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					  Nonleptonic Decays and
the Soft Collinear Effective
          Theory
               Iain Stewart
                    MIT

   Super B Factory Workshop, Hawaii, 2004
Two body nonleptonic decays.
          Simple?
                         B



          


                             Note: Nonleptonic B-decays are
                             not Gold Plated Observables for
                                      Lattice QCD
B                    
Measuring CP violation in “unclean” decays requires

    1. Use SU(2) or SU(3) to relate amplitudes so data can
       be used to reduce uncertainties.

       • Flavor symmetries of QCD,

    2. Factorization from QCD to reduce the amplitudes to
       simple universal nonperturbative parameters.

       • Expand in
 These two possibilities are not exclusive.

            The important thing to keep in mind is
                 “what are the uncertainties”.
        Factorization in QCD
• Beneke, Buchalla, Neubert, Sachrajda proposed a QCD
  factorization theorem for           , QCDF .
• Amplitude is reduced to simpler matrix elements
                                 ,            ,
• At LO in           strong phases are perturbative,

  , and therefore small.                    Keum, Li, Sanda:
                                           pQCD Factorization




 form factor         hard spectator
PP = 21 + 13
  decays       eg. SU(3) analysis   Chiang et al.

PV = 40 + 23       QCDF analysis Beneke & Neubert
  decays
VV = 21 + 13
  decays
           Effective Field Theory
•   Separate physics at different momentum scales
•   Power expansion
•   Make symmetries explicit
•   Model independent, systematically improvable
       Soft - Collinear Effective
                Theory
                                        Bauer, Pirjol, Stewart
                                              Fleming, Luke


• An effective field theory for energetic hadrons,
Degrees of freedom in SCET
 Introduce fields for infrared degrees of freedom (in operators)




                               Energetic jets




                               Energetic hadrons
                       Factorization



                                        Bauer, Pirjol, I.S.




Universal functions:            Calculate T,
Universal hadronic parameters
Theory:




Phenomenology:
with HQET for                          get
 not a convergent expansion

            is complex, new mechanism for rescattering
Tests and Predictions
              Tests and Predictions




ie. same Br and same strong phases

 All predictions so far are independent of the form of

       and
                 Lessons
• nonperturbative strong phases                  are
  natural

• Nonperturbative J vs. Perturbative J

• With the entire amplitude power suppressed the
  polarization issue in B to VV is non-trivial
SCET Result
Chay, Kim
     operators, exponentiation of soft & collinear gluons


Bauer, Pirjol, Rothstein, I.S. (to appear)

    hard spectator & form factor terms                     same operators
      unique function                        which is also in
     long distance charming penguins
     analysis for PP, PV, VV
                 Operators
QCD



      Integrate out   fluctuations




                        ...

                                ...
Long Distance



dangerous region near threshold
                     ,
          NRQCD          couple to b, spectator
power suppression
                    Polarization
                                     ...

                                             ...




        ...
                                                           No
ie. SCET agrees with A. Kagan for polarization fraction:
                     power suppressed
unless it is spoiled by charming penguins!
                 Same Jet function as




New Nonperturbative Result in           :




    fit   , calculate T’s
Hard Coefficients




                 Note: have not
                used isospin here
Open Issues in
    Factorization formula with charming
                 penguins?
Role of other degrees of freedom:
   messenger modes,                Becher, Hill, Neubert
   Glaubers
                                 ie.
Power Corrections:
   expect nonperturbative phases


  “chirally” enhanced terms, annihilation

       can use SCET, but there is
         a lot of work left to do
                     Outlook

SCET




   We have only seen
  the tip of the iceberg

				
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posted:10/17/2012
language:English
pages:34