BdKmm Angular Distributions and EvtGen Will Reece

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Bd-gtKmm Angular Distributions and EvtGenWill
Reece
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The Operator Product Expansion

• Separate Long Short Range Forces
• Same principle as Fermi theory of b-decay

Coupling given by Wilson Coefficient

• Local Operators ? Long Range Effects
• Wilson Coefficients ? Short Range Effects

Right handed (suppressed)
Left handed
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Bd?Kmm

• FCNC ? Proceeds by Penguin and Box
• Branching Ratio 9.8x10-7 (HFAG 07)
• Sensitive to C7, C9 and C10 (and others)
• Right and left handed contributions
• New Physics Particles May Run in Loop
• Expect NP affects only Wilson Coefficients
• SM Predictions well Known

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Kinematics

• Decay in terms of 3 Angles and 1 Invariant Mass
• ?l, ?K, f and the invariant mass of muon pair
• Angles are defined in transversity basis

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Angular Distribution
C.S. Kim et al.Phys Rev D 62, 034013 (2000)

• HL,R(1,0,-1) are Functions of C(L,R)7,9,10 and q2

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Variables to Measure
g, g, h, f and a are Hadronic form factors

• Wilson Coefficients are Perturbative
• SM values well known (NNLO)
• Hadronic Form Factors Hard to Calculate
• Larger theoretical uncertainties
• Variables where Form Factors Cancel
• Asymmetries ? Small theoretical uncertainties

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Variables to Measure
B. Aubert et al,Phys. Rev. D 73, 092001 (2006)

• 1st Measurements AFB, FL and Zero Crossing
• Need Several Variables to Constrain C7,9,10
• Signs and Magnitudes

• More Data AT1,2 and Maybe Others
• Powerful NP constraints

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F. Kruger and J. Matias, Phys. Rev. D 71, 094009
(2005)
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Full Angular Fit

• HL,R(1,0,-1) are complex ? 12 numbers
• Fix 1 arg and 2 phases (R L dont interfere) ?
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• Work on Fit is ongoing
• Extra constraints to aid convergence?
• Will be able to extract AT1,2, FL and AFB
• AT1 can only be extracted from full angular fit

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EvtGen and Bd?Kmm

• EvtGen Decays Bs from Pythia
• Uses Model EvtbTosllBall
• Based on A. Ali et al, Phys Rev D61, 074024
  (2000)
• Compare with Full Angular Model

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?K Full Angular Model and EvtGen
RooFit Full Angular Model
EvtGen bTosllBall Model
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?l Full Angular Model and EvtGen
RooFit Full Angular Model
EvtGen bTosllBall Model
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f Full Angular Model and EvtGen
RooFit Full Angular Model
EvtGen bTosllBall Model
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What Makes an EvtGen Model?

• Calculate Decay Amp
• All spin configs required
• Require
• B?K form factor
• Low q2 QCD factorisation
• Evolution of C7,9,10eff
• and help from
• Patricia Ball
• Roman Zwicky
• Aoife Bharucha

UML Diagram of EvtbTosllBall
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Improving the EvtGen Model

• EvtGen Seems to Handle K Decay Correctly
• Keep as three body decay
• Update Model to use State-of-Art Calculations
• Inclusion of Benchmark NP Models
• MSSM, UED, Little Higgs Model
• Should be configurable via decay file
• Access to State-of-Art SM Prediction
• LHCbs Model Discrimination can be Studied