Bs Mixing at CDF History of an easy measurement

1
Bs Mixing at CDFHistory of an easy measurement
F. Bedeschi, INFN-Pisa, for the CDF
collaboration CKM 2006 Nagoya, 15/12/2006

• Introduction
• The challenge
• Signals
• Flavor tagging
• Proper time resolution
• The result
• Some implications of this result

2
Introduction (1)

• Neutral B mesons can turn into their
  anti-particle
• In SM described by box diagrams? measure
  Vts(d)
• ? ms(d) GF2mt2? F(mt2/mW2)/6?2
  mBs(d)f2Bs(d)BBs(d)Vts(d)Vtb2
• Many uncertainties cancel in the ratio

• Neutral B mesons can turn into their
  anti-particle
• In SM described by box diagrams? measure
  Vts(d)
• ? ms(d) GF2mt2? F(mt2/mW2)/6?2
  mBs(d)f2Bs(d)BBs(d)Vts(d)Vtb2
• Many uncertainties cancel in the ratio

1
Oscill. Freq.
Known factors
From lattice O(30) error
Theory error O(5) in ratio!
3
Introduction (2)

• Measurement of yields measurement of UT
  side
• with
  O(5) theory error
• Test of SM/Input for global fits

4
Mixing signal model

• Usual exponential proper decay time distribution
  changes after selection of mixed/unmixed events
• Un-mixed B flavor at production same as flavor
  at decay
• Mixed B flavor at production different
  from flavor at decay
• Measure ?ms from study of this time evolution
• Many experimental effects affect this simple
  relation

5
Experimental effects

• Signal quality
• Number of signal and background events (and
  background shape)
• Decay time resolution
• Finite detector resolution, ?, smears theory
  distribution
• Need resolution better than oscillation period
• Need to know what it is
• Flavor tagging
• Flavor at decay defined by decay mode
• Flavor at production needs complex algorithms
• D dilution 1-2w where w probability of
  wrong tag
• ? tagger efficiency
• Selection bias
• Event selection (trigger/analysis) can bias c?
  distribution

6
Looking for oscillations

• Do we have an oscillation?
• Common approach is search for peak in frequency
  space (Fourier transform)
• Normalize to expected peak height ? Amplitude
  scan
• A 1 at mixing frequency
• A 0 elsewhere
• Figure of merit
• A/?A at peak 1/ ?A
• Expected statistical power

Tagging power
Resolution
7
Yellow book 2001

• Expectation was that this would be an easy
  measurement with the first few hundred pb-1 of
  data

• In practice it turned out to be much harder
• Until 2005 CDF only improves lower limits on ?ms
• Apr 2006 first evidence 3? level
• Sept 2006 5? observation with same data set ?
  Significant analysis improvement

8
Why so difficult? (1)

• Need large samples of exclusive decays
• Proper time resolution insufficient using
  semileptonic decays for large ?ms
• Complex trigger on secondary vertices (SVT)
• A great success ?
• However
• Signal yield smaller than originally expected
• Y.Book prediction (1 fb-1) 33,000 fully
  reconstructed events ? observed 5,600 (3,100
  part. reconstructed)
• Major work on trigger upgrade/optimization with
  varying luminosity conditions to preserve yield

?next
9
CDF SVT trigger

• Dedicated impact parameter trigger
• Select hadronic B decays at L2

8 VME crates Find tracks in Si in 20 ms with
offline accuracy
Resolution
Efficiency
80
?back
10
Why so difficult? (2)

• Flavor tagging much harder than expected
• Opposite side flavor tagging performance
  disappointing
• Y.Book expectation ?D2 7.1 ? 1.8 observed
• Saved by Same Side Kaon Tagging!
• Y. Book expectation 4.2 ? 3.5 (hadronic) 4.8
  (S.L.) observed
• PID with TOF and dE/dx were critical to make this
  so powerful
• However
• Difficult to understand
• Took time to incorporate into the analysis

?
?next
11
PID at CDF

• Time of Flight
• dE/dx in COT

dE/dx in COT K/p sep. gt1.5?_at_Ptgt2GeV
1.5 GeV/c
TOF gt1? K/p separation up to p2 GeV
?back
12
Why so difficult? (3)

• Good proper time resolution requires excellent
  tracking as close as possible to the interaction
  point
• Excellent tracking with large drift chamber
  followed by a 6 layers silicon detector
• Inserted Layer 00 at about 1 cm from beam
• A very innovative and difficult detector
• However
• Real life calls for large resolution scale
  factors
• Noise problems reduce L00 efficiency and
  resolution
• Y. Book ct resolution on fully reconstructed
  events 45 fs ? observed 86 fs

13
The final analysis with 1fb-1

• What we achieved in spite of all the setbacks
• Emphasize improvements relative to the April 2006
  3? evidence analysis

14
Bs hadronic decay signals

• New
• Use decays with lost ? or ?0 in golden mode
  Ds(??)? (Dp/p 2)
• Improve selection with PID and NN

15
Bs semileptonic decay signals

• New
• Improve selection with PID
• 100 S/N improvement in ?? and KK modes
• Add new trigger paths
• Yield 61,500 (was 37,000)
• Exploit lDs mass in oscillation fit
• More sensitivity
• Dp/p 3 high mass
• Dp/p 20 low mass

16
Huge Control Signals

• Hadronic decays
• B (J/yK, D0p, D03p) 50
  k
• B0( J/yK, D-p, D-p, D-3p, D-3p ) 60 k
• Semileptonic decays
• lD0 (D0 ? Kp) 540 k events
• lD- (D- ? D0p) 75 k events
• lD- (D- ? Kpp) 300 k events
• Very important to calibrate and
• understand taggers and other aspects of the
  analysis

17
Flavor tagging (1)

• Combined same side and opposite side tags
  assuming no correlation
• Opposite side electrons, muons, kaons, jet
  charge
• Same Side tag with selected kaon close to Bs

18
Flavor tagging (2)

• Use parameterized taggers
• Sensitivity increased
• ltDgt ?
• New
• Opposite side - 1.8 (20)
• Add OST kaons ?D2 0.23
• Combine all OST with NN
• Same side - 3.5 / 4.8 (0 had./ 9 semi)
• Add NN in SSKT for better
• ?-K separation

19
OST tagger calibration/?md

• OST dilutions calibrated
• Use B/B0 samples
• 1 calibration constant/tagger type
• Important for setting limit, NOT essential for
  observation
• Makes sure A 1 _at_ mixing frequency
• Bd mixing by-product and cross-check of analysis

B
B0
hadronic Dmd 0.536 0.028 (stat)
0.006 (syst) ps-1 (355 pb-1) semileptonic Dmd
0.509 0.010 (stat) 0.016 (syst) ps-1 (1000
pb-1) world average Dmd 0.507 0.004 ps-1
(from HFAG site)
20
Time resolution

• Time resolution is calibrated on large D track
  data sample
• Good for high frequency measurement

21
The September 2006 result
22
Amplitude scans (1)
Golden mode
A/?A 3.74
A/?A 4.45
A/?A 1.82
A/?A 1.76
23
Amplitude scans (2)

• Combined amplitude scan all samples

A/?A 6.05
24
Alternate views

• Log of likelihood ratio between signal and no
  signal hypothesis
• p-value 8x10-8 (5? 5.7x10-7)

• Proper time domain plot
• No oscillation for other choice of ?ms

25
The final result
A. Abulencia et al., hep-ex/0609040, Phys. Rev.
Lett., 97, 242003 (2006)

• Having firmly established the observation
• we fit the oscillation frequency
• Calculate Vtd/Vts (best measurement)
• Experimental error exceeds theory error by 1
  order of magnitude!

(M. Okamoto, hep-lat/0510113)
26
Effect on global picture

• Compared to expectations

• Rho-eta plane

K. Trabelsi CKM2006
27
Model independent limits on NP (1)

• .
• ?ms 2M12, arg(M12) 2bs (also called c)
• Combined measurement of mixing frequency and
  mixing phase provides model independent limits on
  new physics contributions
• Information on phase from
• Bs ! ?? ang. analysis ?CP
• Lepton asymmetry

ICHEP 2006
Mostly from recent Tevatron results (see
talks D. Casey, CKM 2006 M. Bona, CKM 2006)
28
Model independent limits on NP (2)
Dms, DGs and ASL

• NP constraint in Bs sector
• Rather impressive!
• Large LQCD errors
• Tevatron error on ?s will improve
• ICHEP2006 D0 measurement (see D. Casey talk)

M. Bona CKM2006
29
Conclusions

• First firm observation of Bs mixing from CDF
  after nearly 20 years of efforts!
• and a lot of efforts in the last few years!
• Effect on global fits limited by large theory
  error
• We hope it will be reduced good prospects
• First limits on NP in the Bs sector
• Now need to reduce the error on ?s
• The Tevatron has an opportunity to significantly
  improve this measurement maybe by next CKM
  conference

30
Backup slides

• Backup slide list
• CDF detector schematics
• Vtd/Vts from radiative decays at B factories
• Analysis techniques
• Fourier
• Significance
• Amplitude scan
• Limit setting
• Likelihood ratio
• Data sets
• Trigger
• SL backgrounds
• SSKT
• P-values
• Systematics/Zoomed likelihood
• Vtd/Vts calculation

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Previous measurements (2)

• Other measurements of
• Use ratio of BR from the reactions
• B0d ! ? (?) ? relative to
• B0d ! K0 ?
• Vtd/Vts 0.1790.0140.020 BaBar
  (hep-ex/0607099 ICHEP06)
• Vtd/Vts 0.2070.0160.027 Belle (PRL 96,
  221601(2006) after reanalysis in hep-ph/0603232)
• HFAG Vtd/Vts 0.1920.014(th)0.016(exp)
  (hep-ex/0603232))

back
32
Analysis techniques

• Bs mixing signal is difficult to observe
• Need to establish a signal before fitting for a
  value
• Many specific techniques developed to look for Bs
  mixing
• Detailed tutorial
• H.G.Moser and A.Roussarie, NIM A384, 491 (1997)

back
33
Analysis techniques (1)

• Time domain
• Frequency domain (Fourier transform)
• If signal ? observe peak in difference of Fourier
  transforms of un-mixed and mixed data
• Signal is reduced by background (fs), dilution
  (D) and ct-resolution (?)

back
34
Analysis techniques (2)
back

• and are completely
  data driven
• Model independent search by plotting
• Expected significance of resonance
• NS, NB signal, background
• events before flavor tagging
• ? flavor tagging efficiency
• ? D2 flavor tagging power

35
Amplitude scan

• Define amplitude, A, as Fourier transform
  normalized to expected peak size if ?ms ?
• A 1 on resonance, A 0 off resonance
• Amplitude can be obtained by fitting for A in
  ct-space at constant ? the fitting function

Data driven
Model dependent
back
36
Setting limits
back

• For any given ?
• If A(?) 1.645 ?(A(?)) lt 1
• Exclude ? at 95 CL since
• If NO signal ltA(?)gt 0
• ?s sensitivity when
• 1.645 ?(A(?s)) 1
• Must include
• systematic errors

Fall 2005 CDF result
37
Likelihood ratio

• Alternate approach
• ?log L1 log(L(A1)/L(A0))
• If minimum is significant than give bounds on ?
  ms values
• Natural way to evaluate ? ms uncertainty
• Lower and upper bound

back
38
Key detector features
back
Central muon
Central calorimeters
Solenoid
Triggers L1 XFT L2 SVT
Essential for Bs mix. anal.
TOF
Endplug calorimeter
Silicon and drift chamber trackers
Forward muon
39
Data sets

• 3 data taking periods
• 1 355 pb-1
• 2 410 pb-1
• 3 230 pb-1
• Period covered
• Feb. 2002 - Jan. 2006

back
40
Getting signals the trigger

• Many variations to optimize yield with luminosity
• Hadronic decays (typical selection)
• L1
• 2 tracks opp. charge p_Tgt 2 GeV pt1pt2
  gt5.5 GeV - ? ? lt135o
• L2
• Match to SVT tracks with d gt 120 mm Lxy gt 200
  mm
• L3 confirm L2 with full offline accuracy
• Semileptonic decays (typical selection)
• Most leptonic decays from hadronic trigger above
• L1 e or ? with pT gt 4 GeV 2 GeV pT track - ?
  ? lt 100o
• L2 match track to SVT d gt 120 mm - 2o lt ? ? lt
  100o
• L3 confirm L2 with full offline accuracy

back
41
Bs semileptonic backgrounds

• Backgrounds
• Physics bck. from MC
• B?D D X ( 2 6 )
• Combinatorial from mass sidebands
• Fake lepton real D
• Shapes inverting lepton selection cuts
• Fraction from fits to lepton-D mass

back
42
SSKT
back

• Particles closer to B in fragmentation carry
  information on B type at production
• Bs likely to have a K
• Use TOF/dE/dx for K/p separation
• Tune MC
• Reproduce B, Bd
• Determine systematics
• Apply to Bs

43
P-Values
back

• Probability of fake signal 810-8 ? measure ?ms
• Significance from toy MC and tag randomization
  consistent

44
Systematics in measurement of ?ms
back

• Systematics dominated by ct-scale uncertainty

45
Vtd/Vts
back

• Inputs
• m(B0)/m(Bs) 0.98390 (PDG 2006)
• x 1.21 0.047 -0.035 (M. Okamoto,
  hep-lat/0510113)
• Dmd 0.507 0.005 (PDG 2006)
• Vtd/Vts 0.206 0.0081 (th) 0.0007
  (statsyst)
• -0.0060
• Consistent with SM indirect bounds and B-factory
  measurements of b? d(s) g transitions