Rare Hadronic Semi-Inclusive DecaysRare Hadronic Semi-Inclusive Decays

Xiao-Gang He

NTU

1. Why rare hadronic semi-inclusive decays?

2. The Branching ratio for B to K X3. The CP Asymmetry for B to K X4. Beyond the Standard Model5. 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 ; <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)

Eaxmple:Eaxmple:

Factorization involve only decay constant:

Factorization involve only form factor:

More complicated case:

Measurements:Measurements:

BackgroundBackground

Signals:Signals:

( Browder, Datta, He, Pakvasa)( Browder, Datta, He, Pakvasa)

2. 2. The Branching ratio for B to K XThe Branching ratio for B to K X

Decay Modes:

QCDF calculationsQCDF 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 (Initial b bound state effect (He, Ma, Wu; He, Jin, MaHe, 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 Xf(x) universal for B to gamma X, l nu X, K X

Branching ratios as functions of gammaBranching ratios as functions of gamma

Solid: K^- X, Dashed: K^0 X

3. The CP Asymmetry for B to K X3. The CP Asymmetry for B to K X

Leading contributions:

Solid: K^- X,

Dashed: K^0 X

Problems? = - Problems? = - 0.11+(-)0.020.11+(-)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.

4. 4. Beyond the Standard ModelBeyond the Standard Model Example: SUSY gluonic dipole interactionExample: 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 parametersConstraints from B to Xs gamma on SUSY parameters

(He, Li and Yang, hep-ph/0409338)(He, Li and Yang, hep-ph/0409338)

B to K X with new gluonic dipole interactionsB to K X with new gluonic dipole interactions

Cg = -0.143exp[ia] Cg = -0.246exp[ia]Cg = -0.143exp[ia] Cg = -0.246exp[ia]

Br vs. a; Asy vs. aBr vs. a; Asy vs. a

5. Discussions5. 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 (Many other modes (Cheng and SoniCheng and Soni))

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