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Rare Hadronic Semi-Inclusive Decays

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

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Rare Hadronic Semi-Inclusive Decays

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

  2. 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 ; <P1 P2|O|B> = <P1|j1|0><P2|j2|B> + Fierz transformed terms <P1 X|O|B> = <P1|j1|0><X|j2|B> + <X|j1|0><P1|j2|B> + 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)

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

  4. Measurements: Background Signals: ( Browder, Datta, He, Pakvasa)

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

  6. 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.

  7. 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

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

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

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

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

  12. Problems? = - 0.11+(-)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.

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

  14. Constraints from B to Xs gamma on SUSY parameters(He, Li and Yang, hep-ph/0409338)

  15. B to K X with new gluonic dipole interactionsCg = -0.143exp[ia] Cg = -0.246exp[ia]Br vs. a; Asy vs. a

  16. 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.

  17. Many other modes (Cheng and Soni)

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

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