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CP VIOLATION IN NEUTRAL KAON DECAYS
J. Repellin
To cite this version:
J. Repellin. CP VIOLATION IN NEUTRAL KAON DECAYS. Journal de Physique Colloques, 1971, 32 (C3), pp.C3-59-C3-66. �10.1051/jphyscol:1971308�. �jpa-00214589�
JOURNAL DE PHYSIQUE Colloque C3, supplkment au no 10, Tome 32, Octobre 1971, page C3-59
CP VIOLATION IN NEUTRAL KAON DECAYS
J. P. REPELLIN
AccClCrateur LinCaire, Orsay, France CERN, Genbve, Suisse
RBsum6. - La violation de CP dans les dksintkgrations des mksons K neutres est analyske en fonction des resultats expkrimentaux actuellement connus et des mkthodes utiliskes pour les mesurer, ainsi que des rksultats attendus des prochaines expkriences.
Abstract. - The violation of CP in the decays of the neutral K system is presented after a survey of the experimental results, the methods used, and the expected results of new experiments.
The aim of these notes is to survey CP violation in the KK system, or more precisely :
- the general features of CP violation in the KK system ;
- the experimental methods, and the present results ;
- the implications of these results in the problem of T and CPT symmetries, and superweak interaction.
Most of the experimental results or averages, will be taken from J. M. Gaillard's talk at the Daresbury Study week-end on K decay [I].
I. General remarks. - Until the discovery of the decay K: + z + 7t- [2] it was assumed, that the total Hamiltonian for K decay including the weak part was invariant under the product CP (charge conjugation times parity).
In this scheme the two vector-basis used to span the neutral kaon system were [3] :
- either K and K the eigenvectors of the strong and electromagnetic part of the Hamiltonian and strangeness S, with the relative phase defined by
- or K, and K, : the CP symmetric and anti- symmetric combination of KO and KO :
The Wigner Weisskopf method which treats the weak part of the Hamiltonian as a perturbation, can be applied to solve the time-dependent Schrodinger equation.
This leads to a mass matrix equation for the KK part of the wave function
and with the assumption that H,,,, is invariant under CP symmetry K, and K, are the eigenvectors of the mass matrix equation.
As a consequence, K, can decay rapidly into two pions, though K, cannot unless CP is violated. For this reason K, is the short lived component, and K, the long lived one.
This picture is no longer valid since the discovery [2]
of the decay K, -t nf n-, so that we look for CP violation.
It will show up directly in the following decays :
which connects states of opposite values of CP.
It will also appear indirectly in decays which are not eigenvalues of CP, but for which interference effects are observed between the two components K, and K,.
More precisely an interference in a decay involving only pions and gammas, is evidence for CP violation in this decay [4].
Until now CP violation has been seen in the
- K, -t n+ n- and K, + no no decay modes ; - and in the charge asymmetry of the leptonic decay K, -t n1v (at least assuming CPT symmetry).
The characteristic pattern of a KK system decay into a common final state deserves a special introduc- tion.
Assuming the initial K wave function to be a linear combination :
where
are the vectors which undergo an exponential decay law, and p = 1 p 1 eiVP is the amplitude of KL relative to Ks at 0 time.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971308
C3-60 J.-P. REPELLIN We introduce the usual notation for the ratio of the
decay amplitudes in a common final state A :
so that the decay intensity of the wave in that particular mode is :
Of these three terms the first and the second ones arise from KL and Ks decay in the mode A, the last term is due to interference between K, and Ks.
11. K into 3 n decay. - A state of 3 no is odd under CP so that Ks cannot decay into it unless CP is violated.
The decay Ks -+ n + n- no is not completely for- bidden since the n + n- no can be even under CP, at the price of having total isotopic spin I = 2 and a P wave, which reduces strongly the decay due to centrifugal barrier.
In spite of the possibility of such non - CP -
violating processes an experimental limit on the charged decay mode of the Ks is of interest as we will see later.
The limit can be expressed in terms of the parameter :
which, to be small, is just defined as the inverse of our general notation.
Four new experiments have given the following limits :
from the CERN hydrogen bubble chamber (F. James et al.) [5]
from the Orsay-CERN-Vienne wire chamber spectro- meter (J.-J. Aubert et al.) [6]
Re q+-, = .30 + .28 Im y,-, = .08 + .58
from the ZGS magnetic spectrometer (A. Abashian et al.) [7]
R e v + - , = . 4 7 f .20 I m y + - , = - . I 0 + .37
- .32 from the BNL bubble chamber (Y. Cho et al.) 1391.
The present world average is then :
The difficulty of reducing this limit is obvious from equation 2, which reads here (p = 1 for Ks obtained from KO). Rate :
+ 2(Re y+-, cos 6, t - Im q+-, sin 6, t) x exp [ -
" :
t ]- for a low limit on q, the first term, due to KL decay becomes dominant ;
- measurements at early time are very important to constrain the real part ;
- the expected effect from CP violation is by far below the experimental limit.
For instance if the CP violation comes from a smal admixture of K, into KL and K, into Ks :
then y ,-,, roo,, q + - , qoo are of the same order of magnitude, that is 2 to 3 x
There is no measurement of 3 .no decay, but one expects that the limit for y+ -, is valid for Y ~This ~ ~ . would follow from a pure I = 1 amplitude for the 3 n, that is if there are no A1 > 512 amplitudes in CP conserving, and in CP violating transitions.
Another test of CP conservation in the decays Kf + n f n' n- and K- -+ n- n- n + compares their decay rates, and also the slopes of the distribution of the odd pion in the Dalitz plot.
The experiment of Ford et al. [8] gave the values :
and
which are compatible with CP conservation.
111. K into 2 n decay. - The parameters of the CP violation in the 2 n decay are :
Each of these parameters has already been experi- mentally measured.
1. MODULUS OF y + -. - This parameter is the easiest to measure, and this is confirmed by the agree- ment between the different experiments. The normali- zation is done with respect to all charged modes.
CP VIOLATION IN NEUTRAL KAON DECAYS
The world average is : Averaging these values, we obtain :
2. PHASE OF q + -. - AS seen in formula 2, the time dependence for the decay of a K, KL wave into n+ n- depends on the combined phase q, -t- p+ - due to the interference term.
The sensitivity to the interference term is maximum when p and y + - are of the same importance.
Since q + - is a few p has to be of this order of magnitude. There are two ways to reach such values which give two types of experiments.
Phase measurements by regeneration. - One way is to produce the Ks amplitude by coherent regeneration in a block of matter, usually copper is used. 20 cm of copper gives a regeneration intensity of 1 % at 2 GeV/c.
A fit to the time distribution curve determines the phase.
Four experiments [lo], [13] have measured the phase with this method, once the small mass correction has been applied, they all agree, and the average is :
The geometrical part of the phase of p has been subtracted and cp, = arg (i(f - f)) where f and f are the amplitudes for K and K scattering.
Regeneration Phase. - The previous experiments
With this regeneration method the y + - phase is :
Phase measurement by <( vacuum regeneration D. - Instead of producing a K, amplitude of the right magnitude by regeneration, one can start from a KO, and observe the interference pattern at a distance such that the Ks amplitude has decreased to the needed value.
The interference term is now :
The relative phase q, disappears in this method, but one pays back this improvement because the uncer- tainty in 6, is amplified by the time factor t which is about 13.
Two experiments [17], [18] have used this so-called
<( vacuum regeneration w, and give an averaged value :
These values are computed with an average mass difference :
need a separate determination of the regeneration such a precise mass difference results from three phase P,. This phase can be obtaineddirectl~ fromthe experiments [13], 1181, [19] using the gap method.
charge asymmetry of the Ke3 decay of a s u ~ e r ~ o s i t i o n These experiments are very precise and agree quite of KL and K,, the Ks being created from KL by cohe- well.
rent regeneration in the same material. This method Finally the present value of q+ - obtained from the
gives a value (1 4) : combination of the two methods is :
Another determination [15] of cp, can be obtained from an independent knowledge of the imaginary part, and of the modulus of f - f. The imaginary part has been computed from the total cross section of K*
interaction with copper. The modulus can be directly measured.
With this method the value for copper is :
3. MODULUS OF yo,. - Concerning this parameter, the experimental situation is not yet as clear as for the charged parameters. The detection of the gamma rays obviously makes these experiments quite difficult. The normalization is also one of the problems.
The different values are spread over a range too wide to be averaged, so I will list the different experiments of table I.
RCA experiment [20], [21] used optical spark chambers to observe the showers from the gamma Measured Values of I yo, I
Normalization Experiment I Too l2 X lo6 I Too I X lo3 Regeneration 3
- - -
RCA [20, 211 11.8 + 3.4 3.4 + 0.5
Bartlett et al. [22] - 2 k 7
Banner et al. [23] 4.9 + 1.2 2.2 k 0.3
Bugadov et al. [25] 3.5 + 1.7 1.9 k 0 . 5 Cence et al. [24] 14.1 + 3.4 3.72 + 0.45
Barmin et al. [26] 4.07 $- 0.88 2.02 f 0.23
C3-62 J.-P. REPELLIN
rays. The 2 no signal from KL decays is observed over ing the determination of the modulus of yo, gives a an important background of events due to the 3 z0 preliminary result :
decay. The subtraction of this background needs a
Monte-Carlo simulation. The normalization has been ~ o o / ( f - f)/k = (1.04 k .09) x 10 -3statistlcal done with respect to regeneration and to 3 z0 decays.
Bartlett et al. [22] did not see 2 z0 decays. but the values of (f - f)/k at 2 GeV/c in fm2 (the Banner et al. [23] measured the branching ratio momentum at which the experiment was run), are K, -+ 2 nO/K, -+ 3 no. The authors measured carefully quite uncertain by now, as seen in figure 2.
- -
one of the gamma rays. The requirement of a momen- tum transverse to the beam of at least 165 MeV/c for this gamma ray elipimates most of the 3 no events. In addition, the showers developed in spark chambers by 2 or 3 of the other gamma rays were used to reduce the background. Also a time of flight measurement of the kaon was used to constrain the fit of the event. The result needs a good knowledge of the conversion pro- bability.
~ e n c e et al. [24] have observed the decays in spark chambers, and normalized to 3 no. The background is important, and has been subtracted using a Monte- Carlo calculation.
The two experiments of Bugadov et al. [25], and Barmin et al. [26] are quite similar. The decays are observed in heavy liquid bubble chamber, the first filled with heavy freon, the second with xenon. Both experiments are analysed in the same way. The second has a better conversion efficiency, so that the 3 no background is less important (Fig. 1). The background subtraction can be done by using genuine 6 y events.
The 2 no signal is normalized to the 3 no.
illo)-iio)l
h lor Coppr
FIG. 2. - Regeneration amplitude on copper.
The CERN-Aachen-Torino experiment [28] used wire spark chambers to determine the gamma ray direc- tions, and lead glass counters to measure their energy (Fig. 3). The 2 no events obtained from four observed
FIG. 1. - Mass spectrum of the 2 no obtained by Barmin et al.
FIG. 3. - Experimental set up of CAT experiment [28].
gamma rays are well separated from 3 no events (Fig. 4). The experiment measures I yoo/p I by compar- ing 2 no decays from KL and Ks, the kaon flux for these two conditions is monitored by the 3 no events.
This measurement is combined with a value of 1 y + - / p ] obtained in similar conditions, and the result is then :
I ~ o o l ~ + - I = (1.0 f .06).
Besides these published values, two experiments are
nearly completely analysed. To conclude this part, I would say that the results of The CERN-Orsay experiment [27] used roughly the the last experiments seem to converge to such an same apparatus as the RCA one. The analysis concern- attractive relation as y+ - = yo,.
CP VIOLATION I N NEU ITRAL KAON DECAYS C3-63
FIG. 4. - Mass spectrum of 2 xo obtained by CAT experiment, when 4 gammas are converted in the spark chambers.
4. PHASE OF qoo. - The experimental situation is here much clearer since there is only one measurement, except for an experiment [29] on Ks + 2 n which gave indications that qoO was in the first quadrant.
The qoo phase has been measured by Chollet et al.
The gamma rays convert in optical spark chambers.
The directions are measured on the photographs, and the energy is obtained from spark counting. Despite the poor resolution on the decay point, the interaction term of equation 2 can be extracted from the time
FIG. 5. - Time distribution of the 2 no decay, and chi square contour from J. C. Chollet et al. [30].
distribution of the decays after a copper regenerator (Fig. 5).
The result is : cpoo = 51" + 30".
IV. CP violation in the leptonic decays. - I don't want to describe fully the K13 decays, but only the part which concerns CP violation.
For simplicity we assume the CPT symmetry, and define as usual :
x = g*lfis the well known parameter used to describe the violation of the AQ = AS rule, and that parameter should be real if CP symmetry is good.
Then the charge asymmetry in the leptonic decay of KL is :
E is the Tviolating part of the admixture of K, into KL as seen from formula 3.
Such an asymmetry has been observed in both Ke, and Kp3 decays of long lived kaons. The values of the asymmetry are :
Assuming that AQ = AS, one gets the real part of Re E = (1.62 f .16) x l o p 3
or
R e & = (1.68 + .17) x
if one takes
V. Test of CPT and T symmetries. - ORIGINE OF
THE C P VIOLATION. - Many attempts were made to preserve CP symmetry in spite of the 2 n decay of the long lived kaon. All the <( ad hoc >) models have been ruled out one after the other by the experiments.
Once the CP violation is well established, one has to question the CPT or T symmetry. As we will see, the phase of qoo is a crucial test, and even with the large error, one can establish that T is violated.
The mass matrix elements of equation 2 can be expressed in the KK basis :
p - 6 A A =
where
C3-64 J.-P. REPELLIN
and The more careful1 analysis of Schubert et al. shows
contain already four measurable parameters.
m, and m, are the KL Ks masses and r, T , the life
times, of the total 8 parameters, the last four are E and 6.
CPT invariance implies 6 = 0 ; T invariance implies E = 0 ;
CP invariance implies both E = 6 = 0 [ 3 ] .
In the KL Ks basis which diagonalizes A, unitary gives the relation [34] :
The sum on the right hand side runs over all obser- vable decay states.
The scalar product :
contains information about CPT or T violation, and can be determined provided the sum is calculated.
Let us separate the contribution of the 2 n ( I = 0) states in the sum :
where to a good approximation :
For clarity let us assume, that the 2 n I = 0 states saturate the unitary relation. The contributions of other states are analysed in the paper of Schubert et al. [35] and are small.
In this approximation the equation 4 gives :
using the known values of y + and qoO one gets :
yo, has been left explicitly in the formula to show that any of the values measured do not change the conclu- sion that E is definitely not 0, while 6 is compatible with 0.
that this conclusion holds also for Im E, and Re g
(where g is slightly different from 6).
We can then conclude, that the observed CP violation in KO decays is predominantly due to the CPT conserv- ing amplitude E , and that time reversal invariance T is violated.
This conclusion does not solve completely the problem of the origin of the violation, and we will see now what new measurements are important.
To describe the KL Ks decay into 2 no we have already introduced the parameter 8,. Let us define also [36] :
These quantities have been measured by Gobbi et al. [29, 371 :
E~ = (- 3.3 + 4.0) - i(5.8 + 4.0)
o = (.044 .013) exp i ( - 39" $. 18") .
In the approximation where o is small compared to 1, an isospin decomposition leads to :
Yo0 = Eo - 42 E z .
Among the models for CP violation one of the simplest has been developed by Wolfenstein [38], and is known as the superweak model. It attributes the CP violation to an imaginary part in the off diagonal element MI, of the Hermitian part M of the mass matrix :
. A L = M + i T .
R e a l
FIG. 6. - WU and Yang diagram.
CP VIOLATION IN NEUTRAL KAON DECAYS C3-65
In this scheme superweak interaction would allow where a A S = 2 transition t o produce a n imaginary part
in M I , through the term tg p, = 2(mL - m,)/T', E,/ JZ = y + - - Re & ( I + i tg 9,) .
Since all the phases are near 45", one can say roughly that (Fig. 6) :
I n the Wolfenstein model, there is no important CP - the difference of the modulus of y+ - and yo, violating effect in the KK decays so that 8, = 0. measures the component of E~ parallel to 8,
E, which measures the difference between y+ - and - p+ - - q o o measures the component of 82 yo, is then an important parameter : perpendicular to e,
- finally Re 8 measures the real part of 8,.
42 Precise experiments along these three lines are in
E 2 = $y+- - ~ 0 0 )
progress, and should definitively settle the problem.
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