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An upper limit on D0−D̄0 mixing
Volume 199, number 3
PHYSICS LETTERSB
24 December 1987
AN UPPER LIMIT ON D°-I) ° MIXING ARGUS Collaboration H. ALBRECHT, A.A. ANDAM 1, U. BINDER, P. B()CKMANN, R. GL~,SER, G. HARDER, A. NIPPE, M. SCHAFER, W. SCHMIDT-PARZEFALL, H. SCHRC)DER, H.D. SCHULZ, R. WURTH, A. YAGIL 2.3 DESE D-2000 Hamburg, Fed. Rep. Germany
J.P. DONKER, A. DRESCHER, D. KAMP, H. KOLANOSKI, U. MATTHIESEN, H. SCHECK, B. SPAAN, J. SPENGLER, D. WEGENER lnstitutj~r Physik a, Universitat Dortmund, D-6400 Dortmund, Fed. Rep. Germany
J.C. GABRIEL, T. RUF, K.R. SCHUBERT, J. STIEWE, K. STRAHL, R. WALDI lnstitut~r Hochenergiephysik s Universitiit Heidelberg, D-6900 Heidelberg, Fed. Rep. Germany
K.W. EDWARDS 6, W.R. FRISKEN 7, D.J. GILKINSON 8, D.M. GINGRICH 8, H. KAPITZA 6, P.C.H. KIM s, R. KUTSCHKE 8 D.B. MACFARLANE 9, J.A. McKENNA 8, K.W. McLEAN 9 A.W. NILSSON 9, R.S. ORR 8, p. PADLEY 8, J.A. PARSONS 8, P.M. PATEL 9, J.D. PRENTICE 8, H.C.J. SEYWERD 8, J.D. SWAIN 8, G. TSIPOLITIS 9, T.-S. YOON 8, J.C. YUN 6 Institute of Particle Physics m. Canada
R. AMMAR, S. BALL, D. COPPAGE, R. DAVIS, S. KANEKAL, N. KWAK University of Kansas ' ~, Lawrence, KS 66045, USA
B. BOSTJANCIC, G. KERNEL, M. PLESKO lnstitut J. Stefan and Oddelek za fiziko ~2, Univerza v Ljubljani, 61111 Ljubljana, Yugoslavia
L. JONSSON Institute of Physics ~3, University of Lund, 8-22362 Lund, Sweden
A. BABAEV, M. DANILOV, B. FOMINYKH, A. GOLUTVIN, I. GORELOV, V. LUBIMOV, V. MATVEEV, V. RYLTSOV, A. SEMENOV, V. SHEVCHENKO, V. SOLOSHENKO, V. TCHISTILIN, I. TICHOMIROV, Yu. ZAITSEV Institute of Theoretical and Experimental Physics, 117259 Moscow, USSR
R. CHILDERS, C.W. DARDEN, R.C. FERNHOLZ and Y. OKU University of South Carolina ~4, Columbia, SC 29208, USA
Received 10 August 1987
For footnotessee next page.
0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
447
Volume 199, number 3
PHYSICS LETTERS B
24 December 1987
We have searched for D°-IT)° mixing in the cascade decay of D *+, using the excellent particle identification of the ARGUS detector. No mixing was observed, leading to an upper limit of 1.4% (90% CL) for F(D°--,17)°-~X')/F(D°--,X).
Quark flavour is not conserved in weak interactions. One manifestation o f this is the K ° ~ I ~ ° transition, which is allowed via the A S = 2 box d i a g r a m [ 1 ]. The analogue for neutral c h a r m mesons, D°-13 ° mixing is, however, highly suppressed in the six-quark s t a n d a r d model o f electroweak interactions [2] ~ , even after accounting for the long-distance effects [4]. Therefore, a recent report by the M A R K III collaboration [5] o f possible D°-13 ° mixing at about 1.6% level has generated considerable interest. While e x p e r i m e n t a l sensitivities are still orders of magnitude away from the values p r e d i c t e d in the s t a n d a r d model, mixing searches are nevertheless desirable as a test for the high level D°-13 ° mixing p r e d i c t e d by some o f the theoretical ideas which go b e y o n d the s t a n d a r d m o d e l [ 6]. The two most c o m m o n m e t h o d s used to search for D°-13 ° mixing are (i) the study o f the d i - m u o n events (or t r i - m u o n events in the case o f g-scattering exp e r i m e n t s ) arising from the semi-leptonic decays of the c h a r m - a n t i - c h a r m h a d r o n pairs [ 7 ] and (ii) full reconstruction o f the D o meson from its daughter particles in the cascade decay o f the D* + [8 ] ~2. The first m e t h o d is m o d e l - d e p e n d e n t , since it requires On leave from University of Science and Technology, Kumasi, Ghana. 2 Weizmann Institute of Science, 76100 Rehovot, Israel. 3 Supported by the Minerva Stiftung. Supported by the German Bundesministerium f'tir Forschung und Technologie under contract number 054DO5 I P. 5 Supported by the German Bundesministerium ftir Forschung und Technologie under contract number 054HD24P. ~'Carleton University, Ottawa, Ontario, Canada KIS 5B6. v York University, Downsview, Ontario, Canada M3J 1P3. University of Toronto, Toronto, Ontario, Canada, M5S IA7. McGill University, Montreal, Quebec, Canada H3A 2T8. u~Supported by the Natural Sciences and Engineering Research Council, Canada. f~ Supported by the US National Science Foundation. ~2Supported by Raziskovalna skupnost Slovenije and the Internationales Btiro KfA, Jiilieh. ~3Supported by the Swedish Research Council. ~4Supported by the US Department of Energy under contract DEAS09-80ER 10690. ~ See ref. [3] for a review. ~" In this paper references to a particular particle state should be taken to imply both the particle and its anti-particle. 448
a s s u m p t i o n s about the c h a r m p r o d u c t i o n cross section, the semi-leptonic branching fractions of all c h a r m e d particles, and the fraction o f D o mesons p r o d u c e d in c h a r m e d quark fragmentation. We fully reconstruct the D O mesons from D *+ decays, a m e t h o d which is completely m o d e l independent. D* + decays are also particularly suited to obtaining a signal essentially flee o f c o m b i n a t o r i a l background. This is due to the small Q-value for the decay D *+ ~ D ° x +, which leads to an excellent mass resolution for the D *+, if the mass o f the D o decay products is constrained by a k i n e m a t i c fit to the n o m i n a l D O mass. Moreover, mixing searches are possible because the charge of the soft p i o n tags whether a D Oor I3 0 was produced. In the weak decay o f the D ° ( c l i ) , the c quark decays to an s quark, and so the sign of the charged daughter kaon is negative; thus, the sign o f the charged kaon from the D Odecay is opposite to the sign o f the pion from the D* + decay. If mixing were to occur, the signs would be the same, The a m o u n t o f mixing can be d e t e r m i n e d by c o m p a r i n g the signal with the same-sign combination versus that with the opposite-sign c o m b i n a t i o n . We call the opposite-sign m o d e a right-charge combination, a n d the same sign-mode a wrong-charge combination. The data sample used for our study corresponds to an integrated luminosity o f 199 p b - J, o b t a i n e d with the A R G U S detector at the D O R I S II storage ring on the "f(2S) and "f(4S) resonances, and in the nearby continuum. The configuration and performance o f the A R G U S detector, and i n f o r m a t i o n on multihadron event selection and trigger conditions can be found in previous publications [ 9 ]. F o r this analysis we have used mostly information from the main drift c h a m b e r ( m o m e n t u m resolution o f ap/p=O.O12 at 1 GeV/c and dE/dx resolution o f 5.4%) and the timeof-flight ( T O F ) counters ( t i m e resolution o f a(t) = 220 ps). The m e t h o d o f particle identification for charged particles is the same as used previously [ 9 ]. F o r each charged track, the e, p, x, K and p particle assignments are used to obtain a corresponding Z 2 from the d E / d x and T O F m e a s u r e m e n t s for each particle hy-
Volume 199, number 3
PHYSICS LETTERS B
pothesis. A likelihood ratio, l,, for each of these particle hypotheses is then calculated: wi e x p ( - Z ~ / 2 ) li=zjwj e x p ( - z ~ / 2 ) '
0 . 5 ~leV/c 2
P,ot(K+g-)/P~o,(K-n + ) < 10 -3
,
ARGUS
40
i,j=e, p, x, K, p,
where the w, are a priori weights. Weights are set to 1 for all hypotheses except that for n, which is set to 5, a rough a p p r o x i m a t i o n to the observed abundances. A track is used for all particle hypotheses for which the likelihood ratio exceeds 10%. D t~mesons are reconstructed in the decay channel D ° ~ K - n +. A mass-constraining k i n e m a t i c fit is applied to all K - n + c o m b i n a t i o n s with an invariant mass within 30 MeV/c 2 o f the D Omass. Next, we a d d a second pion o f appropriate charge and compare the n u m b e r o f events above background at the D *+ mass in the D°n + and D ° n - mass distributions. Since the fragmentation o f c h a r m e d quarks produces a h a r d D* + m o m e n t u m spectrum, a requirem e n t that the scaled m o m e n t u m o f the D *+ system, x~,=-PD,+/P. . . . . exceed 0.6 greatly reduces the combinatorial background. The d i s t r i b u t i o n o f cos 0~, where 0* is the angle between the kaon and D o flight direction in the D ° rest frame, should be isotropic. In contrast, the distribution from r a n d o m combinations o f particles from the same jet tends to peak strongly at small forward angles. Therefore, we require cos 0* < 0.85 to further suppress c o m b i n a t o r i a l background. A d d i t i o n a l cuts were a p p l i e d to r e m o v e correlated b a c k g r o u n d sources arising from particle misidentification. R e m o v a l o f such backgrounds is critical, since single-particle misidentification for the Cab i b b o - s u p p r e s s e d D ° - - . K + K - and x +n - decays, and double misidentification o f the allowed D ° - * K - n + mode, can feed events from the right-charge into the wrong-charge category. To suppress a m b i g u i t y in the identification of the daughter particles o f the D O, the ratio o f the kaon to p i o n likelihood, lK/l~, must exceed unity for those particles used as kaons. Likewise, IJlK> 1 was required for those particles used as pions. F u r t h e r cuts are m a d e using the total probability, P, ot, d e r i v e d from the sum o f the Z2'S from the particle identification o f daughter particles and the Z 2 for the D O mass hypothesis. Specifically, the following ratios must be satisfied:
24 December 1987
30 20
10
0 .00
2.02
.01
M(D°,<)
,03
[CeV/o~]
Fig. 1. Invariant mass distribution for right-sign combinations, ( K - x + )x +, shown by the histogram, and wrong-sign combinations, ( K - 7t + ) x -, shown by the solid points.
and P~ot ( K+ K - )/P,o, ( K - ~ + ) < 10 -2 , P,o,(X + n - )/P,o, ( K - n + ) < 10 -2 , where the correct assignment is taken to be ( K - x + ). Contributions from doubly Cabibbo-suppressed decays, e.g., I ) ° ~ K - x +, are expected [ I 0 ] to have a rate p r o p o r t i o n a l to sin40c, and are therefore neglected. Fig. 1. shows the D°x invariant mass plots for both sign modes. We take 2 . 0 0 8 5 < M ( D ° n ) < 2 . 0 1 1 5 GeV/c 2 as the signal region and find 162 events in the right-sign and no events in the wrong-sign categories, respectively. This yields an upper limit o f 1.4% (90% CL) for r = F ( D ° - , O ° - , X ' ) / F ( D ° - , X ) . The cuts have been chosen to m i n i m i z e the ratio o f the expected n u m b e r o f background events to the number o f right-sign signal events, where the former was estimated by extrapolating from the observed distribution above 2.015 GeV/c 2. I f the expected background drops much below one event, it becomes selfdefeating to continue optimizing. The procedure is unbiased, except that the actual n u m b e r o f background events is discrete. I f we restrict ourselves to the case where no wrong-sign events are observed, then the limit changes between 1.2 and 1.4% as the cuts are varied. I f one event appears, the limit ranges from 1.6 to 1.9%. The mixing rate is related to the mass difference 449
Volume 199, number 3
PHYSICS LETTERS B
( g m ) a n d the difference in the decay w i d t h s ( S F ) o f the two C P mass eigenstates [ 11 ], ( S m / F ) "- + ( S F / 2 F ) 2 r=2+ (Sm/F)2 - (SF/2F) 2 ,
where F is the m e a n decay width. F r o m o u r l i m i t , we f i n d that g r n / F is less t h a n 0.17 (90% C L ) , ass u m i n g 5 F < < g m . U s i n g a D o lifetime 4 . 3 X 10 -~3 s [ 12] this i m p l i e s that ~ m ~ < 2 . 6 × 10 - 4 eV. In c o n c l u s i o n , we have o b s e r v e d n o e v i d e n c e for D ° - I ) ° m i x i n g a n d set a n u p p e r l i m i t o f 1.4% at the 90% c o n f i d e n c e level. This l i m i t holds also for the d o u b l y C a b i b b o - s u p p r e s s e d decay D ° - ~ K + x - . I n c o m p a r i s o n , the o b s e r v a t i o n s by M A R K III o f three e v e n t s with strangeness +_2, w h i c h m a y possibly be d u e to D ° - D ° m i x i n g , a n d 162 e v e n t s with strangeness 0 [5] in a s a m p l e o f ~ " ~ D ° I T ) ° decay corres p o n d s to a m i x i n g rate o f a b o u t 1.6% [ 11 ]. However, it s h o u l d be n o t e d that d u e to c o h e r e n c e effects, a n d the fact that M A R K III uses several D o decay c h a n nels in c o m b i n a t i o n , the two search m e t h o d s have different sensitivities to the c o n t r i b u t i o n o f d o u b l y C a b i b b o - s u p p r e s s e d decays [ 10 ].
It is a pleasure to t h a n k U, D j u a n d a , E. K o n r a d , E. Michel a n d W. R e i n s c h for their c o m p e t e n t technical help in r u n n i n g the e x p e r i m e n t a n d processing the data. We t h a n k Dr. H. N e s e m a n n , B. Sarau a n d the D O R I S group for the good o p e r a t i o n o f the storage ring. T h e v i s i t i n g groups wish to t h a n k the D E S Y directorate for the s u p p o r t a n d k i n d h o s p i t a l i t y ext e n d e d to them,
450
24 December 1987
References
[ 1] M.K. Gaillard and B.W. Lee, Phys. Rev. D 10 (1974) 897. [2] T. Inami and C.S. Lira, Progr. Theor. Phys. 65 (1981) 297; A. Datta and D. Kumbhakar, Z. Phys. C 27 (1985) 515. [3] L.L. Chau, Phys. Rep. 95 (1983) 1. [4] L. Wolfenstein, Phys. LeU. B 164 (1985) 170; J.F. Donoghue et al., Phys. Rev. D 33 (1986) 179. [5 ] R.H. Schindler, Proc. SLAC Summer Institute of Particle Physics (1985 ). [6] A. Datta, Phys. Lett. B 154 (1985) 287, and references therein. [ 7 ] EM Collab., J.J. Aubert et al., Phys. Lett. B 106 ( 1981 ) 419; A. Bodek et al., Phys. Lett. B 113 (1982) 82; A.C. Benvenuti et al., Phys. Lett. B 158 (1985) 531; W.C. Louis et al., Phys. Rev. LeU. 56 (1986) 1027. [8] G. Feldman et al., Phys. Rev. Lett. 38 (1977) 1313; G. Goldhaber et al., Phys. Lett. B 69 (1977) 503; CLEO Collab., P. Avery et al., Phys. Rev. Lett. 44 (1980) 1309; ACCMOR Collab., R. Bailey et al., Phys. Lett. B 132 (1983) 237; TASSO Collab., M. Althoffet al., Phys. Lett. B 138 (1984) 317; ARGUS Collab., H. Albrecht et al., Phys. Lett. B 150 (1985) 235; DELCO Collab., H. Yamamoto et al., Phys. Rev. Lett. 54 (1985) 522; HRS Collab., S. Abachi et al., Phys. Lett. B 182 (1986) 101; TPC Collab., H. Aihava et al., Phys. Rev. D 34 (1986) 1945. [9] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 134 (1984) 137;B 150 (1985) 235;B 156 (1985) 134. [ 10] I. Bigi and A.I. Sanda, Phys. Lett. B 171 (1986) 320. [ 11 ]L.B. Okun, V.I. Zakharov and B.M. Pontecorvo, Nuovo Cimento Lett. 13 (1975) 218; R.L. Kingsley et al., Phys. Rev. D l 1 (1975) 1919; A. Pais and S.B. Treiman, Phys. Rev. D 12 (1975) 2744. [ 12 ] Particle Data Group, M. Aguilar-Benitez et al., Review of particle properties, Phys. Lett. B 170 (1986) 1.
PHYSICS LETTERSB
24 December 1987
AN UPPER LIMIT ON D°-I) ° MIXING ARGUS Collaboration H. ALBRECHT, A.A. ANDAM 1, U. BINDER, P. B()CKMANN, R. GL~,SER, G. HARDER, A. NIPPE, M. SCHAFER, W. SCHMIDT-PARZEFALL, H. SCHRC)DER, H.D. SCHULZ, R. WURTH, A. YAGIL 2.3 DESE D-2000 Hamburg, Fed. Rep. Germany
J.P. DONKER, A. DRESCHER, D. KAMP, H. KOLANOSKI, U. MATTHIESEN, H. SCHECK, B. SPAAN, J. SPENGLER, D. WEGENER lnstitutj~r Physik a, Universitat Dortmund, D-6400 Dortmund, Fed. Rep. Germany
J.C. GABRIEL, T. RUF, K.R. SCHUBERT, J. STIEWE, K. STRAHL, R. WALDI lnstitut~r Hochenergiephysik s Universitiit Heidelberg, D-6900 Heidelberg, Fed. Rep. Germany
K.W. EDWARDS 6, W.R. FRISKEN 7, D.J. GILKINSON 8, D.M. GINGRICH 8, H. KAPITZA 6, P.C.H. KIM s, R. KUTSCHKE 8 D.B. MACFARLANE 9, J.A. McKENNA 8, K.W. McLEAN 9 A.W. NILSSON 9, R.S. ORR 8, p. PADLEY 8, J.A. PARSONS 8, P.M. PATEL 9, J.D. PRENTICE 8, H.C.J. SEYWERD 8, J.D. SWAIN 8, G. TSIPOLITIS 9, T.-S. YOON 8, J.C. YUN 6 Institute of Particle Physics m. Canada
R. AMMAR, S. BALL, D. COPPAGE, R. DAVIS, S. KANEKAL, N. KWAK University of Kansas ' ~, Lawrence, KS 66045, USA
B. BOSTJANCIC, G. KERNEL, M. PLESKO lnstitut J. Stefan and Oddelek za fiziko ~2, Univerza v Ljubljani, 61111 Ljubljana, Yugoslavia
L. JONSSON Institute of Physics ~3, University of Lund, 8-22362 Lund, Sweden
A. BABAEV, M. DANILOV, B. FOMINYKH, A. GOLUTVIN, I. GORELOV, V. LUBIMOV, V. MATVEEV, V. RYLTSOV, A. SEMENOV, V. SHEVCHENKO, V. SOLOSHENKO, V. TCHISTILIN, I. TICHOMIROV, Yu. ZAITSEV Institute of Theoretical and Experimental Physics, 117259 Moscow, USSR
R. CHILDERS, C.W. DARDEN, R.C. FERNHOLZ and Y. OKU University of South Carolina ~4, Columbia, SC 29208, USA
Received 10 August 1987
For footnotessee next page.
0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
447
Volume 199, number 3
PHYSICS LETTERS B
24 December 1987
We have searched for D°-IT)° mixing in the cascade decay of D *+, using the excellent particle identification of the ARGUS detector. No mixing was observed, leading to an upper limit of 1.4% (90% CL) for F(D°--,17)°-~X')/F(D°--,X).
Quark flavour is not conserved in weak interactions. One manifestation o f this is the K ° ~ I ~ ° transition, which is allowed via the A S = 2 box d i a g r a m [ 1 ]. The analogue for neutral c h a r m mesons, D°-13 ° mixing is, however, highly suppressed in the six-quark s t a n d a r d model o f electroweak interactions [2] ~ , even after accounting for the long-distance effects [4]. Therefore, a recent report by the M A R K III collaboration [5] o f possible D°-13 ° mixing at about 1.6% level has generated considerable interest. While e x p e r i m e n t a l sensitivities are still orders of magnitude away from the values p r e d i c t e d in the s t a n d a r d model, mixing searches are nevertheless desirable as a test for the high level D°-13 ° mixing p r e d i c t e d by some o f the theoretical ideas which go b e y o n d the s t a n d a r d m o d e l [ 6]. The two most c o m m o n m e t h o d s used to search for D°-13 ° mixing are (i) the study o f the d i - m u o n events (or t r i - m u o n events in the case o f g-scattering exp e r i m e n t s ) arising from the semi-leptonic decays of the c h a r m - a n t i - c h a r m h a d r o n pairs [ 7 ] and (ii) full reconstruction o f the D o meson from its daughter particles in the cascade decay o f the D* + [8 ] ~2. The first m e t h o d is m o d e l - d e p e n d e n t , since it requires On leave from University of Science and Technology, Kumasi, Ghana. 2 Weizmann Institute of Science, 76100 Rehovot, Israel. 3 Supported by the Minerva Stiftung. Supported by the German Bundesministerium f'tir Forschung und Technologie under contract number 054DO5 I P. 5 Supported by the German Bundesministerium ftir Forschung und Technologie under contract number 054HD24P. ~'Carleton University, Ottawa, Ontario, Canada KIS 5B6. v York University, Downsview, Ontario, Canada M3J 1P3. University of Toronto, Toronto, Ontario, Canada, M5S IA7. McGill University, Montreal, Quebec, Canada H3A 2T8. u~Supported by the Natural Sciences and Engineering Research Council, Canada. f~ Supported by the US National Science Foundation. ~2Supported by Raziskovalna skupnost Slovenije and the Internationales Btiro KfA, Jiilieh. ~3Supported by the Swedish Research Council. ~4Supported by the US Department of Energy under contract DEAS09-80ER 10690. ~ See ref. [3] for a review. ~" In this paper references to a particular particle state should be taken to imply both the particle and its anti-particle. 448
a s s u m p t i o n s about the c h a r m p r o d u c t i o n cross section, the semi-leptonic branching fractions of all c h a r m e d particles, and the fraction o f D o mesons p r o d u c e d in c h a r m e d quark fragmentation. We fully reconstruct the D O mesons from D *+ decays, a m e t h o d which is completely m o d e l independent. D* + decays are also particularly suited to obtaining a signal essentially flee o f c o m b i n a t o r i a l background. This is due to the small Q-value for the decay D *+ ~ D ° x +, which leads to an excellent mass resolution for the D *+, if the mass o f the D o decay products is constrained by a k i n e m a t i c fit to the n o m i n a l D O mass. Moreover, mixing searches are possible because the charge of the soft p i o n tags whether a D Oor I3 0 was produced. In the weak decay o f the D ° ( c l i ) , the c quark decays to an s quark, and so the sign of the charged daughter kaon is negative; thus, the sign o f the charged kaon from the D Odecay is opposite to the sign o f the pion from the D* + decay. If mixing were to occur, the signs would be the same, The a m o u n t o f mixing can be d e t e r m i n e d by c o m p a r i n g the signal with the same-sign combination versus that with the opposite-sign c o m b i n a t i o n . We call the opposite-sign m o d e a right-charge combination, a n d the same sign-mode a wrong-charge combination. The data sample used for our study corresponds to an integrated luminosity o f 199 p b - J, o b t a i n e d with the A R G U S detector at the D O R I S II storage ring on the "f(2S) and "f(4S) resonances, and in the nearby continuum. The configuration and performance o f the A R G U S detector, and i n f o r m a t i o n on multihadron event selection and trigger conditions can be found in previous publications [ 9 ]. F o r this analysis we have used mostly information from the main drift c h a m b e r ( m o m e n t u m resolution o f ap/p=O.O12 at 1 GeV/c and dE/dx resolution o f 5.4%) and the timeof-flight ( T O F ) counters ( t i m e resolution o f a(t) = 220 ps). The m e t h o d o f particle identification for charged particles is the same as used previously [ 9 ]. F o r each charged track, the e, p, x, K and p particle assignments are used to obtain a corresponding Z 2 from the d E / d x and T O F m e a s u r e m e n t s for each particle hy-
Volume 199, number 3
PHYSICS LETTERS B
pothesis. A likelihood ratio, l,, for each of these particle hypotheses is then calculated: wi e x p ( - Z ~ / 2 ) li=zjwj e x p ( - z ~ / 2 ) '
0 . 5 ~leV/c 2
P,ot(K+g-)/P~o,(K-n + ) < 10 -3
,
ARGUS
40
i,j=e, p, x, K, p,
where the w, are a priori weights. Weights are set to 1 for all hypotheses except that for n, which is set to 5, a rough a p p r o x i m a t i o n to the observed abundances. A track is used for all particle hypotheses for which the likelihood ratio exceeds 10%. D t~mesons are reconstructed in the decay channel D ° ~ K - n +. A mass-constraining k i n e m a t i c fit is applied to all K - n + c o m b i n a t i o n s with an invariant mass within 30 MeV/c 2 o f the D Omass. Next, we a d d a second pion o f appropriate charge and compare the n u m b e r o f events above background at the D *+ mass in the D°n + and D ° n - mass distributions. Since the fragmentation o f c h a r m e d quarks produces a h a r d D* + m o m e n t u m spectrum, a requirem e n t that the scaled m o m e n t u m o f the D *+ system, x~,=-PD,+/P. . . . . exceed 0.6 greatly reduces the combinatorial background. The d i s t r i b u t i o n o f cos 0~, where 0* is the angle between the kaon and D o flight direction in the D ° rest frame, should be isotropic. In contrast, the distribution from r a n d o m combinations o f particles from the same jet tends to peak strongly at small forward angles. Therefore, we require cos 0* < 0.85 to further suppress c o m b i n a t o r i a l background. A d d i t i o n a l cuts were a p p l i e d to r e m o v e correlated b a c k g r o u n d sources arising from particle misidentification. R e m o v a l o f such backgrounds is critical, since single-particle misidentification for the Cab i b b o - s u p p r e s s e d D ° - - . K + K - and x +n - decays, and double misidentification o f the allowed D ° - * K - n + mode, can feed events from the right-charge into the wrong-charge category. To suppress a m b i g u i t y in the identification of the daughter particles o f the D O, the ratio o f the kaon to p i o n likelihood, lK/l~, must exceed unity for those particles used as kaons. Likewise, IJlK> 1 was required for those particles used as pions. F u r t h e r cuts are m a d e using the total probability, P, ot, d e r i v e d from the sum o f the Z2'S from the particle identification o f daughter particles and the Z 2 for the D O mass hypothesis. Specifically, the following ratios must be satisfied:
24 December 1987
30 20
10
0 .00
2.02
.01
M(D°,<)
,03
[CeV/o~]
Fig. 1. Invariant mass distribution for right-sign combinations, ( K - x + )x +, shown by the histogram, and wrong-sign combinations, ( K - 7t + ) x -, shown by the solid points.
and P~ot ( K+ K - )/P,o, ( K - ~ + ) < 10 -2 , P,o,(X + n - )/P,o, ( K - n + ) < 10 -2 , where the correct assignment is taken to be ( K - x + ). Contributions from doubly Cabibbo-suppressed decays, e.g., I ) ° ~ K - x +, are expected [ I 0 ] to have a rate p r o p o r t i o n a l to sin40c, and are therefore neglected. Fig. 1. shows the D°x invariant mass plots for both sign modes. We take 2 . 0 0 8 5 < M ( D ° n ) < 2 . 0 1 1 5 GeV/c 2 as the signal region and find 162 events in the right-sign and no events in the wrong-sign categories, respectively. This yields an upper limit o f 1.4% (90% CL) for r = F ( D ° - , O ° - , X ' ) / F ( D ° - , X ) . The cuts have been chosen to m i n i m i z e the ratio o f the expected n u m b e r o f background events to the number o f right-sign signal events, where the former was estimated by extrapolating from the observed distribution above 2.015 GeV/c 2. I f the expected background drops much below one event, it becomes selfdefeating to continue optimizing. The procedure is unbiased, except that the actual n u m b e r o f background events is discrete. I f we restrict ourselves to the case where no wrong-sign events are observed, then the limit changes between 1.2 and 1.4% as the cuts are varied. I f one event appears, the limit ranges from 1.6 to 1.9%. The mixing rate is related to the mass difference 449
Volume 199, number 3
PHYSICS LETTERS B
( g m ) a n d the difference in the decay w i d t h s ( S F ) o f the two C P mass eigenstates [ 11 ], ( S m / F ) "- + ( S F / 2 F ) 2 r=2+ (Sm/F)2 - (SF/2F) 2 ,
where F is the m e a n decay width. F r o m o u r l i m i t , we f i n d that g r n / F is less t h a n 0.17 (90% C L ) , ass u m i n g 5 F < < g m . U s i n g a D o lifetime 4 . 3 X 10 -~3 s [ 12] this i m p l i e s that ~ m ~ < 2 . 6 × 10 - 4 eV. In c o n c l u s i o n , we have o b s e r v e d n o e v i d e n c e for D ° - I ) ° m i x i n g a n d set a n u p p e r l i m i t o f 1.4% at the 90% c o n f i d e n c e level. This l i m i t holds also for the d o u b l y C a b i b b o - s u p p r e s s e d decay D ° - ~ K + x - . I n c o m p a r i s o n , the o b s e r v a t i o n s by M A R K III o f three e v e n t s with strangeness +_2, w h i c h m a y possibly be d u e to D ° - D ° m i x i n g , a n d 162 e v e n t s with strangeness 0 [5] in a s a m p l e o f ~ " ~ D ° I T ) ° decay corres p o n d s to a m i x i n g rate o f a b o u t 1.6% [ 11 ]. However, it s h o u l d be n o t e d that d u e to c o h e r e n c e effects, a n d the fact that M A R K III uses several D o decay c h a n nels in c o m b i n a t i o n , the two search m e t h o d s have different sensitivities to the c o n t r i b u t i o n o f d o u b l y C a b i b b o - s u p p r e s s e d decays [ 10 ].
It is a pleasure to t h a n k U, D j u a n d a , E. K o n r a d , E. Michel a n d W. R e i n s c h for their c o m p e t e n t technical help in r u n n i n g the e x p e r i m e n t a n d processing the data. We t h a n k Dr. H. N e s e m a n n , B. Sarau a n d the D O R I S group for the good o p e r a t i o n o f the storage ring. T h e v i s i t i n g groups wish to t h a n k the D E S Y directorate for the s u p p o r t a n d k i n d h o s p i t a l i t y ext e n d e d to them,
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References
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