- Email: [email protected]
Charm decays and D0-D̄0 mixing
~ILICLEAR ~HYSICS
Nuclear Physics A675 (2000) 291c-296c
ELSEVIER
Charm
A
www.elsevier.nl/locate/npe
decays and D°-D ° mixing
M. A l e p p o ~ ~Dipartimento di Fisica, Universit~ di Milano, and I.N.F.N. sezione di Milano, Via Celoria 16, 20133 Milano, I t a l y The LEP1 d a t a sample (4 million hadronic Z decays) recorded by the A L E P H detector is analysed to s t u d y charmed particle decays. The measurements of t h e hadronic branching ratios D O -+ K-~r+, and of the purely leptonic decays D~ --* ~-u and Ds --+ #u are presented. T h e L = I charmed mesons D** and D** are reconstructed in several exclusive decay channels and their production rates are measured. The contributions from charm quark fragmentation and from b hadron decays are disentangled. A s t u d y of decays D *+ --+ D%r +, with D O decaying D o --* K-~r + and D O --+ K % r - is shown. T h e relative branching ratio B(D ° --~ K % r - ) / B ( D ° --~ K - r +) is measured and t h e contribution to D o --+ K % r - decay given b y D°-I) ° mixing is extracted with a s t u d y of D o proper t i m e distribution. 1. T H E
BRANCHING
RATIO
D O -~ K-~r +
T h e branching ratio for the decay D o --4 K - r + enters several D meson analysis and m a n y measurements involving B hadron decays. A precise measurement of this quantity is obtained by fully reconstructing t h e signal events in t h e cascade D *+ -+ D%r +, D o --* K-~r + and comparing t h e m with an inclusively selected sample of D *+ --* D%r+ decays [1]. Both the exclusive and t h e inclusive selections m a k e use of t h e low m o m e n t u m ( s o f t ) p i o n ~r8 to tag t h e D* decay. The branching ratio is then e x t r a c t e d from the formula B(D o --+ g _ r + ) -
NDO~K-~+ ND.+_~D%+
x
¢~'~z e:~cl
- -
(1)
where ND,+_,D0~+ is t h e n u m b e r of events selected in the inclusive analysis, NDO-~K-~÷ is t h e n u m b e r of events exclusive reconstructed in the decay chain D *+ --+ D%r+~D ° --+ K-~r +, c~cl and e ~ d are the respective selection efficiencies. Each of t h e two samples is divided in six subsamples selecting the ~rs in m o m e n t u m bins of width 0.5 GeV/c. 1.1. E x c l u s i v e a n a l y s i s Tracks with m o m e n t u m in the range between 1 and 4 G e V / c are taken as ~rs candidates. Two oppositely charged tracks are added to form a D o candidate assigning the kaon mass to t h e t r a c k with charge opposite to the ~rs and t h e pion to the other one. The combinations are retained if t h e decay angle of the kaon in the D o rest frame 9~< satisfies I cos 0~: I< 0.8 and if 1835 M e V / c 2 <1 M(K~r) I< 1865 M e V / c 2. N u m b e r of candidates is counted in t h e region 0.1435 G e V / c 2 <1 M(Zr~rs) - M(Z~r) I< 0.1475 G e V / c 2. 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0375-9474(00)00268-2
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M. Aleppo /Nuclear Physics A675 (2000) 291c-296c
1.2. I n c l u s i v e a n a l y s i s The signal relies on observed 7r, transverse m o m e n t u m relative to the D *+ line of flight. Soft pion candidates are selected as in the exclusive analysis. The axis of the nearest jet to the ~r, is taken as D *+ direction. ND,+_~O0~+ is calculated with a fit to the p~ distribution. Background distribution is parameterised with an inverse polynomial function. Signal distribution is given by a sum of three contributions: Z -4 ce, Z --+ bb and gluon splitting. The shapes are taken from Monte Carlo, while the relative fractions are estimated using previous measurements [2,3] and the value of Rb = FZ_+bD/FZ~haa and R~ = l~z--+ce/i~Z~had fixed to Standard Model values. 1.3. C o n c l u s i o n s The branching ratio is calculated according to eq. 1 for each ~rs m o m e n t u m bin. The results are combined giving B(D ° --+ K-~r +) = (3.90 ± 0.09 ± 0.12)%, at present the best single measurement result [7]. 2. L E P T O N I C
D E C A Y S O F Ds M E S O N S
The rate of the leptonic D mesons decays depends on to the quark-antiquark wave function at the origin, which is described by decay constant fD~- The B - B mixing rates are proportional to square of the corresponding decay constants, that at present can not be measured directly. The large uncertainties affecting the calculation of fB do not allow to translate the precise measurement of the mass difference between the B ° mass eigenstates into tight constrains on the Vtd element of the CKM matrix. A fD, precise measurement is a valid check of the theoretical calculation of meson decay constants and can be used as constraint for lattice QCD and QCD sum-rules evaluations. Preliminary measurements of B(D~ -+ Tu) and/3(Do -+ #u) are presented [4]. 2.1. D~ --+ Tu a n a l y s i s The candidates are searched in the decay chain c+e - -+ c5, c -4 Ds, Ds -4 TU, T ---~ eff~u~or T --+ #ffUV~. Each event is divided into two hemispheres according to the plane orthogonal to the thrust axis. Hemispheres with an identified lepton and large missing energy are retained. Electron identification is based on the shower shape in the Electromagnetic Calorimeter and on the specific ionization loss measured into the T P C ( d E / d x ) , while muon identification relies on digital patterns in the Hadronic Calorimeter and hits in muon chambers. Sets of high rapidity and low rapidity tracks are defined in each hemisphere. The confidence levels that these sets originate from the interaction point are then calculated. Cuts are applied on the confidence leve] for the low rapidity tracks in each hemisphere to reduce the bb background, and on the high rapidity tracks to suppress c~ background. Do energy and m o m e n t u m are determined requiring four m o m e n t u m conservation and imposing the mass constraint [ E ~ - p~)~]1/2 = MD~. The background is reduced requiring ED~ > 25 GeV. Several variables are linearly combined to create two discriminating variables U~ and Us to separate signal from cg and bb backgrounds respectively. From the signal extracted from a two-dimensional unbinned maximum likelihood fit to the U~ vs Ub distribution B(D~ -4 ru) = [4.93 -t- 1.43(star.) + 2.05(syst.) -'- 1.62(BR)] and [4.87 J: 0.93(star.) +
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1.63(syst.) 4- 1.37(BR)] are measured in the muon channel and in the electron channel, respectively. The errors labelled BR are due to the error on B(D~ --+ ¢~r) measurement, that enters in the calculation of normalisation term P(c -4 D~) [5,6]. The two results are combined, giving B(Ds .4 ru) = [4.9 3: 0.9(star.) + 1.6(syst.) + 1.4(BR)]. 2.2. D~ --+ #u a n a l y s i s The selection strategy is similar to the strategy in D, .4 Tu analysis. Loose requirements in the muon identification algorithm are used. The missing neutrino is reconstructed performing a two-constraint kinematic fit, in which the missing mass is constrained to be zero and muon and neutrino momenta and the interaction point are constrained to lie in the same plane. The bb and c~ backgrounds are reduced with the same techniques. Two discriminant variables U~ and Ub are defined analogously to the D~ --+ Tu analysis. The signal is measured from a fit to slices of M(#u) in 36 bins (6 x 6) in the (Ub, U~) plane. The branching ratio in the muon channel is measured to be B(D, --+ #u) = [0.64 + 0.08(stat.)d: 0.21(syst.)4-0.15(BR)], where again the error labelled BR. comes from the uncertainty on B(D~ -+ ¢~r). 2.3. C o n c l u s i o n s Preliminary measurements of B(D~ .4 Tu) and B(D~ -+ #u) are presented. The results from the two channels are combined to evaluate the D~ decay constant: fD~ = 261 3: 20(star.) 3:43(syst.)3:35(BR). This value is consistent with the previous measurements [7].
3. O R B I T A L L Y
EXCITED
CHARMED
DECAYS
In the heavy quark limit, H Q E T predicts the cC1 mesons with L = I to split in two degenerated doublets according to the angular momentum j of the light quark. One (j = ½) doublet with j R = 0 +, 1+, usually referred to as D(*~)0 and D(*~)a, and one (j = ~) doublet j R = 1 +, 2 +, indicated with D(~)l and D(*)2. It is expected that the decays of these charmed and charmed-strange mesons are dominated by two body decays to D(*)~r and D(*)K, respectively. Only the members of doublets j = 2, that can decay only through Dwave and are therefore narrow, are observed in A L E P H [4,8]. The member of the doublet j = 1 decay through S-waves and are expected to be wide. 3.1. T h e D + a n d D~*+ m e s o n s d e c a y s D~*+ state is reconstructed in the decay to D°K + ,while D + in the decays to D*°K + and D*+K}. D *+ mesons are reconstructed in the decay channel D *+ --+ D%r +, and the D o mesons are reconstructed in the decays to K-~r +, K-~r+~r-Tr + and K-~r+~r °. Charged kaons and pions are separated using dE/dx. Signal is extracted fitting the mass difference distribution A M = M ( D *+, K}) - M(D *+) - M(K}) + M t ~ ( K ° ) . The combinatorial background shape is parameterised with a function
dN d(AM)
-- n - ( A M -- a) b. e -~(AM-a)
(2)
The signal is fitted with a Breit Wigner function convoluted with a Gaussian. D *° mesons decay into D O by emitting a pion or a photon. No attempt is made to reconstruct these particles. According to Monte Carlo this doesn't significantly worsen the resolution. In the
M. Aleppo /Nuclear Physics A675 (2000) 291c-296c
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two decay channels D + --+ D*°K + and D *+ --+ D°K + signal is determined with an unbinned m a x i m u m likelihood to the mass difference distribution A M = M ( D °, K +) - M ( D ° ) . Only t h e best signal to background ratio channel D o --+ K-Tr + is used. The fitting function is t h e same used in the D*+K~ channel, except for D *+ decay in which combinatorial background is parameterised with a linear function. In order to determine the production rates c --+ D** and b --* D~* one sample enriched in c~ and one in bV~ are selected. The properties of long lifetime of b hadrons and harder energy spectrum of D mesons produced in fragmentation of p r i m a r y c quarks are used. Cuts on the probability of all tracks in the hemisphere of t h e D~* meson to come from the p r i m a r y vertex in the hemisphere of t h e D** meson, scaled energy of D~* mesons and on the distance of the reconstructed D o vertex to the p r i m a r y vertex are applied.
3.2.
The D1 and D~ mesons decays
D~+ state is reconstructed in the decay D~+ ~ D%r + , D~° in the decays D~° --+ D*+Tr-, D+Tr - and D o in t h e decay D O -+ D*+Tr- . D *+ and D o mesons are reconstructed in the same channels as in D** analysis. Charged D mesons are reconstructed in the decay D + --+ K-Tr+Tr +. The background is reduced applying cuts the angle between the sphericity axis of the D O/+ system and the D O/+ direction in the D O/+ rest frame, on kaon m o m e n t u m and on the measured dE/dx. A b / c contribution are separated analogously as in t h e D** analysis. Signal is e x t r a c t e d from t h e mass difference distribution A M = M(D(*), 7 r s ) - M(D(*)). The combinatorial background shape is parameterised with the function 2, in which the p a r a m e t e r a is fixed to nominal value of pion mass. The signal is fitted as described in Sec. 3.1. 3.3. C o n c l u s i o n s From t h e observed number of D** mesons in t h e c and in t h e b enriched samples, assuming t h a t D1 --* D*Tr and D~ --+ D(*)~r only and t h a t D~a -+ D*K only and B(D *+ --+ D°K +) = 45%, t h e production rates from c and b quarks are: c --+ D1
--
c --+ D~ =
(3.2 + 0.9)%, c ~ D~I = (0.77 4- 0.22)% (9.4 4- 1.9)%, c --~ D~2 = (1.3 4- 0.5)%
b --* D1
=
(4.6 -t- 1.4)%, b --+ D~I = (1.1 4- 0.4)%
b --+ D~
<
3.9%(95%CL),b --+ D*2 = (2.2 + 0.9)%
4.
T H E B(D ° -~ K % r - ) / B ( D ° -+ K - r +) A N D D ° - D ° M I X I N G
Both mass and width differences between weak eigenstates of t h e D°-~) ° system can cause mixing. The rate of such a mixing is predicted from t h e S t a n d a r d Model to be orders of m a g n i t u d e below t h e current experimental limits, while m a y approach t h e m in extensions of the S t a n d a r d Model. A search for D°-D ° mixing is performed using the decay chain D *+ --~ D%r +, D o --~ K+~r - . The K % r - system can be produced by a D o both in a direct Doubly Cabibbo Suppressed Decay (DCSD) and by an oscillation followed by a Cabibbo Favoured Decay I) ° --~ K % r - . The contribution of each component is obtained from a s t u d y of D O proper t i m e distribution. Assuming small mixing and neglecting
M. Aleppo /Nuclear Physics A675 (2000) 291c-296c
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CP-violating terms, the time evolution for D O --+ K%r- decay has the following form
[.o.,o
+
o-,-,
(3)
where r is the D O lifetime (r = 0.415 ps), RDCSD is the ratio B(D ° --+ K+zc-)/B(D ° K-Tr+), ~ is the ratio B(D ° -+ I) ° --+ K % r - ) / B ( D ° ---* K - z +) and cos ¢ is the phase angle parameterising the interference between the two processes. Measurement o f B(D ° ---+K % r - ) / B ( D ° --+ K - r +) Each pair of oppositely-charged tracks are combined with the two mass assignments K-rr + and ~r-K +. The signal is identified by selecting candidates in the region I M(KIr) MD 0 l< 30 M e V / c 2. If both hypotheses satisfy the mass cut the event is rejected. The decay angle of the kaon in the D O rest frame 0~ is required to satisfy I cos 0~¢ l< 0.8. Only combinations in which the two tracks form a common vertex and each track have at least one V D E T hit are kept. The d E / d x of each track is used to suppress misidentification of a pion with a kaon and vice versa. An extra pion zrs is added to build D* candidates. The background is suppressed requiring ED,/Eb > 0.5, where Eb is the beam energy. The rightsign ( K-~r%r + combinations ) and wrong-sign ( K+~r-~r + combinations ) signal candidates are counted selecting events in the window 0.1435 GeV/c 2 < l M(K~rzrs) - M(Krr) l< 0.1475 G e V / c 2 (fig. 1). After combinatorial background has been subtracted the number of signal events found in the right-sign sample and in the wrong-sign sample are NRs = 1038.8 4- 32.5(star.) -4- 4.3(syst.) and Nws = 21.3 4- 6.1(stat.) 4- 3.4(syst.), respectively. The number of physics background events in the wrong-sign sample is estimated using 4.1.
18 I
300
• Data
16
Combinatorial Background
ALEPH
14
%, 250
•
Data
~
Combinatorial Background Comi
(b)
~o
10
÷ 50
0 0.13
?
ALEPH
100
÷
J--.' 2'." 0.14
0.15
0.16
0.17
M(K-rr÷n'*,) - M(K-'~*) (OeV/c=)
0.18
i O--i
0.13
i *! 0.14
0.15
0.16
0.17
0.18
u(K*~-~:) - U(K',~-) (ZeV/o9
Figure 1. Mass difference distribution for D *+ --+ D°zr+, D O --+ K-Tr + candidates (a) and D O --+ K % r - candidates (b)
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M. Aleppo/Nuclear Physics A675 (2000) 291c-296c
real and Monte Carlo data to be 2.2 ± 1.0; this is subtracted from the selected sample leading to a signal of NDO-~K+,- = 19.1 ± 6.1(star.) ± 3.5(syst.). The physics background contamination in the right-sign sample is negligible. 4.2. P r o p e r t i m e s t u d y The proper time of a D o candidate is calculated from the distance between the primary vertex projected along the direction of flight of the D o and the reconstructed momentum and mass of the candidate. Results are obtained with a binned maximum likelihood fit. Details of the probability density function used are in [10]. Setting the interference term to zero (cos ¢ = 0) the result of the fit to the proper time distribution of the wrong-sign sample is NocsD = 20.8+s:4(stat.) ± 4.0(syst.), N ~ = -2.0±4.4(stat.) + 1.1(syst.). The negative value of Nmi~, outside a physical region, implies that no mixing is observed. Constraining Nmlx to be positive the number of Doubly Cabibbo Suppressed Decay events is found to be NDOSD = 18.4+6:s2(stat.) ± 3.2(syst.), +060 which translates to RDCSD = (1.77_0:56(star.) ± 0.31(syst.)) %. An upper limit of R~x < 0.92% at 95% CL. is obtained. The effect of interference is studied by fitting the data with fully constructive (cos ¢ = +1) and fully destructive interference (cos ¢ = - 1 ) , finding, at 95% CL, Rm~ < 0.96% and ~ < 3.6%, respectively. 4.3. Conclusions The decays D *+ --+ D%r+ with D O --+ K - x + and D o -+ K+~r- are reconstructed. The relative branching ratio of the two decay modes is found to be B(D ° --+ K+rc-)/B(D ° --+ K - r +) = (1.84 4- 0.59(star.) -4-0.34(syst.))%. From the study of the proper time distribution the mixing and DCDS components are, giving RDCSD = (1.77+0°:~O(stat.) ± 0.31(syst.)) %, R,fix < 0.92% at 95% CL. The results are in good agreement with the previous measurements [11-13]. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
R. Barate et al. (ALEPH Collaboration), Phy. Lett. B403 (1997) 367 D. Buskulic et al. (ALEPH Collaboration), Z. Phys. C62 (1994)1 R. Akers et al. (OPAL Collaboration), Phys. Lett. B353 (1995) 595 ALEPH Collaboration, EPS-HEP 99, Tampere, 15-21 July. Abstract # 5_393 LEP Heavy Flavour Working Group, preprint LEPHF/98-01 (1998) D. Buskulic et al. (ALEPH Collaboration), Phys. Lett. B388 (1996) 648 C. Caso et al. Eur. Phys. J. C3 (1998) 1 and 1999 off-year partial update for the 2000 edition available on the PDG WWW pages (URL: http://pdg.lbl.gov/) ALEPH Collaboration, EPS-HEP 99, Tampere, 15-21 July. Abstract # 5-411 ALEPH Collaboration, EPS-HEP 99, Tampere, 15-21 July. Abstract ~ 5_409 R. Barate et al. (ALEPH Collaboration), Phy. Lett. B436 (1998) 211 D. Cinabro et aI. (CLEO Collaboration), Phy. Rev. Lett. 72 (1994) 1406 J.C Anjos et al. (E691 Collaboration), Phy. Rev. Lett. 60 (1988) 1239 E.M. Aitaia et al. (E791 Collaboration), Phy. Rev. D57 (1998) 13
Nuclear Physics A675 (2000) 291c-296c
ELSEVIER
Charm
A
www.elsevier.nl/locate/npe
decays and D°-D ° mixing
M. A l e p p o ~ ~Dipartimento di Fisica, Universit~ di Milano, and I.N.F.N. sezione di Milano, Via Celoria 16, 20133 Milano, I t a l y The LEP1 d a t a sample (4 million hadronic Z decays) recorded by the A L E P H detector is analysed to s t u d y charmed particle decays. The measurements of t h e hadronic branching ratios D O -+ K-~r+, and of the purely leptonic decays D~ --* ~-u and Ds --+ #u are presented. T h e L = I charmed mesons D** and D** are reconstructed in several exclusive decay channels and their production rates are measured. The contributions from charm quark fragmentation and from b hadron decays are disentangled. A s t u d y of decays D *+ --+ D%r +, with D O decaying D o --* K-~r + and D O --+ K % r - is shown. T h e relative branching ratio B(D ° --~ K % r - ) / B ( D ° --~ K - r +) is measured and t h e contribution to D o --+ K % r - decay given b y D°-I) ° mixing is extracted with a s t u d y of D o proper t i m e distribution. 1. T H E
BRANCHING
RATIO
D O -~ K-~r +
T h e branching ratio for the decay D o --4 K - r + enters several D meson analysis and m a n y measurements involving B hadron decays. A precise measurement of this quantity is obtained by fully reconstructing t h e signal events in t h e cascade D *+ -+ D%r +, D o --* K-~r + and comparing t h e m with an inclusively selected sample of D *+ --* D%r+ decays [1]. Both the exclusive and t h e inclusive selections m a k e use of t h e low m o m e n t u m ( s o f t ) p i o n ~r8 to tag t h e D* decay. The branching ratio is then e x t r a c t e d from the formula B(D o --+ g _ r + ) -
NDO~K-~+ ND.+_~D%+
x
¢~'~z e:~cl
- -
(1)
where ND,+_,D0~+ is t h e n u m b e r of events selected in the inclusive analysis, NDO-~K-~÷ is t h e n u m b e r of events exclusive reconstructed in the decay chain D *+ --+ D%r+~D ° --+ K-~r +, c~cl and e ~ d are the respective selection efficiencies. Each of t h e two samples is divided in six subsamples selecting the ~rs in m o m e n t u m bins of width 0.5 GeV/c. 1.1. E x c l u s i v e a n a l y s i s Tracks with m o m e n t u m in the range between 1 and 4 G e V / c are taken as ~rs candidates. Two oppositely charged tracks are added to form a D o candidate assigning the kaon mass to t h e t r a c k with charge opposite to the ~rs and t h e pion to the other one. The combinations are retained if t h e decay angle of the kaon in the D o rest frame 9~< satisfies I cos 0~: I< 0.8 and if 1835 M e V / c 2 <1 M(K~r) I< 1865 M e V / c 2. N u m b e r of candidates is counted in t h e region 0.1435 G e V / c 2 <1 M(Zr~rs) - M(Z~r) I< 0.1475 G e V / c 2. 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0375-9474(00)00268-2
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M. Aleppo /Nuclear Physics A675 (2000) 291c-296c
1.2. I n c l u s i v e a n a l y s i s The signal relies on observed 7r, transverse m o m e n t u m relative to the D *+ line of flight. Soft pion candidates are selected as in the exclusive analysis. The axis of the nearest jet to the ~r, is taken as D *+ direction. ND,+_~O0~+ is calculated with a fit to the p~ distribution. Background distribution is parameterised with an inverse polynomial function. Signal distribution is given by a sum of three contributions: Z -4 ce, Z --+ bb and gluon splitting. The shapes are taken from Monte Carlo, while the relative fractions are estimated using previous measurements [2,3] and the value of Rb = FZ_+bD/FZ~haa and R~ = l~z--+ce/i~Z~had fixed to Standard Model values. 1.3. C o n c l u s i o n s The branching ratio is calculated according to eq. 1 for each ~rs m o m e n t u m bin. The results are combined giving B(D ° --+ K-~r +) = (3.90 ± 0.09 ± 0.12)%, at present the best single measurement result [7]. 2. L E P T O N I C
D E C A Y S O F Ds M E S O N S
The rate of the leptonic D mesons decays depends on to the quark-antiquark wave function at the origin, which is described by decay constant fD~- The B - B mixing rates are proportional to square of the corresponding decay constants, that at present can not be measured directly. The large uncertainties affecting the calculation of fB do not allow to translate the precise measurement of the mass difference between the B ° mass eigenstates into tight constrains on the Vtd element of the CKM matrix. A fD, precise measurement is a valid check of the theoretical calculation of meson decay constants and can be used as constraint for lattice QCD and QCD sum-rules evaluations. Preliminary measurements of B(D~ -+ Tu) and/3(Do -+ #u) are presented [4]. 2.1. D~ --+ Tu a n a l y s i s The candidates are searched in the decay chain c+e - -+ c5, c -4 Ds, Ds -4 TU, T ---~ eff~u~or T --+ #ffUV~. Each event is divided into two hemispheres according to the plane orthogonal to the thrust axis. Hemispheres with an identified lepton and large missing energy are retained. Electron identification is based on the shower shape in the Electromagnetic Calorimeter and on the specific ionization loss measured into the T P C ( d E / d x ) , while muon identification relies on digital patterns in the Hadronic Calorimeter and hits in muon chambers. Sets of high rapidity and low rapidity tracks are defined in each hemisphere. The confidence levels that these sets originate from the interaction point are then calculated. Cuts are applied on the confidence leve] for the low rapidity tracks in each hemisphere to reduce the bb background, and on the high rapidity tracks to suppress c~ background. Do energy and m o m e n t u m are determined requiring four m o m e n t u m conservation and imposing the mass constraint [ E ~ - p~)~]1/2 = MD~. The background is reduced requiring ED~ > 25 GeV. Several variables are linearly combined to create two discriminating variables U~ and Us to separate signal from cg and bb backgrounds respectively. From the signal extracted from a two-dimensional unbinned maximum likelihood fit to the U~ vs Ub distribution B(D~ -4 ru) = [4.93 -t- 1.43(star.) + 2.05(syst.) -'- 1.62(BR)] and [4.87 J: 0.93(star.) +
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1.63(syst.) 4- 1.37(BR)] are measured in the muon channel and in the electron channel, respectively. The errors labelled BR are due to the error on B(D~ --+ ¢~r) measurement, that enters in the calculation of normalisation term P(c -4 D~) [5,6]. The two results are combined, giving B(Ds .4 ru) = [4.9 3: 0.9(star.) + 1.6(syst.) + 1.4(BR)]. 2.2. D~ --+ #u a n a l y s i s The selection strategy is similar to the strategy in D, .4 Tu analysis. Loose requirements in the muon identification algorithm are used. The missing neutrino is reconstructed performing a two-constraint kinematic fit, in which the missing mass is constrained to be zero and muon and neutrino momenta and the interaction point are constrained to lie in the same plane. The bb and c~ backgrounds are reduced with the same techniques. Two discriminant variables U~ and Ub are defined analogously to the D~ --+ Tu analysis. The signal is measured from a fit to slices of M(#u) in 36 bins (6 x 6) in the (Ub, U~) plane. The branching ratio in the muon channel is measured to be B(D, --+ #u) = [0.64 + 0.08(stat.)d: 0.21(syst.)4-0.15(BR)], where again the error labelled BR. comes from the uncertainty on B(D~ -+ ¢~r). 2.3. C o n c l u s i o n s Preliminary measurements of B(D~ .4 Tu) and B(D~ -+ #u) are presented. The results from the two channels are combined to evaluate the D~ decay constant: fD~ = 261 3: 20(star.) 3:43(syst.)3:35(BR). This value is consistent with the previous measurements [7].
3. O R B I T A L L Y
EXCITED
CHARMED
DECAYS
In the heavy quark limit, H Q E T predicts the cC1 mesons with L = I to split in two degenerated doublets according to the angular momentum j of the light quark. One (j = ½) doublet with j R = 0 +, 1+, usually referred to as D(*~)0 and D(*~)a, and one (j = ~) doublet j R = 1 +, 2 +, indicated with D(~)l and D(*)2. It is expected that the decays of these charmed and charmed-strange mesons are dominated by two body decays to D(*)~r and D(*)K, respectively. Only the members of doublets j = 2, that can decay only through Dwave and are therefore narrow, are observed in A L E P H [4,8]. The member of the doublet j = 1 decay through S-waves and are expected to be wide. 3.1. T h e D + a n d D~*+ m e s o n s d e c a y s D~*+ state is reconstructed in the decay to D°K + ,while D + in the decays to D*°K + and D*+K}. D *+ mesons are reconstructed in the decay channel D *+ --+ D%r +, and the D o mesons are reconstructed in the decays to K-~r +, K-~r+~r-Tr + and K-~r+~r °. Charged kaons and pions are separated using dE/dx. Signal is extracted fitting the mass difference distribution A M = M ( D *+, K}) - M(D *+) - M(K}) + M t ~ ( K ° ) . The combinatorial background shape is parameterised with a function
dN d(AM)
-- n - ( A M -- a) b. e -~(AM-a)
(2)
The signal is fitted with a Breit Wigner function convoluted with a Gaussian. D *° mesons decay into D O by emitting a pion or a photon. No attempt is made to reconstruct these particles. According to Monte Carlo this doesn't significantly worsen the resolution. In the
M. Aleppo /Nuclear Physics A675 (2000) 291c-296c
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two decay channels D + --+ D*°K + and D *+ --+ D°K + signal is determined with an unbinned m a x i m u m likelihood to the mass difference distribution A M = M ( D °, K +) - M ( D ° ) . Only t h e best signal to background ratio channel D o --+ K-Tr + is used. The fitting function is t h e same used in the D*+K~ channel, except for D *+ decay in which combinatorial background is parameterised with a linear function. In order to determine the production rates c --+ D** and b --* D~* one sample enriched in c~ and one in bV~ are selected. The properties of long lifetime of b hadrons and harder energy spectrum of D mesons produced in fragmentation of p r i m a r y c quarks are used. Cuts on the probability of all tracks in the hemisphere of t h e D~* meson to come from the p r i m a r y vertex in the hemisphere of t h e D** meson, scaled energy of D~* mesons and on the distance of the reconstructed D o vertex to the p r i m a r y vertex are applied.
3.2.
The D1 and D~ mesons decays
D~+ state is reconstructed in the decay D~+ ~ D%r + , D~° in the decays D~° --+ D*+Tr-, D+Tr - and D o in t h e decay D O -+ D*+Tr- . D *+ and D o mesons are reconstructed in the same channels as in D** analysis. Charged D mesons are reconstructed in the decay D + --+ K-Tr+Tr +. The background is reduced applying cuts the angle between the sphericity axis of the D O/+ system and the D O/+ direction in the D O/+ rest frame, on kaon m o m e n t u m and on the measured dE/dx. A b / c contribution are separated analogously as in t h e D** analysis. Signal is e x t r a c t e d from t h e mass difference distribution A M = M(D(*), 7 r s ) - M(D(*)). The combinatorial background shape is parameterised with the function 2, in which the p a r a m e t e r a is fixed to nominal value of pion mass. The signal is fitted as described in Sec. 3.1. 3.3. C o n c l u s i o n s From t h e observed number of D** mesons in t h e c and in t h e b enriched samples, assuming t h a t D1 --* D*Tr and D~ --+ D(*)~r only and t h a t D~a -+ D*K only and B(D *+ --+ D°K +) = 45%, t h e production rates from c and b quarks are: c --+ D1
--
c --+ D~ =
(3.2 + 0.9)%, c ~ D~I = (0.77 4- 0.22)% (9.4 4- 1.9)%, c --~ D~2 = (1.3 4- 0.5)%
b --* D1
=
(4.6 -t- 1.4)%, b --+ D~I = (1.1 4- 0.4)%
b --+ D~
<
3.9%(95%CL),b --+ D*2 = (2.2 + 0.9)%
4.
T H E B(D ° -~ K % r - ) / B ( D ° -+ K - r +) A N D D ° - D ° M I X I N G
Both mass and width differences between weak eigenstates of t h e D°-~) ° system can cause mixing. The rate of such a mixing is predicted from t h e S t a n d a r d Model to be orders of m a g n i t u d e below t h e current experimental limits, while m a y approach t h e m in extensions of the S t a n d a r d Model. A search for D°-D ° mixing is performed using the decay chain D *+ --~ D%r +, D o --~ K+~r - . The K % r - system can be produced by a D o both in a direct Doubly Cabibbo Suppressed Decay (DCSD) and by an oscillation followed by a Cabibbo Favoured Decay I) ° --~ K % r - . The contribution of each component is obtained from a s t u d y of D O proper t i m e distribution. Assuming small mixing and neglecting
M. Aleppo /Nuclear Physics A675 (2000) 291c-296c
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CP-violating terms, the time evolution for D O --+ K%r- decay has the following form
[.o.,o
+
o-,-,
(3)
where r is the D O lifetime (r = 0.415 ps), RDCSD is the ratio B(D ° --+ K+zc-)/B(D ° K-Tr+), ~ is the ratio B(D ° -+ I) ° --+ K % r - ) / B ( D ° ---* K - z +) and cos ¢ is the phase angle parameterising the interference between the two processes. Measurement o f B(D ° ---+K % r - ) / B ( D ° --+ K - r +) Each pair of oppositely-charged tracks are combined with the two mass assignments K-rr + and ~r-K +. The signal is identified by selecting candidates in the region I M(KIr) MD 0 l< 30 M e V / c 2. If both hypotheses satisfy the mass cut the event is rejected. The decay angle of the kaon in the D O rest frame 0~ is required to satisfy I cos 0~¢ l< 0.8. Only combinations in which the two tracks form a common vertex and each track have at least one V D E T hit are kept. The d E / d x of each track is used to suppress misidentification of a pion with a kaon and vice versa. An extra pion zrs is added to build D* candidates. The background is suppressed requiring ED,/Eb > 0.5, where Eb is the beam energy. The rightsign ( K-~r%r + combinations ) and wrong-sign ( K+~r-~r + combinations ) signal candidates are counted selecting events in the window 0.1435 GeV/c 2 < l M(K~rzrs) - M(Krr) l< 0.1475 G e V / c 2 (fig. 1). After combinatorial background has been subtracted the number of signal events found in the right-sign sample and in the wrong-sign sample are NRs = 1038.8 4- 32.5(star.) -4- 4.3(syst.) and Nws = 21.3 4- 6.1(stat.) 4- 3.4(syst.), respectively. The number of physics background events in the wrong-sign sample is estimated using 4.1.
18 I
300
• Data
16
Combinatorial Background
ALEPH
14
%, 250
•
Data
~
Combinatorial Background Comi
(b)
~o
10
÷ 50
0 0.13
?
ALEPH
100
÷
J--.' 2'." 0.14
0.15
0.16
0.17
M(K-rr÷n'*,) - M(K-'~*) (OeV/c=)
0.18
i O--i
0.13
i *! 0.14
0.15
0.16
0.17
0.18
u(K*~-~:) - U(K',~-) (ZeV/o9
Figure 1. Mass difference distribution for D *+ --+ D°zr+, D O --+ K-Tr + candidates (a) and D O --+ K % r - candidates (b)
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M. Aleppo/Nuclear Physics A675 (2000) 291c-296c
real and Monte Carlo data to be 2.2 ± 1.0; this is subtracted from the selected sample leading to a signal of NDO-~K+,- = 19.1 ± 6.1(star.) ± 3.5(syst.). The physics background contamination in the right-sign sample is negligible. 4.2. P r o p e r t i m e s t u d y The proper time of a D o candidate is calculated from the distance between the primary vertex projected along the direction of flight of the D o and the reconstructed momentum and mass of the candidate. Results are obtained with a binned maximum likelihood fit. Details of the probability density function used are in [10]. Setting the interference term to zero (cos ¢ = 0) the result of the fit to the proper time distribution of the wrong-sign sample is NocsD = 20.8+s:4(stat.) ± 4.0(syst.), N ~ = -2.0±4.4(stat.) + 1.1(syst.). The negative value of Nmi~, outside a physical region, implies that no mixing is observed. Constraining Nmlx to be positive the number of Doubly Cabibbo Suppressed Decay events is found to be NDOSD = 18.4+6:s2(stat.) ± 3.2(syst.), +060 which translates to RDCSD = (1.77_0:56(star.) ± 0.31(syst.)) %. An upper limit of R~x < 0.92% at 95% CL. is obtained. The effect of interference is studied by fitting the data with fully constructive (cos ¢ = +1) and fully destructive interference (cos ¢ = - 1 ) , finding, at 95% CL, Rm~ < 0.96% and ~ < 3.6%, respectively. 4.3. Conclusions The decays D *+ --+ D%r+ with D O --+ K - x + and D o -+ K+~r- are reconstructed. The relative branching ratio of the two decay modes is found to be B(D ° --+ K+rc-)/B(D ° --+ K - r +) = (1.84 4- 0.59(star.) -4-0.34(syst.))%. From the study of the proper time distribution the mixing and DCDS components are, giving RDCSD = (1.77+0°:~O(stat.) ± 0.31(syst.)) %, R,fix < 0.92% at 95% CL. The results are in good agreement with the previous measurements [11-13]. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
R. Barate et al. (ALEPH Collaboration), Phy. Lett. B403 (1997) 367 D. Buskulic et al. (ALEPH Collaboration), Z. Phys. C62 (1994)1 R. Akers et al. (OPAL Collaboration), Phys. Lett. B353 (1995) 595 ALEPH Collaboration, EPS-HEP 99, Tampere, 15-21 July. Abstract # 5_393 LEP Heavy Flavour Working Group, preprint LEPHF/98-01 (1998) D. Buskulic et al. (ALEPH Collaboration), Phys. Lett. B388 (1996) 648 C. Caso et al. Eur. Phys. J. C3 (1998) 1 and 1999 off-year partial update for the 2000 edition available on the PDG WWW pages (URL: http://pdg.lbl.gov/) ALEPH Collaboration, EPS-HEP 99, Tampere, 15-21 July. Abstract # 5-411 ALEPH Collaboration, EPS-HEP 99, Tampere, 15-21 July. Abstract ~ 5_409 R. Barate et al. (ALEPH Collaboration), Phy. Lett. B436 (1998) 211 D. Cinabro et aI. (CLEO Collaboration), Phy. Rev. Lett. 72 (1994) 1406 J.C Anjos et al. (E691 Collaboration), Phy. Rev. Lett. 60 (1988) 1239 E.M. Aitaia et al. (E791 Collaboration), Phy. Rev. D57 (1998) 13