Volume
PHYSICS
21. number 5
FURTHER
RESULTS
FROM
THE
THE
7~+n-
LETTERS
15 June 1966
INTERFERENCE
DECAY
MODES
C. ALFF-STEINBERGER,
W.HEUER*,
K. KLEINKNECHT**,
J. STEINBERGERt,
M. J. TANNENBAUMtt
OF
C. RUBBIA,
KS
AND
KL
IN
A. SCRIBANO***
and K. TITTEL*
CERN, Geneva, Switzerland
Received
2 May 1966
Previous measurements
on K” decay and the interference of KL and K3 in the n’n- decay modes have been
extended. We find that the interference term has the predicted coefficient with an experimental uncertainty of about 15%, that the KI - K3 mass difference is + (0.445 f 0.034), the phase Cp= ‘pn- ‘pf is x (1.41 +
0.18) and we find no evidence for the lenton
.
.pair decays of KL. With 90% confidence IL B+cl_/FL < 2 x 10-4
IL,e+e-/FL
< 1.6 x 10-4.
Recently we presented experimental results
on the interference in the Kg and KE two-pion
modes [l]. The experiment has been extended
statistically and slightly refined systematically.
It is the purpose of the present note to give
briefly the new results, especially more precise values of the mass difference Am = ML ikfs and the relative phase cp of the two interfering amplitudes, and to make one or two
comments which were omitted before. A detailed account of the technique is in preparation for publication elsewhere; for the present
we refer to our previous letter for the experimental procedure and for the notation.
The experimental changes are the following:
1) We now monitor by means of the leptonic
decays in the same film. These are selected
by taking events outside the invariant mass
peak: m < 485 MeV or m > 515 MeV and outside
the forward cone: LY> 4, and in the second half
of the fiducial decay volume along the beam
direction. In this way we have an essentially
pure sample of leptonic decays which are found
and measured with the same efficiency as the
two-pion decays in the several exposures. There
remains one correction, for the case of the
This is due to the differheavy regenerator.
* Visitor from III. Phys. Inst. der TH, Aachen.
** Visitor from Max-Planck Inst. f. Kernphysik,
Heidelberg.
*** Visitor from Istituto di Fisica dell7Jniversita,
Pisa.
t On leave from Columbia University, New York
+t U.S. National Science Foundation Postdoctoral
Fellow.
ence in effective nuclear attenuation of the kaons
in the regenerator for 271decay and leptonic
decay. In the case of the 2s decay, the angular
resolution is such that diffraction-scattered kaons
are rejected. The effective cross-section in this
case is therefore the total cross-section.
In the
case of the leptonic decays, the direction of the
kaon cannot be determined exactly, since the
neutrino escapes detection. The diffraction-scattered kaons can therefore not be separated in
general from the undeflected beam. Using a
Monte Carlo calculation, we find that the detection efficiency of the diffraction-scattered kaons
in the leptonic mode is 60% of that for the undefleeted kaons.
In a subsidiary experiment we find (970 f 100)
mb for the total cross-section of KL in our
momentum interval. Using the optical theorem
and an optical model calculation, the diffraction
scattering cross-section is 260 mb. The corresponding multiplicative factor in the leptonic rate
for the dense regenerator was taken to be 0.85 f
0.05.
2) As before, events are selected by plotting all
events in the mass region 489 MeV < m < 507
MeV as function of (Y ( a measure of the deviation
from the beam) and taking those events with
o! < 2. The background is subtracted by extrapolating the rates at larger angles into the forward cone. This background consists of leptonic
decays and diffraction-scattered kaons decaying
to two pions. We have refined the extrapolating
by calculating the distribution in o! for these decays, and making this calculation the basis of the
extrapolation.
595
Volume
21,
number
HEAVY
;
I
PHYSICS
5
REGENERATOR
ia1
LlGHT
1.5 June
m-
REGENERATOR
k
NO
1966
REGENERATOR
1 k
( 10-%ec)
Fig. I. Proper
time distributions
copper
of density
8.9 g/cm2.
for the three regenerator
conditions.
The light regenerator
is 12 cm copper
The experimental results are shown in the form
of prop+er_time distributions of the decays
for
KO-+~T 71, aligned with the beam direction,
the three regenerator conditions: dense regenerator, light regenerator,
and no regenerator
(fig. 1). The calculated time-dependent
efficiencies, normalized to the level of the KL decay,
are also shown.
The theoretical expectations [l eq. (l)], were
fitted to the data of fig. 1, to find the best values
of IP i, i 77i, rs, A m, and (D. This might deserve
a word of explanation: Am and (D are the quanti ties we are trying to determine.
The KL -~+7rintensity relative to the beam monitor and the
regeneration intensity are also not initially
known, and are given by 1~1~ and (p/q 12, respectively.
The decay constant rs is quite adequately known, but we find that we do not increase the errors in am and q by also leaving
Q to be determined.
The resultant measurement of I’s agrees with previous determinations.
The distributions
corresponding
to the best
fit solutions are drawn in fig. 1. Thex 2 for this
fit is 30.6 against an expectation of 30. The
values of the fitted parameters are: jp/q I=
21.2 f 1.0, this is the regeneration amplitude in
12 cm of copper of normal density, an average
momentum of 2.7 GeV/c,
relative to the relative
amplitudes of KL and KS in ~T+T-decay; rs =
1.155 f 0.021 X 10WIO set-l; Amm/l?s = f (0.445 f
0.034); q = v)~ - qf = f (1.41 f 0.18) rad.
The errors include the statistical errors and
estimates _of the systematic uncertainties.
pf is
arg MO) -f(O)] + $r wheref(0)
and?(O) are the
forward scattering amplitudes of KS and KL,
596
LETTERS
The dense regenerator
is 12 cm
of average
density
0.356 g/cm2.
Fig. 2. Experimental
tic terms
according
to exhibit
data after subtracting
to the best fit solutions,
the interference
term.
the quadrain order
respectively,
in copper. The relative sign of cp
and Am/rS is the same, the over-all sign is not
determined in this experiment.
The data of fig. 1 can be treated in such a
way as to exhibit the interference term. This can
be done by subtracting the quadratic terms accord.
ing to the fitted parameters p and 1, and then
dividing by 21 p/q lexp(-$ FST). This has been done
for both the dense and light regenerators,
and
the results are combined in fig. 2. The resultant
distribution should have the form cos (Am7 - cp)
and gives perhaps some insight into the sensitivity of the experiment to cp and Am.
A least square fit of the data in which the size
of the interference terms is allowed to vary,
indicates that experimentally
this is 1.20 f 0.14
Volume
PHYSICS
21, number 5
-4HKExprmMENT
_BYfT
BZIENHAtJSENetCd.
FITCHet al
+ FIRESTONE et al.
:
I
d2
I
T
3112
rL, p+b-/
2a
Fig.3. Comparison of experimental results on the relative phase of the amplitudes KL -+a’lr- and KS -+~+8with the prediction of the “weak CP’ model.
of the expectation. The models of KL two-pion
decay of Kabir and Lewis [2] and Laurent and
Roos [3] predict a smaller interference term,
under our conditions approximately one-half as
large, and can be rejected on the basis on this
experiment.
We now turn to the phase qn. There is a
particularly simple expectation for this phase
shared by all “weak CP” models, that is, for
those models in which the CPviolating amplitude is no more than a few per cent of the CP
conserving amplitude in any channel. In these
= 0.73 f 0.04 rad.
models ‘pn N arctan (2 m/F,)
In the case of the superweak model of Wolfenstein [4] this prediction is exact.
In fig. 3 this phase is compared with the
results of this and other experiments [5-71.
Exact agreement among the experiments cannot be expected, since the regenerator materials
and the kaon momenta are not the same, and
the regeneration phase pf must differ to some
extent. However, the experiments do not disagree with each other. They also do not disagree with the predictions of the “weak CP”
models, except for this experiment, perhaps on
account of its smaller errors. We find
"weak CP =
exp
9
15 June 1966
quired size. The latter possibility is not in conflict with anything presently known, experimentally or theoretically, about regeneration in
copper at these momenta. In any case, given this
uncertainty, no experimental check of the phase
prediction of the “weak CP’ models can be considered to exist to a better accuracy than of the
order of one radian.
We have also used the apparatus to search
for the decays KL + /J+ + /J- and KL - e+ + e-.
We find no evidence for these decay modes, and
give upper limits, with 90% confidence:
- “WEM c P” MOOELS
-+I
LETTERS
-9
(‘p?7- cpf)exp - q’lweak cp” =0.69 f 0.18 rad.
We must conclude that either the “weak CP”
models are incorrect, or the regeneration amplitude in our case has a phase ‘pf = 0.69 f 0.18 rad.
A phase difference of about 7 degress between
the K” and K” forward scattering amplitudes on
copper would produce a value of ‘Pf of the re-
FL,e+e-
l-L < 2 x 10-4
/ FL < I.6
X mm4
Two other negative results of substantially the
same sensivity have been reported [8-91.
We wish to thank Mr. F. Blythe for his help
in the mechanical design and construction, Mr.
L. Thornhill for the construction of the counters, Prof. R. Friedberg for his contribution to
the experiment in its early stages, Dr. I. Manelli
and the Istituto di Fisica, Universita: degli Studi,
Pisa, for computational assistance, and Columbia University for some help in measurement,
and Prof.V. F. Weisskopf for his support.
References
W,Heuer,
K.Kleinknecht,
C.
1. C.Alff-Steinberger,
Rubbia, A.Scribano,
J.Steinberger,
M. J. Tannenbaum and K.Kittel,
Physics Letters 20 (1966)
20.
and R.R.Lewis,
Phys. Rev. Letters 15
2. P.K.Kabir
(1965) 306.
3. B. Laurent and M. Roos, Physics Letters 15 (1965)
104.
Physics Letters 13 (1964) 562.
4. L. Wolfenstein,
R.F.Roth,
J.S.Ross
and W.Vernon,
5. K.L.Fitch,
Phys. Rev. Letters 15 (1965) 73.
X.De Bouard, D.G.Cassel,
6. M.Bott-Bodenhausen,
D.Dekkers,
R. Felst, R.Mermod,
I.Savin, P.
Scharff, M.Vivargent,
T.R. Willitts and K. Winter
Physics Letters 20 (1966) 212.
A.Firestone,
J.K.Kim,L.Lach.J.Sandweiss,
H.D.Taft,
V.Barnes,
H.W. J.Foelsche,
T.Morris,
Y .Oren and M. Webster, Phys . Rev. Letters 16
(1966) 556.
D. W. Carpenter,
A. Abashian. R. F. Abrams,
C. P.
Fisher,
B.M.K.Nefkens
and J.H.Smith,
Phys.
Rev. 142 (1966) B871.
X.De Bouard, D .Dekkers,
B. Jordan, R. Mermod,
T .R . Willitts, K. Winter, P. Scharff, L. Valentin,
M.Vivargent,
M. Bott-Bodenhausen,
Physics
Letters 15 (1965) 58.
597