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Experimental evidence against particle mixture models of CP violation
Volume
29B,
number 2
PHYSICS
EXPERIMENTAL
EVIDENCE
LETTERS
AGAINST OF
P. DARRIULAT,
CP
14 April 1969
PARTICLE
MIXTURE
MODELS
VIOLATION
J. P. DEUTSCH *, K. KLEINKNECHT,
C. RUBBIA and CERN.
Geneva.
Received
K .TITTEL Switzerland
21 March 1969
Predictions of particle mixture models which propose to preserve CP invariance at the price of an additional long-lived kaon state with CP = +1 are found in disagreement with interference experiments on two pion decays.
A recent paper [l] has revived the interest in a class of models [2-71 which propose to reconcile the experimental results on long-lived kaon decay and CP conservation by postulating still another particle K’, very nearly degenerate with Kl and K2 states. As long as those models are consistent with experiments, CP violation is not proven but simply one of the possible explanations of the experimental observations. The Kl, K2 and K’ states are assumed to be CP eigenstates: CPIKl
) = +\Kl ), C
P
K2 > = -/K2 CP
),
K’ > =+/K’
).
The Kl and K2 have the same properties as before the discovery of Christenson et al. [8]. The K’ particle, which has a two-pion decay mode, is adjusted ‘ad hoc’ in order to explain all findings normally attributed to CP violation in the long-lived kaon state. In particular, 7K1 N rK2 and mK, N ??zK2. The strongly interacting states (Kg ) and (K8 ) are described as linear superpositions of the K 1, K2, and K’ states [ 11:
I$)
=TTll;;z)
t tK2 ) + t’]K’
IK$
= a)
[ 1K2 ) - 5’ ]K’ >I
are two diffeerent long-lived states generated from an initial Kg or KO state, respectively. It is possible to decide experimentally between particle mixture models (PMM) and CP violation (CPV). A test has been proposed by Lipkin [ 11, who has remarked that the charge asymmetry for leptonic decays, 6 _ N(n+l - v) - N(n- I+ v) N(r+l - v) + N(n- I+ v) ’ has opposite signs for KL and KL states. Additional effects are expected in the interference between short- and long-lived two-pion decays. We wish to consider two cases: i) Two-pion decays from initial Kg and Kg states. Then, for PMM (27~T~KO)
=( 24T/KO) oc(211/T]K1)+
/Ko>
=&[(l-
)I
a &:2”iTIK’
)+(l+?/K;)] and for CPV,
/Kg)=~[(1-51)~Kl:-(l+~t2)~K~)],
( 2?i 1T]KO ) m ! 27i 1T]KS ) + ( 2n 1T]KL )
where tf2 = 251 - 5; is a small quantity and
( 27i 1T/E0 > m ( 2771T/KS ) - ( 2n / T/KL >.
*
According to PMM, the interference phase is the same for an initial Kg or i?o state; instead CPV predicts opposite interference effects.
On leave
from the Centre de Physique Nucleaire, Universite de Louvain, Heverle-Louvain, Belgium.
132
:
PHYSICS
Volume 29B, number 2
LETTERS
ii) Two-pion decays after a regenerator placed in the long-lived beam. The effect is described according to PMM as an interference between K’ and KI regenerated (mainly) from the K2 component of the Ki and Ki states. According to PMM, the interference term changes sign for experiments performed with long-lived kaons originated from a MO or a RO. No difference is expected in the case of CPV.
Usually, neutral kaon beams are produced by collisions of a high-energy proton beam on a dense target. Then the initial state is not a pure state but an incoherent mixture of KO and RO states. Incoherence is the result of strangeness conservation since it is possible, at least in principle, to determine if a KO or a KO was produced by observing the other products of the reaction. The r+n- decay intensity is therefore the sum of the rates expected for a K. and a KO state, weighted by the corresponding production probabilities. The time dependence of the rfx- decay intensity is of the general form:
- l-sf/2
where: o(P) =
i’pp (P)
b(P) e
is the ratio of the shorttudes at kaon momentum q+_
= Iv+-
and long-lived p and t = 0;
ampli-
1 el@+-
is the usual ratio between the two pion decay amplitudes for the long-lived and short-lived states; Am, rs are the mass difference and the short-lived decay rate, respectively. Let also S(p) and s(p) be the KO and KO yields at production. In the case of interference close to the production point (f = 0), we have p(p) = = 1, ‘pp = 0 and A(V)(p)
= 1
for PMM and
Instead, behind a thin regenerator long-lived beam:
AtR)
=
m+
@) = 1
for PMM and for CPV.
An additional test of PMM has been suggested in the case in which the regenerator is thick enough to produce an appreciable attentuation of the incident beam [6,7]. The total cross-section on complex nuclei of the Kl and K2 states is large and approximately constant in the energy range of experimental interest (1.0 to 10.0 GeV). On the other hand, the K’ state could have considerably different interactions with matter. Indeed, ref. 1 to 7 have all assumed that the K’ particle is interacting much more weakly than ordinary kaons. Allowing for a difference in the K’ and Kl.K2 absorption cross-sections, formula (1) becomes: I,+,-(t,P)
a
+ 2A(R) (p) e
I&)
2e-rSf+
q+-(2e-(u’-u12)Nz
+
-(o’-312)NZ/2
-rs t/2 Iv+-IP@)
e
X
(2)
where:
cos(Amt+@$d -cp+-1,
-t-2AW77+IIP(P)e
A@) (P)
xcos(A~f+cpp(Pbcp+-),
evrst +/77+-l2+
f,+,-(f,P) m IP(
14 April 1969
placed
in the
N is the number of scattering centres per unit of volume of the regenerator; 7 is the regenerator length; u’ and u12 are the total cross-sections for the K’ and K2, (Kl) states, respectively. Note that Kl and K2 states have equal total cross-sections. We have reanalysed two recent experiments [9, lo] on interference between long-lived and short-lived &T- decays in order to test the predictions of PMM. Both experiments were performed in a 140 mrad beam line derived from the extracted proton beam of the CERN Proton Synchroton. In the first one we have observed high-energy neutral kaons (average momentum 6.5 GeV/c) decaying between 2.4 and 5.9 metres from the production target, corresponding to the time interval from 6/Q to 16/PS. The data have been fitted to a distribution of the form (l), with p(p) = 1. v,(p) = 0, in order to extract simultaneously A(V) and Q+-. In a second experiment [lo] we have observed the n+n- decay intensity after five different copper regenerators of equal lengths (25 cm) and different densities, located far from the production target (= 10 metres), where only the longlived component has survived.
133
PHYSICS
Volume 29B, number 2
14 April 1969
LETTERS
A@)
lb12IO-
O.S-
os-
o.c-
0.2-
0'
I
I
I
1
I
I
3
4
5
6
7
6
Kaon Momentum
(GcVk)
Fig. 1. Amplitude of the interference term between the short-lived and long-lived sf7r- decays. AR (p) is the amplitude as observed behind a regenerator placed in a long-lived beam. The dashed region is the result of the fit of the T+~T- decay intensity observed close to the production target in the same beam.
Diluted regenerators consist of a large number of closely spaced copper plates. The actual densities were: 8.9, 4.63, 2.26, 0.914, 0.448 g/cm3. Data have been fitted to an expression of type (2). Events have been divided in kaon momentum bins 500 MeV/c wide. The regeneration amplitude (p(p) 1, the inter ference phase cp,(p) - cp+-, and the size of the interference term A(P) (p), can vary independently for each momentum bin. The mass difference Am, the short-lived decay rate Ps, and the difference between the cross-sections u’ - al2 are variables common to all momentum bins. The results of the fit are the following: i) the attenuation cross-section for the hypothetical K’ state is about equal to 012, namely (012 - a’)/012 = (5 f 5) X 10-2. So, if K’ exists, its interaction with matter is comparable to that of Kl and K2. This is contrary to what was surmised by authors of refs. 1 to 7. ii) The amplitude of the interference term is given in fig. 1. In the same figure we have also reported the value of At’) (p) , as determined from the fit of the interference experiment close to the production target. Experimental results are clearly incompatible with the PMM prediction: A(R) (p) -’ A(V) (p) = 1 and fully consistent 134
with CPV viz.:
A(V) (p) =SA(R) (p) = 1. Previous interference experiments [ll, 121 behind a regenerator in long-lived neutral beams derived at large angles from high-energy accelerators have reported an interference term A(R) (p) close to unity. It is unlikely that in these experimental conditions s(a) >> @K). If, for instance, neutral KO and charged kaons have proportional production yields [ 131, PMM would predict A = 0.29 to be compared with A = = (1.0 f 0.2) for the experiment of ref. 11 and A = 0.5 instead of A = (1.20 * 0.14) for ref. 12. This is an additional piece of evidence against particle mixture models.
References 1. H. J. Lipkin,
Phys. Rev. Letters
22 (1969) 213.
2. J. L. Uretsky, Phys. Letters 14 (1965) 154, 3. A. Abashian and H. J. Lipkin, Phys. Letters 14 (1965) 151.
4. K. Nishijima 5. 6. 7. 8. 9.
and M. H. Saffouri, Phys. Rev. Letters 14 (1965) 205. H. Ezawa, Y. S. Kim, S. Oneda and J. C. Pati, Phys. Rev. Letters 14 (1965) 673. L. B. Okun’ and I. Ya. Pomeranchuk, Phys. Letters 16 (1965) 338. P. K. Kabir and R. R. Lewis, Phys. Rev. Letters 15 (1965) 306. J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay, Phys. Rev. Letters 13 (1964) 138. P. Darriulat, K. Kleinknecht, C. Rubbia, J. SandWeiss, H. Faissner, H. Foeth, A. Staude, K. Tittel,
Volume 29B, number 2
PHYSICS
LETTERS
14 April
1969
11. V. L. Fitch, R. F. Roth, J.S. Russ and W. Vernon, Phys. Rev. Letters 15 (1965) 73. 12. C. Alff-Steinberger, W. Heuer, K. Kleinknecht, C. Rubbia, A. Scribano, J. Steinberger. M. J. Tannenbaum and K. Tittel, Phys. Letters 20 (1966) 207 and Phys. Letters 21 (1966) 595. 13. J. R. Sanford, C. L. Wang, Empirical formulas for particle productions, BNL International Report, 1 May 1967.
M. I. Ferrer0 and C. Grosso, naoer presented at the Topical Conference on Weak Interactions, CERN. Januarv 1969. and to be submitted to Phys. Letters: 10. A.Boehm. P. Darriulat. C. Grosso, V.Kaftanov. K.Kleinknecht, H. L. Lynch. C. Rubbia, H. Ticho and K. Tittel, Phys. Letters 27B (1968) 321, and Nucl. Phys. (to be published).
*****
135
29B,
number 2
PHYSICS
EXPERIMENTAL
EVIDENCE
LETTERS
AGAINST OF
P. DARRIULAT,
CP
14 April 1969
PARTICLE
MIXTURE
MODELS
VIOLATION
J. P. DEUTSCH *, K. KLEINKNECHT,
C. RUBBIA and CERN.
Geneva.
Received
K .TITTEL Switzerland
21 March 1969
Predictions of particle mixture models which propose to preserve CP invariance at the price of an additional long-lived kaon state with CP = +1 are found in disagreement with interference experiments on two pion decays.
A recent paper [l] has revived the interest in a class of models [2-71 which propose to reconcile the experimental results on long-lived kaon decay and CP conservation by postulating still another particle K’, very nearly degenerate with Kl and K2 states. As long as those models are consistent with experiments, CP violation is not proven but simply one of the possible explanations of the experimental observations. The Kl, K2 and K’ states are assumed to be CP eigenstates: CPIKl
) = +\Kl ), C
P
K2 > = -/K2 CP
),
K’ > =+/K’
).
The Kl and K2 have the same properties as before the discovery of Christenson et al. [8]. The K’ particle, which has a two-pion decay mode, is adjusted ‘ad hoc’ in order to explain all findings normally attributed to CP violation in the long-lived kaon state. In particular, 7K1 N rK2 and mK, N ??zK2. The strongly interacting states (Kg ) and (K8 ) are described as linear superpositions of the K 1, K2, and K’ states [ 11:
I$)
=TTll;;z)
t tK2 ) + t’]K’
IK$
= a)
[ 1K2 ) - 5’ ]K’ >I
are two diffeerent long-lived states generated from an initial Kg or KO state, respectively. It is possible to decide experimentally between particle mixture models (PMM) and CP violation (CPV). A test has been proposed by Lipkin [ 11, who has remarked that the charge asymmetry for leptonic decays, 6 _ N(n+l - v) - N(n- I+ v) N(r+l - v) + N(n- I+ v) ’ has opposite signs for KL and KL states. Additional effects are expected in the interference between short- and long-lived two-pion decays. We wish to consider two cases: i) Two-pion decays from initial Kg and Kg states. Then, for PMM (27~T~KO)
=( 24T/KO) oc(211/T]K1)+
/Ko>
=&[(l-
)I
a &:2”iTIK’
)+(l+?/K;)] and for CPV,
/Kg)=~[(1-51)~Kl:-(l+~t2)~K~)],
( 2?i 1T]KO ) m ! 27i 1T]KS ) + ( 2n 1T]KL )
where tf2 = 251 - 5; is a small quantity and
( 27i 1T/E0 > m ( 2771T/KS ) - ( 2n / T/KL >.
*
According to PMM, the interference phase is the same for an initial Kg or i?o state; instead CPV predicts opposite interference effects.
On leave
from the Centre de Physique Nucleaire, Universite de Louvain, Heverle-Louvain, Belgium.
132
:
PHYSICS
Volume 29B, number 2
LETTERS
ii) Two-pion decays after a regenerator placed in the long-lived beam. The effect is described according to PMM as an interference between K’ and KI regenerated (mainly) from the K2 component of the Ki and Ki states. According to PMM, the interference term changes sign for experiments performed with long-lived kaons originated from a MO or a RO. No difference is expected in the case of CPV.
Usually, neutral kaon beams are produced by collisions of a high-energy proton beam on a dense target. Then the initial state is not a pure state but an incoherent mixture of KO and RO states. Incoherence is the result of strangeness conservation since it is possible, at least in principle, to determine if a KO or a KO was produced by observing the other products of the reaction. The r+n- decay intensity is therefore the sum of the rates expected for a K. and a KO state, weighted by the corresponding production probabilities. The time dependence of the rfx- decay intensity is of the general form:
- l-sf/2
where: o(P) =
i’pp (P)
b(P) e
is the ratio of the shorttudes at kaon momentum q+_
= Iv+-
and long-lived p and t = 0;
ampli-
1 el@+-
is the usual ratio between the two pion decay amplitudes for the long-lived and short-lived states; Am, rs are the mass difference and the short-lived decay rate, respectively. Let also S(p) and s(p) be the KO and KO yields at production. In the case of interference close to the production point (f = 0), we have p(p) = = 1, ‘pp = 0 and A(V)(p)
= 1
for PMM and
Instead, behind a thin regenerator long-lived beam:
AtR)
=
m+
@) = 1
for PMM and for CPV.
An additional test of PMM has been suggested in the case in which the regenerator is thick enough to produce an appreciable attentuation of the incident beam [6,7]. The total cross-section on complex nuclei of the Kl and K2 states is large and approximately constant in the energy range of experimental interest (1.0 to 10.0 GeV). On the other hand, the K’ state could have considerably different interactions with matter. Indeed, ref. 1 to 7 have all assumed that the K’ particle is interacting much more weakly than ordinary kaons. Allowing for a difference in the K’ and Kl.K2 absorption cross-sections, formula (1) becomes: I,+,-(t,P)
a
+ 2A(R) (p) e
I&)
2e-rSf+
q+-(2e-(u’-u12)Nz
+
-(o’-312)NZ/2
-rs t/2 Iv+-IP@)
e
X
(2)
where:
cos(Amt+@$d -cp+-1,
-t-2AW77+IIP(P)e
A@) (P)
xcos(A~f+cpp(Pbcp+-),
evrst +/77+-l2+
f,+,-(f,P) m IP(
14 April 1969
placed
in the
N is the number of scattering centres per unit of volume of the regenerator; 7 is the regenerator length; u’ and u12 are the total cross-sections for the K’ and K2, (Kl) states, respectively. Note that Kl and K2 states have equal total cross-sections. We have reanalysed two recent experiments [9, lo] on interference between long-lived and short-lived &T- decays in order to test the predictions of PMM. Both experiments were performed in a 140 mrad beam line derived from the extracted proton beam of the CERN Proton Synchroton. In the first one we have observed high-energy neutral kaons (average momentum 6.5 GeV/c) decaying between 2.4 and 5.9 metres from the production target, corresponding to the time interval from 6/Q to 16/PS. The data have been fitted to a distribution of the form (l), with p(p) = 1. v,(p) = 0, in order to extract simultaneously A(V) and Q+-. In a second experiment [lo] we have observed the n+n- decay intensity after five different copper regenerators of equal lengths (25 cm) and different densities, located far from the production target (= 10 metres), where only the longlived component has survived.
133
PHYSICS
Volume 29B, number 2
14 April 1969
LETTERS
A@)
lb12IO-
O.S-
os-
o.c-
0.2-
0'
I
I
I
1
I
I
3
4
5
6
7
6
Kaon Momentum
(GcVk)
Fig. 1. Amplitude of the interference term between the short-lived and long-lived sf7r- decays. AR (p) is the amplitude as observed behind a regenerator placed in a long-lived beam. The dashed region is the result of the fit of the T+~T- decay intensity observed close to the production target in the same beam.
Diluted regenerators consist of a large number of closely spaced copper plates. The actual densities were: 8.9, 4.63, 2.26, 0.914, 0.448 g/cm3. Data have been fitted to an expression of type (2). Events have been divided in kaon momentum bins 500 MeV/c wide. The regeneration amplitude (p(p) 1, the inter ference phase cp,(p) - cp+-, and the size of the interference term A(P) (p), can vary independently for each momentum bin. The mass difference Am, the short-lived decay rate Ps, and the difference between the cross-sections u’ - al2 are variables common to all momentum bins. The results of the fit are the following: i) the attenuation cross-section for the hypothetical K’ state is about equal to 012, namely (012 - a’)/012 = (5 f 5) X 10-2. So, if K’ exists, its interaction with matter is comparable to that of Kl and K2. This is contrary to what was surmised by authors of refs. 1 to 7. ii) The amplitude of the interference term is given in fig. 1. In the same figure we have also reported the value of At’) (p) , as determined from the fit of the interference experiment close to the production target. Experimental results are clearly incompatible with the PMM prediction: A(R) (p) -’ A(V) (p) = 1 and fully consistent 134
with CPV viz.:
A(V) (p) =SA(R) (p) = 1. Previous interference experiments [ll, 121 behind a regenerator in long-lived neutral beams derived at large angles from high-energy accelerators have reported an interference term A(R) (p) close to unity. It is unlikely that in these experimental conditions s(a) >> @K). If, for instance, neutral KO and charged kaons have proportional production yields [ 131, PMM would predict A = 0.29 to be compared with A = = (1.0 f 0.2) for the experiment of ref. 11 and A = 0.5 instead of A = (1.20 * 0.14) for ref. 12. This is an additional piece of evidence against particle mixture models.
References 1. H. J. Lipkin,
Phys. Rev. Letters
22 (1969) 213.
2. J. L. Uretsky, Phys. Letters 14 (1965) 154, 3. A. Abashian and H. J. Lipkin, Phys. Letters 14 (1965) 151.
4. K. Nishijima 5. 6. 7. 8. 9.
and M. H. Saffouri, Phys. Rev. Letters 14 (1965) 205. H. Ezawa, Y. S. Kim, S. Oneda and J. C. Pati, Phys. Rev. Letters 14 (1965) 673. L. B. Okun’ and I. Ya. Pomeranchuk, Phys. Letters 16 (1965) 338. P. K. Kabir and R. R. Lewis, Phys. Rev. Letters 15 (1965) 306. J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay, Phys. Rev. Letters 13 (1964) 138. P. Darriulat, K. Kleinknecht, C. Rubbia, J. SandWeiss, H. Faissner, H. Foeth, A. Staude, K. Tittel,
Volume 29B, number 2
PHYSICS
LETTERS
14 April
1969
11. V. L. Fitch, R. F. Roth, J.S. Russ and W. Vernon, Phys. Rev. Letters 15 (1965) 73. 12. C. Alff-Steinberger, W. Heuer, K. Kleinknecht, C. Rubbia, A. Scribano, J. Steinberger. M. J. Tannenbaum and K. Tittel, Phys. Letters 20 (1966) 207 and Phys. Letters 21 (1966) 595. 13. J. R. Sanford, C. L. Wang, Empirical formulas for particle productions, BNL International Report, 1 May 1967.
M. I. Ferrer0 and C. Grosso, naoer presented at the Topical Conference on Weak Interactions, CERN. Januarv 1969. and to be submitted to Phys. Letters: 10. A.Boehm. P. Darriulat. C. Grosso, V.Kaftanov. K.Kleinknecht, H. L. Lynch. C. Rubbia, H. Ticho and K. Tittel, Phys. Letters 27B (1968) 321, and Nucl. Phys. (to be published).
*****
135