rare hadronic semi-inclusive decays xiao-gang he ntu 1.why rare hadronic semi-inclusive decays?...
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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
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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)
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Eaxmple:Eaxmple:
Factorization involve only decay constant:
Factorization involve only form factor:
More complicated case:
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Measurements:Measurements:
BackgroundBackground
Signals:Signals:
( Browder, Datta, He, Pakvasa)( Browder, Datta, He, Pakvasa)
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2. 2. The Branching ratio for B to K XThe Branching ratio for B to K X
Decay Modes:
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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.
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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
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CKM matrix elements (PDG)
S12=0.2243, S13=0.0037, S23=0.0413, gamma= 60 dgree.
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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
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Branching ratios as functions of gammaBranching ratios as functions of gamma
Solid: K^- X, Dashed: K^0 X
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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
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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.
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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
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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)
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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
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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.
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Many other modes (Many other modes (Cheng and SoniCheng and Soni))
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Another type: ~ Form factor (Another type: ~ Form factor (He, Kao, Ma and PakvasaHe, Kao, Ma and Pakvasa))