IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06
18
IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06 Gabriel López Castro Physics Department Cinvestav, México City Model-dependent electromagnetic corrections to → decay
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IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06. Model-dependent electromagnetic corrections to → decay. Gabriel L ó pez Castro Physics Department Cinvestav, M é xico City. Necessity for radiative corrections. - PowerPoint PPT Presentation
Transcript of IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06
IX International Workshop On Tau Lepton Physics Pisa, 19-22 September 06
Gabriel López CastroPhysics DepartmentCinvestav, México City
Model-dependent electromagnetic corrections to → decay
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 [ –e+e- based data]
Up to 10% discrepancy in Fe+e-(s)/F(s)2 [KLOE data]
Necessity for radiative corrections
Isospin symmetry breaking
23
2
2
23
2320
0
)(12
)()(
),(2
1132
)(
tFs
t
tMt
MtVMG
dtd udF
Isospin symmetry breaking : and (Cirigliano et al, 01,02)
(t)GEM EWLDSD Sdtd
dtd
dtd 00
1
1.02010.0003(Marciano-Sirlin 88Braaten-Li 90)
00 ,mmmm
Kinematics
Virtual and real photon corrections to have an infrared safe result
Kinematics of three-body decay (tree-level + virtual corrections)
),(2
utfdtdud
Kinematics of four-body decay (real photon corrections)
),,cos,,,(cos
5
xutFddtdudxd
d
t=(p-p)2 =(p- +p0) 2 and u=(p- p- )2
framerestin),( and ,invariants)(,)( 220 ppxppt
Long-distance electromagnetic corrections
dtd
dt
d
dtd
dt
dr110
)(2 )(
)(
0
,1
)(0
0
,11
0)(2 1)(),()(
tregEMg
hardr
tEMG
softr
EMEM
dtddt
d
dtd
dtd
dtd
tGtGdtd
dt
d
Important for photon inclusive measurements (→+→)
Model-dependent contributions (Cirigliano et al, JHEP 2002)
Resonant and a1 exchangefixed 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
G0EM(t)
Cirigliano et al, JHEP 2002
G0EM(t)
)(for,106.1
)(full,100.11
)(1
)()(
)(4
1010
10
4
)(
3
max
2 tG
tG
tGdt
d
tKtK
tdtKaEM
EM
EM
t
m
Vector meson dominance
model (Flores et al, PRD 2005;
hep-ph/0608084)
Couplings fixed from low-energyprocesses: →, l+l-, →, Γa1 , Weinberg sum rule (fa1)
Large q2 in decays allows the production and decayof resonances
Alternative calculation
54322 2776.3735.995.10667.5326.1107.1)/( xxxxxMtxGEM
)(for,106.1
)(full,108.31
)(1
)()(
)(4
1010
10
4
)(3
max
2 tG
tG
tGdt
d
tKtK
tdtKaEM
EM
EM
t
m
Excluding the contribution of (782) meson
)1()()),(( 0 LDE 300 -0.31 ----
400 -0.27 ----
500 -0.23 ----
600 -0.19 ----
700 -0.16 ----
800 -0.15 ----
max -0.15 -0.38
0 (%) Cirigliano
(MeV) This work 2002
If photons with E 0 arediscriminated
Hard photon radiative events
MeV80~20 2005 PRD
Yndurain-Troc. de%,8.0log~
workThis%,17.0
00
mM
Corrections to the decay rate
Radiative → decays
Can help to discriminate between two models
Photon spectrum Hadron spectrum
Effects of (770) magnetic dipole moment
]')()'[(0 gpgpgkgkgppieie
Electromagnetic vertex, magnetic moment =(e/m)
→ →0
=100
=200
=1 =2 =3
=100
=200
y=cos
x=2E/m
GLC+toledo, PRD, 1999 Flores et al, PRD, 2005
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.
Sources of isospin breaking corrections (M. Davier et al EPJ C27, 2003)
Current best test of CVC
0+ (A,Z+1)→0+ (A,Z)e+
0+T_ 0+=2
Hardy and Towner, EPJ A25, 2005
)19)(15)(11(97377.0 )2(SUF
Vud G
GV
Marciano & Sirlin, PRL 96, 2006
Isospin symmetry breaking
23
2
2
23
2320
0
203000
20
)(12
)()(),(
211
32)(
)(12
)()(),(
4)(
sFs
ssM
t
M
tVMG
ds
d
sFs
sss
ee
udF
Isospin symmetry (CVC): (s)= 0(s)
Isospin breaking: (s)0(s) and,
(s)GEM EWLDSD Sdsd
dsd
dsd 00
1
1.02010.0003(Marciano-Sirlin 88Braaten-Li 90)
