Bphysics theory

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B-physics theory

• Thomas Becher, Fermilab
• The Tevatron Connection,
• June 24, 2005

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Overview

• CKM status and news
• Exclusive Vub from the lattice
• sin(2?) trees vs. penguins
• B-physics with collider physics methods
• Heavy-to-light decays Factorization,
  Soft-Collinear Effective Theory,
• Scope, limitations and relevance for B-physics
  program at the Tevatron

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The CKM matrix
?-
?
W-
b
c

• Flavor changing quark interactions
• Unitary. 4 parameters including 1 complex CP
  violating phase

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Wolfenstein parameterization

• . (A?0.8, ??0.2,
  ??0.3)
• Almost diagonal. Hierarchical.
  

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Constraints on ?,? the unitarity triangle
KK -mixing
ACP(t) in B?J/?KS
b?u semileptonic
Bd Bd -mixing
Combined constraint from Bd-mixing and bound on
Bs -mixing
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New constraints ? and ?

• ? from ACP(t) in B???, B???, B??? isospin
  analysis
• ? from B??D0, D0K? ? f K?

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Exclusive Vub from B??l?

• New Dynamical (nf3) lattice calculations of
  semileptonic form factors.

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sin(2?) from loop dominated processes
Tree (penguin)
Penguin
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Questions

• Babar vs. Belle?
• Theoretical uncertainties?
• Contribution from small amplitudes?
• Suppressed by
• Calculable in QCDF/SCET

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Collider physics methods in B-physics?

• Factorization, Soft and Collinear particles,
  Jet-functions, Distribution Amplitudes

WHAT IS WRONG WITH THE B-THEORISTS?
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Hard scattering for mb ? ?

• In heavy-to-light decays, the decay products are
  typically energetic, e.g.
• Large momentum transfer ? factorization?

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Remember? (1980)

• ?? form factor at large Q2

?
TH
Wave functions (LCDAs) non-perturbative
Hard-scattering kernel
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Factorization for mb ? ??
K-
Wave functions (LCDAs)
TH
Bs
K
Factorization FAILS!
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Ways out?

• Ignore the problem Naïve factorization.
• Assume that non-factorizable effects are small
  after Sudakov resummation pQCD.
• Give up on complete factorization. Allow for
  non-factorizable form factor piece QCD
  factorization.

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Example ?b??c?
Form factor (from semileptonic decay)
1O(?s)

• Note Obtain naïve factorization result to lowest
  order in ?s.
• Decays to two light hadrons also contain a
  completely factorizable piece.

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CDF

• Theory prediction?
• Leibovich et al. hep-ph/0312319
• Needs F(q2?0) as an input!
• same F(q2) gives

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Soft-Collinear Effective Theory

• Effective Lagrangian instead of diagrammatic
  language systematic and transparent analysis of
  factorization properties.
• The HQET for heavy-to-light processes.
• Complicated field content
• Soft-fields partons of b- (and c-) hadrons
• Collinear fields partons of energetic light
  particles
• Messenger fields low energy interactions between
  soft and collinear partons. Absent for
  factorizable quantities.
• Hard scattering kernels TH ? Wilson coefficients
  of operators in SCET
• Based on Strategy of Regions. Fields in SCET ?
  Relevant momentum regions for expansion of
  diagrams.

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?b??c? analysis in SCET
?-
Messenger
Collinear
Hard
Soft
?b
?c
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Applications

• Factorization analysis (M light meson)
• Bs,d ? Ds,d M, ?b ? ? c M
• Bs,d ? M1 M2, B?M l?
• Bs,d ? M ?, Bs,d ? M ? ?-, B ? ?l?
• B? Xu l?, B? Xs ? (end-point region)
• Sudakov resummation
• B?M l?, B ? K ?, B ? ?l?
• B? Xu l?, B? Xs ?
• ?/mb power corrections
• B? Xu l?, B? Xs ? (subleading shape functions)
• B0 ?D()0?0
• partial results for Bs,d ? M1 M2

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Hadronic input for two-body decays

• Need form-factors at q20 as well as meson wave
  functions as input.
• Have B?D form factor
• Some knowledge on B?? form factors (exp.,
  lattice)
• Little lattice info on wave functions. B-meson
  wave function is especially difficult.
• Can use SU(2) and SU(3) to relate hadronic
  parameters.
• Many factorization predictions rely on
  (light-cone) sum rule determinations for form
  factors and wave functions.

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Strategies for charmless decays

• Beneke et al. QCDF (B?PP, B ? VP)
• Use sum rule input for leading power
• Estimate enhanced power corrections
• chiral enhancement, annihilation
• Bauer et al. SCET (B? ??)
• Use B? ?? data to determine hadronic parameters.
• Do not attempt to factorize charming penguins
• To retain predictability drop power and ?s(mb)
  corrections.
• CKM fitter group fit to charmless decays in QCDF.

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The Bs,d ? M1 M2 landscape
wealth of exp. information The Landscape
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CDF results for Bs,d?hh

• CDF sample of Bd?hh is as large as BaBar sample
  (and growing faster).
• Only a few decay channels measured up to now, but
  with competitive accuracy

• In future Bs?KK,K?,??,

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The first Bs charmless two-body decay!
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Outlook (see talks of U. Nierste and R. Harr
at INT workshop)

• Bd,s?hh-, Bs???,
• Updated Br() results
• more theoretical work on VV decays
• Bs???, Bs?KK- lifetime measurements?
• Sensitive to CP phase in b?qqs
• Isospin violating decay Bs??0??
• Time-dep. CP asymmetries?
• Baryonic decays ?b?p(?,K)
• Direct CP asymmetry
• Factorization analysis (hadronic parameters?)
• Rare decay Bs????-
• ? from B?D0K

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sin(2?) from penguin dominated modes

• Beneke (hep-ph/0505075) evaluates the corrections
  to sin(2?) from the small amplitudes.
• Scans over all input parameters, (require BRs to
  3?). Gives resulting range.
• Positive contribution to ?S. Strengthens the
  discrepancy!

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Summary

• With the exception of sin(2?) from penguin
  dominated modes all measurements are consistent
  with the CKM picture of the flavor sector.
• theoretical uncertainty on sin(2?) extraction is
  small.
• Bd?M M- decays
• Theoretically challenging understand the limit
  mb??
• Power corrections, hadronic input.
• Tevatron measurents of Bd?M M- are competitive
  with B-factories.
• I look forward to Bs?M M- ,
• Apologies. Much more B-physics at the Tevatron
  than in my talkjust keep listening!

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Extra slides
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B?D M
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A. Hoecker at SLAC/INT Workshop, Seattle 2005
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U. Nierste, Chicago Flavor seminar
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