_ will make no difference). the result of Ref. 33 can be averaged with that of Ref. 32

to give

(0 z 13)·.

III.6� The Charge Asymmetry in K -1TlvL�

It is defined as�

-164­

The overall result for the combined K Kf13 channels ise 3,

3•6 = (3.Z0 ± 0.Z9) x 10­

e, f1

3. Note that the experiment of McCarthy et al. 34 has initially given the result 6 =(Z.1 + 1)

x 10- However, recent investigation by another Berkeley group35 has shown an~bservable difference between the ranges of positive and negative muons. Introducing a correction for this

-3 range difference changes the result dramatically to 6f1 = (6.0 ± 1.4) x 10 . This result has not

been included in the average.

Assuming CPT, * the charge asymmetry is directly related to the real part of the CP mixing O

in the wave function of the long -lived K state 3.

6/Z = Re(€) = (1.60 ±0.17) x 10­

This result is compared with the prediction of the super-weak models in Table III.1. The agree­

ment is good for both values of 1]+_, mainly because of the relatively large experimental errors.

Table III.1. Charge Asymmetry in K - 1T± 1 +v , L

-10 -10 T = 0.865 X 10 sec T S = 0.900 x 10 secS

311] I = 1.96 X 10- I1]+_I = Z.35 x 10-3 +­

3 -3Re(€ )SW = (1.43 ± 0.OZ3) x 10- Re(€)sw = (1.71 ± 0 ..03) x 10

36/Z = Re(€) = (1.60 ± 0.17) x 10­

exp

o + - 0III. 7 The K - 31T , 1T 1T 1T Decays

S A search for CP-violating amplitudes in 31T decays has been reported at the conference. Let

us define as

+ - 0A(K 1T 1T )

1] = S-1T +-0 + - 0

A(K -1T 1T 1T )L

36The CERN-Saclay-Brussels collaboration has reported a result from Hz bubble chamber

+.17 Re (1]+_0) = 0.17

-.Z3

+0.18 Im (1]+_0) = 0.01

-0.40

37The Moscow-ITEP group has reported an Xe bubble chamber study of the process K L

S,0

31T , with the result

or(K - 31T )s

< r.z.or(K 31T )

L­

*In principle also the L'.Q=L'.S rule has to be assumed. However, the experimentally measured charge asymmetry after a regenerator can be injected in the experimental results, requiring no further a priori assumption,

-165 ­

Note that

1. one would expect 11)+_0I = 11)+_'. Therefore the experiments do not have the sensitivity

one� would like. 0

2. K - 3,,0 is exactly forbidden by CP conservation; K _"+" -,, (a-wave pions) is alsoS S

forbidden. However, higher angular momentum states can contribute to CP-conserving decays.

We would expect

+ - 0 R (K S -" " " , CP conserving) 3 4

10- -10-. + - 0 ~

R(KL -""" )

+ - 0 +­Ilf.B The Decays 1)-" " " , " " Y

Although it is not a weak process, it is directly related to the question of CP violation. A

very precise result on charge asymmetry in the Dalitz plot has been reported to the conference by

the Columbia group38

"'3" = (-0.005 ± 0.0022), ~ 2 X 105 events

4 a = (0.005 ± 0.006), ~ 3.6 x 10 events.

"Try

No evidence for C violation is observed.

III.9 Overall Fit of K Decays, CPT and T Violationso The results on 17]00fTJ+-' and "'00 -'" +_ can be used to set limits to the allowed domain for

E I, where

are the usual parametrizations. We obtain for

1 - TJoofTJ+_E'a:::­EO 2 + TJoo!TJ+_

the values

Re(a) = 0.00 ±0.02�

Im(a) = 0.05 ± 0.10.�

This is illustrated in Fig. S(a). The result, compatible with a= 0, is in agreement with theories 0

which concentrate the CP violation in the K wave function, rather than in the decay matrix

elements.

A more general approach is the one of Schubert et al. 39 who separate EO = 2TJ+_f3 + TJOOf3

into a CPT-conserving, T-violating part E, and a T-conserving. CPT-violating part 6, according

to

The result of a new fit gives

-166­

-3Re (f) = (1.39 ± 0.25) x 10

-31m (f) = (1.1.6 ± 0.26) x 10

~ -3Re (6) = (0.01 ± 0.25) X 10

3.1m (6) = (-0.24 ± 0.30) X 10­

The result, illustrated in Fig. S(b) is compatible with absence of CPT violation.

OIlL10 Direct Proof of CP or CPT Violation in K Decays

OAny difference observed in the decay distributions from K and KO

mesons would constitute

either CP or CPT violation independent of any theoretical formalism or parametrization. An O

experiment to compare the vacuum regeneration interference from K and KO has been reported O

at the conference. 40 The interference term is expected to change sign from K to KO• The K

mesons were obtained by charge exchange on a carbon target in a K+!K- beam. The decay into

1T+1T- pairs was observed by spark chambers. The result shows a clear difference between KO

and KO decays (probability for the same distribution -10 -4). The fitted values of the relevant

parameters are in good agreement with the known values.

Similar direct tests have been already provided by the non-zero value of the asymmetry

parameter 6, and by the dilution factor of the vacuum regeneration experiments, which is appre­

ciably less than one.

IV. Neutral Currents and Other Forbidden Processes

IV.1 Introduction

One of the most remarkable and as yet unexplained properties of the weak interactions is the

one of retaining only those processes in which a unit of charge is transferred to the leptons.

Several theoretical considerations would on the contrary suggest that weak neutral currents exist,

perhaps at a somewhat reduced strength, in addition to the experimentally observed weak charged

ones. (For detail we refer to the report of B. W. Lee, p. 249.)

Even if primitive neutral currents are indeed absent, one expects higher order weak pro­

cesses to generate analogous effects. These diagrams are essentially uncalculable at present,

and they appear to be badly divergent. Still, we know from the K -K mass difference that second­L S

order effects exist, and that they are much smaller than the first-order weak interactions. Finally,

combined weak and electromagnetic effects can also simulate apparent neutral current effects. to

the first or second order in the constant a and to the first order in Gil. If confirmed, the dis­+ ­covery of the decay K - fL + fL is very likely an example of this type.

L The search for strangeness-conserving neutral currents is the domain of the neutrino­

induced reactions. A number of decays can instead probe very accurately the existence of

strangeness-violating currents. The main results are discussed in the following paragraphs. + + + +

From a comparison of processes like K - Tfee/K - nev , K -TryV IK -c rrev and K - ........ /K - f.Lv.�L4 one can state that the coupling constant of the neutral currents cannot exceed 10-1":10- of the

standard Fermi coupling.

+ + + +IV.2 Searches for K -fL +v+v+vandK -1T +v+v

An experiment to search for the process K+ - vvvfL+ is reported by a Chicago-LBL group. 41

The experiment consists of stopping K+, observing K-fL-e chain, measuring the range of the fL+

-167­

and rejecting events with other charged particles or v-rays from K+ - mry or K+- f1vy (Fig. 9).

This is achieved with a high-efficiency y detector surrounding completely the K+ stopper and the

f1-range telescope. Seven events have been found. However, the background is such that one can

neither identify them as good events nor subtract them as background. The corresponding upper

limit to the branching ratio is

+� + R(K -vvv!" ) '" 7 x fO- 6 (90% conf.).

R(K+- all)

The occurence of the process may be the result of

f. A primitive strong v -v interaction of the form sugge sted by Bialynicka et al, and Bardin 42

et al.

-2The result gives F s 0.90 m , to be compared to the usual weak interaction constant, G.. =

p-5 vv ,.. fO m ' p

2.� A process which in lowest order causes the emission of four leptons. as suggested by 4 3

Vanzha et al. They refer to this process as a six-fermion interaction. The interaction coupling

constant G 6 can be related to G by a proportionality constant of the dimension of mass cubed13

-3 . r.:'G G }. /",2.6 = 13

The negative result sets the limit}." 575 MeV (90% conf, ).

The same apparatus has been used to search for the process K+ - vv"+ leading to pions in

the kinetic energy range 60-fOO MeV. Since only part of the pion spectrum is observed, the

negative result can be interpreted as an upper limit on the branching ratio only if the form of the

interaction is specified. For a vector interaction the limit is

R(K +

-vv,,} < 7.5 x fO- 7 (90% conr.), R(K+-all)

+ + + ­IV.3 Search for K -'Q' +e +e

'!'his process, which is similar to the decay K+

- V\l1T +

, has been searched for by a Wisconsin

group44 with a counter and spark chamber arrangement. The result (preliminary) sets a limit

R(K+-ee,,) s 3.5 x fO- 7 (90'. conf. ).

R(K+ -all)

+ - + ­IV.4 Search for K -" +" +e +e

L + - + ­A Duhna group has searched for the process K

L -e rr Tt e e in a f -m streamer chamber ex-

Oposed to a long-lived K beam. 45 Appropriate cut-off criteria remove the background due to + .. 0 +-+-

Dalitz pairs K Tt Tt " -" " e e. No valid candidate has been foundL

­

+ - + ­R(KL -" " e e ) -5

R(K -all) s 3 x ro (90% conf.). L

We remark that the actual sensitivity of the process is greatly reduced by the 4-body phase space.

For instance the corresponding allowed decay K+- ""ev has an observed branching ratio of -5

3.7 x ro !

-f68­

+ ­lV.5 TheK -flo +flo Puzzle

L + ­The decay K - flo flo • if observed, could be generated to the first order by a primitiveL

neutral current. Evidence for such a current would, of course, be of great interest. Even in

absence of such a primitive weak interaction, the process can be induced by higher-order corr­

tributions of ordinary weak interactions such as the diagram of Fig. to(a). Such diagrams. badly

divergent, are essentially uncalculable by present theories. A simpler type of diagram is the one

of Fig. to(b), representing the combined effect of first order weak and second order ·electromag­

netic interaction. A lower bound to the diagram can be estimated including only the "on mass

shell" photons. This contribution, which corresponds to an absorptive part, adds incoherently

with the real part and is related to the known K - yy rate by unitarity considerations. With theL

assumption that contributions from other intermediate states can be neglected, the "on mass shell" 46

two-photon contribution gives a lower bound

+ ­R(K -flo flo)L

R(K -yy) '" L

Theoretical estimates of the maximum interference possible from other likely intermediate

states can reduce this lower bound at most by ~ 200/0. From the experimental value

R(K -yy) -4L R(K -all) =(5.6"'0.5) to

L

taking into account the maximal contribution from states other than the yy, we get the so called

"unitaetty limit"

+ ­R(KL-floflo) -9

'" 4.8 X 10 .R(K -all)L

47 This prediction is in disagreement with the experiment of Clark et al who have reported the

sensational result

(900/0 coni. level).

IT both the theory and the experiments on the K - yy are correct. the probability of obtainingL

the result above is < 2 x 10 -3. The newer value of T/+_ would decrease somewhat the disagree­

ment by raising the result about 400/0, i. e. ,

+ ­since the branching ratio had been normalized to the K -1T 1T decay observed by the same appa-L

ratus.

A number of theoretical speculations have attempted to explain the effect in a number of

ingenious ways, challenging one by one almost all the assumptions used for the derivation of the

unitarity bound. 48

-169­

The value for the branching ratio K - YY is an average of several experiments, all in goodL

agreement with each other. Instead, at least until this conference, the experiment of Clark et al,

has stood as the unique evidence against the prediction of the unitarity limit. A very interesting

contribution49 to this conference by the Columbia-CERN-NYU collaboration has challenged the

validity of the result with the observation of six events which satisfy their criteria for the decay + ­

K -1'1' .L� The experiment was situated in a long-lived neutral beam derived from the G-10 internal�

O� target of the Brookhaven AGS. K decays occurring within the evacuated decay region were de­

L tected with a spectrometer (Fig. tt) employing three X-Y multiwire proportional chambers

(MWPC). The chambers (5000 wires altogether) have 2-mm spacing between signal wires and the

left and right halves of the horizontal wires are divided to allow independent readout. The spec­

trometer magnet was operated at 210.6 MeV Ie transverse momentum, between the maximum values

possible for ........ and 1T1T decays. The total time resolution of the MWPC's for> 990/0 efficiency is

40 nsec. Electrons are identified by an atmospheric pressure hydrogen gas Cerenkov counter 2

with 12 optical sectors. Muons are identified by penetration of 900 g/cm of heavy concrete.

Three scintillation counter hodoscopes register the passage of muons with momentum greater than

1.6 GeV/c.

Data were recorded when either of two trigger conditions were satisfied:

1. Correct number of MWPC track segments present, at least one hit in each of the three

scintillation counter hodoscopes, and at least two hits in either of the last two hodoscopes.

2. Correct number of MWPC track segments present, and at least one counter hit in the

first scintillatlon counter hodoscope. To avoid cumbersome data analysis, only 1 in 64 of this

trigger was actually recorded. O

Examples of the decay K - ........ were sought in type 1 triggers, whereas type 2 triggers provide�L

Onormalization through other K decay modes. Approximately 850/0 of the total data is reported in

L this contribution. Track reconstruction was accomplished by calculating the particular circular

orbit through the magnet which provides a continuous trajectory for the three points measured by

the MWPC's. O

The resolution of the apparatus was studied by means of several thousand examples of K ­L

O1T1T decays contained in the type 2 triggers [ see Fig. 12( a)]. In the K -momentum interval 4-5

2 OGeV [c , the mass resolution o is less than 1.4 MeV Ic , and averaged over the K -momentum

L2

spectrum is 1.8 MeV Ic . In computing the i, the observed momentum dependences of the kink, o +­

vertex, and 9 resolutions are included. With the above cuts, the total number of K - 1T 1T k L

6 2 Odecays recorded (multiplied by 64) is 1.1 x 10 in the mass interval ±3.5 MeV Ic about the K

mass. O O

The candidates for K - 1'1' were treated with exactly the same cuts as the K -1T1T decays,L L

but with additional requirements relevant to muon detection. These are

1. No shared counters in any hodoscope

2. No more than 5 counters hit in the last 2 hodoscopes

3. The projected trajectory must intersect the hit counter or miss by a distance compatible

with multiple scattering.

-170­

The distribution in invariant mass for K -1'1' candidates is shown in Fig. 1Z(b). There are sixLO

O� Z,events within the interval ,1,3.5 MeV// of the K mass, one event at -51Z MeV/c and no events

Oat higher mass. Using the K momentum dependent mass resolution, the l sum:.f. (M.-M )Z/(1.Z" L 1 K 1

4.1� corresponding to a 70% confidence limit. On the other hand, the probability that the observed Z

distribution of the seven events above 490 MeV /c arises from a monotonic background is negli­Z

gibly small. For example, a flat background in the interval 490 to 5Z0 MeV /c corresponds to a

probability of < 1 x 10 -3. On this basis, the data provide conclusive evidence for the decay 0+­

K -I' I' .L

The nature of the background events can be seen more clearly in a scatter plot of mass vs� Z Z_ Z Z 0 .�

Ok' where Ok =0kx + 0ky' About 100 K L -1TT' events are shown m Fig. 13 (top) to indicate the

resolution, and all available 1'-1'- data are shown in Fig. 13 (bottom). In these plots, the l sum for

the track kinks and the vertex size is less than 6.Z5. o� 0

~e relevant number of K decays, Neff' for K - 1'1', can be found from the detectedL� L K

LO -e rr IT - events, suitably corrected for the relative geometric acceptance of the spectrometer,

'I'-:P' ,,:P, the efficiency of the muon detector, '1'-1" pion decays in flight and the K O-"+,,­

L branching ratio. Thus,

, sp

N "01'1' x x x 1 xN eff ,sp 'I'I'- Pdecays BR"" rrn

""

" 0.74 x 0.85 x 0.~5 x 0.0~157 x 1.1 x 106

8." 5 x 10

OThe branching ratio for K - 1'+1'- decays is thenL

BRI'I' " (NI'I' - NBackground)/Neff

= 5/(5 x 10 8) = 10 x 10-9 (Preliminary). 49

Here one has explicitly allowed for the possibility that one event is background in computing the

branching ratio.

If the new value for !71+_1 presented at this conference by Steffen et a1. 2 is employed, one

obtains

BR = 14 x 10-9 (Preliminary).1'-1'­

In either case, no conflict exists with regard to the lower bound imposed by the unitarity conditions.

The result cannot be reconciled on a purely statistical basis with the work of Clark et al.

However, so far no valid effect has been noticed which could have introduced severe event losses

in that experiment. Furthermore, the Columbia-CERN-NYU experiment is still at a preliminary

stage. EVidently the solution of the puzzle rests on more experimental investigations. A sharp

drop in the number of theoretical speculations on the subject is to be forecast for the near future.

+ ­IV.5 Search for the Decay K I' I' S

-

The search for the decay K - 1'-1' is specifically motivated by a suggestion of Christ andS

Lee50 that an unexpectedly large CP-violating decay K 1'-lJ. could overcome the difficultiesS

­

-171­

encountered in the explanation of the result of Clark et al. on K ....... The suggestion of Christ�L ­51

and Lee was generalized by M. K. Gaillard and embodied in a model by Dass and Wolfenstein. 52

A CP violating 1<1- ...... amplitude is assumed, in order to cancel the unitarity amplitude K YY- .......�L ­52

This sets the limits

-6 R(KS - ......> -6 12.5 x 10 '" '" 1.1 x 10 .R(K -all)

S

The less� specific arguments of Christ and Lee and of Gaillard give the less restrictive limits 7 7,z 5 x 10- and," 2.8 x 10- respectively. Note that these numbers are somewhat affected by the

recent possible changes in the values of 11+_. The CERN-Heidelberg group53 has reported a search

for the decay which has given a negative result. The experiment is essentially a by-product of the

vacuum regeneration experiment described in Ref. 2. Muons were identified by penetration in a

light concrete block. The invariant ......-mass distribution for the events meeting the selection

criteria is shown in Fig. 14. There is no event in the mass range 491-507 MeV. The nux was + ­

normalized from the number of observed 1T 1T decays. After several corrections the result is

R(KS - ...... ) -7 R(K -all) :S4X10

S

and it excludes the model of Dass and Wolfenstein.

References

10 . Skjeggestad et al., CERN/D. Ph. II/phys 72-28 and Paper 267.�

2p . Steffen et al., Oral presentation by P. Steffen to the conference.�

3L. Krisch and P. Schmidt, Phys. Rev. 147, 939 (1966).� 4� ­

R. A. Donald et al.. Phys. Letters 27B. 58 (1968).�

5D. G. Hill et al; , Phys. Rev. 171, ~ (1968) and private communication. (The new value has�

been corrected for CP effects differently. )�

6F. S. Crawford et al., Phys. Rev. Letters 2, 266 (1959).�

7L. Bertanza et aI., preprint (1962). ­

8M. Chretien et al., Phys. Rev. 131. 2208 (1963).

9 M. N. Kreisler et al, , Phys. Re::-136B, 1074 (1964).

fO C. AUf-Steinberger et al., Phys. Letters 21, 595 (1966).

tiL. Auerbach et al., Phys. Rev. 149. 1052(;"966).

12C. Baltay et al., Phys. Rev. 142~32 (1966). 13� ­

S. H. Aronson et aI., Phys. Rev. Letters 25, 1057 (1970).

14R. K. Carnegie et al., Phys. Rev. D4, 1 (1971).

15M. Cullen et al., Phys. Letters 32B, 523 (1970).

16J • H. Christenson et al., Phys. ~. 140B. 74 (1965).

17 L. B. Okun, unpublished.

18p. SOding et al,.; Particle Data Group, Phys. Letters 39B, 1 (1972).

-172­

1.9D. A. Jensen et al., Phys. Rev. Letters 23, 61.5 (1.969).

20private communication of V. L. Telegdi and collaborators.

21J. H. Christenson et al,.; Phys. Rev. Letters 13, 1.38 (1964).

22 W. Galbraith et al., Phys. Rev. Letters 1.4, 383 (1.965).

23 p• Basile et al.. in Proceedings of the Balaton Conference (1.965), unpublished.

24M• Bott-Bodenhausen et al., Phys. Letters 23, 277 (1966). 25 -­

X. De Bouard et al., Phys. Letters 15, 58 (1.965).

26V• L. Fitch et al., Phys. Rev. 1.64,771.1. (1.967).

27 H. Wahl, private communication-.­

Z8F or details see the report of G. Giacomelli in these Proceedings, Vol. 3, p. 219.

29 C• Rubbia and J. Steinberger, Phys. Letters ~4B, 531. (1.967).

30M. Holder et al; , Phys. Letters 40B, 141 (1972). 31 --­

M. Banner et al., Phys. Rev. Letters 28, 1.597 (1.972).

32p. Darriulat et al,.; private communica~n. 33J • C. Chollet et al., Phys. Letters 31B, 658 (1.970); B. Wolffet al; , Phys. Letters 36B, 517

(1971).

34R. L. McCarthyet al., Phys. Rev. D7, 687 (1973).

35A. R. Clark et al., Phys. Letters 41.B, 229 (1.972).

36F. James et al,.; Paper 266.

37V. V. Barmin et aI., Paper 828b.

38J• G. Layter et al,.; Papers 237, 238.

39K • R. Schubert et al., Phys. Letters 31B, 662 (1970).

40D. Banner et a1.. Paper 480. --­

41G. D. Cable et al,.; Papers 213, 214.

42 Z• Bialynicka-Birula, Nuovo Cimento 33A, 1.484 (1.964); D. Yu, Bardin et al., Phys. Letters

32B, 121 (1970).

43~Vanzhaet al., Yad. Fiz. 12, 595 (1970), [Sov. J. Nuc1. Phys. 12, 325 (1971.)].

44 D. B. Clarke, private communication quoted in Ref. 41 and Abstract in Bull. Am. Phys. Soc , ,

DJ10, April 1.972.

45 M. H. Anikina et al,.; Paper 888. 46

L. M. Segahl, Nuovo Cimento 45A, 785 (1966); Phys. Rev. 183, 1511 (1969). Also B. R. Martin

et al., Phys. Rev. D2, 179 (1970). 47 -­

A. R. Clark et al., Phys. Rev. Letters 26, 1.667 (1971).

48 F o r a complete review of the subject we ::::-fer to the paper of A. D. Dolgov, L. B. Okun, and

V. I. Zakharov, The Decay K -2.. (Review), ITEP preprint No. 924, Moscow, 1972.L

49 w. C. Carithers et aI., Oral presentation by D. R. Nygren at this conference.

50N. Christ and T. D. Lee, Phys. Rev. D4, 209 (1971).

51 M. K. Gaillard. Phys. Letters 36B, 1;;(1971).

52G. V. Dass and L. Wolfenstein, Phys. Letters 38B, 435 (1972).

53S. Gjesdal et al,.; Paper 687.

-173­

l1: 11. UJ 010,

~ UJ ~0.05

~ 1000 UJ

(!)

o 5 10 15 20 TIME (10-1) sec)

- 100 ~ z UJ [ij

~ 0::

~ 10 ~

~

o 23456 7 8 TIMEINUNITSOF 10-10 sec

+ ­Fig. 1. The time distribution of K _"" of the bubble chamber experiment of Ref. 1. The con-S

tinuous lines show the best fit and the world's average of older results.

-174­

5 ( 10-10_ )

+ ­Fig. Z. Time distribution of K-1T 1T of the CERN-Heidelberg experiment of Ref. Z. The two

sets of dots show the effect of the interference term. Note the drop at early times due to changes in the detection efficiency.

-175­

·---- noinlerfer~

--i~

• Experiment

o 2 4 6 8 14 16 l8 20�

Fig. 3. The same distribution as of Fig. 2, corrected for the detection efficiency.

-f 76­

1. 00

0.96�

0 ",�

-$2 0.92 )(

w t-----_ ..... ____::E - - - - - - - - -,-+- -­~ , 2 ... w 0.88u,-J

-J

?, :J f2 +

O<J)

:s:: 0.84 101 t 4

I I 11

8 9I 3

0.80 1958 1962 1966 1970 1974

YEAR

Fig. 4. Comparison of the result of Refs. 1 and 2 on T with the results 0' c.'her experiments. Reference numbers are shown with theS

data points.

-----

------ - --- - -- ---

GAP METHOD

---- -- It·L a)K CD ~- <D+®<1t_

I

l..., ex> ZERO-CROSS METHOD I

i ,- - - - - - - - - - - - ­

CD It+ K CD I------

S ;:® _L

L,____' ----- CD__® -- --------It b)

Fig. 5. The principle of the gap and zero cross methods [5( a) and 5(b) I to determine the K -Kg mass difference.L

2.6 x103

I - 1'7+_ I

Vacuum Reg. I 6.- ...-----~ Aronson I T =0.856

SI Vacuum Reg. 16.-~ SteffenI T =0.856

I I I ~ FitchKL-1T1TIKL-('7rev+1Tfl-v)

I I ~ De Brouard

;. KL-1T'7r/KC('7rev+1Tfl-v)

I -J I I

-<> KL-1T1TIK~all charged ~ Bott- Bodenhausen

I II I

I f I Basile I I

II I _, I Galbraith I I

II I ~ I Christenson

2 3 4 xlO­

R=KL-1T+1T-1 [KL1TeV+KC1Tfl-v]

Fig. 6. Comparison of the world's results on 1'1+_'.

'P+-vs L'1 m (U.C. - WC.C. data)

for 't s =(0.899±0.005) x10-l°sec

55°

50°

L'1 m=0.052 ±0.006

0.530 0.535 0.540 0.545 0.550 L'1m/h (Xl0~S-1)

Fig. 7. The dependence of Arg (7)+J on the value of the KL -K S

mass difference zxm, The pre­diction of the superweak models, Arg (7)+J = arc tan (rLl.m T S) is also shown.

-f80­

-0.10 -0.05 Re(a)

Fig. S(a). Allowed regions for the ratio a=!' /E ' (b). Allowed regions for the T-violating. CPT-conserving amplitude E and for theO CPT-violating, T-conserving amplitude 5.

(0) v C Radiators

T8 T7 T6 T5

89

810 87

86

K4 K3 K2 Veto

Againsty's

85 84 83

r;ilI I

82 81 KC KI

~ p,T,7T+Degroder +

~ K Degrader-yConverter !§:,:.:-;:;., Scinto Coupled to Pb Glass ~ Light Pipe

+ ~ K Stepper

Fig. 9. The experimental setup of the Chicago-LBL experiment on neutral currents (Ref. 41).

-182­

(a)

(b)

Fig. 10. Diagrams contributing to the decay KL - f1f1: (a) Second-order weak interaction; (b) First order weak and second-order elecTromagnetic interaction.

-183­

---

.......�

l 00 ... I

..---­

~ ~ r-t­

t-> k f::: I..­f::::

....

-...,. f::: L- I

L- 1 -L-­

49 Fig. 1:1. The experimental setup of the Columbia-CERN-NYU experiment on K - fLfL. Top part is the horizontal view; the lower part

Lis the vertical view. The neutral beam is absorbed in a lead-uranium insert in the muon filter.

800

N 700

~ ~6oo ~ - 500 <,

ffi 400 m ~ :::> 300 Z

200

100

480 485 490 495 500 505 510 5/5 520

K~ - 7f tr INVARIANT MASS MeV/c 2

Fig. 12( a) The invariant mass distribution for K _,,+,,- events. 49L

N

~ ~ :E MUON -PAIR MASS SPECTRUM

~ 20 X2 (5 DOF)< 10 I­Z w >w

~ 10

a:: w m :E :::> Z

480 490 520

Fig. 12(b). The invariant mass distribution for KL

_,,+,,- events. 49

-185­

40 7T.7T INVARIANT MASS vs. 8 2

N 30 CJ:)

~20 N

CD 10 .. ..... .-,. .. ­... 480 485 490 495 500505 510 515 110 M7T7T

100 ."

90 ·· ... jJ;J.L INVARIANT MASS vs. 82

80 ." ..�

70 '..: N CJ:) ••••• o 60" ... , '." .,

\. .. I. ••Q:, 50 .' . .

40 :!:' ': .� 30 ...-. ..

i \ '. 20 :1. I. .. . .,- . .�10 -:.•. I

I••t.. ••

1-· ,. ~ a ".1 .. . .

480 485490495500 505510 515 MJ.LI.L

49Fig. 13. (top). Scatter plot of K -,'" events. (Bottom). The same for K fLl'-events. The

L-

distributions are plotted in theL

invariant mass- 6 Z plane. The variable 6 Z has been dividedK Kby the appropriate resolution for each event.

-186­

100 5000

't ~

Ion 80 I000O ­§ ~ '::1. ~ +::1. .~

\! 60 3000

Fig. 14. Invariant mass distribution for KS

- f'fL and KS

-1T1' events of the CERN-Heidelberg experiment. 53

-187­

DISCUSSION

V. L. Telegdi (Chicago): I would like to make some comments:

1. Our vacuum regeneration data fits the new (Steinberger) 111+_1 with the Steinberger TS

as input just as well as it fits the old (Handbook) 111+_1 with the handbook TS as input. That is, our

conclusion is that we have no conclusion.

Z. We are going to analyze the leptonic events from this experiment to get an independent

measurement of 111+_1. 3. The important question is not what is TS or l!.m, but what is 1/>+_. Perhaps my arithmetic

is different from yours but our group finds that the new T gives us a new l!.m which in turn gives usS

us a 1/>+_ which differs from the superweak prediction by Z standard deviations.

C. Rubbia: The value for the phase comes from two sources:

1. Vacuum Regeneration (your experiment) and (Z) Regeneration Amplitude experiments.

The former method is most sensitive to changes in l!.m. In my calculation I have taken the average

of all these experiments and have thus diluted the effect of TS

on 1/>+_.

H. J. Frisch (Chicago): On the existence or absence of K -I'+', I don't know if we have the moreL

relevant truth or not. Our experiment was very carefully looked at. In view of the results re­

ported here (Ref. 49), we will now throw out some of our constraints and reanalyze our data, but

I do not expect a change in our result.

C. Rubbia: Is the following correct, Dr. Frisch? If the Columbia result is correct, you should

have seen S-ZO events, where you saw none in vacuum and one in Helium.

H. J. Frisch: Yes, let me add if the new 111'+_1 is taken our result is consistent with the unitarity

limit, but the two experiments are still significantly statistically inconsistent.

-188­