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CP violation in K decay
Nuclear Physics B (Proc. Suppl.) 3 (1988) 367-388 North-Holland, Amsterdam
367
CP VIOLATION IN K DECAY
Italo MANNELLI NA31 Collaboration *), CERN, Geneva, Switzerland, and Dipartimento di Fisica, Universit~ di Pisa and INFN Sezione di Pisa, Pisa, Italy
Since the original discovery ] in 1964 that both Ks and KL decay into 7r%r-, which represents clear evidence for CP violation, the challenge has been to devise experiments and theoretical models that could elucidate the nature of this phenomenon and its source. A number of implications have been analysed2: for example, it was pointed out in 19673 that CP violation, combined with a very small baryon instability, could have produced, in the early explosive development of the Universe, the matter-antimatter imbalance as manifested today by the measured ratio = 109.
Nbaryons/Nphotons
Despite intensive research efforts, no CP-violation effects have been detected outside the neutral K system. In addition to the two-pion channel, CP violation is detected in the charge asymmetry of semileptonic KL decays. All results appear to be consistent with CPT invariance and what is clearly demonstrated is that in K ° --, ~o mixing the amplitude for the transition K ° -~ ~o is different from the amplitude for the time-reversed transition ~o ~ K 0. The superweak model 4, linking CP violation to ]ASl = 2 transitions, is empirically still valid 5. In this model, the KL decay to two pions is due only to the impurity c of the eigenstate Kt with CP = + in the composition of the KL = (K= + 6K1).(1 + Id2) -1/2 itself (K2 is the eigenstate with CP = - ) , and A0 and A2, the amplitudes for K° to decay to two pions in isotopic spin I = 0 and I = 2 respectively, are relatively real. The ratios of the amplitudes for KL and Ks decay to two pions *) The members of the NA31 Collaboration are: CERN: H. Burkbardt, P. Clarke, D. Coward, D. Cundy, V. Gibson, N. Doble, L. Gatignon, R. Hagelberg, G. Kesseler, J. van der Lans, T. Miczaika, H.G. Sander, A.C. Shaffer, P. Steffen, J. Steinberger, H. Taureg, H. Wahl, C. Youngman; Dortmund: G. Dietrich, F. Eisele, W. Heinen; Edinburgh: R. Black, D.J. Candlin, J. Muir, K.J. Peach, B. Pijlgroms, I. Shipsey, B. Stephenson; Mainz: H. Blfimer, M. Kasemann, K. Kleinknecht, B. Panzer, B. Renk, S. R6hn; Orsay: E. Auge, R.L. Chase, M. Corti, L. Iconomidou-Fayard, D. Fournier, P. Heusse, A.M. Lutz; Pisa: L. Bertanza, A. Bigi, M. Calvetti, M. Carosi, R. Casali, C. Cerri, R. Fantechi, S. Galeotti, I. Mannelli, E. Massa, A. Nappi, D. Passuello, G. Pierazzini; Siegen: C. Becker, D. Heyland, M. Holder, G. Quast, M. Rost, W. Weihs, G. Zech. Their dedication and hard work has made possible the performance of the experiment, the results of which on e'/e are reported here for the first time. 0920-5632/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
368
L Mannelli / CP violation in K decay
T/+_ = (Tr%r-lTIKL)/(Ir+r-ITlKs)
= ~
and
~/oo = (Tr°Tr°lTIKL)/(r°~r°lTlKs/ =
are hence both equal to ~, and ~/+ _ hloo = 1. The phase of ~ is fixed by the mass and total decay rate of Ks and KL: arg (~) = tan -~ 2(mL -- ms)/(Vs - VL) = 4 3 . 7 °. In the more general case, w h e r e CP-violating amplitudes could be present in the K t w o - p i o n decay, to a good a p p r o x i m a t i o n T/oo=~-
2~' ,
r/+_ = ~ + ~ '
w i t h ~' = i/~f2 Im (A2/Ao) exp [i(62 - 60)], w h e r e (50 and 62 are the ~rTr phase shifts for I = 0andl
= 2, a t ~ / s = mK. Experimentally, 62 - 6o = - 5 3
_+ 5 ° and h e n c e a r g (~') =
62 - 6o + lr/2 = 3 7 _+ 5 °. Therefore taking ~' and ~ as relatively real and for le'/~l ~ 1 Ir/ooh/+ -12 = 1 - 6E'/~ w i t h *) arg ~/+ _ - arg ~/0o. It w a s first realized in 1 9737 t h a t it is possible to incorporate CP violation into the standard e l e c t r o w e a k gauge t h e o r y if three generations of quarks exist, as n o w appears very plausible. From this point of v i e w only an accidental cancellation could produce Also CP-violation p h e n o m e n a could be e x p e c t e d in cases similar to the neutral K, in particular for the neutral B mesons, for w h i c h B ° --* ~o mixing, a prerequisite for CP violation, has recently been observed by the UA1 Collaboration at the CERN Collider s and by A R G U S at DORIS 9. The results of the first a t t e m p t s to measure f~/oo/~+-I are reported in Table 1 t o g e t h e r w i t h more accurate results published in 19851°. The main features of the 1 9 8 5 e x p e r i m e n t s are summarized in Table 2. M o r e recently ]~ the C h i c a g o - F e r m i l a b - P r i n c e t o n - S a c l a y
Collaboration (experiment
E731 at Fermilab) have given a preliminary result, ~'/~ = 0 . 0 0 3 5 + 0 . 0 0 3 (stat.) + 0 . 0 0 2 (syst.), based on a sample of 6 7 3 8 27r° decays, obtained from an improved set-up at Fermilab w h i c h is ultimately e x p e c t e d to yield some 1 0 0 , 0 0 0 27r° decays and reach an a c c u r a c y of + 1 x 10-3 for ~'l~. A t CERN the N A 3 1 e x p e r i m e n t has n o w produced its first result,
*) The experimental value for arg ~/oo - arg 7/+_ = 9.8 ° + 5 . 4 ° is 2 standard deviations from zero 5. A difference from zero w o u l d imply CPT non-invariance 6.
369
L Mannelli / CP violation in K decay
~'/~ = (3.5 + 1.4) x 10 -3,
and most of the remainder of this paper will be concerned with this experiment. The principle is to measure
e'/e = (1 - R)/6, where R is the double ratio of the decay rates R = [r(KL --*
2~r°)/r(KL -* 7r+lr-)]/[r(Ks --* 2~r°)/r(Ks -* ~r%r-)].
Charged and neutral decays are detected at the same time, alternatively for KL and Ks. Switching from KL to Ks was done with a periodicity of about a day. The overall stability of the detection system was checked in several ways. In particular, the ratio of charged to neutral decays for Ks changed by less than _ 1.5% over a time equal to 20
Table 1 Measurements of ~'/~ = [1 -
(In0o/n+-12)]/6
Year
Authors
l~/ooh/+ -I
1972
Holder et al.
1.00 + 0 . 0 6
1972
Banner et al.
1.03 + 0 . 0 7
1979
Christenson et al.
1.00 + 0 . 0 9
Average
1.01 + 0 . 0 4 R = 17/ooh/+-I2 = 1.02 + 0 . 0 8
Year
Authors
1985
Black et al.
1985
Bernstein et al.
Average
e'/e 0.002 + 0.007 + 0.004 -0.005
+ 0.005 + 0.002
-0.003
_+ 0 . 0 0 5
R = I~oo/~+_12 = 1.015 _+ 0 . 0 3
Experiment
0 . 2 % of Ks --' 7r÷Tr
Incoherent Ks: 1.5 _+ 0 . 5 % o f Ks ~ 27r°
KL semileptonic d e c a y s
n interactions in He
KL ~ 37r° ~ 63'
12 = R = 0 . 9 9 0 _+ 0 . 0 4 3 +_ 0 . 0 2 6
Backgrounds:
t~oo/n+
Main s y s t e m a t i c s :
_+0.2
f o r 7r+ ;r
a c c e p t a n c e c o r r e c t i o n (KL u p s t r e a m o f Ks regenerator)
inelastic r e g e n e r a t i o n of Ks
u n c e r t a i n t i e s in b a c k g r o u n d (KL -~ 37r°, n interaction)
_+1.3
_+0.5 f o r 27r°
+_ 0 . 0 0 5 3 +_ 0 . 0 0 2 4
KL/Ks
R = 1 . 0 2 8 + 0 . 0 3 2 _+ 0 . 0 1 4
~'/E = - 0 . 0 0 4 6
error
correction
Total systematic
Acceptance
_+0.1 1.7 _+ 0.1 0.2
25751
K s -* ~+Tr-
20960
Ks --* lr+Tr -
~'/E = 0 . 0 0 1 7 _+ 0 . 0 0 8 2
_+1.0 _+0.2
0.4_+0.1 3.1 _+ 0 . 2
10638
KL --~ 7r+~ -
2.0_+1
8506
0.6_+0.1
5663
KL --} 7r+Tr -
_+0.6 2 . 9 _+ 0 . 3
8 . 4 _+ 0 . 4
3152
1 4 . 9 _+ 0 . 5
KL --~ 27r°
Ks --* 27r °
1.2 _+ 0 . 2
17.5_+3
1122
3317
Systematics (%) Inelastics (%)
Background (%)
No. of e v e n t s
et al., 1 985)
Experiment
K s --* 27r °
Background (%)
(Bernstein
Chicago-Saclay
Table 2b
KL --~ 27r °
No, o f e v e n t s
(Black et al., 1985)
BNL-Yale
Table 2a
L~J 0
I. Mannelli / CP violation in K decay
3 71
so-called miniperiods, i.e. sets of KL and Ks data takings, each one sufficient to give a value of ~'/e independently of any change of acceptance between miniperiods. Binning the events in momentum pK and decay vertex longitudinal position Zv, for small enough bins (10 GeV/c was used for pK and 1.2 m for Zv), the relative acceptances cancel out in the double ratio to better than 1%, so the ratio of the number of reconstructed events needs only a small Monte Carlo computed correction in order to represent the ratio of decay rates. The experimental set-up ~2 is sketched in Fig. 1, where transverse dimensions are enhanced by a factor of 50 relative to the longitudinal ones. The KL beam is produced by 450 GeV/c protons at 3.6 mrad. The KL intensity is such that in total about 105 decays (to any final state) occur per SPS pulse, Over the 120 m following the beginning of the useful decay region. Once collimated, 48 m after the production target, the neutral beam remains in vacuum up to the dump which follows the whole set-up. For Ks an attenuated proton beam is brought to a target, located on a train supporting
also
suitable
deflecting
magnets,
proton
beam
dump,
and
a Ks
beam-defining collimator, which can move in steps of 1.2 m over 48 m so as to imitate the flat KL longitudinal decay distribution. An anticoincidence counter, preceded by 7 mm of Pb, is normally inserted in the Ks beam to define precisely the beginning of the decay region. As shown in Fig. 2 the evacuated decay volume is terminated by a thin [4 x 10 -3 radiation lengths (r.l.)] Kevlar window and followed by a helium tank, at the plastic window\ an~ings "~
50 cm Ks/anti 0
anti-rings
j 0
DETECTOR
J
10 ,m vacuum
PROTONS
I I KL co[hmator
i
[~[
KL target KS
collimator I
SOm REGION
wire chamber 1
250 m
FIGURE 1 Overall schematic view of the NA31 experimental set-up
~r'Muon veto • Hadron CAL LA CAL
wire chamber 2
372
L Mannelli / CP violation in K decay
extremities of which are minidrift chambers to detect the trajectories of charged particles with 0.5 mm space resolution. The second set of chambers is followed by a suitably segmented scintillation-counter hodoscope. The basic detector for photons is a liquid-argon calorimeter which represents a major improvement with respect to previous experiments. Its total thickness is 27 r.l. The sampling is done in strips of 1.25 x 120 cm connected in such a way as to integrate the charge collected in the two halves of the calorimeter independently. The point of impact of a photon with energy greater than 5 GeV can be reconstructed to better than 0.5 ram. The measured energy resolution and linearity of response are shown in Figs. 3a and b. In order to get a well-timed pretrigger for neutral decays, a segmented plane of plastic scintillator is inserted between the two longitudinal halves of the calorimeter. Its output
is
read
out,
via
wavelength
shifters
and
light
guides,
by
external
photomultipliers; the scintillator and wavelength shifter work immersed in the liquid argon. The invariant mass M of a system of n photons--originating from a common vertex at a distance Z~ from the detector, at which the energy Ei and the transverse coordinates x~, y~ of each photon
are measured--is
given to
a very good
approximation, in our geometrical situation, by
K°- DETECTORPART ElectroCH 1
Counter 3
"'oom "el Net l'el Beam
k ~
1 ~.I,.,I~L
,'
.e
I
__
~
_
/%
Counter ~ CH 2 shower
Hadron Calorimeter
/
," / A
Muon
_
"\ "A /
/~
", X
/~
\ X /',\
\ .
- IL, m -25m !
~
J..__:j.~___ ..,. From collimator
~...,_.
-,m.-
"26m
_~,
___.___~_-5 4m
-28m
~
-3Z.rn
.,,.
_ _
~- TRIGGER HODOSCOPE ~+
TRIGGER COUNTERS
~o~o
FIGURE 2 The detector region of the NA31 set-up
.
373
I. Mannelli / CP violation in K decay
M = [ ~ Ei/Z~] [
with
Eixil~ Ei, 1
(x} =
1
Eixil~ Ei 1
1
and similarly for (y2> and (y). Assuming that a K decay into 27r° produced four detected photons, its longitudinal decay vertex position is obtained from 4
Z~ = [ ~ Eilmx] [ _ 2],/2. I
10.0 9.5
I
-
I
1
I
I
a)
Energy reso[ufion
9.0 8.5
+
8.0 ~'
I
+
7.5
....
7.0 6.5 6.0
I
0
20
I ~0
i 60
I 80
l 100
I 120
1L,0
Electron energy (GeV)
1.0
i
i
i
i
b) 0.5 I -
0
?T
~ -0.5 w -1.o
20
L0
6~
8'0
1~0 1~0
1~0
elecfron energy (GeV)
FIGURE 3 a) Measured energy resolution for electrons in the NA31 liquid-argon calorimeter, b) Linearity of calorimeter response
374
L Mannelli / CP violation in K decay
Figures 4a and b show the precision with which the beginning of the decay region, typically 120 m in front of the calorimeter, is reconstructed for 7r°Tr° and 7r+Tr- events. The curves are simple Monte Carlo predictions incorporating the measured resolution. It should be noticed that, for example, a shift of 0.8% in the absolute energy calibration of the calorimeter would result in a shift of 1 m in Zv. In fact, knowing the longitudinal geometry of the detector with about 1 cm accuracy, checking that the same position of the Ks anticounter is reconstructed from the neutral and from the charged decays, and that the transverse geometrical scale is the same for the chambers and the liquid-argon calorimeter, the momentum scale for p K as reconstructed for 7r°Tr° and 7r%r- (see later the method of measurement for 7r+Tr - , which depends essentially on geometry and known values of masses) can be fixed to better than 0.4 x 10 -3. As an illustration of the quality of the photon detection in this experiment, we have determined, from a sample of Ks -~ 27r° decays with a particularly good geometrical configuration and a photon energy in a restricted range, the ratio of the mass of the K ° to that of the 7r°.
3
.10 7
5
,10 7
a)
0 -2
I 0
b)
I 2
I 4-
~ 6
VERTEX DISTRIBUTION
I 8 KS ~ Pl0 P/0
I 10
I 12 METER
0 -2
t 0
t 2
I 4
VERTEX DISTRIBUTION
I 6
I B KS =~ PI+ P I -
L 10
I I 12 METER
FIGURE 4 Distribution of the distance of the reconstructed decay vertex from the position of the counter defining the beginning of the accepted decay region: a) for Ks --* ~r°Tr° and b) forKs -~ 7r+Tr-
375
I. Mannelli / CP violation in K decay
Taking m~o = 134.964 + 0 . 0 0 4 (Ref. 5) we find mKo = 4 9 7 . 5 6 _+ 0.01 (stat.) _+ 0.03 (syst.), to be compared with the present world average mKo = 4 9 7 . 7 2 _+ 0.07 (Ref. 5) which is due mostly to an e+e - ~ ~ --, KIK2 experiment 5. Of course, out of the three possible pairings of the four photons one can choose the one which is the best fit to the assumption that the photons come from 2~r°. Within the resolution of the system the invariant mass of the t w o pairs would coincide with the ~r° mass for true K -* 27r° decays. This appears to be precisely the case for Ks (Fig. 5). For KL the plot of the masses of t w o pairs shows some background (Fig. 6). The curves traced in the figure are elliptical rings of fixed area. The ratio of the axes of the ellipses is determined by the different
K° ~ / T ° / T ° 0-35M
;...::-.,-...;:',
;-., .;.'.~ .-:.~ .,,.':..:--.~
..;':.;.,..~:': ".;.... ::, : ...., .:..;..:~.:...~:. •
-/.:.':.'.,..;; ,.:::..:...:,-.:-' ::...:.. :.-.:.....-: :..¢.,;.-~.,?~....,..'...:-..~....:; o~6 :....~..:....: :.- !:.. ;..: ~::......"::'/"".",'::'.":" ;..i:::."' '.~,'"-"~'.':;,'.,~":"~ o ls
":': :"-': ":'"~i' ....:....,:...::-: :, "."..........:.~~.~...~ .',.:., .j. :.:
"':"~"'?'" "':" :':'"" "'" '" "*:" ..:-, .'., "'.':....: ;; y.:'.". :'. . ;. ;.:;.'.':;'.'.~:'.'~' ~ ., .....::...:....:: :: :.
•: ... ..... : -...~.. --%.: o.I,L :".'.'.~'".:.
.; ;,~.~ :' ...*.. -.
...: ~.:: :'...:.. ::"...'. ,
o iiii!i!ili! i! .J..'" ~ :~".;...
o
iiii!i!!i;:" 0.11
0.12
,. ,..,..-.~,.
:ilili!ii! .0.13
0.1~.
MPI01 .VS. MPI02
FIGURE 5 Lego plot for the invariant mass of the 23, pairs for Ks -4 7rOaro
". "~::'~"~;".'"
0.15
016
KL"~2PIO
FIGURE 6 Density distribution for KL --' ~r°Tr°, as a function of the mass of the 23, pairs
376
L Mannelli / CP violation in K decay
resolution in the sum and in the difference of the masses of the pairs, due to the constraint of the K mass imposed on the four photons. Except for the first rings, the population is almost exactly constant (Fig. 7a), a fact expected from Monte Carlo for KL ~ 37r° events for which two photons have escaped detection. The comparison with K s, where no such background is visible (Fig. 7b), and the flat dependence with respect to the number of the ring, allow for a precise background subtraction. It should be noticed in Fig. 8 that the background is a strong function of the distance of the decay vertex from the beginning of the KL decay region, which coincides with the end of the KL cleaning collimator. In fact, the reconstructed distance of the K decay vertex from the detector is equal to the true distance multiplied by the ratio of the invariant mass of the photons detected to the mass of the K. This is the reason for the shift in Zv for the background, which is of the order of 25 m for the case when one of the r°'s from KL ~ 37r° is missed by the detector. For the energy determination of the 7r+ and 7r-, the experiment again employs calorimetry rather than magnetic deflection. This improves the acceptance while, in the 70 to 1 70 GeV/c K momentum range used in the experiment, it is quite possible, as we
10 6
10 6
a)
b)
10 5
I0 5
__
iO 4
__
=
10 4
O.
I 2.5
f 5.
f 7,5
I 10.
I 12.5
I 15.
I 17.5
I 20.
--1 | O.
RING NO,
2.5
I 5.
I 7.5
I 10.
I 12.5
I 15.
I 17.5
I 20,
RING NO.
FIGURE 7
a) Number of events KL --* 43' as a function of the number of the elliptical ring in which they fall according to the values of the invariant mass of 23' pairs, b) Same for Ks -~ 4%
377
L Mannelli / CP violation in K decay
24
Bockground 11-°71.0 2O
16
12
}+++++
8
+4-+
+4-
÷÷+
4
+++÷ +
0
*+++++I+++++++++ 10
I
20
++ I
30
I
40 50 Z-decoy in meters
FIGURE 8 Dependence of the background from KL --* 3~r° decays on the distance of the decay vertex from the end of the Kr cleaning collimator
will show, to obtain good K momentum determination and background rejection. For this purpose the liquid-argon calorimeter is followed by an iron-plastic scintillator sampling calorimeter which, in conjunction with it, gives an energy resolution of = 65%/V-E (GeV) as shown in Fig. 9. The position of the decay vertex is found directly from extrapolation of the tracks in the chambers; the momentum of K is determined using the relation Px = (1 + 1/RE) [REm~-- (1 + RE)ZmZ~r]I/Z/0, where 0 is the angle between the two pions and RE is the ratio of the higher to the lower of the two pion energies. The above relation is remarkably accurate in our range of application. It is interesting to point out that px changes by only 5% when 1 < RE <
378
I. Mannelli / CP violation in K decay
1.0
I
I
I
I
I
÷
+
I
I
I
I
0.8
>=o.6
,+÷÷+
\
0.2
0
I
I
I
20
40
60
Energy
resolution
I
80 100 120 versus hadron energy (fieV)
I
1/,0
FIGURE 9 Energy resolution versus hadron energy for charged pions in the NA31 calorimetric measurement
5.6 and we in fact (also to reject A --* pTr- decays) only accept 1 < RE < 2.5. In this way the resolution in PK is typically 1%. In order to reject background it is necessary to compute the 7r+~r- invariant mass, using the calorimetric measured energy for each pion. Figure l Oa shows the Ks reconstructed mass. An analogue plot for KL, Fig. l o b , shows a very similar peak, with however a secondary peak at its left, interpreted as misidentified KL -* 7r%r-Tr° decays with the ~r° missed by the detector. In order to appreciate more generally the problem of backgrounds, Table 3 summarizes the size of the two-pion signal for KL and the main background sources, the importance of the latter relative to the signal, and the amount of background we finally had to subtract, after employing all rejection criteria that we found useful. These criteria give for both decay modes a rejection factor of about 5000. We have already briefly discussed the criteria used for subtraction of the background induced by KL -* 3 r °. For the charged decay modes we illustrate the main points in the following. For 7r+Tr-Tr°, with
both
photons from
the 7r° escaping the detector,
the
reconstructed invariant mass is too low to contribute to the accepted KL ~ r % r region. Occasionally one of the photons could, however, closely overlap with the r + or 7r- and be added to it, giving a higher invariant mass. The number of these events is estimated by looking at the photon density in events detected as 7r%r-3' and normally rejected. For K ~ rep decays, the rejection comes mostly from the fact that an electron produces a shower which is almost always fully absorbed in the 27 r.I. thick
379
I. Mannelli / CP violation in K decay
,lO 900 I" ~o
8
a)
b)
:~ 800
500
300
0
o'2
0',
5
0,4
o',
\
0.,
o
o'.2
0.3
0.4
o'~
0.6
FIGURE 10 a) Invariant mass distribution for 7r+Tr - pairs in Ks decays, b) Same in KL decays.
liquid-argon calorimeter. That rejection criteria, based only on shower development, still leave a small residue of electrons is shown in Figs. 11a and b, where we compare the distributions of the events for Ks and KL in the distance, dtarget, from the K production target to the reconstructed decay plane, suitably normalized to take into account the different extrapolation distances from the wire chambers to the Ks and KL targets. The rather flat tail for KL is interpreted as residual K -~ Trey, as supported by a detailed examination of the events and Monte Carlo simulation for the shape of the distribution. Looking at the distribution of large-dtarget events as a function of the distance Zv of the decay vertex from the end of the KL cleaning collimator (Fig. 1 2) a peak is seen at small Zv which, after detailed study, can be attributed to inelastic regeneration in the collimator itself. Although we can calculate, from this regenerated Ks, the number of scattered KL, which turns out to be negligible, we decided for this preliminary analysis simply to reject both 7r+Tr- and ~r°vr° decays with Zv < 10.5 m, because it is rather difficult to ensure the same dependence of the acceptance for the t w o decay modes as a function of the scattering angle. The decays K--* 7r#v are rejected, at trigger level, by the veto counters following the iron walls behind the calorimeters; at the reconstruction stage, they are rejected by the
380
L Mannelli / CP violation in K decay
Table 3 KL signal and background sources
Decay
Branching
Ratios
Background
modes
ratios
relative
to signal
tO
ratio
7rTr
(%) KL - ' 21r°
(%)
0.094 21.5
37r° KL ~ 7r+Tr ~ey q¢ + ~-- .A.0 ~ e v I,
230
0.203 38.7
190
27.1
130
12.4
61
1.3
6
-0
0.02
-0
4.4 x 10 -3
7r~*y
4
106
0.7 0.1
~10 6
a)
b)
105
105
10 4
10 4
10 3
10 3
10 2
10 2
L
d~ltarmeto torget
[cm]
distonce to tor~et
[cm]
FIGURE 1 1 a) Distribution of KL --* Ir + 7r- reconstructed events as a function of the distance,
dtarget,
of the K-production t a r g e t from the r e c o n s t r u c t e d d e c a y plane, b) S a m e for Ks --* ./i. + 71. -
I. Mannelli / CP violation in K decay
381
24
#.
Background ~+~-
+ +
+++ ÷**÷÷÷÷÷÷*÷**** 110
20 '
÷+÷
÷+~÷
2o
÷÷÷
&
÷÷÷~
,o
FIGURE 12 Distribution of large-dtar~et events as a function of the decay vertex distance from the end of the KL cleaning collimator
Z-relax in me'~or3
requirements on the energy ratio of the two tracks, on their invariant mass, and on other kinematical quantities. The background subtraction has been carried out bin by bin. The data analysed consist of 32 self-contained Ks and KL data sets, or miniperiods, during which the experimental set-up and running conditions were kept as stable as possible. The double ratio R of the final number was calculated miniperiod by miniperiod for each of 10 x 32 bins of pKand Zv, for 70 < PK < 170 GeV/c and 10.5 < Zv < 48.9 m. Given the measured resolution in p K and Zv, and the chosen bin sizes, the effects of the different beam sizes, different beam divergences, and momentum spectra between KL and Ks are such that the double ratio of the numbers of reconstructed events, as shown by Monte Carlo studies, cannot possibly differ by more than 1% from the double ratio of the rates of decay, implying a total Monte Carlo correction on ~'/E of -I x l O -3. About 2 0 0 , 0 0 0 KL -~ ~r°Tr°, IO~KL -~ 7r*Tr - , and 12 x 106Ks -* 27r, i.e. more than 20 times the integrated number of KL --* 7r°~r° events of all previous experiments, were collected in 1986 and a large fraction of them are used for the analysis. The high statistics allow us to study the dependence of the result on various parameters. As an illustration, the double ratio R is given in Figs. 13a, b, and c as a function of Z,, of pK, and of the chronological number of the miniperiods. Our work is still in progress regarding the degree of possible systematic distortions. Up to now we have evaluated, in a preliminary fashion, the differential effect on the four types of
382
L Mannelli / CP violation in K decay
o 1.2 P ~
1.1
L a) ,+,4..
1. I
"I~,,
T't'-l-t+ ,rt+
+I
+ ++ +÷ +I~ + +-I-~ + + +÷
0.9 0.8 0.7 0,6 I 15
0.5
I 20
I 25
J 30
I 4-0
35
DOUBLE RATIOVERSUS Z V
l 45 Z-ve~(ex [m]
o 1.2
b)
o ~0
3
1.1 1.
--I--
~
---t-
__~.
__~_
I
-I-
+
~-I-
0.9 0.8 0.7 0.6 ().5
I 8O
I 100
I 120
I 140
I 160 P K [OeV]
DOUBLE RATIOVERSUS HOMENTUM
o 1.2 o
.~ 1.1 1.
,,,, ~..I 1 ÷
+~ +.~ ' ,~,~ ÷+÷++ +÷÷+ ' '÷~ 'T'~
T~IT 0.9 0.8 0.7 0.6 0:5
I 12
l 16
I 20
I 24
DOUBLE RATIOVERSUS TIME
I 28
I 32
36 time
FIGURE 1 3 a) Double ratio: [N(KL -~ 21r°)/N(KL -* ~ + ~ - ) ] / [ N ( K s -~ 21r°)/N(Ks -~ 7 r + ~ - ) ] as a function of decay vertex position; b) S a m e as a function of momentum; c) S a m e as a function of time.
L Mannelli / CP violation in K decay
383
events selected due to all sources we could think to be relevant. The most important of them are briefly described below:
a)
Trigger efficiency By looking at a sample of events recorded with a much looser trigger requirement
than the standard one, we have continuously monitored the trigger efficiency and found it to be, on an average: in the 2~ ° mode, (99.87 ± 0 . 2 5 ) % for the KL trigger and (99.76 ± 0 . 0 4 ) % for the Ks one; in the r + ~ - mode, (100 ± 0 . 0 0 8 ) % for the KL trigger and (99.99 ± 0 . 0 0 3 ) % for the Ks one. This implies ~R = (0.11 ± 0 . 2 7 ) % for the double ratio.
b)
Event losses by accidental events By overlapping with normal events the content of events taken in correspondence
with a random trigger, adjusted to occur during the burst at a frequency proportional to the instantaneous beam intensity, we have determined the fraction of events which have been lost because of the disturbance induced by an accidental event. We have decided, for the moment, to apply no correction and to assign an error on R of 0 . 5 % (0.8 x 10 -3 on e'/~), i.e. 2.5 times the statistical uncertainty of the effect measured, to cover possible imperfections of the method. We have also other ways of studying the effect of accidentals, because for each event we have recorded the instantaneous beam intensity and the time history, in 64 time slices of 50 ns each, centred around the time of occurrence of the event, for 96 channels comprising all relevant detector elements.
c)
Relative energy scale for T+x - and 7r°Tr° This could, in principle be an important effect, but a good understanding of the
geometry allows sufficient precision to be achieved.
d)
Uncertainty in background subtraction The largest background subtracted is in KL - ' 2 r °, where it amounts to 4%. The
procedure to estimate it is, however, straightforward and we estimate that we have determined it to an accuracy o f ± 5%. The subtraction of the background for 7r+;r- is much smaller (0.7%), but only k n o w n with 50% uncertainty. The summary of the systematic uncertainties and our present result for e'/~ are given in Table 4 and s h o w n in Fig. 14. In Fig. 14, in addition to comparing our results with all previous determinations, we indicate 13 the most recent best guess on the value of ~'/E as (2 ± 1) × 10 -3, according to the Standard Model. Combining
quadratically the statistical error with the present limit on the
systematic uncertainties, the result for ~'/~ is 2.5 standard deviations from zero. Given
384
L Mannelli / CP violation in K decay
Table 4 Summary of systematic uncertainties
2~ °
7 r + ,/l- -
Ks/KL
Ks
energy scale
+ 0 . 4 x 10 -3
background
+ 0 . 3 x 10-3
stability Ks/KL
± 0 . 4 x 10 -3
background
_+0.6 x 10-3
beam divergence accidentals
+0.1 x 10-3 + 0 . 8 x 10-3
scattering
_+0.2 x 10 -3
anticounter inefficiency
+0.1 x 10-3
Total systematic error
_ 1.2 x 10 .3
Preliminary result
~'/~ = (3.5 _ 0.7 _+ 0.4 ___ 1.2)
statistical error Monte Carlo statistical error systematic error x 10 -~
this result we plan, in addition to completing in its final form the analysis of the present data, to apply for a new SPS run in 1988 with improvement to the experimental equipment, in particular to the veto coverage close to the beam pipe, a better KL cleaning collimator system, and additional electron identification. We plan also to take data in a wider range of instantaneous intensities and to introduce some refinements in monitoring and data-taking procedure. At present we are running in order to measure arg ~/o0 - arg ~/+ _ with a projected accuracy of - 1 o Concerning future developments in this field by other groups, the E731 experiment is running already with an improved, higher-acceptance detector, in a beam with better KL/neutron ratio, with an 'active' regenerator, a faster and more selective dataacquisition system, and finally with better calibration and resolution for the Pb-glass calorimeter. It is conceivable that ultimately a precision of 1 x 100,000 KL -* 27r°, will be reached.
10 -3 on ~'/E, with
385
L Mannelli / CP violation in K decay
103 Rec'/¢
Holder et al 72 Banner et al 72 Christenson et al 79
15 -
Black et al 85 10
-
E731 (preliminary) I 5
. . ~ A 3 1 (preliminaryl
"--z'--+ (3.5 -~ 1.4) x 10-3 I
0
,T_
/
I
,
"S'I'ANDARD HODEL" L.P. SYHPOSIUH 198'/
-,5
Bernsfein ef al 85 -10
-
FIGURE 14 Present preliminary result of the NA31 experiment for e'/~. In the error indicated, we have combined quadratically statistical and systematic errors.
An experiment (PS 195) based on quite different principles is in preparation at the CERN Low-Energy Ant(proton Ring (LEAR) ~4. It is aimed at an accuracy of 1.5 x 10 -3 for c '/e, while detecting CP-violation effects in other channels such as K -4 23, and K 3~r, and checking various aspects of discrete symmetries. By detecting the sign of the charged kaon produced in association with a neutral one in ant(proton-proton annihilations at rest, pp-~ K+~r-K°
and
pp-* K-Tr+K °,
the strangeness at t = 0 of the neutral K is determined and, for instance, an integrated asymmetry can be defined from the probability of an initial K° and ~ decaying into 2~r within a time interval to:
to
tO
to
tO
+ 0
For to >- 20Ts
0
0
0
386
L Mannelli / CP violation in K decay
A+_ = 2 R e ~ + 4 R e e ' , Aoo = 2 R e ~ -
8Re~',
from which we get ~'/c = [1 - (Ao0/A+-)]16. More than 109 K --* ~r°Tr° decays will have to be collected to reach the required statistical accuracy, and a good fraction of the events will have to be analysed in detail to check sources of systematic distortion. A recent Letter of Intent has been submitted at Brookhaven (No. 749) by the BNL-Yale Collaboration, which needs a primary proton beam of such intensity that will only become available with the future AGS Booster. The neutral K beam would be produced by charge exchange from a charged K beam and the coherent mixture of KL and Ks could be altered, with hopefully no effect on the detecting apparatus, in such a w a y as to enhance or reduce the normal K2 component of KL and hence the ratio of 7r°Tr° to lr+~r - decays in case ~'/~ is different from zero. The sensitivity is again estimated to be 1 x 10 -3. In conclusion, the present experiment and those which will give results in the next few years may reasonably be expected to definitely settle the question of the existence of direct CP violation in weak interactions, according to the Standard Model.
387
L Mannelli / CP violation in K decay
REFERENCES 1) J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Phys. Rev. Lett. 13 (1964) 138. 2) See, for example, V.L. Fitch, Rev. Mod. Phys. 53 (1981) 367; J.W. Cronin, Rev. Mod. Phys. 53 (1981) 373; L. Wolfenstein, Annu. Rev. Nucl. Part. Sci. (1986). 3) A. Sakharov, Zh. Exp. Teor. Fiz. Pis'ma v Red. 5 (1967) 32 [Transl.: JETP Lett. 5 (1967) 24]. 4) L. Wolfenstein, Phys. Rev. Lett. 13 (1964) 569. 5) Review of Particle Properties, Phys. Lett. 170B (1986) 1. 6) V.V. Barmin et al., Nucl. Phys. 247B (1984) 293. 7) M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49 (1973) 652. 8) C. Albajar et al., Phys. Lett. 186B (1987) 247. 9) H. Albrecht et al., Phys. Lett. 192B (1987) 245. 10) M. Holder et al., Phys. Lett. 40B (1972) 141. M. Banner et al., Phys. Rev. Lett. 28 (1972) 1597. J.A. Christenson et al., Phys. Rev. Lett. 43 (1979) 1209. J.K. Black et al., Phys. Rev. Lett. 54 (1985) 1628. R.H. Bernstein et al., Phys. Rev. Lett. 54 (1985) 1631. 11 ) B. Winstein, CP and other tests of the Standard Model, to appear in Proc. APS-DPF Meeting, Salt Lake City, January 1987. 12) H. Burkhardt et al., The beam and detector for a high energy measurement of CP violation in neutral kaon decays, CERN-EP/87-166 (1987) submitted to Nucl. Instrum. Methods. 13) M. Shifman, Theoretical status of weak decays, Report to this Symposium. 14) L. Adiels et al., Test of CP violation with K° and ~ CERN/PSCC/85-6, January 1985.
at LEAR, Proposal
388
I. Mannelli / CP violation in K decay
DISCUSSION
J.A. Thompson, Univ. of Pittsburgh You mentioned that K L -~ ~0~07r0 was the main source of background for K L -~ ~0~0 (4%). What were the main background sources in the decay KL _, ~+~-, KS _~ ~0~0, KS _, n+n-, and how large were they ? Answer: For the K L -* ~+~-, the main background were again 3-body decays, which were detected by observing the distance of the K 0 production target from the decay plane. Their relative importance is shown in table 3. For K S decay the backgrounds were small, mostly connected with scattering from the lips of the collimator and the K S anti counter material
367
CP VIOLATION IN K DECAY
Italo MANNELLI NA31 Collaboration *), CERN, Geneva, Switzerland, and Dipartimento di Fisica, Universit~ di Pisa and INFN Sezione di Pisa, Pisa, Italy
Since the original discovery ] in 1964 that both Ks and KL decay into 7r%r-, which represents clear evidence for CP violation, the challenge has been to devise experiments and theoretical models that could elucidate the nature of this phenomenon and its source. A number of implications have been analysed2: for example, it was pointed out in 19673 that CP violation, combined with a very small baryon instability, could have produced, in the early explosive development of the Universe, the matter-antimatter imbalance as manifested today by the measured ratio = 109.
Nbaryons/Nphotons
Despite intensive research efforts, no CP-violation effects have been detected outside the neutral K system. In addition to the two-pion channel, CP violation is detected in the charge asymmetry of semileptonic KL decays. All results appear to be consistent with CPT invariance and what is clearly demonstrated is that in K ° --, ~o mixing the amplitude for the transition K ° -~ ~o is different from the amplitude for the time-reversed transition ~o ~ K 0. The superweak model 4, linking CP violation to ]ASl = 2 transitions, is empirically still valid 5. In this model, the KL decay to two pions is due only to the impurity c of the eigenstate Kt with CP = + in the composition of the KL = (K= + 6K1).(1 + Id2) -1/2 itself (K2 is the eigenstate with CP = - ) , and A0 and A2, the amplitudes for K° to decay to two pions in isotopic spin I = 0 and I = 2 respectively, are relatively real. The ratios of the amplitudes for KL and Ks decay to two pions *) The members of the NA31 Collaboration are: CERN: H. Burkbardt, P. Clarke, D. Coward, D. Cundy, V. Gibson, N. Doble, L. Gatignon, R. Hagelberg, G. Kesseler, J. van der Lans, T. Miczaika, H.G. Sander, A.C. Shaffer, P. Steffen, J. Steinberger, H. Taureg, H. Wahl, C. Youngman; Dortmund: G. Dietrich, F. Eisele, W. Heinen; Edinburgh: R. Black, D.J. Candlin, J. Muir, K.J. Peach, B. Pijlgroms, I. Shipsey, B. Stephenson; Mainz: H. Blfimer, M. Kasemann, K. Kleinknecht, B. Panzer, B. Renk, S. R6hn; Orsay: E. Auge, R.L. Chase, M. Corti, L. Iconomidou-Fayard, D. Fournier, P. Heusse, A.M. Lutz; Pisa: L. Bertanza, A. Bigi, M. Calvetti, M. Carosi, R. Casali, C. Cerri, R. Fantechi, S. Galeotti, I. Mannelli, E. Massa, A. Nappi, D. Passuello, G. Pierazzini; Siegen: C. Becker, D. Heyland, M. Holder, G. Quast, M. Rost, W. Weihs, G. Zech. Their dedication and hard work has made possible the performance of the experiment, the results of which on e'/e are reported here for the first time. 0920-5632/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
368
L Mannelli / CP violation in K decay
T/+_ = (Tr%r-lTIKL)/(Ir+r-ITlKs)
= ~
and
~/oo = (Tr°Tr°lTIKL)/(r°~r°lTlKs/ =
are hence both equal to ~, and ~/+ _ hloo = 1. The phase of ~ is fixed by the mass and total decay rate of Ks and KL: arg (~) = tan -~ 2(mL -- ms)/(Vs - VL) = 4 3 . 7 °. In the more general case, w h e r e CP-violating amplitudes could be present in the K t w o - p i o n decay, to a good a p p r o x i m a t i o n T/oo=~-
2~' ,
r/+_ = ~ + ~ '
w i t h ~' = i/~f2 Im (A2/Ao) exp [i(62 - 60)], w h e r e (50 and 62 are the ~rTr phase shifts for I = 0andl
= 2, a t ~ / s = mK. Experimentally, 62 - 6o = - 5 3
_+ 5 ° and h e n c e a r g (~') =
62 - 6o + lr/2 = 3 7 _+ 5 °. Therefore taking ~' and ~ as relatively real and for le'/~l ~ 1 Ir/ooh/+ -12 = 1 - 6E'/~ w i t h *) arg ~/+ _ - arg ~/0o. It w a s first realized in 1 9737 t h a t it is possible to incorporate CP violation into the standard e l e c t r o w e a k gauge t h e o r y if three generations of quarks exist, as n o w appears very plausible. From this point of v i e w only an accidental cancellation could produce Also CP-violation p h e n o m e n a could be e x p e c t e d in cases similar to the neutral K, in particular for the neutral B mesons, for w h i c h B ° --* ~o mixing, a prerequisite for CP violation, has recently been observed by the UA1 Collaboration at the CERN Collider s and by A R G U S at DORIS 9. The results of the first a t t e m p t s to measure f~/oo/~+-I are reported in Table 1 t o g e t h e r w i t h more accurate results published in 19851°. The main features of the 1 9 8 5 e x p e r i m e n t s are summarized in Table 2. M o r e recently ]~ the C h i c a g o - F e r m i l a b - P r i n c e t o n - S a c l a y
Collaboration (experiment
E731 at Fermilab) have given a preliminary result, ~'/~ = 0 . 0 0 3 5 + 0 . 0 0 3 (stat.) + 0 . 0 0 2 (syst.), based on a sample of 6 7 3 8 27r° decays, obtained from an improved set-up at Fermilab w h i c h is ultimately e x p e c t e d to yield some 1 0 0 , 0 0 0 27r° decays and reach an a c c u r a c y of + 1 x 10-3 for ~'l~. A t CERN the N A 3 1 e x p e r i m e n t has n o w produced its first result,
*) The experimental value for arg ~/oo - arg 7/+_ = 9.8 ° + 5 . 4 ° is 2 standard deviations from zero 5. A difference from zero w o u l d imply CPT non-invariance 6.
369
L Mannelli / CP violation in K decay
~'/~ = (3.5 + 1.4) x 10 -3,
and most of the remainder of this paper will be concerned with this experiment. The principle is to measure
e'/e = (1 - R)/6, where R is the double ratio of the decay rates R = [r(KL --*
2~r°)/r(KL -* 7r+lr-)]/[r(Ks --* 2~r°)/r(Ks -* ~r%r-)].
Charged and neutral decays are detected at the same time, alternatively for KL and Ks. Switching from KL to Ks was done with a periodicity of about a day. The overall stability of the detection system was checked in several ways. In particular, the ratio of charged to neutral decays for Ks changed by less than _ 1.5% over a time equal to 20
Table 1 Measurements of ~'/~ = [1 -
(In0o/n+-12)]/6
Year
Authors
l~/ooh/+ -I
1972
Holder et al.
1.00 + 0 . 0 6
1972
Banner et al.
1.03 + 0 . 0 7
1979
Christenson et al.
1.00 + 0 . 0 9
Average
1.01 + 0 . 0 4 R = 17/ooh/+-I2 = 1.02 + 0 . 0 8
Year
Authors
1985
Black et al.
1985
Bernstein et al.
Average
e'/e 0.002 + 0.007 + 0.004 -0.005
+ 0.005 + 0.002
-0.003
_+ 0 . 0 0 5
R = I~oo/~+_12 = 1.015 _+ 0 . 0 3
Experiment
0 . 2 % of Ks --' 7r÷Tr
Incoherent Ks: 1.5 _+ 0 . 5 % o f Ks ~ 27r°
KL semileptonic d e c a y s
n interactions in He
KL ~ 37r° ~ 63'
12 = R = 0 . 9 9 0 _+ 0 . 0 4 3 +_ 0 . 0 2 6
Backgrounds:
t~oo/n+
Main s y s t e m a t i c s :
_+0.2
f o r 7r+ ;r
a c c e p t a n c e c o r r e c t i o n (KL u p s t r e a m o f Ks regenerator)
inelastic r e g e n e r a t i o n of Ks
u n c e r t a i n t i e s in b a c k g r o u n d (KL -~ 37r°, n interaction)
_+1.3
_+0.5 f o r 27r°
+_ 0 . 0 0 5 3 +_ 0 . 0 0 2 4
KL/Ks
R = 1 . 0 2 8 + 0 . 0 3 2 _+ 0 . 0 1 4
~'/E = - 0 . 0 0 4 6
error
correction
Total systematic
Acceptance
_+0.1 1.7 _+ 0.1 0.2
25751
K s -* ~+Tr-
20960
Ks --* lr+Tr -
~'/E = 0 . 0 0 1 7 _+ 0 . 0 0 8 2
_+1.0 _+0.2
0.4_+0.1 3.1 _+ 0 . 2
10638
KL --~ 7r+~ -
2.0_+1
8506
0.6_+0.1
5663
KL --} 7r+Tr -
_+0.6 2 . 9 _+ 0 . 3
8 . 4 _+ 0 . 4
3152
1 4 . 9 _+ 0 . 5
KL --~ 27r°
Ks --* 27r °
1.2 _+ 0 . 2
17.5_+3
1122
3317
Systematics (%) Inelastics (%)
Background (%)
No. of e v e n t s
et al., 1 985)
Experiment
K s --* 27r °
Background (%)
(Bernstein
Chicago-Saclay
Table 2b
KL --~ 27r °
No, o f e v e n t s
(Black et al., 1985)
BNL-Yale
Table 2a
L~J 0
I. Mannelli / CP violation in K decay
3 71
so-called miniperiods, i.e. sets of KL and Ks data takings, each one sufficient to give a value of ~'/e independently of any change of acceptance between miniperiods. Binning the events in momentum pK and decay vertex longitudinal position Zv, for small enough bins (10 GeV/c was used for pK and 1.2 m for Zv), the relative acceptances cancel out in the double ratio to better than 1%, so the ratio of the number of reconstructed events needs only a small Monte Carlo computed correction in order to represent the ratio of decay rates. The experimental set-up ~2 is sketched in Fig. 1, where transverse dimensions are enhanced by a factor of 50 relative to the longitudinal ones. The KL beam is produced by 450 GeV/c protons at 3.6 mrad. The KL intensity is such that in total about 105 decays (to any final state) occur per SPS pulse, Over the 120 m following the beginning of the useful decay region. Once collimated, 48 m after the production target, the neutral beam remains in vacuum up to the dump which follows the whole set-up. For Ks an attenuated proton beam is brought to a target, located on a train supporting
also
suitable
deflecting
magnets,
proton
beam
dump,
and
a Ks
beam-defining collimator, which can move in steps of 1.2 m over 48 m so as to imitate the flat KL longitudinal decay distribution. An anticoincidence counter, preceded by 7 mm of Pb, is normally inserted in the Ks beam to define precisely the beginning of the decay region. As shown in Fig. 2 the evacuated decay volume is terminated by a thin [4 x 10 -3 radiation lengths (r.l.)] Kevlar window and followed by a helium tank, at the plastic window\ an~ings "~
50 cm Ks/anti 0
anti-rings
j 0
DETECTOR
J
10 ,m vacuum
PROTONS
I I KL co[hmator
i
[~[
KL target KS
collimator I
SOm REGION
wire chamber 1
250 m
FIGURE 1 Overall schematic view of the NA31 experimental set-up
~r'Muon veto • Hadron CAL LA CAL
wire chamber 2
372
L Mannelli / CP violation in K decay
extremities of which are minidrift chambers to detect the trajectories of charged particles with 0.5 mm space resolution. The second set of chambers is followed by a suitably segmented scintillation-counter hodoscope. The basic detector for photons is a liquid-argon calorimeter which represents a major improvement with respect to previous experiments. Its total thickness is 27 r.l. The sampling is done in strips of 1.25 x 120 cm connected in such a way as to integrate the charge collected in the two halves of the calorimeter independently. The point of impact of a photon with energy greater than 5 GeV can be reconstructed to better than 0.5 ram. The measured energy resolution and linearity of response are shown in Figs. 3a and b. In order to get a well-timed pretrigger for neutral decays, a segmented plane of plastic scintillator is inserted between the two longitudinal halves of the calorimeter. Its output
is
read
out,
via
wavelength
shifters
and
light
guides,
by
external
photomultipliers; the scintillator and wavelength shifter work immersed in the liquid argon. The invariant mass M of a system of n photons--originating from a common vertex at a distance Z~ from the detector, at which the energy Ei and the transverse coordinates x~, y~ of each photon
are measured--is
given to
a very good
approximation, in our geometrical situation, by
K°- DETECTORPART ElectroCH 1
Counter 3
"'oom "el Net l'el Beam
k ~
1 ~.I,.,I~L
,'
.e
I
__
~
_
/%
Counter ~ CH 2 shower
Hadron Calorimeter
/
," / A
Muon
_
"\ "A /
/~
", X
/~
\ X /',\
\ .
- IL, m -25m !
~
J..__:j.~___ ..,. From collimator
~...,_.
-,m.-
"26m
_~,
___.___~_-5 4m
-28m
~
-3Z.rn
.,,.
_ _
~- TRIGGER HODOSCOPE ~+
TRIGGER COUNTERS
~o~o
FIGURE 2 The detector region of the NA31 set-up
.
373
I. Mannelli / CP violation in K decay
M = [ ~ Ei/Z~] [
with
Eixil~ Ei, 1
(x} =
1
Eixil~ Ei 1
1
and similarly for (y2> and (y). Assuming that a K decay into 27r° produced four detected photons, its longitudinal decay vertex position is obtained from 4
Z~ = [ ~ Eilmx] [
10.0 9.5
I
-
I
1
I
I
a)
Energy reso[ufion
9.0 8.5
+
8.0 ~'
I
+
7.5
....
7.0 6.5 6.0
I
0
20
I ~0
i 60
I 80
l 100
I 120
1L,0
Electron energy (GeV)
1.0
i
i
i
i
b) 0.5 I -
0
?T
~ -0.5 w -1.o
20
L0
6~
8'0
1~0 1~0
1~0
elecfron energy (GeV)
FIGURE 3 a) Measured energy resolution for electrons in the NA31 liquid-argon calorimeter, b) Linearity of calorimeter response
374
L Mannelli / CP violation in K decay
Figures 4a and b show the precision with which the beginning of the decay region, typically 120 m in front of the calorimeter, is reconstructed for 7r°Tr° and 7r+Tr- events. The curves are simple Monte Carlo predictions incorporating the measured resolution. It should be noticed that, for example, a shift of 0.8% in the absolute energy calibration of the calorimeter would result in a shift of 1 m in Zv. In fact, knowing the longitudinal geometry of the detector with about 1 cm accuracy, checking that the same position of the Ks anticounter is reconstructed from the neutral and from the charged decays, and that the transverse geometrical scale is the same for the chambers and the liquid-argon calorimeter, the momentum scale for p K as reconstructed for 7r°Tr° and 7r%r- (see later the method of measurement for 7r+Tr - , which depends essentially on geometry and known values of masses) can be fixed to better than 0.4 x 10 -3. As an illustration of the quality of the photon detection in this experiment, we have determined, from a sample of Ks -~ 27r° decays with a particularly good geometrical configuration and a photon energy in a restricted range, the ratio of the mass of the K ° to that of the 7r°.
3
.10 7
5
,10 7
a)
0 -2
I 0
b)
I 2
I 4-
~ 6
VERTEX DISTRIBUTION
I 8 KS ~ Pl0 P/0
I 10
I 12 METER
0 -2
t 0
t 2
I 4
VERTEX DISTRIBUTION
I 6
I B KS =~ PI+ P I -
L 10
I I 12 METER
FIGURE 4 Distribution of the distance of the reconstructed decay vertex from the position of the counter defining the beginning of the accepted decay region: a) for Ks --* ~r°Tr° and b) forKs -~ 7r+Tr-
375
I. Mannelli / CP violation in K decay
Taking m~o = 134.964 + 0 . 0 0 4 (Ref. 5) we find mKo = 4 9 7 . 5 6 _+ 0.01 (stat.) _+ 0.03 (syst.), to be compared with the present world average mKo = 4 9 7 . 7 2 _+ 0.07 (Ref. 5) which is due mostly to an e+e - ~ ~ --, KIK2 experiment 5. Of course, out of the three possible pairings of the four photons one can choose the one which is the best fit to the assumption that the photons come from 2~r°. Within the resolution of the system the invariant mass of the t w o pairs would coincide with the ~r° mass for true K -* 27r° decays. This appears to be precisely the case for Ks (Fig. 5). For KL the plot of the masses of t w o pairs shows some background (Fig. 6). The curves traced in the figure are elliptical rings of fixed area. The ratio of the axes of the ellipses is determined by the different
K° ~ / T ° / T ° 0-35M
;...::-.,-...;:',
;-., .;.'.~ .-:.~ .,,.':..:--.~
..;':.;.,..~:': ".;.... ::, : ...., .:..;..:~.:...~:. •
-/.:.':.'.,..;; ,.:::..:...:,-.:-' ::...:.. :.-.:.....-: :..¢.,;.-~.,?~....,..'...:-..~....:; o~6 :....~..:....: :.- !:.. ;..: ~::......"::'/"".",'::'.":" ;..i:::."' '.~,'"-"~'.':;,'.,~":"~ o ls
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.; ;,~.~ :' ...*.. -.
...: ~.:: :'...:.. ::"...'. ,
o iiii!i!ili! i! .J..'" ~ :~".;...
o
iiii!i!!i;:" 0.11
0.12
,. ,..,..-.~,.
:ilili!ii! .0.13
0.1~.
MPI01 .VS. MPI02
FIGURE 5 Lego plot for the invariant mass of the 23, pairs for Ks -4 7rOaro
". "~::'~"~;".'"
0.15
016
KL"~2PIO
FIGURE 6 Density distribution for KL --' ~r°Tr°, as a function of the mass of the 23, pairs
376
L Mannelli / CP violation in K decay
resolution in the sum and in the difference of the masses of the pairs, due to the constraint of the K mass imposed on the four photons. Except for the first rings, the population is almost exactly constant (Fig. 7a), a fact expected from Monte Carlo for KL ~ 37r° events for which two photons have escaped detection. The comparison with K s, where no such background is visible (Fig. 7b), and the flat dependence with respect to the number of the ring, allow for a precise background subtraction. It should be noticed in Fig. 8 that the background is a strong function of the distance of the decay vertex from the beginning of the KL decay region, which coincides with the end of the KL cleaning collimator. In fact, the reconstructed distance of the K decay vertex from the detector is equal to the true distance multiplied by the ratio of the invariant mass of the photons detected to the mass of the K. This is the reason for the shift in Zv for the background, which is of the order of 25 m for the case when one of the r°'s from KL ~ 37r° is missed by the detector. For the energy determination of the 7r+ and 7r-, the experiment again employs calorimetry rather than magnetic deflection. This improves the acceptance while, in the 70 to 1 70 GeV/c K momentum range used in the experiment, it is quite possible, as we
10 6
10 6
a)
b)
10 5
I0 5
__
iO 4
__
=
10 4
O.
I 2.5
f 5.
f 7,5
I 10.
I 12.5
I 15.
I 17.5
I 20.
--1 | O.
RING NO,
2.5
I 5.
I 7.5
I 10.
I 12.5
I 15.
I 17.5
I 20,
RING NO.
FIGURE 7
a) Number of events KL --* 43' as a function of the number of the elliptical ring in which they fall according to the values of the invariant mass of 23' pairs, b) Same for Ks -~ 4%
377
L Mannelli / CP violation in K decay
24
Bockground 11-°71.0 2O
16
12
}+++++
8
+4-+
+4-
÷÷+
4
+++÷ +
0
*+++++I+++++++++ 10
I
20
++ I
30
I
40 50 Z-decoy in meters
FIGURE 8 Dependence of the background from KL --* 3~r° decays on the distance of the decay vertex from the end of the Kr cleaning collimator
will show, to obtain good K momentum determination and background rejection. For this purpose the liquid-argon calorimeter is followed by an iron-plastic scintillator sampling calorimeter which, in conjunction with it, gives an energy resolution of = 65%/V-E (GeV) as shown in Fig. 9. The position of the decay vertex is found directly from extrapolation of the tracks in the chambers; the momentum of K is determined using the relation Px = (1 + 1/RE) [REm~-- (1 + RE)ZmZ~r]I/Z/0, where 0 is the angle between the two pions and RE is the ratio of the higher to the lower of the two pion energies. The above relation is remarkably accurate in our range of application. It is interesting to point out that px changes by only 5% when 1 < RE <
378
I. Mannelli / CP violation in K decay
1.0
I
I
I
I
I
÷
+
I
I
I
I
0.8
>=o.6
,+÷÷+
\
0.2
0
I
I
I
20
40
60
Energy
resolution
I
80 100 120 versus hadron energy (fieV)
I
1/,0
FIGURE 9 Energy resolution versus hadron energy for charged pions in the NA31 calorimetric measurement
5.6 and we in fact (also to reject A --* pTr- decays) only accept 1 < RE < 2.5. In this way the resolution in PK is typically 1%. In order to reject background it is necessary to compute the 7r+~r- invariant mass, using the calorimetric measured energy for each pion. Figure l Oa shows the Ks reconstructed mass. An analogue plot for KL, Fig. l o b , shows a very similar peak, with however a secondary peak at its left, interpreted as misidentified KL -* 7r%r-Tr° decays with the ~r° missed by the detector. In order to appreciate more generally the problem of backgrounds, Table 3 summarizes the size of the two-pion signal for KL and the main background sources, the importance of the latter relative to the signal, and the amount of background we finally had to subtract, after employing all rejection criteria that we found useful. These criteria give for both decay modes a rejection factor of about 5000. We have already briefly discussed the criteria used for subtraction of the background induced by KL -* 3 r °. For the charged decay modes we illustrate the main points in the following. For 7r+Tr-Tr°, with
both
photons from
the 7r° escaping the detector,
the
reconstructed invariant mass is too low to contribute to the accepted KL ~ r % r region. Occasionally one of the photons could, however, closely overlap with the r + or 7r- and be added to it, giving a higher invariant mass. The number of these events is estimated by looking at the photon density in events detected as 7r%r-3' and normally rejected. For K ~ rep decays, the rejection comes mostly from the fact that an electron produces a shower which is almost always fully absorbed in the 27 r.I. thick
379
I. Mannelli / CP violation in K decay
,lO 900 I" ~o
8
a)
b)
:~ 800
500
300
0
o'2
0',
5
0,4
o',
\
0.,
o
o'.2
0.3
0.4
o'~
0.6
FIGURE 10 a) Invariant mass distribution for 7r+Tr - pairs in Ks decays, b) Same in KL decays.
liquid-argon calorimeter. That rejection criteria, based only on shower development, still leave a small residue of electrons is shown in Figs. 11a and b, where we compare the distributions of the events for Ks and KL in the distance, dtarget, from the K production target to the reconstructed decay plane, suitably normalized to take into account the different extrapolation distances from the wire chambers to the Ks and KL targets. The rather flat tail for KL is interpreted as residual K -~ Trey, as supported by a detailed examination of the events and Monte Carlo simulation for the shape of the distribution. Looking at the distribution of large-dtarget events as a function of the distance Zv of the decay vertex from the end of the KL cleaning collimator (Fig. 1 2) a peak is seen at small Zv which, after detailed study, can be attributed to inelastic regeneration in the collimator itself. Although we can calculate, from this regenerated Ks, the number of scattered KL, which turns out to be negligible, we decided for this preliminary analysis simply to reject both 7r+Tr- and ~r°vr° decays with Zv < 10.5 m, because it is rather difficult to ensure the same dependence of the acceptance for the t w o decay modes as a function of the scattering angle. The decays K--* 7r#v are rejected, at trigger level, by the veto counters following the iron walls behind the calorimeters; at the reconstruction stage, they are rejected by the
380
L Mannelli / CP violation in K decay
Table 3 KL signal and background sources
Decay
Branching
Ratios
Background
modes
ratios
relative
to signal
tO
ratio
7rTr
(%) KL - ' 21r°
(%)
0.094 21.5
37r° KL ~ 7r+Tr ~ey q¢ + ~-- .A.0 ~ e v I,
230
0.203 38.7
190
27.1
130
12.4
61
1.3
6
-0
0.02
-0
4.4 x 10 -3
7r~*y
4
106
0.7 0.1
~10 6
a)
b)
105
105
10 4
10 4
10 3
10 3
10 2
10 2
L
d~ltarmeto torget
[cm]
distonce to tor~et
[cm]
FIGURE 1 1 a) Distribution of KL --* Ir + 7r- reconstructed events as a function of the distance,
dtarget,
of the K-production t a r g e t from the r e c o n s t r u c t e d d e c a y plane, b) S a m e for Ks --* ./i. + 71. -
I. Mannelli / CP violation in K decay
381
24
#.
Background ~+~-
+ +
+++ ÷**÷÷÷÷÷÷*÷**** 110
20 '
÷+÷
÷+~÷
2o
÷÷÷
&
÷÷÷~
,o
FIGURE 12 Distribution of large-dtar~et events as a function of the decay vertex distance from the end of the KL cleaning collimator
Z-relax in me'~or3
requirements on the energy ratio of the two tracks, on their invariant mass, and on other kinematical quantities. The background subtraction has been carried out bin by bin. The data analysed consist of 32 self-contained Ks and KL data sets, or miniperiods, during which the experimental set-up and running conditions were kept as stable as possible. The double ratio R of the final number was calculated miniperiod by miniperiod for each of 10 x 32 bins of pKand Zv, for 70 < PK < 170 GeV/c and 10.5 < Zv < 48.9 m. Given the measured resolution in p K and Zv, and the chosen bin sizes, the effects of the different beam sizes, different beam divergences, and momentum spectra between KL and Ks are such that the double ratio of the numbers of reconstructed events, as shown by Monte Carlo studies, cannot possibly differ by more than 1% from the double ratio of the rates of decay, implying a total Monte Carlo correction on ~'/E of -I x l O -3. About 2 0 0 , 0 0 0 KL -~ ~r°Tr°, IO~KL -~ 7r*Tr - , and 12 x 106Ks -* 27r, i.e. more than 20 times the integrated number of KL --* 7r°~r° events of all previous experiments, were collected in 1986 and a large fraction of them are used for the analysis. The high statistics allow us to study the dependence of the result on various parameters. As an illustration, the double ratio R is given in Figs. 13a, b, and c as a function of Z,, of pK, and of the chronological number of the miniperiods. Our work is still in progress regarding the degree of possible systematic distortions. Up to now we have evaluated, in a preliminary fashion, the differential effect on the four types of
382
L Mannelli / CP violation in K decay
o 1.2 P ~
1.1
L a) ,+,4..
1. I
"I~,,
T't'-l-t+ ,rt+
+I
+ ++ +÷ +I~ + +-I-~ + + +÷
0.9 0.8 0.7 0,6 I 15
0.5
I 20
I 25
J 30
I 4-0
35
DOUBLE RATIOVERSUS Z V
l 45 Z-ve~(ex [m]
o 1.2
b)
o ~0
3
1.1 1.
--I--
~
---t-
__~.
__~_
I
-I-
+
~-I-
0.9 0.8 0.7 0.6 ().5
I 8O
I 100
I 120
I 140
I 160 P K [OeV]
DOUBLE RATIOVERSUS HOMENTUM
o 1.2 o
.~ 1.1 1.
,,,, ~..I 1 ÷
+~ +.~ ' ,~,~ ÷+÷++ +÷÷+ ' '÷~ 'T'~
T~IT 0.9 0.8 0.7 0.6 0:5
I 12
l 16
I 20
I 24
DOUBLE RATIOVERSUS TIME
I 28
I 32
36 time
FIGURE 1 3 a) Double ratio: [N(KL -~ 21r°)/N(KL -* ~ + ~ - ) ] / [ N ( K s -~ 21r°)/N(Ks -~ 7 r + ~ - ) ] as a function of decay vertex position; b) S a m e as a function of momentum; c) S a m e as a function of time.
L Mannelli / CP violation in K decay
383
events selected due to all sources we could think to be relevant. The most important of them are briefly described below:
a)
Trigger efficiency By looking at a sample of events recorded with a much looser trigger requirement
than the standard one, we have continuously monitored the trigger efficiency and found it to be, on an average: in the 2~ ° mode, (99.87 ± 0 . 2 5 ) % for the KL trigger and (99.76 ± 0 . 0 4 ) % for the Ks one; in the r + ~ - mode, (100 ± 0 . 0 0 8 ) % for the KL trigger and (99.99 ± 0 . 0 0 3 ) % for the Ks one. This implies ~R = (0.11 ± 0 . 2 7 ) % for the double ratio.
b)
Event losses by accidental events By overlapping with normal events the content of events taken in correspondence
with a random trigger, adjusted to occur during the burst at a frequency proportional to the instantaneous beam intensity, we have determined the fraction of events which have been lost because of the disturbance induced by an accidental event. We have decided, for the moment, to apply no correction and to assign an error on R of 0 . 5 % (0.8 x 10 -3 on e'/~), i.e. 2.5 times the statistical uncertainty of the effect measured, to cover possible imperfections of the method. We have also other ways of studying the effect of accidentals, because for each event we have recorded the instantaneous beam intensity and the time history, in 64 time slices of 50 ns each, centred around the time of occurrence of the event, for 96 channels comprising all relevant detector elements.
c)
Relative energy scale for T+x - and 7r°Tr° This could, in principle be an important effect, but a good understanding of the
geometry allows sufficient precision to be achieved.
d)
Uncertainty in background subtraction The largest background subtracted is in KL - ' 2 r °, where it amounts to 4%. The
procedure to estimate it is, however, straightforward and we estimate that we have determined it to an accuracy o f ± 5%. The subtraction of the background for 7r+;r- is much smaller (0.7%), but only k n o w n with 50% uncertainty. The summary of the systematic uncertainties and our present result for e'/~ are given in Table 4 and s h o w n in Fig. 14. In Fig. 14, in addition to comparing our results with all previous determinations, we indicate 13 the most recent best guess on the value of ~'/E as (2 ± 1) × 10 -3, according to the Standard Model. Combining
quadratically the statistical error with the present limit on the
systematic uncertainties, the result for ~'/~ is 2.5 standard deviations from zero. Given
384
L Mannelli / CP violation in K decay
Table 4 Summary of systematic uncertainties
2~ °
7 r + ,/l- -
Ks/KL
Ks
energy scale
+ 0 . 4 x 10 -3
background
+ 0 . 3 x 10-3
stability Ks/KL
± 0 . 4 x 10 -3
background
_+0.6 x 10-3
beam divergence accidentals
+0.1 x 10-3 + 0 . 8 x 10-3
scattering
_+0.2 x 10 -3
anticounter inefficiency
+0.1 x 10-3
Total systematic error
_ 1.2 x 10 .3
Preliminary result
~'/~ = (3.5 _ 0.7 _+ 0.4 ___ 1.2)
statistical error Monte Carlo statistical error systematic error x 10 -~
this result we plan, in addition to completing in its final form the analysis of the present data, to apply for a new SPS run in 1988 with improvement to the experimental equipment, in particular to the veto coverage close to the beam pipe, a better KL cleaning collimator system, and additional electron identification. We plan also to take data in a wider range of instantaneous intensities and to introduce some refinements in monitoring and data-taking procedure. At present we are running in order to measure arg ~/o0 - arg ~/+ _ with a projected accuracy of - 1 o Concerning future developments in this field by other groups, the E731 experiment is running already with an improved, higher-acceptance detector, in a beam with better KL/neutron ratio, with an 'active' regenerator, a faster and more selective dataacquisition system, and finally with better calibration and resolution for the Pb-glass calorimeter. It is conceivable that ultimately a precision of 1 x 100,000 KL -* 27r°, will be reached.
10 -3 on ~'/E, with
385
L Mannelli / CP violation in K decay
103 Rec'/¢
Holder et al 72 Banner et al 72 Christenson et al 79
15 -
Black et al 85 10
-
E731 (preliminary) I 5
. . ~ A 3 1 (preliminaryl
"--z'--+ (3.5 -~ 1.4) x 10-3 I
0
,T_
/
I
,
"S'I'ANDARD HODEL" L.P. SYHPOSIUH 198'/
-,5
Bernsfein ef al 85 -10
-
FIGURE 14 Present preliminary result of the NA31 experiment for e'/~. In the error indicated, we have combined quadratically statistical and systematic errors.
An experiment (PS 195) based on quite different principles is in preparation at the CERN Low-Energy Ant(proton Ring (LEAR) ~4. It is aimed at an accuracy of 1.5 x 10 -3 for c '/e, while detecting CP-violation effects in other channels such as K -4 23, and K 3~r, and checking various aspects of discrete symmetries. By detecting the sign of the charged kaon produced in association with a neutral one in ant(proton-proton annihilations at rest, pp-~ K+~r-K°
and
pp-* K-Tr+K °,
the strangeness at t = 0 of the neutral K is determined and, for instance, an integrated asymmetry can be defined from the probability of an initial K° and ~ decaying into 2~r within a time interval to:
to
tO
to
tO
+ 0
For to >- 20Ts
0
0
0
386
L Mannelli / CP violation in K decay
A+_ = 2 R e ~ + 4 R e e ' , Aoo = 2 R e ~ -
8Re~',
from which we get ~'/c = [1 - (Ao0/A+-)]16. More than 109 K --* ~r°Tr° decays will have to be collected to reach the required statistical accuracy, and a good fraction of the events will have to be analysed in detail to check sources of systematic distortion. A recent Letter of Intent has been submitted at Brookhaven (No. 749) by the BNL-Yale Collaboration, which needs a primary proton beam of such intensity that will only become available with the future AGS Booster. The neutral K beam would be produced by charge exchange from a charged K beam and the coherent mixture of KL and Ks could be altered, with hopefully no effect on the detecting apparatus, in such a w a y as to enhance or reduce the normal K2 component of KL and hence the ratio of 7r°Tr° to lr+~r - decays in case ~'/~ is different from zero. The sensitivity is again estimated to be 1 x 10 -3. In conclusion, the present experiment and those which will give results in the next few years may reasonably be expected to definitely settle the question of the existence of direct CP violation in weak interactions, according to the Standard Model.
387
L Mannelli / CP violation in K decay
REFERENCES 1) J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Phys. Rev. Lett. 13 (1964) 138. 2) See, for example, V.L. Fitch, Rev. Mod. Phys. 53 (1981) 367; J.W. Cronin, Rev. Mod. Phys. 53 (1981) 373; L. Wolfenstein, Annu. Rev. Nucl. Part. Sci. (1986). 3) A. Sakharov, Zh. Exp. Teor. Fiz. Pis'ma v Red. 5 (1967) 32 [Transl.: JETP Lett. 5 (1967) 24]. 4) L. Wolfenstein, Phys. Rev. Lett. 13 (1964) 569. 5) Review of Particle Properties, Phys. Lett. 170B (1986) 1. 6) V.V. Barmin et al., Nucl. Phys. 247B (1984) 293. 7) M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49 (1973) 652. 8) C. Albajar et al., Phys. Lett. 186B (1987) 247. 9) H. Albrecht et al., Phys. Lett. 192B (1987) 245. 10) M. Holder et al., Phys. Lett. 40B (1972) 141. M. Banner et al., Phys. Rev. Lett. 28 (1972) 1597. J.A. Christenson et al., Phys. Rev. Lett. 43 (1979) 1209. J.K. Black et al., Phys. Rev. Lett. 54 (1985) 1628. R.H. Bernstein et al., Phys. Rev. Lett. 54 (1985) 1631. 11 ) B. Winstein, CP and other tests of the Standard Model, to appear in Proc. APS-DPF Meeting, Salt Lake City, January 1987. 12) H. Burkhardt et al., The beam and detector for a high energy measurement of CP violation in neutral kaon decays, CERN-EP/87-166 (1987) submitted to Nucl. Instrum. Methods. 13) M. Shifman, Theoretical status of weak decays, Report to this Symposium. 14) L. Adiels et al., Test of CP violation with K° and ~ CERN/PSCC/85-6, January 1985.
at LEAR, Proposal
388
I. Mannelli / CP violation in K decay
DISCUSSION
J.A. Thompson, Univ. of Pittsburgh You mentioned that K L -~ ~0~07r0 was the main source of background for K L -~ ~0~0 (4%). What were the main background sources in the decay KL _, ~+~-, KS _~ ~0~0, KS _, n+n-, and how large were they ? Answer: For the K L -* ~+~-, the main background were again 3-body decays, which were detected by observing the distance of the K 0 production target from the decay plane. Their relative importance is shown in table 3. For K S decay the backgrounds were small, mostly connected with scattering from the lips of the collimator and the K S anti counter material