Implications%20of%20%20%20%20%20%20%20%20%20Decays%20on%20%20%20%20%20%20%20%20%20%20%20%20Decays

1
Implications of Decays on
Decays

• Chun-Khiang Chua
• Academia Sinica, Taipei
• HEP2005, Lisbon

2
Color-suppressed Decays

• Color-suppressed (CS) modes were observed
• D()0?0, D()0?, D()0?, (Belle,
  CLEO, 2001)
• Ds K-, D0K0 (Belle,
  BaBar, 2002)
• D0?0
  (BaBar, Belle, 2004)
• Rates are significantly larger than (naive
  factorization) expectations.
• B(D0?0) ?104 ? 0.5 ? 2.5, ...
• Non vanishing strong phases (D? triangle, ? ?
  30?).
• Hint at the present of Final State Interactions
  (FSI).
• (Xing, Cheng, CKC, Hou, Yang, Gronau,
  Fleischer, QCDF, SCET, pQCD groups, Soni )

3
Final State Interaction

• Through FSI CS (D0h0) rates can be easily fed
  from the CA (D?-) one.
• B(D?-)(27.6?2.5) ? 10-4
• B(D0?0)(2.53?0.20) ? 10-4
• B(D?-)B(D0?0) ? 101
• FSI generates strong phases. Watson Theorem.
• ACP ? sin?Weak sin?Strong
• ACP(K-?) , see Sonis talk.

4
The color and CKM -suppressedDK- mode is
important in the ? extraction

• The ? determination methods
• Gronau-London-Wyler
• Atwood-Dunietz-Soni
• DK Dalitz plot (Giri et al, Belle)
• The interference effect is controlled by some
  common phases and parameters
• ?(f3) the goal of the analysis.
• rB ratio of D0K-/D0K- amps.
• ?B relative phase of the amps.

5
Expt. Results from DK Dalitz method

• Belles and BaBars ?3/? are similar.
• Belle rB gt BaBar rB ( a factor 2) ?
• ? Belle ?? lt BaBar ??
• rB is important in the ? determination.
• Not much theoretical predictions on rB.

6
What is the implication of D0h0 on rB?

• Naïve factorization expectation
• rB ? 0.07.
• The CS D0h0 rates are enhanced,
• perhaps rB A(D0K-)/A(D0K-) will be too.
  (Gronau,2002)
• What is the implication of D0h0 on rB?

7
QCD respects Charge Conjugation SU(3)Lessons
learned from D0h0 ? DK
8
Quasi-elastic scattering
Flavor Flow Diagram.

• FSI in B cannot be neglected.
• (Donoghue et al, Cheng CKC Soni)
• May have cancellation in in-elastic rescattering.
• Statistical approach. Random phase (Suzuki,
  Wolfenstein)
• Fac. in D?-, QCDF (BBNS)
• Concentrate on quasi-elastic rescattering,
• The large source D?- is included
• A working assumption.
• The Flavor Flow analysis is equivalent to the
  SU(3) sym. approach.

Exchange
Annihilation
Singlet Exch.
9
In the light of SU(3) decomposition

• DPD(3)?(8)1563, D(3)?1(1)3
• DPD(3)?(8), D(3)?1(1)
• Need three phases (?, ?, s) and one mixing angle
  (?).

6,3,3
10
Use D0h0 rates (6) to extract a1,2eff (2) and
rescattering parameters (4)

• AS1/2A0, use naïve fac. amplitude as A0
• avoid double counting
• a1,2eff values as expected
• Exchange rescattering dominating.
• Small 3 3 mixing 3 , 3 (D0 ?1) decoupled

11
Prediction for B(DK)
Errors from B(D0 h0) uncertainties
12
Prediction for B(DK)
Errors from B(D0 h0) uncertainties

• Source D-s?0 (I1).
• DK (I0,1) can be fed. D-s?(0) (I0) cannot be
  fed.
• The D0K- rate is enhanced (through rexchange) by
  65.
• D0?0 enhanced by 5 times.
• D0K0 enhanced by 6 times.

13
Comparing FSI effects in DK and DK.

• Both governed by exchange rescattering
• Source for DK and the rescattering m.e. are
  smaller.

C.G.
14
Implication on rB
Use Vub3.67x10-3

• Our rB prefers the BaBar value.
• Consistence with UTfit and pQCD (Keum) results.
• Upper sign is preferable by
• comparing to D0h0 amplitudes from pQCD and
  Cheng-CKC-Soni calculations.
• ?B data

15
How about rB (DK)?

• SCET ?D? ? ?D?. So
• rB? rB? 0.1
• Compare with data (DK Dalitz)
• Belle 0.12 0.160.11 ? 0.02 ? 0.04
• BaBar 0.17 ? 0.10 ? 0.03 ? 0.03

16
Conclusion

• FSI effects on rB is investigated using the
  quasi-elastic approach.
• Rescattering parameters are fitted from D0h0
  data.
• The enhancement on rB is mild (30).
• Our result favors the BaBars value.
• Agree with UTfit and pQCD results.
• Need more statistics to extract ?/?3.