Upload
clover
View
18
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Test of FSR in the process at DA F NE. G.Pancheri, O. Shekhovtsova, G. Venanzoni. INFN/LNF. EURIDICE Midterm Collaboration Meeting 8-12 Feb. 2005 Frascati. F p (s). F p (s). FSR in sQED (sQED VMD ). F p (s). But how good is this approximation? - PowerPoint PPT Presentation
Citation preview
Test of FSR in the process at DANE
G.Pancheri, O. Shekhovtsova, G. Venanzoni
ee
EURIDICE Midterm Collaboration Meeting
8-12 Feb. 2005 Frascati
INFN/LNF
FSR in sQED (sQEDVMD)
But how good is this approximation?
sQED VMD is reasonable for the final state.
F(s)
But what about final state ?
Can we use for FSR the same value of F(s) as for
An additional contribution is model-dependent,
and probably very small. But must be estimated.
F(s)
F(s)
Global structure of FSR tensor for
• charge conjugation symmetry
• photon crossing symmetry and
• gauge invariance
)()()()(* kppP
),,( lkPM F
ppl
** ||)()(||)()( jppSpp
kP
,0),,( PlkPM F 0),,(
klkPM F
P2 = s)(
p
)( p
)(* P
)( 3322112 fffieM F
0lim
)()(
)(2lim
)()(
)(2lim
330
22220
22110
sQEDk
sQEDk
sQEDk
ff
lkPk
sFff
lkPk
sFPkff
Limit of soft photon (what we callsQED), in fact VMD*sQED
At threshold (very hard photon) this approximation could not work
i gauge invariant tensors:
),,( klkPsfi scalar (model dependent) functions
)()(
)()(
3
2
1
klPkPlPlkklgs
kPlklklklgPlkl
kPgPk
fi=fisQED+fi
FSR in ChPT with and a1 mesons(S. Dubinsky et al,hep-ph/041113)
The contribution with +,-
(instead of a1), turns out to be negligible
)(2
)(
)()
(12
)(
11A
02V
02V
20V
aaFf
eFB
Bf
eG
f
iG
fF
eF
BeBieBL
)(
BBF
G.Ecker et al., Nucl. Phys B321, 311 (1989)
)(* P
Meson M(GeV) GV (GeV) FV (GeV) FA (GeV)
0.775 0.0066 0.156 -
a1 1.23 - - 0.122
4 model parameters: f , FV, GV, FA
keV 246 640)(
MeV 2.9 .7501)(
keV 0.11 6.85)(
MeV4.92
1
0
0
a
ee
f
We calculate fi in ChPT (S. Dubinsky et al,hep-ph/0411113)
1. contribution to a(analytical results)
2. Contribution to d/dQ2 spectrum and charge asymmetry (Monte
Carlo)
contribution to a
max
24
,
2
2,had
)(
)()(,)()(
3
s
m s
ssRsKsR
s
dsa
Differential contribution to , where is hard ( >Ecut)
,hada
,hada
a (~ 500(5) 10-10
a (sQED 5 10-10
a (CHPT 0.1 10-10
below current experimental precision
10-9
10-13
10-8
10-12
Contribution of FSRCHPT to d/dQ2
spectrum and charge asymmetryThe following matrix element has been introduced in a MC,for e+e- (based on EVA structure):
))Re((2
||||||*
222
MMM
MMMMMMd
sQED
CHPTCHPT
FSRISR
FSRISRFSRISR
•We neglect the contributions from found to be negligible in hep-ph/0411113)
•We included the direct decay important at s=m2. This
contribution (which is model dependent) affects also the low Q2 region.
Charge asymmetry can help to distinguish between various models (see the talk of H. Czyz)
•We consider KLOE large angle analysis: 50o< 10o, 50o<10o
(S. Mueller talk)
S. Binner et al. Phys. Lett. B 459 (1999)
We included decay in our calculation, by looking to the channel (similar to H. Czyz et al. hep-ph/0412239)
))()(Re(
),(2
)(
2222
)(
2
2
2222
0000
2
200
QmQm
e
m
Q
m
mI
m
gggQf
ffff
Qi
KKK
ff
B
22.3
29.14
962.0
2
2
2
2
0
0
0
0
f
KKf
KKf
f
g
gR
GeVg
GeVm
CAVEAT: For the moment we consider only the contribution of f0 (no meson).This could be too crude for low Q2 !
We use the Achasov 4quark parametrization with the parameters of the model taken from the fit of the KLOE data .is related to by isospin symmetry)
m(MeV)
dBR
/dm
x 1
08 (M
e V-1)
(Analytical) Comparisons (at s=m2):
= FSRsQED+f
Since MFSR*M |M|2 at low Q2
f can be relevant only for destructive interference (we willconsider only this case in the following)
0o<10o
0o<10o
= resonant cont.
= FSRsQED
= f
Q2(GeV2)
What happens for s<m2 ?
d
/dQ
2 (n
b/G
eV2 )
The comparison at s=1 GeV2 (off peak):
= FSRsQED+f
0o<10o
0o<10o
= 100·resonant cont.
= FSRsQED
= f
Q2(GeV2)
Multiplied by a factor 100
1/|D(s)|2
In this case the interference MFSR*M is expected to be >>|M|2
d
/dQ
2 (n
b/G
eV2 )
We could not neglect the interference contribution (i.e. contr.), but the work off the resonance region is attractive (3 background is much less)
1.04 GeV1 GeV s 1.04 GeV
Numerical results:differential cross section…
s=m2
50o<10o
50o<10o
= ISR+FSRsQED +
= ISR+FSRCHPT +
= ISR+FSRsQED
d/d
Q2 (n
b/G
eV2 )
dTOT/dsQED
dsQED/dsQED
dTOT/dsQED
Q2(GeV2) Q2(GeV2)
Effect al low Q2…however the contribution of is not much accurate(no interference with has been taken into account)
A closer look at the threshold region:
= ISR+FSRsQED +
= ISR+FSRCHPT +
= ISR+FSRsQED
d/d
Q2 (n
b/G
eV2 )
Q2(GeV2)
dTOT/dsQED
dsQED/dsQED
dTOT/dsQED
Up to 30% of contribution beyond sQED
at the threshold. Results are sensitive to FSR model
0.35 Q2(GeV2)
0.35
And asymmetry…
Q2(GeV2)
= ISR+FSRCHPT +
= ISR+FSRsQED +
= ISR+FSRsQED
-25%
Conclusions and outlook
•First MC results on a generalization of FSR using ChPT with and a1 mesons have been presented.
•A sizeable effect can be seen on the cross section (at low Q2 only).
•The situation on the asymmetry is more complicate.the result strongly depends on the parametrization of the direct decay.
For the near future:
• Improve the simulation:• better parametrization of (including also the meson)• study of the dependence of results on the various parameters of
the models in MC • New theoretical tasks
• improve the knowledge on the phi decay (in particular at low Q2): to consider the phi decay in ChPT
• try to take into account and ' mesons contribution in ChPT• Try to disentangle the various contributions:
• asymmetry, and other kinematical variables (angular distributions)
• Model independent analysis of fi different kinematics region?
• Work off resonance
Disclaimer: all our numerical results are preliminary!!!
The theoretical results is only the first step out sQED!!!
BACKUP SLIDES
Q2(GeV) Q2(GeV)
ISR+FSRsQED
ISR+FSRsQED +
Asymmetry