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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?
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Test of FSR in the process at DAFNE G.Pancheri, O. Shekhovtsova, G. Venanzoni INFN/LNF EURIDICE Midterm Collaboration Meeting 8-12 Feb. 2005 Frascati
Fp(s) Fp(s) FSR in sQED (sQEDVMD) Fp(s) But how good is this approximation? sQED VMD is reasonable for the pp final state. But what about ppg final state ? Can we use for FSR the same value of Fp(s) as for pp ? An additional contribution is model-dependent, and probably very small. But must be estimated.
Global structure of FSR tensor for P2 = s • charge conjugation symmetry • photon crossing symmetry and • gauge invariance e*
gauge invariant tensors: scalar (model dependent) functions Limit of soft photon (what we call sQED), in fact VMD*sQED At threshold (very hard photon) this approximation could not work fi=fisQED+Dfi
(S. Dubinsky et al,hep-ph/041113) FSR in ChPT with and a1 mesons G.Ecker et al., Nucl. Phys B321, 311 (1989) The contribution with r+,- (instead of a1), turns out to be negligible
4 model parameters: f , FV, GV, FA We calculate fi in ChPT(S. Dubinsky et al,hep-ph/0411113) • ppg contribution to am (analytical results) • Contribution to dsppg/dQ2pp spectrum and charge asymmetry (Monte Carlo)
ppg contribution to am 10-9 10-8 10-13 10-12 Differential contribution to , where is hard ( >Ecut) am (pp) ~ 500(5) 10-10 am (ppgsQED) 5 10-10 Dam (ppgCHPT) 0.1 10-10 below current experimental precision
Contribution of FSRCHPT to dsppg/dQ2pp spectrum and charge asymmetry The following matrix element has been introduced in a MC, for e+e- p+p-g (based on EVA structure): S. Binner et al. Phys. Lett. B 459 (1999) • We neglect the contributions from g*rp p+p-g (found • to be negligible in hep-ph/0411113) • We included the direct decay f p+ p- g, important at s=mf2. This contribution (which is model dependent) affects also the low Q2pp region. Charge asymmetry can help to distinguish between various models (see the talk of H. Czyz) • We consider KLOE large angle analysis: 50o< qg< 130o, 50o<qp< 130o (S. Mueller talk)
We included fp+ p- g decay in our calculation, by looking to the channel f p0p0g (similar to H. Czyz et al. hep-ph/0412239) We use the Achasov 4quark parametrization with the parameters of the model taken from the fit of the KLOE data f p0p0g. (fp+ p- g is related to fp0 p0 g by isospin symmetry) dBR/dm x 108 (MeV-1) CAVEAT: For the moment we consider only the contribution of f0 (no s meson). This could be too crude for low Q2 ! mpp(MeV)
(Analytical) Comparisons (at s=mf2): 0o<qp< 180o 0o<qg< 180o = FSRsQED+Df dsppg /dQ2 (nb/GeV2) =fp+ p- g resonant cont. = FSRsQED Since MFSR*Mf |Mf|2 at low Q2 Df can be relevant only for destructive interference (we will consider only this case in the following) = Df Q2(GeV2) What happens for s<mf2 ?
The comparison at s=1 GeV2 (off fpeak): 0o<qp< 180o 0o<qg< 180o = FSRsQED+Df dsppg/dQ2 (nb/GeV2) =100·fp+ p- g resonant cont. Multiplied by a factor 100 = FSRsQED = Df 1/|Df(s)|2 s 1.04 GeV 1.04 GeV 1 GeV Q2(GeV2) In this case the interference MFSR*Mf is expected to be >>|Mf|2 • We could not neglect the interference contribution (i.e. f contr.), but the work off the resonance region is attractive (3 p backgroundis much less)
s=mf2 50o<qp< 130o 50o<qg< 130o Numerical results:differential cross section… dsTOT/dssQED ds/dQ2 (nb/GeV2) dssQED+f/dssQED = ISR+FSRsQED = ISR+FSRsQED + f dsTOT/dssQED+f = ISR+FSRCHPT + f Q2(GeV2) Q2(GeV2) Effect al low Q2…however the contribution of f is not much accurate (no interference with s has been taken into account)
A closer look at the threshold region: dsTOT/dssQED ds/dQ2 (nb/GeV2) dssQED+f/dssQED = ISR+FSRsQED dsTOT/dssQED+f = ISR+FSRsQED + f = ISR+FSRCHPT + f 0.35 0.35 Q2(GeV2) Q2(GeV2) Up to 30% of contribution beyond sQED at the threshold. Results are sensitive to FSR model
And asymmetry… = ISR+FSRsQED = ISR+FSRCHPT + f = ISR+FSRsQED + f -25% Q2(GeV2)
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 ismore complicate. • the result strongly depends on the parametrization of the f direct decay.
For the near future: • Improve the simulation: • better parametrization of f (including also the s 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!!!
Asymmetry ISR+FSRsQED + f ISR+FSRsQED Q2(GeV) Q2(GeV)