1. Lifetime and Mixing Chunlei Liu / University of Pittsburgh
On behalf of CDF and D0 collaborations
FPCP 2008
May 5-9

2. Part I Lifetime
Motivation and Experiments
B0s , Bc lifetimes
Part II Mixing
B0s mixing from D0
D0 mixing from CDF

3. Decay of B Hadrons Pauli interference prolongs lifetimes:
kinetic and chromomagnetic operator
weak annihilation and Pauli interference
Pauli interference prolongs lifetimes:
+5% for B+, +3% for Lb
Spectator model: all b hadron
lifetimes are equal.
Heavy Quark Expansion (HQE):
Lifetime ratios are better predicted:
t(B+)/t(B0), t(Bs)/t(B0), t(Lb)/t(B0)…
Weak annihilation or scattering
reduces lifetimes -7% Lb

4. The Bc - Doubly Heavy Meson
• Doubly heavy with b and c quark – interesting lab for studying QCD
• Both quarks decay or annihilate, shorter lifetime than light B mesons
theory prediction:
t(Bc) : ps
arXiv:hep-ph/ v1
Phy Rev. D 64, (2001)
Phy Lett. B 452, 129 (1999)
hep-ph/ ( and references within)

5. B0s Lifetime and Decay Width Difference
B0s →J/y f W c s c
Eigenstates: Bslight and Bsheavy => GL and GH
Gs= (GL+GH)/2 , DG = GL-GH
Two kinds of lifetime measurements:
Measure 1/Gs and DG directly (need to identify CP eigenstates)
Treat GL and GH together as one exponential, measure t
e.g flavor specific channel:

6. Combine ts and DG
DG: theoretically calculable and sensitive to new Physics
Probe to New Physics : DG= 2|G12|cos(fs)

7. Latest HFAG (by 03/08) New measurements today:
Bs lifetime –direct measurement
Bs lifetime – flavor specific
Bc lifetime
Theory references:
PRD 68, (2003)
PRD 70, (2004)
hep-ph/ (2007)

8. Tevatron pp collisions at 1.96 TeV
3.4 fb–1 data on tape (recorded at D0)
Initial instantaneous luminosity up to 3x1032cm–2s–1
Main Injector
& Recycler
Tevatron
p source
Booster
CDF DØ
Apr 2002 – Apr 2008

9. CDF II Detector DØ Detector
Central tracking: silicon vertex detector drift chamber
=> dpT/pT = pT
excellent vertex resolution
Particle identification: dE/dX and TOF
Excellent muon coverage
Good tracker coverage
Silicon layer 0 installed in 2006 improves track parameter resolution
tracker

10. Measure ts and DG from B0s→J/y fq
ct=L/bg
=Lxy/sinq/bg
=LxyM/PT
CP conservation (bs=0)
|BsH> : CP odd eigenstate ~ %
|BsL> : CP even eigenstate ~ %
S, D waves: CP even
P wave: CP odd
Angular distribution in transversity basis => separate CP eigenstates

11. Events Selection at CDF/D0
Di-muon trigger
Neural Network selection at CDF ~ 2500 signal events
Cuts based selection at D0 ~ signal events

12. Measure ts and DG (bs free) =1.52 ± 0.05(stat)±0.01(syst) ps
DG=0.19±0.07(stat) (syst) ps-1
(bs=0) t=1.53 ± 0.06(stat) ps DG=0.14 ± 0.07(stat) ps-1
(arXiv:/ [hep-ex])
(bs=0) t=1.52 ± 0.04(stat) ± 0.02(syst) ps DG=0.08 ± 0.06(stat) ± 0.01(syst) ps-1
World’s best measurement!
Phys. Rev. Lett. 100, (2008)

13. Bs Lifetime Measurement from Bs→ Ds+(fp) p- X - CDF
x2 stats
fully and partially reconstructed channel such as: Bs→ Ds-1 r(p+ p0)
Double statistics!
“K” factor accounts for missing momentum and mass
Extensive test on B0, B+ control samples

14. Events Selection and Fit Strategy
Data (1.3 fb-1) collected by displaced-vertex trigger ( 120mm<d0<1mm )
~ 1100 fully reconstructed events
~ 2000 partially reconstructed events
=> cut on lifetime ( events with ct<d0 removed)
modeled with “trigger efficiency curve” from MC
Two-step fit, 1)mass fit
=> relative fraction of various modes and background
2) lifetime fit (shape from MC, fraction from mass fit)
=> extract lifetime only

15. Lifetime Result (CDF) Fix fractions from mass fit
t(Bs) only free parameter
= ± 0.041(stat.) ± 0.025(syst.) ps (
Lifetime for control samples:
B0→ D-(K+p-p-) p B0→ D*-(D0(K+p-)p-) p B+ →D0(K+p-) p+
Agrees well with PDG
D0 had Bs semileptonic lifetime in 2006 from Bs→Ds-m+nX
t=1.398±0.044(stat) (syst) ps
PRL 97, (2006)

16. Bc Semileptonic Lifetime
Missing momentum, correct pseudo-lifetime: ct= K x ct*
K= pT(J/y l)/ pT(Bc)
Main challenge is multiple backgrounds:
real J/Ψ + fake lepton
fake J/Ψ + real lepton
real J/Ψ + real lepton → from bb events
prompt J/Ψ + lepton
residual conversion (J/y+e only)

17. Bc→J/y+m+X from D0 (1.35 fb-1)
Mass – lifetime simultaneous fit used to
disentangle small signal fraction among
large fraction of backgrounds

18. Bc→J/y+l+X from CDF (1.0 fb-1)
Lifetime fit only
Muon channel Electron channel
ct= (stat) mm ct= (stat) mm
combined (by likelihood):
t= (stat) ± 0.018(syst) ps (

19. Combine Bc Lifetime from D0 and CDF
Bc lifetime measurements have been exclusive to Tevatron
Weighted average: t=0.459 ± ps
Theory prediction:
t=0.47 – 0.59 ps

20. Part I Lifetime
Motivation and Experiments
B0s , Bc lifetimes
Part II Mixing
B0s mixing from D0
D0 mixing from CDF

21. B0s Mixing two eigenstates and
Dms  mH – mL , Gs ( GH + GL)/2, DG  GL – GH
DmsTheo =19.3 ± 6.4 ± 1.9
(arXiv: /hep-ph)
Dms/Dmd ∝ |Vts|2/|Vtd|2
CDF measured at: ± 0.10(stat) ± 0.07(syst) ps
Show D0 new result today !

22. Dms Measurement Strategy
Opposite Side
Same Side

23. Final States Reconstruction at D0
Data collected by inclusive single and di-muon triggers, 2.4 fb-1
Final cuts maximizing S/ sqrt(S+B)
D0 Run IIa
D0 Run IIb innermost layer of silicon added resolution improved

24. Measure Dms at D0 Introduce amplitude, P(t) ~ 1  AD cos(Dmst)
Fit for A at different Dms
Δms = ± 0.93(stat) ± 0.30(syst) ps-1
2.9 s significance
( DO conference note 5618)
Agrees with what CDF measured in 2006:
Δms = ± 0.10(stat) ± 0.07(syst) ps-1

25. D0 Mixing DM/G DG/G discovered K0 0.474 0.997 1964
D0 mixing in SM occurs through either:
‘short range’ processes ‘long range’ processes
(negligible in SM)
DM/G DG/G discovered K
B < Bs
D < <
Recent D0 mixing evidence :
Compare D0 → ππ, KK (CP eigenstates) with D0 → Kπ ( Belle)
2) Compare doubly Cabibbo suppressed (DCS) D0 →K+π- with Cabibbo favored (CF) D0 →K-π+ (Babar )
Lifetime ratio:
where x=DM/DG , y=DG/2G, d is strong phase between DCS and CF modes

26. Evidence for D0 Mixing at CDF (1.5 fb-1)
CDF : probe longer D0 lifetime than B factories
3.8s significance comparing DCS D0 →K+π- to CF D0 →K-π+
RD (10-3) =3.04± x’2(10-3)=-0.12± y’(10-3)= 8.5±7.6
(Phys.Rev.Lett.100:121802,2008 )
Lifetime ratio fit
Bayesian probability 1-4s contour: closed circle: best fit value open diamond: highest probability point physically allowed (x’2≥0) cross : no mixing point 3.8s

27. Conclusion Best Bs t and DG measurement in the world
Bc lifetime provide better constraint for theory
Bs mixing from D0 confirms CDF measurement
D0 mixing evidence from hadron collider
Expect new Lb lifetime result for the summer

28. Back Up

29. Angular Analysis in Transversity Basis
● Bs->J/y f is P -> VV decay
➔ 3 possible angular momenta:
S, D wave: CP even
P wave : CP odd
● Separation by angular
distribution
➢ Transversity angles q, f ,y 

30. B0s Systematics and Cross Check
Systematics at CDF: ) Background angular distribution ) Mass model ) Lifetime resolution function ) B0 cross feed ) Detector acceptance ) Silicon detector alignment
Cross check sample at CDF:
B0→J/y K*0 for angular analyis
Lifetime: td= 1.52 ± 0.02(stat) ± 0.02(syst) ps
Systematics at D0: ) Procedure test ) Acceptance ) Reconstruction algorithm ) Background model ) Detector alignment

31. Bs→ J/y f angular distribution

32. B0 → J/y K*0 ctd = 456 +/- 6 (stat) +/- 6 (syst) μm
|A0|2 = / (stat) +/ (syst) |A|||2 = / (stat) +/ (syst) δ|| = / (stat) +/ (syst) δ⊥ = / (stat) +/ (syst)

33. Mass components:
Single B templates (MC): (signal): Bs→ Ds(fp) X (bkgd): B0, B+, Lb
Real D + track (background): template comes from fit to wrong-sign sample Ds- p-
Fake D + track (background): template comes from D sidebands

34. Bc Background Summary at CDF

35. One word about Λb Lifetime Status
DØ measurements are in agreement with the theoretical predictions and with
the world average
CDF measurement in is ~3s high w.r.t world average
Expect CDF measurement updates very soon
decay mode CDF lifetime (ps), 1 fb DØ lifetime (ps), fb-1
update expected soon x x
expected soon x