Qiang Zhao

1
Institute of High Energy Physics, CAS
The role of electromagnetic transitions in V ? V
P

• Qiang Zhao
• Theory Division, Institute of High Energy
  Physics, CAS
• Department of Physics, University of Surrey

11-th International conference on Meson-Nucleon
Physics, Jülich, Sept. 13, 2007
2
Topics

• The role of the EM transitions in the explanation
  of ?? puzzle and 12 rule in J/?, ? ? V P (
  V ?, ?, ?, K P ?, ?, ??, K)
• Isospin violations in V ? V P, e.g. ?, J/? ? ? ?0

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Topics

• The role of the EM transitions in the explanation
  of ?? puzzle and 12 rule in J/?, ? ? V P (
  V ?, ?, ?, K P ?, ?, ??, K)
• Isospin violations in V ? V P, e.g. ?, J/? ? ? ?0

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Motivation

• Experimental observation of obvious isospin
  violations in ? ? ? ?0.
• Mechanisms for OZI-rule violation in the low
  energy region.
• Interferences between different isospin-violating
  sources.

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Isospin violation in ? ? ? ?0

• Flavor-changed transition via two processes
• I) Isospin violation via electromagnetic decays
• EM interaction does not conserve isospin
• II) Isospin violation in strong decays
• u and d quark have different masses

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Electromagnetic transition in ? ? ? ?0
? (I0)
?
s
?
?
?
? (I0)
?0
?0
?0 (I1)
?s
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• Vector meson dominance model

??
??
e
e
?
?
V (?, ?, ? )

??
??
e-
e-
EM field in terms of vector meson fields
e
?
V
e-
V? effective coupling
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Isospin violation in ? ? ? ?0
I) EM process in VMD
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Decompose the EM field in terms of vector mesons
in Process-I
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?-?0-?0 coupling
KLOE Collaboration, PLB561, 55 (2003)
is dominated by ?0, we extract
Assuming
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II) Isospin violation in strong decays

• Physical vacuum is not invariant under chiral
  symmetries
• Chiral symmetry is spontaneously broken
• Goldstone boson
• Chiral symmetry is explicitly broken
• mu ? md
• Manifestations
• Light 0? octet mesons (Goldstone bosons), ?, K, ?
• Strong isospin violation m(?0) lt m(??) m(K0) gt
  m(K?) m(p) lt m(n)

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Strong transition in ? ? ? ?0
? (I0)
g
s
? (I0)
?0 (I1)
?s
OZI evading process
K? (u?s)
K0 (d?s)
? (I0)
s
K
? (I0)
?0 (I1)
?s
?K0 (s?d)
K? (s?u)
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• Strong isospin violation
• via intermediate meson exchanges

If mu md, (a) (b) 0 and (c) (d)
0. If mu ? md, (a) (b) ? 0 and (c) (d) ?
0.
Li, Zhao and Zou, arXiv0706.0384hep-ph
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Isospin violated effective couplings
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• t-channel versus s-channel

Previous approach
?
mixing
?
?
?
?-?0, ?-?0 mixing
?0
?0
This approach
?
?
?, VMD
?
?
?
t-channel
?0
?0
?0
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Three schemes for the numerical calculations of
the intermediate meson exchange loops
1. On-shell approximation 2. Feynman integration
with a monopole form factor 3. Feynman
integration with a dipole form factor
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1. On-shell approximation
0, No form factor n 1, monopole
2, dipole
? (GeV) to be determined by experimental data.
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Numerical results
Experimental branching ratio
On-shell approximation underestimates the data.
Exclusive KK(K) loop
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• ?-dependence of the sum of EM and KK(K) loop

EM and KK(K) out of phase
EM and KK(K) in phase
Still underestimate the experimental data.
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2. Feynman integration with a monopole form factor
?
Similarly for the neutral meson loop
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• ?-dependence of the exclusive KK(K) loop with a
  monopole form factor

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• ?-dependence of the exclusive KK(K) loop with a
  monopole form factor

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3. Feynman integration with a dipole form factor
Exclusive KK(K) loop contribution to BR
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Exclusive KK(K) loop contribution to BR
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Inclusive contributions from the isospin
violating transitions
Isospin violation EM ? Strong decay loops
V ? V P is a P-wave decay, favors a dipole form
factor.
In phase
Out of phase
Exp.
Exp.
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A Brief Summary

• The correlation between the OZI-rule violation
  and strong isospin violations makes the
  intermediate meson exchange process a possible
  dynamic solution for the study of isospin
  violations in ? ? ? ?0.
• It provides an explicit way to separate the EM
  and strong isospin violation mechanisms, thus, is
  different from meson mixing scheme.

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• Application to J/?, ? ? VP is useful for the
  study of ?? puzzle (Zhao, Li and Chang, PLB645,
  173(2007) ) and search for pseudoscalar glueball
  (Li, Zhao and Chang, hep-ph/0701020).
• Application to the study of a0(980)-f0(980)
  mixing in J/?? ? a0(980) ? ???0 (Wu, Zhao and
  Zou, PRD 75, 114012 (2007) ).
• Experimental focuses of BES, CLEO-c, KLOE,
  B-factories

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Thanks !