1. Attila Mihalyi University of Wisconsin-Madison
Recent results on the CKM angle a from BaBar DAFNE 2004, Frascati, Italy
Attila Mihalyi
University of Wisconsin-Madison
12/6/2018
Attila Mihalyi - Wisconsin

2. The CKM matrix and Unitarity Triangle
The CKM mixing matrix relates the quarks in the weak interaction basis (d’,s’,b’) and the quark mass eigenstates (d,s,b): (d’,s’,b’)=VCKM (d,s,b)
Wolfenstein parametrization:
Unitarity leads to:
l=sinqC (Cabibbo angle)
Independent parameters: l,r,h, A
The angles of the triangle are related to CP–violation. 1
(r,h) b g a
Measure a from CP-asymmetries in b→uud processes.
B→pp, B→rp, B→rr
12/6/2018
Attila Mihalyi - Wisconsin

3. B-decay modes sensitive to a
Time dependent asymmetry of a B-B system (h=p,r):
where
Decay amplitudes:
T=Tree
P=penguin
aeff directly related to Shh
Due to the presence of both tree and penguin amplitudes we have:
The extraction of a is complicated by penguins!
12/6/2018
Attila Mihalyi - Wisconsin

4. Isospin analysis for B→pp and B→rr
Two triangular (isospin) relations can be constructed from the decay amplitudes.
M. Gronau, D. London, Phys. Rev. Lett., 65, 3381 (1990)
d=0 if no penguins
Unknowns: Decay amplitudes
Observables: Branching ratios, CP asymmetries
Solvable but a 4-fold ambiguity on a remains:
Common base: EW penguins neglected
One can set a limit on the shift from penguins, a-aeff (useful only if the B→ h0h0 BR is small):
Gronau-London-Sinha-Sinha Phys. Lett. B514, 315 (2001)
Y. Grossman, H. R. Quinn, Phys. Rev., D58, (1998)
12/6/2018
Attila Mihalyi - Wisconsin

5. Prospects of a from B0→p+p-
113 fb-1 of data Preliminary,LP03
From 81fb-1 of data, taken in : PRL (2002), PRL (2003)
HFAG average:
The B0→ p0p0 BR was recently measured at BaBar, PRL (2003), and also at Belle.
BR comparable to B0→ p+p- and B+→ p+p0 but not large enough to measure the B0 - B0 asymmetry.
Implies large penguin contributions: |a-aeff |<48o at 90% c.l Not easy to get a from B→pp !
12/6/2018
Attila Mihalyi - Wisconsin

6. Prospects of a from B→rp
rp is not a CP eigenstate:
Both tree and penguin processes contribute.
Time dependent decay rate:
S: CPV in interference between mixing and decay
C: direct CPV
DC, DS: parameters related to rp not being a CP eigenstate.
ACP: asymmetry between r+p- and r-p+
Babar Results from 113 fb-1 with a quasi-2-body approach. (Select the r bands on the Dalitz plot)
PRL (2003)
12/6/2018
Attila Mihalyi - Wisconsin

7. Lipkin, Nir, Quinn, Snyder, PRD 44, 1454,1991
rp Isospin Analysis
Neutral and charged B decay amplitudes:
Construct an SU(2) pentagon relationship to solve for a:
Lipkin, Nir, Quinn, Snyder, PRD 44, 1454,1991
Even in the absence of penguins there’s an eightfold ambiguity on a.
Analysis is complicated by penguins (aeff) and the non-CP eigenstates
No model independent constraints yet on a, from B→ rp The next step is a full Dalitz analysis. (Quinn-Snyder, PRD 48, 2139, 1993)
12/6/2018
Attila Mihalyi - Wisconsin

8. Prospects of a from B→rr
Penguin
Both tree and penguin amplitudes contribute.
If no penguins:
With penguin contributions:
Tree
Using the Grossman-Quinn bound to limit Da=|a-aeff|
Decay is penguin dominated.
B0→r0r0 branching ratio is small compared to B+→r+r0 !
12/6/2018
Attila Mihalyi - Wisconsin

9. Attila Mihalyi - Wisconsin
The B→rr decay
B0  + - is a VV-decay The decay can proceed through 3 partial waves: S (L=0, CP even), P (L=1, CP odd), D( L=2, CP even)
3 helicity amplitudes:
l=0 → longitudinal polarization. Pure CP even eigenstate l=±1→ transverse polarization. Mix of CP even and odd eigenstates.
The decay B0  + - has been observed at BaBar and its BR and polarization measured: (PRD 69, (2004) and hep-ex/ , submitted to PRL)
B0  + - is an excellent candidate for measuring a:
§ Longitudinally saturated
§ Relatively large BR
§ Small penguin pollution
§ Two charged tracks in the decay for vertexing
12/6/2018
Attila Mihalyi - Wisconsin

10. Attila Mihalyi - Wisconsin
Analysis Strategy
In a simultaneous fit we measure: signal yield, polarization, Clong and Slong..
Use a Maximum Likelihood fit to model: True-signal, Misreconstructed signal (42% long., 15% trans.), Continuum and 17 B-background modes.
B-background: 209 decay modes simulated. Dominant modes:
Simple assumptions:
§ We neglect interference with other decays to p+p-p0p0 final states (includes non-resonant contributions).
§ I=1 decay amplitudes are also neglected. I=1 absent due to Bose statistics but reintroduced by the finite Gr.. (Falk, Ligeti, Nir, Quinn, Phys. Rev. D69:011502,2004)
12/6/2018
Attila Mihalyi - Wisconsin

11. Attila Mihalyi - Wisconsin
B→rr Signal Selection
B-decay: isotropic Continuum qq: jet-like
Combine event shape variables into a Neural Network.
Also use the r-mass and r-decay angle (helicity) to distinguish signal from background.
Events with clean tags.
B-mass:
Missing energy:
Full likelihood Background Data
12/6/2018
Attila Mihalyi - Wisconsin

12. Attila Mihalyi - Wisconsin
Results:
Babar result from 81fb-1 of data (taken between )
Submitted to PRL
hep-ex/
Recent preliminary Babar result from 113fb-1 of data (presented at Moriond EW):
12/6/2018
Attila Mihalyi - Wisconsin

13. Attila Mihalyi - Wisconsin
Global CKM Fits
More plots at:
Other B→rr used in the SU(2) analysis.
Can’t exclude a large a region with pp.
Includes the Belle B→pp result.
The B→rr system provides the most stringent constraint on a!
Includes Belle
12/6/2018
Attila Mihalyi - Wisconsin

14. Attila Mihalyi - Wisconsin
Summary
No significant constraint on a from B→pp
Non optimal B0→p0p0 BR (large penguins).
B→ rp quasi-2-body analysis performed but no model-independent constraints on a
Non-CP eigenstate and penguins not under control.
B→rr provides the most stringent constraint on a. This analysis has been carried out at BaBar, and the result is (with some simple assumptions):
12/6/2018
Attila Mihalyi - Wisconsin