1. : pQCD analysis in pursuit of determing ϒ
Run-Hui Li
2018/11/19

2. Content Motivation & Background Calculation in pQCD
•background &Frame of pQCD
•Contributions to these channels
Summary
2018/11/19

3. Motivation & background
2018/11/19

4. About γ In SM, the explanation for the CPVCKM
Triangle of CKM in SM (Unitarity)
Important task in Flavor Physics experiments:
Extracting the CKM elements & test the unitarity
2018/11/19

5. γ: the worst precision β : measured in B-> J/ψ KS
γ : B±-> DK±
2018/11/19

6. One method to extract γ
, : CP even(odd) state
definde:
2018/11/19

7. One method to extract γ Two physical observables:
World average [CKMfitter group]:
Observables not sensitive to γ
2018/11/19

8. Dynamics for B->DK in FA
Small
2018/11/19

9. What about the ? ---- some background
: Scalar meson : Tensor meson
in quark model
2018/11/19

10. What about the ? ---- some background
Two scenarios of scalar mesons
Mesons
Scenario I
Scenario II
Around 1 GeV:
f0(600), f0(980), K0*(800), a0(980)
Lowest lying states
4 quark bound states
Around 1.5 GeV:
f0(1370), f0(1500)/f0(1700),
K0*(1430), a0(1450)
Excited states
2018/11/19

11. What about the ? For scalar meson: For Tensor meson: is small
SU(3) breaking effect, tiny
Keenly to be large, physical observables more sensitive to γ
W. Wang,PRD85,051301
2018/11/19

12. What about the ? Already been analyzed in FA.
We will study it in pQCD.
The difference between FA and pQCD.
• FA: Only factorizable emission diagrams;
Amplitude is real number, only give information to
• pQCD: rich dynamics – factorizable, nonfactorizable,
emission, annihilation;
Amplitude with phases, can calculate both
and
W. Wang,PRD85,051301
2018/11/19

13. Calculation in pQCD
2018/11/19

14. Effective Hamiltonian in B physics
In B meson decays, W, Z, top, … are very heavy, and never appear in the external lines. Integrate them out to get effective operators.
Effective operator
2018/11/19

15. Charged Current Wilson coefficient
G. Buchalla, A.J. Buras, M. E. Lautenbacher, Rev. Mod. Phys. 68,1125.
2018/11/19

16. In this calculation, only tree operators contribute.
Charged Current
Tree operators
Flavor Changed Neutral Current
In this calculation, only tree operators contribute.
2018/11/19

17. Deal with Factorization Else LQCD QCDF SCET PQCD LFQM LCSR CollinearkT
Factorization
●●● ●●●
2018/11/19

18. KT Factorization x  0, kT is important. x: momentum fraction
Sudakov factor:
- Eliminate end point divergence
- Suppress end point region
Overlap of soft and collinear contributions
Two body nonleptonic B decay.
Behavior of Sudakov factor from kT resummation.
Resummation to Sudakov
2018/11/19

19. Two body nonleptonic B decay in pQCD
Wave functions: universal inputs
Sudakov factors: process independent functions
Hard kernel: specific to decays
2018/11/19

20. in pQCD In pQCD FA contributions Expected enhancement
Annihilation to be explored
In pQCD
2018/11/19

21. Our process & Preliminary estimation
The analytic expressions are obtained. The expressions for the annihilation diagrams need check.
For a preliminary estimation, the branching ratios of
can reach the order of ,
The similarity channels, whose time dependent observables can also be use to determine γ, will also be investigated:
2018/11/19

22. Summary
decays are expected to have a better performance than decays in the determination of CKM angle ϒ.
We investigate these decays in pQCD approach, which can offer the information of and
The BRs of these channels are estimated, which can reach , which is easy for the observation in experiments.
We will also calculate the similar channel, which can offer information for the determination of γ as well.
2018/11/19