Interactions of mesons with heavy quarks

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Interactions of - mesons with heavy
quarks

• Avakyan E. Z., Avakyan S. L.
•  
• GSTU, Gomel

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MIXING SCHEMES (only u,d,s-quarks)

• 1. Mixing
• Where
• The flavor structure of and

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MIXING SCHEMES only u,d,s-quarks

• 2. MIXING IN THE OCTET SINGLET BASIS
• The pseudoscalar nonet can be displayed as
• So

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HEAVY QUARK ADMIXTURES TO LIGHT PSEUDOSCALAR
MESONS

• Problem ClEO mesuarment of
  branching fraction unexpetedly large. CLEO coll
  ab. B.H.Behrens et.al. Phis.Rev.Lett.80,3710(1998)
  
• 
  Mixing

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WAYS TO DEFINE MIXING PARAMETERS

• The radiative decays of ? mesons
• T.Feldman, P.Kroll and B. Stech, Phys.Rew.
  D58,114006 (1998)
• Radiative ?/? decays
• K.Chao, Nucl.Phys B317,597(1989)
• Rations of weak decays constants

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QUARK MODEL

• The hadronic interactions will be described in
  the Relativistic Constituent Quark Model (RCQM).
• M.A.Ivanov,M.P.Locher and V.E.Lyubovitskij,
  Few-Body Syst. 21,131(1996),
• M.A.Ivanov, V.E.Lyubovitskij, Phys.Lett.,
  B408,435(1997)
• The coupling of the meson M into its constituents
  and is given by Lagrangian
• where are Dirac and Gell-Mann
  matrices.

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QUARK MODEL

• The function characterizes the finite
  size of meson and is given by
• The coupling constant is determined by
  compositeness condition
• where - the derivative of the
  mass function of meson.
• 
  
  

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QUARK MODEL
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QUARK MODEL

• Example of evaluation of one loop diagram
• After calculating Tr and performing
  a-parameterization one finds
• where
• Next we use Cauchy integral representation for

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QUARK MODEL

• We use a-parameterization once more and find
• The contour integral can be done again by
  Cauchys theorem.
• On substitution of and shift
  ,
• after rotation
  ,one receives

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MESON-QUARK INTERACTION CONSTANTS
Pseudoscalar meson constant THE
MIXING
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DECAY

• Decay amplitude
• Decay width
• Experimental values (PDG)

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DECAY
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DECAY

• THE MIXING

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• To define the experimental
  values
• were used.
• For mixing
• For mixing
• So we find the quark content of physical mesons

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RADIATIVE TRANSITIONS BETWEEN LIGHT PSEUDOSCALAR
AND VECTOR MESONS

• Decay amplitude
• Decays width

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RADIATIVE TRANSITIONS BETWEEN LIGHT PSEUDOSCALAR
AND VECTOR MESONS

• NUMERICAL RESULTS FOR RADIATIVE DECAYS

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RADIATIVE TRANSITIONS BETWEEN LIGHT PSEUDOSCALAR
AND VECTOR MESONS

• NUMERICAL RESULTS FOR RADIATIVE DECAYS