1. B Physics Lessons from the Tevatron
Sinéad M. Farrington
University of Oxford
YETI Durham January 2008

2. Observation of Bs Mixing-
In 2006 the phenomenon of mixing was observed for the first time
in the Bs meson system
This analysis required understanding almost every challenge
we face in hadron collider B physics
I will use it to illustrate the lessons we have learned
(Note that there are many other B physics analyses at the Tevatron, but
this one addresses nearly all of the issues)
I will give more examples from CDF, reflecting my experience and affiliation 2

3. The Tevatron
CDF D0 p
1km
Ecom=2TeV -
Ep=0.96TeV
ECoM=2TeV -
Fermilab, Chicago
Currently the world’s highest
energy collider
Hadron collisions can produce a wide spectrum of b hadrons (in a challenging environment)
Bs cannot be produced at the B factories since their Centre of Mass energy is below threshold (except for a special run by Belle) 3

4. Bs Physics Bs Bs Bs b s Bound states: Matterantimatter: b s Vts*
Bound states:
Matterantimatter: b s
u, c, t, ?
u,c,t,? b s Bs
MATTER
ANTIMATTER
NEW PHYSICS?
Vts*
occurs
via Bs Bs W+ W-
Vts
The mass eigenstates (H and L) are superpositions of Bs and Bs
System characterised by 4 parameters:
masses: mH, mL lifetimes: GH, GL (G=1/t)
Difference in mass is related to frequency of oscillation between matter and antimatter particle
Predicted Dms around 20ps-1

5. Measuring ms
In principle: Measure asymmetry of number of matter and antimatter decays:
In practice: Dm is measured by more complex techniques: amplitude scan and
likelihood profile
H. G. Moser, A. Roussarie, NIM A384 (1997)
Measurement interesting because:
New Physics may enter in box diagram
Leads directly to measurement of CKM matrix element Vts 5

6. Mixing Ingredients
Whichever technique is used, the information we need to extract from the events is:
1) Signal samples
- semileptonic and hadronic modes
Time of Decay
Flavour tagging
- was the B in a mixed state when it decayed? 6

7. Signal Samples for BsMixing
Hadronic: fully reconstructed
Semileptonic: partially reconstructed  L
These modes are flavour specific: the charges tag the B at decay
Need to gather large samples of these decays 7

8. Lesson 1: Triggering To trigger leptons: Bs → J/y f, Bs → Ds- l+
B mesons have long lifetimes (~ps)
their decay products have large impact parameter, d0 d0
Secondary
Vertex
Primary
Vertex
Online
accuracy
Require two displaced tracks (CDF):
(pT > 2 GeV/c, 120 m<|d0|<1mm)
Need precision tracking in silicon
vertex detector
To trigger leptons: Bs → J/y f, Bs → Ds- l+
look for activity in muon chambers/ calorimetry
Single- or di- lepton triggers
D0 has superb muon coverage
Trigger in |h| <1.6 (single)
|h|<2 (di)
CDF trigger in |h|<1
The experiments have focussed their analyses in complementary ways

9. Lesson 1: Triggering p = e-t’/  R(t’,t)  (t)
Requiring displaced tracks biases the B lifetime (remember exponential distribution: the most likely value for the proper decay time is actually zero for B mesons)
Correct for this bias using MC
Calculate the “bias” as a function of the B’s proper decay time
p = e-t’/  R(t’,t)  (t)
intrinsic B
lifetime
resolution
0.0
0.2
0.4
proper time (cm)
signal probability
In addition we must confirm the trigger requirements so we take no volunteers

10. Lesson 1: Triggering Application at LHC:
LHCb has displaced track triggers
Made possible by the precision of the silicon
detectors and the trigger hardware
d0 resolution of 30mm for 2GeV track
CMS/ATLAS cannot trigger on displaced tracks per se
ATLAS uses Region of Interest triggering to collect
some hadronic decays
Mostly restrict B analyses to dimuon channels which are easier
to trigger (excellent muon coverage so these results will be powerful in e.g. Bs→mm,Bs→mmf)

11. Lesson 2: Background Estimation
Invariant mass distribution of Dsp:
partially
reconstructed
B mesons
Understand this contribution using MC plus measured branching fractions in constrained fit to data
signal
Bs→ Ds,
Ds → 
 → K+K-
Combinatorial
Background
Extrapolate function
from high sideband
B0→ D- decays

12. Background Estimation Example
Simple case: Average the sidebands
above and below D peak in semileptonic decay
to obtain background estimate under the peak
Harder case: partially reconstructed B mesons
(missing photons/neutrals) populate lower
sideband but not the signal region
In this case can extrapolate from higher sideband into signal region
Thus predict expected background events in signal region

13. Lesson 3: Neural Networks
Tevatron is obviously not the first place to use multivariate techniques, but their power has been manifest
Neural Network selection used in mixing analysis to increase signal yield
Neural net can “learn” the characteristics of signal compared with background
Exploit correlations among
distinguishing variables
More powerful than cuts
based analysis
LHC application
Should not be in the first iteration analysis – requires
understanding MC/data comparisons first
Will be widely used at LHCb/CMS/ATLAS

14. Flavour Tagging To know whether a B meson “mixed” or not, need to know
flavour (B or B) when it was produced
flavour (B or B) when it decayed
To determine B flavour at production, use tagging techniques:
b quarks produced in pairs  only need to determine flavour of one of them
fragmentation K p Bs Ds f p-
Same Side K Tag
Opposite side
Same Side
Opposite side tags
understood well at B factories,
LEP/SLD and applied at Tevatron
Can make huge gains by using
same side tagger 14

15. Lesson 4: Particle Identification
This is the first time this type of tagger has been implemented
Principle:
charge of B and K correlated
Use Time Of Flight detector, dE/dx information from tracking detector to select Kaon track
The kaon is also selected based on its kinematics Bs s b u K+ } 15

16. Lesson 4: Particle Identification
LHCb has excellent PID
RICH: 16

17. Same Side Kaon Tagger CDF Public Note 8206
If MC reproduces distributions well for B0,B+, then rely on MC to predict
tagger performance in Bs (with appropriate systematic errors)
There is no good way to calibrate this tagger using the data.
Enhance kaon fraction by
making selection on particle ID
tagging track
It is then key to assign appropriate systematic errors 17

18. Lesson 5: use data and MC in tandem
We could not have relied on the MC so heavily in this analysis if we
could not compare distributions between data and MC
Is this being fully addressed at LHC?
In many analyses, the answer is yes
(personal opinion) More focus needs to be placed on this approach
Cannot assume that e.g. rates in MC will be accurate in data as we don’t understand, for example, how to tune the underlying event

19. Lesson 6: Fitter Amplitude scan performed on Bs candidates
Inputs for each candidate:
Mass
Decay time
Decay time resolution
Tag decisions
Predicted dilution
Extra power to distinguish signal and background is obtained in the
fitter by fitting to the mass simultaneously
All elements are then folded into the amplitude scan
“With three parameters, I can fit an elephant.” (Kelvin) 19

20. Combined Amplitude Scan
Amplitude consistent with 1
probability of fake from random tags = 8x10-8
Equivalent to 5.4s significance
ms = 17.77±0.10(stat)±0.07(syst) ps-1

21. (aside - Lesson 7: Branching Fractions)
Measure relative branching fractions when possible
To measure an absolute branching fraction have to know trigger efficiency, reconstruction efficiency, b species production fractions etc
Relative branching fraction eliminates all of these concerns
Choose a high statistics normalisation mode
it should be taken with the same trigger ideally
it should be a decay of the same B species, otherwise you have more work to do and you are penalised anyway by fs/fd uncertainties 21

22. Summary Wish list detector
excellent impact parameter resolution
excellent particle identification
excellent mass resolution
high trigger bandwidth and appropriate triggers
muon/electron coverage
LHC has the ideal detectors for furthering the B physics programme
All it needs are…
Wish list students/postdocs
be detector aware – know its capabilities and get the calibration procedures in place fast
trigger aware – figure out now which triggers to use, fight for your bandwidth!
(quick?) fit fitters – get fitters ready early, add variables to get max power
neural net aware – don’t use NN on day 1 data, but get them ready, get ready to make fast data/MC comparisons so you can move to NN
background aware!!! – don’t assume you can use MC to figure out background, figure out now how you’re going to calculate the backgrounds

23. Outlook This measurement decreases uncertainty on CKM triangle apex:
Easter 2006
October 2006
LHCb with 10fb-1

24. 2) Time of Decay Measure pT of decay products Proper time resolution:
Reconstruct decay length by vertexing
Measure pT of decay products
Proper time resolution:
Semileptonic:
Hadronic:
osc. period at ms = 18 ps-1
Crucial: Vertex resolution
(Silicon Vertex Detector, in particular Layer00 very close to beampipe) 24

25. Layer 00
So-called because we already had layer 0 when this device was designed!
UK designed, built and (mostly) paid for this detector!
I.P resolution
without L00
layer of silicon placed directly on beryllium beam pipe
Radius of 1.5 cm
additional impact parameter resolution

26. Systematic Errors A reminder of what we’ve done: modified MC
checked that it compares well with data for Bd, B+
compared efficiency and dilution for Bd, B+ from data and MC
on the basis that they compare well, we extracted efficiency and dilution for Bs from MC
To apply these numbers in our analysis we need a good understanding of the systematic errors
Several sources:
bb production mechanism
fragmentation fraction
particle content around the B
variation within data statistics
B** fraction
particle ID detectors simulation
pile-up
will discuss further 26

27. Efficiency and Dilution in Data/MC
After all the modifications we compare all relevant distributions including efficiency and dilution in data and MC for Bd, B+ B+ Bd
(%)
Eff
Dil
Data
58.4±0.5
25.4±1.4
57.2±0.6
14.2±2.9 MC
55.9 ±0.1
24.5±0.3
56.6±0.1
12.9±0.4
So we conclude that for Bd, B+ there is a good match between data and MC. Thus we use MC for the Bs case. 27

28. bb Production Mechanism
Three main methods for producing bb in proton-antiproton collisions
Flavour Creation, Flavour Excitation, Gluon Splitting (default mix 5:11:4)
In gluon splitting case, the two b’s are close together – could pick up tagging tracks from the opposite b
Systematic error obtained by fitting Df distribution in data and varying MC distribution within the errors
This results in varying Gluon Splitting [-68%,+46%], Flavour Excitation and Creation [-50%,+50%] Q 28

29. Semileptonic Samples: Ds- l+ x
Fully reconstructed Ds mesons:
Bs mesons not fully reconstructed:
Mixing fit range
Particle ID used; new trigger paths added 
The candidate’s m(lDs-) is included in the fit: discriminates against
“physics backgrounds” of the type B0/+ → D+Ds
61500 semileptonic candidates

30. Calibrating Flavour Taggers
e-/m- p+
ne/m b b K+ c Bd K-
Opposite side D-
Same Side p-
Opposite side: can be calibrated with a sample of any B meson:
Take sample of B+/Bd (mixing behaviour known) – “same side”
Calculate how many B’s in that sample mixed
Look on opposite side for leptons
How often is there a lepton? (efficiency, e)
How often is it the correct sign? (dilution, D)
This is a completely data driven method to obtain the tagger power
BUT! We can’t apply this to the same side tagger! 30

31. Comparisons for Bs already showed some comparisons for Bd and B+
here are comparisons for Bs
Limited statistics  statistical error of comparison is included as systematic
error 31

32. Multiple p-p interactions
More than one pp pair can interact in a bunch crossing
Gives rise to additional particles (usually low momentum)
These could be additional SSKT tagging tracks
Pythia does have a switch to simulate this
but in this analysis data is used to simulate additional tracks
1)Calculate how many additional tracks should be added
do this by looking at the (N+1)th event in our data files
count how many tagging tracks are present in the signal region
2)Harvest tagging tracks from data (which fail one or more of the real cuts)
3)Embed these tracks in MC according to fraction determined in 1) 32

33. Fragmentation Function
E. Ben-Haim et al. Phys. Lett. B580, 108 (2004)
The Lund string fragmentation model is used throughout
This has a “z” parameter to define the fraction of energy the B meson takes from the string
Default z parameterisation is symmetric Lund function
use tuning to LEP data specifically for B mesons 33

34. Why is ms interesting? Probe of New Physics
from Dmd
from Dmd/Dms
Lower limit on Dms
Probe of New Physics
- may enter in box diagrams
2) Measure CKM matrix element:
Dmd known accurately from B factories
Vtd known to 15%
Ratio Vtd/Vts Dmd/Dms related
by constants:
 (from lattice QCD) known to ~4%
So: measure Dms gives Vts
CKM Fit result: Dms: (1s) ps-1
Standard Model Predicts rate of mixing, Dm=mH-mL, so
Measure rate of mixing Vts (or hints of NEW physics) 34

35. Modifications to MC
Each of these modifications is driven by previous measurements, and then associated systematic errors are assigned
Data and MC are used in tandem (and consultation with theorists on what are “reasonable” variations to assess systematics)
Multiple proton-antiproton interactions
Fragmentation Model
As well as usual GEANT detector simulation, specific response of particle ID systems treated especially for this analysis
Trigger prescales
After these modifications we make a comparison of all of the relevant variables between MC and data for all B meson types 35

36. Fragmentation
Track multiplicity, transverse momentum of B meson and fragmentation tracks are sensitive to fragmentation function
Tuning made at LEP should apply equally at Tevatron
Variables compare well with data for Bd, B+
No reason to be suspicious of fragmentation used as a default, but systematic errors assigned to cover the possibility of problems
Simultaneous fit to these distributions to determine allowed parameters of the symmetric Lund function
data not sufficient to give a
tight constraint
reasonable variation can be obtained,
beyond which comparison between
MC and data is degraded
The variations are used to
assign systematic errors: 36

37. Particle Content around B Meson
Particle species around the B meson gives insight on fragmentation
Agrees well between data and MC for Bd, B+
Slight discrepancy for Bs: (20.2±1.4)% kaons in data, (23.6±0.2)% in MC
Vary the kaon fraction in the data downwards in two ways:
reweight all events with a kaon tagging track
reweight only those events with prompt kaons from b-string 37

38. Variation within Data Statistics
We claim the comparisons of data and MC are good
but that is only valid within the errors on our data!
MC samples varied within ranges allowed by statistical uncertainties 38

39. Compare again with data
Including all of the systematic errors we can remake the comparisons of data
and MC
Note that the MC distributions envelope the data distributions 39

40. Final SSKT Results Final Tagger Power: eS2<D2>= (4.0+0.9-1.2) %
(Notes:
<D> is the average dilution over all quantities, in reality we bin dilution in momentum, particle ID
variable to get extra power.
S is a scale factor to account for any differences between data and MC in dependency of dilution
on variables. )
MC simulations combined with measurements in data make
this measurement possible 40

41. The Results 41

42. Bs Dilution and Efficiency Results
Statistical errors only: Bs
(%)
Eff
Dil
Data
49.3±2.3
21.8±0.8 MC
52.1±0.3 -
What about the systematic errors? 42