1. Mixing and CP Violation in neutral D meson system
BESIII 物理分析讲习班
2008年6月26日
郑阳恒
中国科学院研究生院

2. Some notations CPV: CP violation DCS: Doubly Cabbibo Suppressed
CF: Cabbibo Favored ( CA: Cabbibo Allowed )
SM: Standard Model
MC: Monte Carlo
RS: Right Sign D0→K-π+
WS: Wrong Sign D0→K+π-
Y. Zheng (GUCAS)
06/26/2008

3. Outline Introduction (formalism and experimental view)
Experimental Apparatus & Analysis Strategy
Measurement status
Summary and Future perspective
Y. Zheng (GUCAS)
06/26/2008

4. Motivation
Universe in 15 billion years ago: high degree of symmetry between matter and antimatter
Matter encounters antimatter  annihilated
Present-day Universe: matter >> antimatter, Why?
Standard Model: CP violation is the KEY
Neutral meson mixing  CPV
Other sources can exist. At least CPV is one of the KEY.
Y. Zheng (GUCAS)
06/26/2008

5. A little history
Before 1956, discrete space-time symmetries were considered to be exact
1956, T.D. Lee and C.N. Yang suggested P violation. (Nobel prize)
1957, C.S. Wu et al., discovered P violation experimentally.
1964, Christenson et al., discovered CP violation in the neutral K system. (Nobel prize)
1973, Kobayashi and Maskawa: KM model with  6 quark flavors  CP violation
1980, Carter, Sanda and Bigi: Large CP asymmetries in B decays.
2001, B-factories observed CP asymmetries in B decays.
How about D decays?
Y. Zheng (GUCAS)
06/26/2008

6. Starting point: Standard Model
Described the elementary building blocks of matter and interactions.
Account for all experimental phenomena to a high degree of precision.
Many predictions verified experimentally.
A successful theory.
CP violation is one of the least constrained sector.
measurements of Mixing and CP violation in neutral D meson system provide a sensitive testing method.
Y. Zheng (GUCAS)
06/26/2008

7. CKM Picture of CP Violation
In Standard Model:
Cabibbo, Kobayashi & Maskawa:
CKM
matrix
SU(2) doublets in standard electroweak model:
u, c, t
d’, s’, b’
Y. Zheng (GUCAS)
06/26/2008

8. Lagrangian W q q’ In a physics system: Lagrangian  the dynamics
Quark flavor transitions: q  Wq’
Lagrangian of charged weak current via W
Under the CP transformation
Vij  Vij* (at least 1 non-real) CP-violation (only source in SM) q’ W q
Vij: CKM matrix element
Y. Zheng (GUCAS)
06/26/2008

9. Parameterization of CKM matrix
free parameters
9 complex matrix elements
9  2 = 18
Unitarity of the matrix, V+V = I -9
5 arbitrary phases of 6 quark field -5
total 4
Wolfenstein parameterization(A,ρ,η, : Cabibbo angle ~ 0.22):
complex phase  CPV
Y. Zheng (GUCAS)
06/26/2008

10. Mass and flavor eigenstates:
Mixing in neutral meson system
Mass and flavor eigenstates:
“Box diagrams” for second order weak processes:
d,s,b W u c _ D0 __
Time evolution:
u,c,t W
b(s) _
B0(s) (K0) __
d(s)
Y. Zheng (GUCAS)
06/26/2008

11. Time dependent decay amplitudes
For any decay final state f, |f  CP|f
Y. Zheng (GUCAS)
06/26/2008

12. Time dependent decay rates
For any decay final state f, |f  CP|f
If CP is conserved:
Y. Zheng (GUCAS)
06/26/2008

13. CP violation categories
CP violation in decay (direct CP violation) :
observed in B decays
CP violation in mixing (indirect CP violation) :
observed in neutral K system
CP violation in interference between decay and w/o mixing (mixing-induced CP violation) :
observed in neutral B system
Y. Zheng (GUCAS)
06/26/2008

14. neutral D decays (to common states)
D0phys(t) D0 f
D0phys(t) D0 f
For convenient:
Y. Zheng (GUCAS)
06/26/2008

15. D→Kπ (non-CP eigenstates)u d
D0K-p+ is a Cabibbo-allowed
favored decay mode (Br=3.8%) W c s K- u u
There are 2 ways that a D0 can decay to the opposite combination K+p-:
Doubly Cabibbo-suppressed
decays (DCS)
2) D0  D0; D0K+p- decays K+ u p- d s u c W d W c p- u s D0 u u K+ D0 D0 c u u
mixing
Cabibbo-allowed D0
decay (CA)
Br ~ 0.014%
Y. Zheng (GUCAS)
06/26/2008

16. D→Kπ (non-CP eigenstates)
f = K-π+ , f = K+π-
δ: strong phase diff. (assume CPV via weak phase only),
φ: weak phase RS WS
Y. Zheng (GUCAS)
06/26/2008

17. Mixing and CPV: D→Kπ If CP is conserved: fit WS distribution → Mixing
For CPV case: fit two WS distribution separately
Direct CP violation in DCS Decay
CP violation in mixing
CP violation in interference between decay and mixing:
Y. Zheng (GUCAS)
06/26/2008

18. CP eigenstates: K+K-, π+π-
CP eigenstates, a simpler case: |f  CP|f = ±|f
CP Asymmetries: (Integrated time-dependant decay rates over time, assume no CPV in decay, AD=0)
Y. Zheng (GUCAS)
06/26/2008

19. Requirements for Measurements
Large D meson source ( Br(Df) ~ )
very high luminosity e+e- collider  B-factories,
BEPCII
B meson reconstruction
high quality ~4 detetor  Belle, BaBar, BESIII
Tag flavor of the D meson
good particle id  dE/dx, Cherenkov, TOF, EMC
Measure proper-decay-time difference (Belle, BaBar)
high precision vertexing (Δz)  silicon strip vertex detector
Likelihood fit to the t distributions
Measure Branching Ratios (BESIII)
Y. Zheng (GUCAS)
06/26/2008

20. Asymmetric e-e+ Colliders@ U(4S)
Colliders: KEKB and PEP-II
Coherent BB production
KEKB:
8 x 3.5 GeV, bg=0.43
PEP-II
B B production threshold
9 x 3.1 GeV,
bg=0.55
s(BB)/shad=0.28
Asymmetric e-e+ U(4S)
Y. Zheng (GUCAS)
06/26/2008

21. Detectors: BaBar and Belle
e- 9 GeV
e+ 3.1 GeV
ECL
KLM
ECL
KLM
DIRC: Quartz bar + water tank ACC: aerogel Cherenkov counters
SVT: 5-layer SVD: 3-layer. (4-layer soon)
… …
high performance vertexing and PID
Y. Zheng (GUCAS)
06/26/2008

22. A typical collision event
Signals:
D*+  D0+
K-+
K+K-
-+
Variables used to separate signal and background
D invariant mass: M(Kp, KK, pp)
Dm = M(Kpptag) – M(Kp)
Y. Zheng (GUCAS)
06/26/2008

23. Proper decay time t=(ldec/p)(m/c) Signals: D*+ → D0(→Kp, KK, pp) p+tag
Y. Zheng (GUCAS)
06/26/2008

24. Analysis Strategy in B-factories
Signals: D*+ → D0(→Kp, K K, pp) p+tag
Backgrounds: shapes from MC, fractions from data
Fitting method: Unbinned maximum likelihood fit.
Proper-time distribution:
Resolution function: from RS data fitting
Fit WS data event-by-event
Several proper time fits are performed.
lifetime (no mixing)
mixing, no CP violation
mixing, CP violation
Monte Carlo: search for systematics and validate statistical significance of results.
Y. Zheng (GUCAS)
06/26/2008

25. Signal selection criteria
Beam-constrained vertex fits of K, p, ptag tracks.
ptag charge gives D flavor at production.
Require fit probability > 0.001
D0 selection
CMS p(D*) > 2.5 GeV/c to eliminate D0’s from B decays
K, p particle identification
DCH hits > 11
1.81 < M(Kp) < 1.92 GeV/c2
decay time error < 0.5 ps
-2 < decay time < 4 ps
ptag
CMS p* < 0.45 GeV/c
lab p > 0.1 GeV/c
SVT hits > 5
Y. Zheng (GUCAS)
06/26/2008

26. Background shapes True D0 combined with a random πs Mis-recon D0
peaked at M(Kp)
does not peak in Dm
Mis-recon D0
peaked at Dm
does not peak in M(Kp)
Combinatorial background
does not peak in both M(Kp) and Dm
Shapes: from MC
Yields: from 2-D fit
Y. Zheng (GUCAS)
06/26/2008

27. RS(top)/WS(bottom) Datasets After Event Selection
Integrated Luminosity Approximately 384 fb-1
x103
BaBar Data
BaBar Data
1,229,000
RS candidates
events/1 MeV/c2
events/0.1 MeV/c2
BaBar Data
BaBar Data
64,000
WS candidates
Y. Zheng (GUCAS)
06/26/2008

28. Resolution function There is no perfect measurement!
Likelihood for proper decay time measurement:
Resolution function models: (from RS signal fit)
Signal: triple-Gaussian model
random πs and Mis-recon D0 : triple-Gaussian model (same as signal)
Combinatorial background model: double-Gaussian (from sideband)
Y. Zheng (GUCAS)
06/26/2008

29. Validation: RS lifetime
BaBar Data
The D0 lifetime is consistent with the Particle Data Group value, within the statistical and systematic errors of the measurement.
Plot selection:
1.843<m<1.883 GeV/c2
0.1445<m< GeV/c2
Y. Zheng (GUCAS)
06/26/2008

30. WS Mixing Fit: No CP Violation
Varied fit parameters
Mixing parameters
Fit class normalizations
Combinatoric shape
BaBar Data
Mixing minus No mixing PDF
Data minus No mixing PDF
BaBar Data
Plot selection:
1.843<m<1.883 GeV/c2
0.1445<m< GeV/c2
Y. Zheng (GUCAS)
06/26/2008

31. Mixing Contours: No CP Violation
y’, x’2 contours computed by change in log likelihood
Best-fit point is in non-physical region x’2 < 0, but one-sigma contour is in physical region
correlation: -0.95
BaBar Data
Accounting for systematic errors, the no-mixing point is at the 3.9-sigma contour
RD: (3.030.160.06) x 10-3
x’2: (-0.220.300.21) x 10-3
y’: (9.74.43.1) x 10-3
Y. Zheng (GUCAS)
06/26/2008

32. Results for Kp Analysis
Y. Zheng (GUCAS)
06/26/2008

33. D0 reconstruction and lifetime fit
Y. Zheng (GUCAS)
06/26/2008

34. ycp , AΓ results
Y. Zheng (GUCAS)
06/26/2008

35. What about Charm factory?
Charm events at threshold are very clean
Ratio of signal to background is optimum
Lots of systematic uncertainties cancellation while applying double tag method
Mixing at threshold
Bad news: no time-dependent information
Good news: Quantum coherence, CP tags
The coherence of two initial D allows simple methods to measure DDbar mixing, strong phase and CP violation
Y. Zheng (GUCAS)
06/26/2008

36. BEPCII/BESIII experiment
Will collect collision data in July!
Will operate at
Y. Zheng (GUCAS)
06/26/2008

37. Coherent D0 – D0 states (3770)  D0D0 / (3770)  D+D-  50/50
(3770) : spin=1, cc bound state, Mass: GeV
D0 : spin=0, Mass: GeV
 D mesons created  at rest in CM
 DD orbit angular momentum L=1
Bose statistics  D0D0 state anti-symmetric
 D0D0 and D0D0 are prohibited
At any time : one D0 one D0 until one D decays
Y. Zheng (GUCAS)
06/26/2008

38. D Pairs at Different Experiments
128 M is expected at BES-III with 4 years’ luminosity.
5 M is expected at CLEO-c until 2008.
700M
500M
128M
5 M
0.2 M
(3770) peak
(4S) Peak
Background free
Higher statistics
Y. Zheng (GUCAS)
06/26/2008

39. Charm tags Single tags Double tags Flavor tags in Mixing language
reconstruct one D meson
Double tags
Both D and Dbar are reconstructed
Flavor tags in Mixing language
Semileptonic modes: K(p)en
CP tags
CP even
CP odd
Y. Zheng (GUCAS)
06/26/2008

40. K,  Identification at BESIII
Y. Zheng (GUCAS)
06/26/2008

41. RM measurements @3.773 GeV Golden channel Semileptonic channel D0Kp
Ken, Kmn, etc
experiment
theory
Double tag measurements. Number of
R.S. tags at BESIII are expected to be
, the sensitivities of Rmix 10-4—10-5
2-body identical final states are
Required in both D hadronic decays
Y. Zheng (GUCAS)
06/26/2008

42. CP eigenstate Tags CP + CP – KSp0(0.012) Ksh (3.9X10-3) KS h' (0.0094)
K+K- (3.89X10-3 )
p+p-(1.38X10-3 )
Ks p0p0
p0p0(8.4X10-4)
KSKS (7.1X10-4)
r0p0(3.2x10-3)
CP –
KSp0(0.012)
Ksh (3.9X10-3)
KS h' (0.0094)
KSr0 (0.0078)
Ksw (0.012)
KSf (4.7X10-3)
Dalitz Analysis
For Ks modes: CPV effect of Ks
need to be considered!
(Prof. Xing/Zhizhong’s suggestion)
In 20fb-1 y(3770) data, we can get
> 4.5x105 CP+ tags and > 3.6x105 CP- tags
With large sample of CP tags, we may improve the measurements
of strong phase, probe the direct CP, and other mixing parameters
Y. Zheng (GUCAS)
06/26/2008

43. CP Violation 1. Direct CP Violation (in decay)
2. Indirect CP Violation (in mixing)
3. CP violation in the interference between decays
with/without mixing
Y. Zheng (GUCAS)
06/26/2008

44. Quantum Coherence Suppose Both D0 decay to CP eigenstate f1 and f2 .
Thus if a final state such as (KK)(pp) observed, we immediately have evidence of CP violation
In 20 fb-1 y(3770) data, > 1000 double CP+ and CP-
tags can be obtained. if 100%CPV, it lead to ACP~10-3 level
Y. Zheng (GUCAS)
06/26/2008

45. Unitarity Triangle - Vub*Vud+Vcb*Vcd+Vtb*Vtd = 0 (r,h) (B system)
B0 pp
B0 rp
Vub*Vud+Vcb*Vcd+Vtb*Vtd = 0
(B system)
nothing but triangles in complex plane
B0 D(*)p
B+ DK
B0 J/yKs
B0 fKs
B0 D(*)D(*)
Y. Zheng (GUCAS)
06/26/2008

46. 3 from B-  D0 K- No hadronic uncertainty Methods Problem: statistics
Gronau-Wyler original method
Atwood-Dunietz-Soni Method
Dalitz method
Problem: statistics
Y. Zheng (GUCAS)
06/26/2008

47. Gronau-Wyler original method3 δB
Theoretically clean
Experimentally challenging
Hadronic D decay modes: hard for D flavor tagging
Semi-leptonic D decays : Background too high
CP eigenstate decays of D: small Branching ratio
Y. Zheng (GUCAS)
06/26/2008

48. Atwood-Dunietz-Soni Method
Use interference between
B+ DK+ and B+ DK+ follows by D (D)  f
To get a common final state f, we need
Double Cabibbo Suppression (DCS): f = K+ - , K+ K-
K - K mixing: f = KS0 , KS+-
D hadronic parameters:
Decay rates:
rD, δD :measured from Charm factory (see next slides)
(rB, δB, 3 ) 3 unknowns, 4 measurements  3
Y. Zheng (GUCAS)
06/26/2008

49. δD from Charm-factory
Get rD from the large tagged D decay samples (B-factory or Charm factory (CLEO-c sensitivity: ~0.05 from 3fb-1))
δD  Charm factory on(3770) accurately measured (Soffer hep-ex/ )
Reconstruct Double Tags: CP and f
CP+: K+ K-, +  -, Ks00
CP- : Ks0 , Ks , Ks
Asymmetry in CP+ and CP- of D decays:
Input RD= rD2 from PDG
BESIII sensitivity: <0.06 from 20fb-1 for cosD
Y. Zheng (GUCAS)
06/26/2008

50. Dalitz method Three body D decays: KS+-,+-0,KSK+K-…
Effect of D – D interference
Y. Zheng (GUCAS)
06/26/2008

51. Formalism (Giri,Grossman,Soffer,Zupan)
B  (KS+-)D K (hep-ph/ )
D hadronic parameters
Partition the Dalitz plot to 2k bins
Label bins below symmetry axis i, above axis i
S12
S13
unknown
Measurable from tagged D
Y. Zheng (GUCAS)
06/26/2008

52. D Decay model Systematic Uncertainty
3 extraction
2k bins  2(B modes) = 4k equations
For the ith bin:
2k+3 unknowns: ci, si, rB, δB, 3  Solvable for k2
Belle results from Dalitz method in 2005:
D Decay model Systematic Uncertainty
Y. Zheng (GUCAS)
06/26/2008

53. ci ,si from Charm-factory
D double tag: (KS+- vs General state: g)
If g= KS+- and j=i  c2i +s2i
If g=CP  sgj=0 , Tgj =Tgj = cgj  ci
Belle studied relationship between systematic error on 3 and # of CP tagged KS+- events in Charm factory (BESIII)
2000 CP+ and CP- tagged events δ3 (sys)~ 1o -2o
Y. Zheng (GUCAS)
06/26/2008

54. Summary
BaBar using Kπ final state, finds a mixing signal at the 3.9 sigma confidence level (assuming CP conservation and including systematic effects):
Belle using CP eigenstate (K+K-, π+π-) final states, finds mixing evidence (>3 sigma) : ycp=1.31±0.32±0.25%
AΓ=1.31±0.32±0.25% (no evidence for CPV)
BES-III contributions will be coming soon (getting more interesting)!
RD: (3.030.160.06) x 10-3
x’2: (-0.220.300.21) x 10-3
y’: (9.74.43.1) x 10-3
No evidence is seen for CPV.
Y. Zheng (GUCAS)
06/26/2008

55. Future persepctive Mixing parameters
Sensitivities (20 fb-1):
Mixing parameters
=(x2+y2)/2 < 10-4 in Kp and Ken channels
Probe y: ΔyCP < 0.7%,
ΔcosdKp < 0.06
CP Violation
ΔACP~10-3 in D+ decays (direct CPV),
contributions to 3/ errors: <2o (CLEO-c: ~5o)
BESIII
Y. Zheng (GUCAS)
06/26/2008

56. 谢谢！