Diapositiva 1

1
IX International Workshop On Tau Lepton
Physics Pisa, 19-22 September 06
Model-dependent electromagnetic corrections to
????? decay
Gabriel López Castro Physics Department Cinvestav,
México City
2
Necessity for radiative corrections
? Current precision in B(????? )O( 0.5 ), PDG
2006. Expected improvement at B
factories. ? Current tests of the CVC
Hypothesis Superallowed 0?0
transitions (at the 10-4 level).
2.9? discrepancy in B(????? )
measured-CVC 2.1?
discrepancy in a???,LO ? ee- based data
Up to 10 discrepancy in
?F?ee-(s)/F??(s)?2 KLOE data
3
Isospin symmetry breaking

• Isospin symmetry breaking
• and (Cirigliano et al, 01,02)

1.0201?0.0003
(Marciano-Sirlin 88 Braaten-Li 90)
4
Kinematics
? Virtual and real photon corrections to have an
infrared safe result ? Kinematics of three-body
decay (tree-level virtual corrections)
t(p?-p?)2 (p?- p?0) 2 and u(p?- p?- )2
? Kinematics of four-body decay (real photon
corrections)
5
Long-distance electromagnetic corrections
Important for photon inclusive measurements
(???????????)
6
Model-dependent contributions (Cirigliano et al,
JHEP 2002)
Resonant ? and a1 exchange fixed by ChPT (Ecker
et al, NPB, 1989) with form factors from
(Guerrero-Pich, PRD, 1997 Kühn-Santamaria, ZPC,
1990)
Anomalous axial couplings (Wess-Zumino, PLB,
1971 Witten, NPB, 1983) fixed by F? . Not
realistic for all energies, but expected to be
small
7
Cirigliano et al, JHEP 2002
G0EM(t)
G0EM(t)
8
Vector meson dominance model (Flores et al, PRD
2005 hep-ph/0608084)
? Large q2 in ? decays allows the production and
decay of resonances
? Couplings fixed from low-energy processes
????, ll-, ????, Ga1 , Weinberg sum rule (fa1)
? Alternative calculation
9
(No Transcript)
10
Excluding the contribution of ?(782) meson
11
Corrections to the decay rate
If photons with E?? ?0 are discriminated
?0 ?() Cirigliano (MeV) This work
2002
Hard photon radiative events
12
Radiative ??????? decays
Can help to discriminate between two models
13
Hadron spectrum
Photon spectrum
14
Effects of ?(770) magnetic dipole moment
Electromagnetic ?????? vertex, magnetic moment
?(e/m?)?
???????
??????0??
?100
?100
?1 ?2 ?3
?200 ycos? x2E?/m?
?200
GLCtoledo, PRD, 1999
Flores et al, PRD, 2005
15
Conclusions

• ? Long-distance corrections to the spectrum to
  the
• dipion spectrum are smaller than in ChPT for
• t ? 0.6 GeV2. Effect in ?a?(??, ? based)
  -3.8x10-10
• ? Long-distance corrections to the decay rate of
• O(-0.1). Well below current (and future?)
• uncertainties.
• ? The decay rate, and the photon and 2?
• spectrum in ?????? can be useful to
  discriminate
• between MDM and ChPT.

16
Sources of isospin breaking corrections (M.
Davier et al EPJ C27, 2003)
17
Current best test of CVC
Hardy and Towner, EPJ A25, 2005
0 (A,Z1)?0 (A,Z)e? ?0?T_ ?0??2
Marciano Sirlin, PRL 96, 2006
18
Isospin symmetry breaking
? Isospin symmetry (CVC) ??(s) ?0(s) ?
Isospin breaking ??(s)??0(s) and,
1.0201?0.0003
(Marciano-Sirlin 88 Braaten-Li 90)