CP Violation in B0s mesons

1

• CP Violation in B0s mesons
• Results from a flavor tagged analysis of B0s ?
  J/y f
• Joe Boudreau
• University of Pittsburgh
• Experimental results from CDF (and other
  experiment)

2
A very brief abstract of this talk first. The
following topics will be developed
VcbVcs
CDF and D0 use B0s ? J/y f to measure CKM
phases. We determine from this decay
the quantity bs. This is in exact analogy to B
factory measurement of the b, an angle of the
unitarity triangle. The standard model makes
very precise predictions for both angles. But
other new particles processes, lurking
potentially in quantum mechanical loops such as
box diagrams and penguin diagrams can change the
prediction.
VubVus
bs
VtbVts
3
The interaction of quarks with the charged weak
current is governed by one Universal coupling
constant modulated by a matrix, the CKM matrix
4
Unitarity triangles, a graphical representation
of the unitarity of the CKM matrix
VubVud VtbVtd VcbVcd0
5
There are six unitarity triangles. The one we
shall talk about today is the (bs) unitarity
triangle, and, especially, its angle bs , which
is predicted precisely, now measured, too
VubVus VtbVts VcbVcs0
VcbVcs
VubVus
bs
VtbVts
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CP Violation
?
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CP Symmetry

• The operator that transforms matter into
  antimatter in quantum
• mechanics is the CP operator.
• CP composition between two transformations
• P (parity) spatial inversion. Left-handed
  particle-gtRight handed
• particle.
• C (charge conjugation) Inverts every internal
  quantum number,
• like electric charge, isospin gt
  turns a particle into
• its antiparticle.
• CP turns a left-handed particle into a
  right-handed antiparticle.
• CP symmetry says H,CP0
• eigenstates of the Hamiltonian are
  eigenstates of CP
• transitions from CP even states to CP odd
  states do
• not occur.

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CP Violation discovered in 1964 (Cronin, Fitch)
attributed in 1973 to the Higgs, Yukawa
sector (Kobayashi, Maskawa)
experimentally validated in this decade by Belle,
Babar CDF
http//ckmfitter.in2p3.fr/
The verification of the model was carried out by
validating its chief prediction, the Unitarity of
the CKM matrix elements.
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There are 12 observed instances of CP
violation. 1. Indirect CP violation in the kaon
system (eK) 2. Direct CP violation in the kaon
system e/e 3. CP Violation in the interference
of mixing and decay in B0 ? J/y K0. 4. CP
Violation in the interference of mixing and decay
in B0-gthK0 5. CP Violation in the interference
of mixing and decay in B0-gtKK-Ks 6. CP Violation
in the interference of mixing and decay in
B0-gtpp- 7. CP Violation in the interference of
mixing and decay in B0-gtDD- 8. CP Violation in
the interference of mixing and decay in
B0-gtf0K0s 9. CP Violation in the interference of
mixing and decay in B0-gtyp0 10. Direct CP
Violation in the decay B0 ?K-p 11. Direct CP
Violation in the decay B ? rp 12. Direct CP
Violation in the decay B ? pp- Also Direct
CP Violation in the decay B- ?K-p0
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B Mixing
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There are two states in the B0s system, the
so-called Flavor eigenstates They evolve
according to the Schrödinger eqn
and M, G Hermitian Matrices
u, c
G Absorptive diagrams
M Dispersive diagrams
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The mixing of eigenstates gives rise to
oscillations of frequency Dm, determined by the
magnitude of the box diagram The phase of
the diagram gives the complex number q/p, with
magnitude of very nearly 1 (in the standard
model).
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Mixing phenomenology
Mixing probability
Mixing occurs when a B0s decays as a B0s.
Decay to a flavor specific final state eg (Dsp-)
tags the flavor at decay. One of three tagging
algorithms tags the flavor at production. Good
triggering, full reconstruction of hadronic
decays, excellent vertex resolution, and high
dilution tagging are all essential for this
measurement, which made news in 2006.
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• There is a similarity here to Faraday rotation,
  in optics rotation of the
• polarization of light

• Start with polarized light.
• Decompose it into two states of circular
  polarization.
• In a sugar solution these states propagate with
  different speeds.
• So one helicity arrives early, or, there is a
  phase difference.
• When the two beams recohere, the polarization has
  rotated.

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In B mesons .
B0
B0
t
b
s
W
W
Bs0
Bs0
s
b
t
I needed two polarizing filters for the
demonstration. CDF needs initial state flavor
tagging, and looks at decays to flavor-specific
final states.
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?ms 17.77 0.10(sta) 0.07(sys) ps-1 Vtd/Vts 0.2060 0.0007 (exp) 0.0081 0.0060 (theor)
?ms 18.56 0.87(stat) ps-1
(PRL 97, 242003 2006)
(D0 CONF Note 5474)
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Many of the new CP observables are CP
violation in the interference of mixing and
decay
B0gt
J/y K0s gt
B0gt
BABAR, BELLE have used this decay to measure
precisely the value of sin(2b) an angle of the
bd unitarity triangle
19
CP violation in the interference of mixing and
decay Imagine we filter for circularly
polarized light, here at the end
B0
B0
Interference of mixing and decay Uses decay to
CP eigenstates to analyze the mixing. Measures
q/p relative to A/A (ratio of decay
amplitudes) Physical observable
Sin(2b) 0.728 0.056(stat) 0.023(syst)
K. Abe et al., Phys. Rev. D71, 072003 (2005).
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There was a fourfold ambiguity in the Belle,
Babar measurement of b. Two are irreducible
all observables upon either sin(2b) or
cos(2b) The B factory experiments resolved this
with a complicated decays B? J/y K0 A decay to
two vector mesons, a final state which is neither
CP even nor odd, but CP-mixed.
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B0s?J/y f. B-gtV V
decay to actually three distinct final states
(S-wave, P-wave, and D-wave). S,D Wave CP
even, short-lived, light. P Wave CP odd,
long-lived, heavy. These final states are
actually intermediate states (final state is
mm-KK-) so there is interference. Pure S,
P,or D wave states would have distinct angular
distributions. With a mix of orbital angular
momentum final states one can separate the
decays on a statistical basis (angular analysis)
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• Spin correlation of the vector mesons resembles
  that of the two photons
• two photons in positronium decay.
• Polarization of vector mesons can be
  perpendicular (CP odd), or parallel (CP even)
• And also longitudinal (CP even)
• Distributions in the angles q, f, and y sensitive
  to polarization.

A. S. Dighe, I. Dunietz, H. J. Lipkin, and J.
L. Rosner, Phys. Lett. B 369, 144 (1996), 184
hep-ph/9511363.
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Time dependence of the angular distributions
A?, A, A0 transition amplitude ltBs0Pgtto
each final states P?, P, P0 A?, A, A0
transition amplitude ltBs0Pgt
In the physical
B0s,phys meson the flavor content changes
(B0s-B0s oscillations) with fast frequency of
17.77 0.12 ps-1 The amplitude ltBs,phys0(t)Pgt
A(t) (amplitude for a particle born as a
B0s to decay into the state Pgt after a time t)
decays and oscillates.
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This innocent expression hides a lot of
richness CP Asymmetries through flavor
tagging. sensitivity to CP without flavor
tagging. sensitivity to both sin(2bs) and
cos(2bs) simultaneously. Width difference
Mixing Asymmetries
formula suggests an analysis of an oscillating
polarization.
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CP Violation in the interference of mixing and
decay for the B0s system Take q/p from
the mixing of B0s - B0s Take A/A from the
decay into P?, P, P0 Form
the (phase) convention-independ
ent and observable quantity
This number is real and unimodular if H,CP0
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Babar, Belle an ambiguity in b by analyzing the
decay B0 ?J/y K0 which is B?V V and
measures sin(2b) and cos(2b) This involves
angular analysis as described previously
J/y K0
P gt
B0gt
P0 gt
mm-K0sp0gt
B0gt
B0gt
P? gt
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Today I will tell you about an analysis of an
almost exact analogy, Bs0gt ? J/y f (but I think
that in the B0s system the phenomenology is even
richer! Because of the width difference! )

J/y f
P gt
Bs0gt
P0 gt
mm-KK-gt
Bs0gt
Bs0gt
P? gt
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This is a complicated business but there is a
nice analogy one can do to understand what
happens to B0s and in the decay to J/y f
CP violation a preferred direction in the space
B0s/B0s in mixing or in the decay.
Birefringent zone/ weak interaction,
box diagrams, DG/G?10.
Interference on the far screen angular analysis
Polarizing Filter initial state flavor tagging.
Filtered slits CP even and odd final states
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The decay B0s?J/y f obtains from the decay B0?J/y
K0 by the replacement of a d antiquark by an s
antiquark
b
d
s
W
W
B0 ?J/y K0
c
W
c
d
b
s
s
W
W
B0 ?J/y f
c
W
c
s
We are measuring then not the bd unitarity
triangle but the bs unitarity triangle
VubVud
VtbVtd
VcbVcs
b
VubVus
bs
VtbVts
VcbVcd
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VubVud O(l3)
VtbVtd O(l3)
With l 0.2272 0.0010 A 0.818 (0.007
-0.017) r 0.221 (0.064-0.028) h
0.340 (0.017-0.045) One easily obtains a
prediction for bs 2bs 0.0370.002
b
VcbVcd O(l3)
VcbVcs O(l2)
b
VubVus O(l4)
VtbVts O(l2)
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bs, the phase of Vts is expected to be close to
zero in the standard model. and should not lead
to detectable CP violation.
Small phase, small CP violation
However there may be other contributions to CP
violation from other sources This is what
makes this an important measurement.




Flavor structure of BSM physics unknown
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Hidden richness
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reference material
An analysis of the decay can be done with either
a mix of B and B mesons (untagged) or with a
partially separated sample (flavor tagged).
Latter is more difficult and more powerful.
B
B
These expressions are used directly to
generate simulated events. expanded, smeared,
and used in a Likelihood function. summed
over B and B (untagged analysis only)
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reference material
For reference expanded, smeared , normalized
rates
obtain the overall time and angular dependence
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reference material
Explicit time dependence is here
then, replace exp, sinexp, cosexp with
smeared functions.
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The analysis of B0s?J/y f can extract these
physics parameters
bs CP phase
DGGH-GL Width difference
t2/(GHGL) Average lifetime
A?? (phase d?) Decay Amplitude t0
A? (phase d? ) Decay Amplitude t0
A0 (phase 0) Decay Amplitude t0
The exact symmetry..
is an experimental headache.
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Curiosity 1 cos(2bs) is easier to measure than
sin(2bs). It can be done in the untagged
analysis for which the PDF contains time
dependent terms
Physically this is accessible because one
particular lifetime state (long or short) decays
to the wrong angular distributions. Needs
DG?0 no equivalent in B0 ?J/y K0. Some fine
print in the interference term, in an untagged
analysis, there is a term including sin(2bs)
however this term does not determine the sign of
sin(2bs) so it does not solve any ambiguity.
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Curiosity 2 Sensitivity to Dms (tagged
analysis only even in the absence of CP)
How much sensitivity? Well, we did not exploit
it yet but it could be important news at the LHC!
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Where does the sensitivity to Dms come from ?
J/y f
P gt
Bs0gt
P0 gt
mm-KK-gt
Bs0gt
Bs0gt
P? gt
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Where does the sensitivity to Dms come from ?
J/y f
P gt
Bs,Lgt
P0 gt
mm-KK-gt
Bs,Hgt
Bs0gt
P? gt
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Big simplification
Time dependence of interference term is contained
in the factor
? Interference terms tag the flavor at decay.
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CDF Detector showing as seen by the B
physics group.
Muon chambers for triggering on the J/y?mm- and
m Identification.
Strip chambers, calorimeter for electron ID
Central outer tracker dE/dX and TOF system for
particle ID r lt 132 cm B 1.4 T
for momentum resolution.
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SVX II
ISL
Excellent vertex resolution from three silicon
subsystems
L00 1.6 cm from the beam. 50 mm strip
pitch Low mass, low M-S.
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CDF, 2506 51 events
.. And in D0, 1967
65 total..
but 2019 73 tagged events, all tagged.
Next, well run through the CDF analysis, show
what you get from flavor tagging, then show the
D0 results.
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The Analysis needs the proper decay time,
decay angles and flavor-at-production of a B0s or
B0s decaying to J/y f.
S
Modeling of detector sculpting
Selection
Proper decay time estimation
S
Likelihood fit
Extraction of confidence region
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• Artificial Neural Network selection trained on
  data MC Uses
• transverse momentum PT and vertex probability
  prob(c2) of B,
• J/y mass and vertex probability of f
• pT and Particle ID (TOF, dE/dx) of K, K-

Candidate events should have NN gt 0.6
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We reconstruct B0s ?J/y f 2.5K 1.7
fb-1 for untagged tagged analysis B0s ?J/y f
2.0K 1.35 fb-1 for flavor-tagged
analysis B0 ? J/y K0 7.8K 1.35 fb-1
B? V V decay for crosscheck of angular
analysis B ? J/y K 19K 1.35 fb-1
Measure dilution of opposite side tagging.
48
Results from 1.7 fb-1 of untagged decays. bs
fixed to its Standard Model value
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Results untagged analysis
arXiv0710.1789 hep-ex
Standard Model Fit (no CP violation)
HQET ct(B0s) (1.000.01) ct(B0) PDG
ct(B0) 459 0.027 mm
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More results, untagged analysis
Applying the HQET lifetime constraint
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An angular analysis can also be applied to the
decay B0-gt J/y K to extract amplitudes CP even
/ Odd fractions in the final state
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Angular fit projections B0 ? J/y f
Angular fit projections B0 ? J/y K0
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A consistent picture of the CP Odd/Even fraction
in B0?J/y K, B0s?J/y f in CDF, Babar, and Belle
experiments
R. Itoh et al. Phys Rev. Lett. 98, 121801, 2007
(Belle) B. Aubert et al. PRD 76 (2007) 031102
(Babar)
B0s
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This plot is Feldman-Cousins confidence region in
the space of the parameters 2bs and DG
The symmetry you see occurs because the untagged
analysis depends almost only on cos(2bs) and
almost not at all on sin(2bs). Clearly the tagged
analysis will remove this ambiguity. As you
are about to see.
55
Results from 1.35 fb-1 of tagged decays.
bs floating
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Tagged analysis likelihood contour in the space
of the parameters bs and DG
One ambiguity is gone, now this one
remains
57
Constrain strong phases d and d? to BaBar
Values (for B0?J/y K !!)
Constrain ts to PDG Value for B0
Apply both constraints.
using values reported in
B. Aubert et al. (BABAR Collaboration), Phys.
Rev. D 71, 032005 (2005).
58
The standard model predictions of 2bs and DG
data consistent with the CDF data at the 15
confidence level, corresponding to 1.5 Gaussian
standard deviations. One dimensional
Feldman-Cousins confidence intervals on 2bs ( DG
treated as a nuisance parameter) 2bs ?
0.32, 2.82 at the 68 CL. Assuming G12
0.048 0.018 and the relation DG
2G12cos(2bs) 2bs ?? 0.24,1.36 U 1.78,
2.90 at the 68 CL. If we additionally
constrain the strong phases d and d? to the
results from B0 ? J/y K0 decays and the Bs mean
width to the world average Bd width, we find
2bs ? 0.40, 1.20 at 68 CL
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A Feldman-Cousins confidence region in the bs-DG
plane is the main result. This interval is based
on p-values obtained from Toy Monte Carlo and
represents regions that contain the true value
of the parameters 68 (95) of the time.
arXiv0712.2397v1
The standard model agrees with the data at the
15 CL
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D0 Result arXiv0802.2255v1
Strong phases varying around the world average
values ( for B0?J/y K !!) Uncertainty taken
to be p/5
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Likelihood contours for just DG and for just
fs-2bs
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Outlook

• Note fs -2bs
• Fluctuation or something more, it does go in the
  same direction.
• CDF estimates confidence level at 15 using
  p-values to obtain Ln(L/L0)
• D0 estimates confidence level a 6.6 using the
  probability to extract a lower
• value than seen in the data, from toy.

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UTFit group has made an external combination.

• re-introduces the ambiguity into the D0
  result.
• does so by symmetrizing.
• cannot fully undo the strong phase constraint.
• I am showing you this conclusion, but not
  endorsing it
• very enthusiastically.

CDF and D0 plan to make an internal combination
for the near future.
64
Elsewhere there is another anomaly that may also
have to do with b?s Direct CP in B?K p0 and
B0? Kp- are generated by the b ?s transition.
These should have the same magnitude. But
Belle measures
(4.4 s) Including BaBar
measurements gt 5s
Lin, S.-W. et al. (The Belle collaboration)
Nature 452,332335 (2008).

• The electroweak penguin can break the isospin
  symmetry
• But then extra sources of CP violating phase
  would be required in the penguin

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Conclusion

• Towards the end of a 20-year program in
  proton-antiproton physics
• some terribly interesting times for the
  physics of the b-quark.
• An anomaly from the B factories
• Are quantum loop corrections to the b?s
  transitions are to blame?
• If so, precision measurements of the CP
  asymmetries in the B0s system are
• a clean way to sort it out.
• D0 and CDF have just demonstrated the
  feasibility of doing those
• measurements.
• Higher precision, higher statistics
• measurements could give us a
• even stronger hint before the LHC
• turns on.

Baseline expectation w/ 6/fb
s 4.5o
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FIN
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Free Bonus Slides
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Phenomenology of the B0s system
B0s a two-state system like the B0, K0, and D0
systems. All of these neutral mesons have (to
varying extent) particle antiparticle
oscillations, can be analyzed in flavor
specific final states, governed by the
parameter Dm width differences governed by
the parameter DG/G CP violation in the
mixing q/p ? 1 CP violation in the
decay A/A ? 1 CP violation in
interference of mixing and decay qA/pA ?
1

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The extent to which these features show up
depends upon numerical values of the constants
governing mixing, decay, direct CP violation and
CP asymmetries
Species xDm/G yDG/G Striking feature
K0 0.474 0.997 Width difference
B0 0.77 lt0.01 CP violation
B0s 27 0.15 Fast Oscillation
D0 ?0.01 ?0.01 None

• The B0s system is characterized by the following
  standard model expectations
• Very fast oscillation frequency.
• Small but observable (10) lifetime difference.
• Very small CP violation in the standard model.

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Contrast this phenomenology with that of B0
mesons.
Slow oscillation Dmd 0.507 0.005 ps-1 ?
Oscillation length cT 3.7 mm Large
Standard Model CP violation
Fast oscillation Dms 18 ps-1 Oscillation
length cT 110 mm Zero Standard Model CP
violation (almost)
http//utfit.roma1.infn.it/
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Higgs Yukawa couplings
Quark mass matrix
Higgs Field vev
involves a matrix, the CKM matrix (unitary!)
The charged weak currents
VCKM ULDL
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CDF Timeline Tevatron starts 1985 First
physics 1988 Run I start 1992
Top quark 1995 Run II start 2001
Unique opportunity for B physics The Tevatron
produces all flavors of B hadrons B, B0, B0s,
Lb, Bc, Sb, Xb, Wb, excited states
74
Luminosity delivered and collected at CDF
tagged analysis up to summer 06 (1.35
fb-1) untagged analysis a little more (1.7
fb-1)
75
Important detail In the standard model
bs?0 To estimate various standard model
parameters with bs?0 The standard model bs
constraint is applied in the fit. Tagging
information is not used. The full data sample
is used. Bounds on bs can be obtained
without flavor tagging. Data sample of 1.7 fb-1
without tagging has been used to perform both
SM fits and to obtain bounds on bs. The best
bound on bs come from a flavor-tagged sample, but
only a subset of CDFs data has calibrated
flavor-tagging Flavor-tagged data sample of
1.3 fb-1 is used to obtain bounds on bs.
76
Proper decay time distance between production
decay..
Beam profile 30 microns.
Lxy
transformed into the rest frame of the B meson
ct Lxy/sinq/bg Lxy?MB/PT
Resolution is about 76 fs for the J/y f decay
mode
77

• Two techniques for initial state
  flavor tagging
• b, b quarks are always produced in pairs
• b quark always opposite b
• b antiquark always opposite b
• Flavor-specific decay modes (eg semileptonic
  decays)
• of the opposite side b, or jet charge can be
  used to
• determine the sign of the b quark on the
  opposite side.

• The fragmentation chain produces weak
• correlations between b quark flavor and the
• sign of nearby pions and kaons in the
• fragmentation chain
• Procedure to select leading p, K can be
• optimized to obtain the highest quality tag.

78
Performance of the flavor tag in CDF

• Each tagger returns
• A decision (B or B)
• An estimate of the quality of that
• decision (dilution D)
• e tag efficiency
• D 1-2w
• w mistag rate

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Tagger performance in J/y f decays
Dilution (274) Efficiency (501)
Dilution (112) Efficiency (961)
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The quality of the Prediction of dilution Can be
checked against the data We reconstruct a
sample Of B decays in which one knows the sign
of the B meson. We then predict the sign of
the meson and plot the predicted dilution vs the
actual dilution.
Separately for B and B- Scale (from lepton
SVT this sample take the difference B/B- as
an uncertainty).
81
Decay angles come from reconstructed track
momentum of K, K-, m m- as determined by CDFs
tracking system. Detector efficiency modifies
the differential rates
Detector efficiency (MC)
F
cos (q)
Sources of inefficiency detector acceptance
limited to h lt 1.0 neural network cuts on
kinematic quantities such as pT
82
- Without detector efficiency, the time and
angular PDF is analytically normalized

• With detector efficiency Likelihood function
  needs normalization

- One technique
Fit the efficiency function in the same
polynomials
This involves a few basis functions Ylm(cosq,f) x
Pk (cos y)
and N is analytic. This speeds up the
numerical task greatly!
83
Other analysis sensitive to bs Semileptonic
asymmetry
Very weak dependence on fs-2bs
Where
DG/DMs (49.7 9.4) 10-4
(hep-ph/0612167)
Black central value Green 68
allowed.
D0 Contours 39CL

• AsSL 0.020 0.028 (CDF)

http//www-cdf.fnal.gov/physics/new/bottom/070816.
blessed-acp-bsemil/

• AsSL 0.0001 0.0090 (stat) (D0)

Phys. Rev. D 76, 057101 (2007)