Measurements of the CKM angle b from BaBar

1
Measurements of the CKM angle b from BaBar

• Soeren Prell, Iowa State University
• for the BaBar Collaboration
• Brookhaven National Laboratory
• HEP Seminar
• January 20, 2005

2
Outline

• Introduction
• SM CP violation Unitarity Triangle
• Measurements
• sin2b and cos2b from charmonium KS
• sin2b from charmless penguins
• Comparison
• Theoretical Uncertainties
• Summary

3
The Weak Interactions of Quarks
p u, c, t
W
gVpq
q d, s, b
Cabbibo-Kobayashi-Maskawa matrix
Complex matrix elements lead to different
amplitudes for quarks and anti-quarks
? CP violation
4
Wolfenstein Parameterization
? 0.220 0.002 A 0.85 0.05 É 0.22
0.09 0.33 0.05
relative magnitudes
Complex matrix elements Vtd and Vub result
in large CP-asymmetries in B decays

5
The B Unitarity Triangle
All CP asymmetries related to single CKM phase
? ? SM CP violation is very predictive IS IT
RIGHT ?
6
B0 B0 - Mixing Amplitude

• B0 ? B0 mixing via 2nd order weak transition
• proportional to (Vtd )2 Vtd2 e-i2b

Phase difference between B0 and B0 is
7
B0 B0 Mixing the Formalism

• Generic neutral B-meson state
• Time evolution governed by Schroedinger Equation
  
• Hamiltonian is diagonal in basis of heavy and
  light mass eigenstates (GGHGL and q/p1)

8
B0 Decay Amplitudes
Time evolution of physical states
Decay amplitudes

• weak phase ?, strong phase d

9
(Time-dependent) Decay Rates
General case
10
Decay Rates to Final States with specific
Flavor (BB Mixing)
No CP asymmetry, if
unmixed
mixed
11
B0B0 Oscillation Measurements
Di-Leptons
B0 ? Dln
D() p/r/a1, J/?K
B0B0 oscillation frequency precisely determined
from flavor specific final states
Dm 0.502 0.006 ps-1 (world average)
B0 ? Dln
12
CP Eigenstate 2 interfering Amplitudes
Vcb
c
b
Without mixing
?
c
B0
s
Vcs
K0
KS
d
d
Vcb
c
b
b
?
With mixing

c
W
B0
B0
BB mixing
s
Vcs
K0
KS
d
d
d
13
Interference of 2 Amplitudes

• Consider pure B0 initial state (B0 is the same)
• ?m?t 0 P(B0?B0) 0 ? no mixing, no
  interference
• ?m?t p P(B0?B0) 1 ? full mixing, no
  interference
• ?m?t p/2 P(B0?B0) 1/2 ? maximal
  interference, resulting in CP violation !

only B0
final state f
BB mixing
only B0
14
B Decay Rates to CP Eigenstate
For CP eigenstate (with single decay amplitude ?
)
?CP CP of final state
15
Golden Decay Modes (cc)K0 decays
B0 decay
K0 mixing
B0 mixing
c
s
d
b
b
d
c
t
W
s
t
s
d
d
b
d
d
?CP -1 (1) for J/y K0S(L)
16
Time-dependent CP Violation
Amplitude ratio
Define CP Asymmetry as
Mixing phase
(single weak decay amplitude)
Difference in decay rate for B0 and B0 ? CP
Violation
17
BABAR Experiment
BABAR Collaboration 10 Countries 77
Institutions 600 Physicists
EMC 6580 CsI(Tl) crystals
e (3.1GeV)
1.5T Solenoid
DIRC (PID) 144 quartz bars 11000 PMs
e- (9 GeV)
Drift Chamber 40 layers
Silicon Vertex Tracker 5 layers, double sided
strips
Instrumented Flux Return iron / RPCs (muon /
neutral hadrons)
18
PEP-II Integrated Luminosity

• PEP-II top luminosity
• 9.2 x 1033 cm-2s-1
  (design 3.0 x 1033 cm-2s-1 )
• Top recorded L/8 h
• 240 pb-1
• Top recorded L/month
• 16 fb-1
• BABAR logging efficiency
• gt 96

Run4
Run3
trickle injection w/o trickle injection top-off
every 30-40 min
Run2
Run1
continuous filling with trickle injection more
stable machine, 35 more lumi
19
B Meson Production at PEP-II
B production
Suppress with event shape variables
ee- ? ?(4S) ? B0B0
Dominant background for charmless B decays
Continuum (jet-structure)

• ee- ? qq (continuum)

BB (spherical)
BB threshold
B0B0 threshold
20
B Meson Reconstruction
Exploit specific kinematics at the ?(4S) for
signal selection
Energy difference
Beam-energy substituted mass
Correctly reconstructed BB events
Combinatorial background
21
Measurement Technique for sin2b
B-Flavor Tagging
0
B
z
tag
9 GeV
3.1 GeV
Coherent BB production (p-wave)
B0
B0
Reconstruction of B decays to exclusive final
states
22
Charmonium Data Samples
MES GeV
MES GeV
CP sample NTAG purity ?CP
J/? KS (KS?pp-) 2751 96 -1
J/? KS (KS?p0p0) 653 88 -1
?(2S) KS (KS?pp-) 485 87 -1
?c1 KS (KS?pp-) 194 85 -1
?c KS (KS?pp-) 287 74 -1
Total for ?CP-1 4370 92 -1
J/? K0(K0? KSp0) 572 77 0.51
J/? KL 2788 56 1
Total 7730 78
BABAR
J/? KL signal
J/? X background
Non-J/? background
(?CP 1)
?E MeV
23
CP Analysis Dt Distributions
perfect flavor tagging time resolution
realistic mis-tagging finite time resolution
CP PDF
Determine flavor mis- tag rates w and Dt
resolution function R from large control
samples of B0 ? D()p/r/a1
and J/?K
BB Mixing PDF
24
B0 Flavor Tagging

• determine flavor of other B (tag B) from its
  charged decay products
• Correlations exploited by multivariate techniques

Lepton, Kaon tagging
Å
e- , m-
s
c
Category e() w() Q()
Lepton 8.6 0.1 3.2 0.4 7.5 0.2
Kaon I 10.9 0.1 4.6 0.5 9.0 0.2
Kaon II 17.1 0.1 15.6 0.5 8.1 0.2
K-p 13.7 0.1 23.7 0.6 3.8 0.2
Pion 14.5 0.1 33.9 0.6 1.7 0.1
Other 10.0 0.1 41.1 0.8 0.3 0.1
Total 74.9 0.2 30.5 0.4
b
K-
B0(b?l-,K-), B0(b?l,K)
Soft and hard pion tagging
?
Tagging performance
B0 fast p-, soft p B0 fast p, soft p-
25
Sin(2b) Fit Results
J/? KL mode (CP 1)
Preliminary
Preliminary
background
hep-ex/0408127

sin2ß 0.722 ? 0.040 (stat) ? 0.023 (syst)
(PRL 89, 201802 (2002) sin(2ß) 0.741
0.067 0.034)
26
Sin(2ß) the Unitarity Triangle
CKM fit with sin(2ß) measurement
CKM fit without sin(2ß) measurement
cos(2ß) lt 0
cos(2ß) gt 0

• Measured value of sin(2ß) in excellent
  agreement with SM expectation
• Strong constraint on apex of Unitarity Triangle
• One solution for b consistent with measurements
  of Unitarity Triangle sides

27
Cos2b with B ? J/? K0(KSp0)

• Decay of pseudo-scalar meson to 2 spin-1 mesons
• Depending on orbital angular momentum L final
  state can be CP-odd (L1) or CP-even (L0,2)
• Many extra terms in time-dependent decay rate,
  two proportional to cos2ß

angular amplitudes in transversity basis
Interference between CP-even and CP-odd
amplitudes
angular amplitudes
Need to measure amplitudes Ai and phases di
first !
decay angles
28
Measurement of Amplitudes Phases

• Amplitudes measured by angular analysis of
• B0?J/y(Kp-)0 (c.c.)
• B?J/y(KSp) (c.c.)
• B?J/y(Kp0) (c.c.)

A02 0.566 0.012 0.005 A2 0.204
0.015 0.005 A?2 0.230 0.015
0.004 d-d0 2.729 0.101 0.052 d?-d0
0.184 0.070 0.046

• With ambiguous solution ( solution II ) d -
  d0 -2.729 d? - d0 2.958

29
cos2b with B0?J/yK0 (KSp0) ?

• Strong phase differences determined up to the
  2-fold ambiguity
• Sign flip of cos(d? - d0) and cos(d?- d)
  between the 2 strong phases solutions
• ? Flips sign of measured cos2b

Solution I
Solution II
? sign of cos2b is ambiguous ! with K(892)
only.
30
Accounting for a Kp S-wave Contribution
BABAR
L 82 fb-1
Kp- invariant mass

• A broad Kp S-wave present in the K(892)
  region, too NPB296
• Add amplitude to describe B?J/y(Kp)S-wave
• relative strengths of the P and S contributions
• and relative phase g dS-d0
• The ambiguity becomes
• But this ambiguity on g can be resolved !

P-wave intensity
S-wave intensity
31
Resolving the Strong Phases Ambiguity

• Wigner causality principle
• Phase of a resonance rotates counterclockwise
  with mass
• In the K(892) region
• P-wave phase moves fast
• S-wave phase moves slow
• Determine g dS-d0 by m(Kp) bin, fixing d-d0
  and d?-d0 to Solution I (2.729, 0.184) or
  Solution II (3.554, 2.958)

Physical behaviour only observed for solution
II !
32
Measurement of cos2b sign
PRELIMINARY
distribution of cos(2ß) results from a set of
2000 data-sized Monte Carlo samples, generated
with cos(2ß)0.68

• cos2b measured by time and angular analysis of
  104 tagged B0?J/y(KSp0)0 events
• Fit with sin2b floating
• Fit with sin2b fixed to 0.731

• Assuming sin2b and cos2b related to same angle
  2b, from Monte Carlo

33
sin2b from Charmless Penguins
Standard Model interference between B mixing and
dominant b?sss or b?sdd penguin
amplitude gives the same e-i2b as
in tree process b?ccs.
However loops can be sensitive to New Physics!
Standard Model

34
Analysis of B0 ? ?K0

hep-ex/0408072
98 18 fKL
114 12 fKS
total background
continuum background
Earlier BaBar-Belle discrepancy resolved
Belle BELLE-CONF-0435
35
Analysis of B0 ? (KK)CPKS
227 ?106 B pairs
(KK-) mass outside f region contributes 85 to
inclusive branching ratio
hep-ex/0408076
KK- S-wave
452 28 KKK S events (excluding ? KS events)
KK- P-wave

• CP of final state not known a priori
• Describe KK- system in terms of S and P-waves
• Determine CP-even fraction (s-wave) from Legendre
  moments of KK helicity angle distribution
• Crosscheck from isospin method Garmash et al.,
  PRD69

36
CP Asymmetry in B0 ? (KK)CPKS
227 ?106 B pairs
CP content
37
Analysis of B0 ? ?KS
227?106 B pairs
hep-ex/0408090
Large branching ratio
819 38 events
Reconstruct in multiple final states
h?rg
Belle BELLE-CONF-0435
SM
BABAR BABAR-CONF-04/040
38
Analysis of B0 ? f0(980)KS

• Other resonances in ppKS Dalitz-plot are treated
  as systematic

hep-ex/0408095
39
Analysis of B0 ? ? 0KS
227 ?106 B pairs
hep-ex/0408062

• Challenging ?t measurement
• only 2 tracks from long-lived KS available to
  determine B decay vertex
• Use beam constraint in vertex fit
• check of method no bias in sin2b from
  sample using only KS tracks

40
Direct CPV
No indication for direct CP violation in b ?
sss decays BaBar
Consistent results from Belle
41
Summary for sin2b from b?sss Decays
-2.9 s difference between sine coefficients from
s-penguin and (cc)s
42
Combined sin2b Results
BABARBelle DS -3.7 s
Belle only Dsin2b -2.9s
but comparison ignores subleading diagrams !
43
Quark Diagrams for B0 ? J/?KS
Tree Diagram
Penguin Diagram
t

• Tree diagram and penguin diagram have same weak
  phase
• Small deviations O(1) between SJ/?K0 and sin2ß
  from
• DG, eK, q/p-1, direct CPV in B ? J/?K0

Ligeti, Grossman, Kagan PLB538
44
b?s Decay Amplitude VtbVts
penguin
t
Dominant amplitude
q
CP asymmetry from tloop contribution is
where
45
b?s Decay Amplitude VcbVcs
CP asymmetry from c-loop contribution is sin2b
rescattering
long distance
short distance
penguin
46
b?s Decay Amplitude VubVus

• Decays involving Vub enter with decay phase g
• Doubly-CKM suppressed w.r.t dominant diagram

long distance
rescattering
short distance
penguin
Contribute to all b ?sss modes
color-allowed tree
color-suppressed tree
Contribute to hKs, f0Ks, wKs, but not fKs in
KKKs (requires ssbar popup from soft g)
Only in non-resonant KKKs (requires ssbar popup
from soft g)
47
Effect on CP Parameters
S measurement (if this amplitude only)

• Contributing
• Amplitudes

QCD
CKM
Need to know

• Total decay amplitude

O(l2)

• Effect on S and C

Need to estimate xf !
48
Naïve Estimate of sin2b
Kirkby,Nir, PLB592 Hoecker, hep-ex/0410069
Upper limits on xf
B0?f xf Dsin2b
J/yKS loop ? l2 0.02
fKS l2 0.06
p0KS, wKS l2 / loop 0.3
hKS,f0KS,KKKS in between
loop mode-dependent (penguin vs. tree)
QCD-suppression factor O(0.2-0.3)
49
Model Calculations
Some limits from QCD factorization
B0?f Dsin2b
fKS 0.025 0.012 0.010
hKS 0.011 0.009 0.010
p0KS 0.13 0.07
Beneke, Buchalla, Neubert, Sachrajda, NPB591
Buras,Fleischer,Recksiegel,Schwab, NPB697 Ciuchini
at al.,hep-ph/0407073
Problems in reproducing exp. values for some BFs
(!) No reliable theoretical predictions for NP
searches
50
SU(3) Flavor Symmetry
Grossman,Ligeti,Nir,QuinnPRD68

• Assuming SU(3) flavor symmetry, express b?sqq
  amplitude in terms of b?dqq modes

• Get limit on tree in b?sqq from limits on b?dqq
  decay rates (tree dominated)

• No model assumptions beside SU(3) symmetry

51
SU(3) Predictions
Upper limits on xf
B0?f SU(3) U-spin Dsin2b
fKS 0.65 0.22 0.3
hKS 0.18 0.07 0.1
KKKS - 0.19 0.2
p0KS 0.18 - 0.2
Grossman, Isidori, Worah, PRD58 Grossman, Liget,
Nir, Quinn, PRD68 Gronau, Rosner, PLB564 Gronau,
Grossman, Rosner, PLB579 Gronau, Rosner, Zupan,
PLB596 Chiang,Gronau,Rosner,Suprun, PRD70

• Typically many b?dqq branching fractions needed
• Additional assumptions about relations between
  BF such as U-spin reduce uncertainties
• Correction for SU(3)/U-spin breaking
• SU(3) breaking correction (ms /LQCD 20) on
  correction to S (not S itself)
• Smaller than current experimental errors on sin2b

52
SM Uncertainty Estimates - Summary
Dsin2b e.g. fKS
Naïve estimates Easy Ignoring strong phases Cannot improve (not good enough for some modes) 0.06
Model calculations Lowest limits Model-dependent Problems with BF predictions lt 0.04
Flavor symmetry No model-dependence Improving with more data Need to measure many suppressed BF Symmetry breaking lt 0.22, U-spin lt 0.65, SU(3)
Flavor symmetry and model calculation could
eventually provide good limits for Dsin2b
53
Conclusions

• Precise measurement of sin2b in charmonium events
• and cos2b lt 0 excluded at 87 C.L.
• Measurement of sin2b in penguin modes
• BaBar and Belle results combined show apparent
  difference of 3.7 s between the two values for
  sin2b
• ... but if contributions from subleading
  diagrams are (naively) accounted for difference
  is only 3s
• average may not be useful, in case of new
  physics contributions
• More effort is needed to reduce theoretical and
  experimental uncertainties !!!

(sin2b)charmonium 0.722 0.040 0.023
?sin2b?penguin 0.42 0.10
54
Outlook
Expect double BABAR luminosity in summer 2006
2004 246 fb-1 2006 500 fb-1
f0KS KSp0 jKS KKKS hKS
Kg
5s discovery region if non-SM physics is 30
effect
2006
2004
55
Backup Slides
56
Direct CP Violation in the B Decay
CP violation through interference of decay
amplitudes

• Not sufficient to extract physical parameters
• measure A and A, but need A1, A2, fwk, dst

57
Mixing Data Samples
yield
yield
MES GeV
MES GeV
Mixing sample NTAG Purity
D- p/?/a1 (6 decay modes) 32974 83.1
D- p/?/a1 (12 decay modes) 35008 89.4
J/? K0(K0? Kp-) (2 modes) 4896 95.8
Total 72878
58
B0B0 Oscillation Measurements
59
Sin2b - (cc)KS Systematic Error
s(sin2b) Description of background
events 0.012 CP content of peaking
background Background shape uncertainties Mistag
differences between BCP and Bflav
samples 0.007 Composition and content of J/y KL
background 0.011 Dt resolution and detector
effects 0.011 Silicon detector alignment
uncertainty Dt resolution model Beam spot
position 0.007 Fixed ?m, t, ?G/G,
? 0.005 Tag-side interference/ DCSD
decays 0.003 MC statistics/bias 0.003 TOTA
L 0.023
Steadily reducing systematic error July 2002
0.033 July 2001 0.05
60
Results on sin2b from ccs, dcc modes
61
The Decay B ? J/? K0(KSp0)
angular amplitudes in transversity basis
62
Kp S-P Wave

• Fast changing P-wave phase and slowly changing
  S-wave phase around K(890) mass
• ? Counter-clockwise phase motion in Argand
  diagram

P-wave
S-wave
Im A
S-wave relative phase
Re A
Physical phase
63
Comparison with LASS data

• Is this behaviour expected for a Kp S-P phase ?
• Compare with LASS data
• Kp?Kp(n)
• I1/2 contribution
• Global phase p added to LASS data points
• Remarkable agreement!
• A bit surprising because very different processes
  !
• Keep Solution II as the physical solution !
• Note solution I is the one reported up to now !

BABAR
LASS data
sol. I
sol. II
Kp- L 82 fb-1
64
Belles cos2b Measurement
Belle uses the non-physical gtgtsolution I ltlt based
on s-quark helicity conservation
argument Belles result
(sin2b fixed to 0.731)
65
IP-Constrained Vertexing
Constrain decay products to beam-spot in x-y
Vertex precision depends on number of hits in
SVT For ?4 hits, Dt resolution as good as with
charged-tracks (60 events) Crosscheck with
J/yKS compare IP-constrained (Ks) and nominal
(J/y) vertex Belle can reproduce this technique
after SVD upgrade
66
Time-Dependent CP Violation in B ?K(KSp0)g
CP violation occurs, if B and B can decay to
same final state
In the SM, mixed decay to Kg requires wrong
photon helicity, thus CP violation is suppressed
SM C -1 S 2 (ms/mb) sin2b 4
105 14 Kg
S 0.25 0.63 0.14 C -0.57 0.32 0.09
67
Likelihood Ratios
Signal
Continuum
B back.
Signal
Background
68
SU(3) Flavor Symmetry

• Limit on tree in fKS with exact SU(3) symmetry

• Dynamical assumption (tree in fK tree in fK0)
  and U-spin symmetry (mdms)

69
S-Wave under fKS
interference terms!

• Nominal estimate angular-moment analysis (s(S)
  lt 0.06)
• Integrate over helicity angle interference
  terms drop out

measurements w/ and w/o cosqH consistent

• Toy studies with S-wave contributions models

70
CP in KKKS Isospin Approach
Garmash et al, PRD69, 012001
CP content depends on ang. momentum between KK-
CP
L?
CP (-)L
CP
Lodd
Leven
Leven

• So the CP-even (Leven) fraction in KK-KS
  decays is

71
BABAR Status

• Sep 30, 2004 Hoisting and rigging near miss
• - nylon sling broke during a move of 4,400-lbs
  steel corner block
• no injuries or damage
• corrective/retraining measures taken by SLAC

• Oct 11, 2004 Electrical arc injury
• Contract-worker seriously injured during
  installation of circuit breaker in 480V panel in
  LINAC Klystron Gallery
• Work suspension by SLAC director
• Widespread safety training (SLAC/DOE)

• Nov 2004 DOE Type A Accident Investigation
• Injured electrician released from hospital
• PEPII still down

• Dec 2004 DOE Type A Accident Investigation
  results published

• Feb 2005 Corrective Action Plan
• PEPII start anticipated