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