C.D. LuMoriond1 Charmless hadronic B s Decays Cai-Dian Lü (IHEP, Beijing) Thanks Ali, Kramer and Li, Shen,Wang The study of hep-ph/

C.D. LuMoriond2 Outline Introduction and motivation BRs and Direct CP asymmetry Test of SU(3) breaking by charmless B 0 and B s decays in pQCD approach Some B s channels for  /  3 measurement Summary

C.D. LuMoriond3 Picture of PQCD Approach Six quark interaction inside the dotted line 4-quark operator b

C.D. LuMoriond4 Do not need form factor inputs All diagrams using the same wave functions (same order in  s expansion) All channels use the same wave functions Number of parameters reduced pQCD approach based on k T factorization

C.D. LuMoriond5 CP Violation in B    (K) (real prediction before exp.) CP(%)FABBNSPQCDExp  + K – +9±3+5±9–17±5–11.5±1.8  + K ± 0.11 ±1– 1.0 ±0.5– 2 ±4  0 K + +8 ± 27 ±9– 13 ±4 +4 ± 4  +  – –5±3–6±12+30±10+37±10 (2001)

C.D. LuMoriond6 pQCD approach in B decays pQCD approach successfully describe the B 0 and B + decays Most of the branching ratios agree well with experiments The right direct CP asymmetry sign with the experiment Using the constrained parameters determined here to predict B s decays

C.D. LuMoriond7 B s distribution amplitude  b =0.45  b =0.50  b =0.55  b =0.4 GeV for B meson = momentum fraction

C.D. LuMoriond8 Form factors derived from light cone wave functions Larger f Bs, but smaller inverse moment of B s meson distribution amplitude QCDF:

C.D. LuMoriond9 BR (x 10 –6 )

C.D. LuMoriond10 BR (x 10 –6 )

C.D. LuMoriond11 Bs  PV BR (x 10 –6 )

C.D. LuMoriond12 Bs  VV BR (x 10 –6 )

C.D. LuMoriond13 Bs  PV BR (x 10 –6 )

C.D. LuMoriond14 Three measurements of BRs in B s SCET QCDF PQCD EXP CDF B s  K – pi + 4.9±1.8 10±6 11 ±6 5.0±1.3 B s  K – K + 18±7 23±27 17 ±9 24 ± 5 B s  phi phi 22 ±30 33 ±13 14 ± 8 |Vub| (10 –3 ) = 3.69 

C.D. LuMoriond15 First measurement of CP in B s B s  K – pi + SCET QCDF PQCD EXP 20 ± 26 –6.7 ± ± 6 39 ± 15 ± 8 pQCD agree with EXP in CP

C.D. LuMoriond16 vs A 

C.D. LuMoriond17 vs S 

C.D. LuMoriond18 vs A K  LO pQCD

C.D. LuMoriond19 vs A K  NLO pQCD

C.D. LuMoriond20 U-spin symmetry (Gronau,Rosner,Lipkin) Results from pQCD Experimental data = –1 = 0

C.D. LuMoriond21 R 3 vs  Red area is pQCD prediction; Shaded area is exp.

C.D. LuMoriond22 SU(3) symmetry  + u B d(s)  – (K – ) d(s) Only leading contribution is related by simple SU(3)

C.D. LuMoriond23 U-spin, SU(3) T = tree PA = penguin annihilation P = QCD penguin P EW = color suppressed E = W exchange electroweak penguin

C.D. LuMoriond24 SU(3) breaking and relative size of different contributions CKM matrix elements already factored out SU(3) breaking is not negligible

C.D. LuMoriond25 Bs   0 K S If tree dominant (V ub ), good for gamma measuremnt. However, Color suppressed tree is comparable with QCD penguin contribution Direct CP large QCDF PQCD 25 ± 60 % 97 ± 30 % Not good for gamma measurement

C.D. LuMoriond26 B s   0  (Fleischer 1994) I = 0  I = 1  I = 1 Both tree and electroweak penguin can give  I = 1 (QCD penguin  I =0) Like B +  pi + pi 0, only  I =3/2 There should be only one strong phase, then no relative strong phase between amplitudes

C.D. LuMoriond27 Bs   0 Bs   0  Color suppressed tree is comparable with electroweak penguin contribution Direct CP small QCDF PQCD 27 ± 40 % 9 ± 2 % good for  /  3 measurement QCDF PQCD BR(10 – 7 )

C.D. LuMoriond28 Polarizations

C.D. LuMoriond29 Summary PQCD can give the right sign for CP asymmetry  the strong phase from PQCD should be the dominant one. The SU(3) breaking effects are not very small as expected

C.D. LuMoriond30 Thank you!