Rare Hadronic Semi-Inclusive Decays Xiao-Gang He NTU 1.Why rare hadronic semi-inclusive decays? 2.The Branching ratio for B to K X 3.The CP Asymmetry for B to K X 4.Beyond the Standard Model 5.Discussions

1.Why rare hadronic semi-inclusive decays? B to l nu X, information about CKM matrix elements. B to gamma X, information about the SM penguin physics. B to eta’ X, surprises, large branching ratio than expected. Theoretically, less uncertainties than exclusive decays: O = j1. j2 ; = + Fierz transformed terms = + + FT Judicially choose initial and final states, let only one term contribute, only one hadronic current involved. Also choose rare decays, such as B to K X, sensitive to new physics. (Browder, Datta, He, Pakvasa; He, Jin, Ma; Atwood, Soni; He, Kao, Ma, Pakvasa; Cheng, Soni; Kim, Lee and Oh)

Eaxmple: Factorization involve only decay constant: Factorization involve only form factor: More complicated case:

Measurements:BackgroundSignals: ( Browder, Datta, He, Pakvasa)

2. The Branching ratio for B to K X Decay Modes:

QCDF calculations A(B to K X) approx A(b to K q) A^q, B^q known functions of Wilson Coefficients and light corn distribution functions.

Initial b bound state effect ( He, Ma, Wu; He, Jin, Ma ) In the heavy b quark limit: A(B to K X) = A(b to K q) There are corrections with finite b quark mass Light corn distribution Heavy quark effective theory

CKM matrix elements (PDG) S12=0.2243, S13=0.0037, S23=0.0413, gamma= 60 dgree.

f(x) universal for B to gamma X, l nu X, K X f(x) universal for B to gamma X, l nu X, K X

Branching ratios as functions of gamma Solid: K^- X, Dashed: K^0 X

3. The CP Asymmetry for B to K X Leading contributions: Solid: K^- X, Dashed: K^0 X

Problems? = (-)0.02 Different sign as = 0.07 QCDF: Dominant factorization contribution=> exclusive B to K pi wrogn sign. Need large hard scattering and annihilation contributions. Problem: End poin divergencies. pQCD: Right sign also with large annihilation contributions. (divergencies regulated by transverse momentum). No imaginary part generated. Does not change CP asymmetry very much.

4. Beyond the Standard Model Example: SUSY gluonic dipole interaction C11,12= C(susy), C’11,12 change delta(LR) to delta(RL) C11 = Cg

Constraints from B to Xs gamma on SUSY parameters (He, Li and Yang, hep-ph/ )

B to K X with new gluonic dipole interactions Cg = exp[ia] Cg = exp[ia] Br vs. a; Asy vs. a

5. Discussions Hadronic semi-inclusive decay can be calculated in QCD factorization. Good contral on branching ratios. Better handel on CP violating asymmetry compared with exclusive decays. New physics can change the situation dramatically. Provide good tests for the SM.

Many other modes ( Cheng and Soni )

Another type: ~ Form factor ( He, Kao, Ma and Pakvasa )