Test of FSR in the process at DAFNE

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

FSR in s. QED (s. QED VMD) Fp(s) But how good is this approximation? s. QED VMD is reasonable for the final state. But what about g 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.

Global structure of FSR tensor for P 2 = s e * • charge conjugation symmetry • photon crossing symmetry • gauge invariance and

gauge invariant tensors: scalar (model dependent) functions Limit of soft photon (what we call s. QED), in fact VMD*s. QED At threshold (very hard photon) this approximation could not work fi=fis. QED+Dfi

(S. Dubinsky et al, hep-ph/041113) FSR in Ch. PT with and a 1 mesons G. Ecker et al. , Nucl. Phys B 321, 311 (1989) The contribution with +, (instead of a 1), turns out to be negligible

4 model parameters: f , F V , GV , F A We calculate fi Meson M(Ge. V) GV (Ge. V) FA (Ge. V) r 0. 775 0. 0066 0. 156 - a 1 1. 23 - - 0. 122 in Ch. PT (S. Dubinsky et al, hep-ph/0411113) 1. pp contribution to am (analytical results) 2. Contribution to dspp /d. Q 2 pp spectrum and charge asymmetry (Monte Carlo)

pp 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 (pp s. QED) 5 10 -10 Dam (pp CHPT) 0. 1 10 -10 below current experimental precision

Contribution of FSRCHPT to dspp /d. Q 2 pp spectrum and charge asymmetry The following matrix element has been introduced in a MC, for e+e- p+p- (based on EVA structure): S. Binner et al. Phys. Lett. B 459 (1999) • We neglect the contributions from g* + -g (found to be negligible in hep-ph/0411113) • We included the direct decay f + - g, important at s=mf 2. This contribution (which is model dependent) affects also the low Q 2 pp region. Charge asymmetry can help to distinguish between various models (see the talk of H. Czyz) • We consider KLOE large angle analysis: 50 o< q < 130 o, 50 o<qp< 130 o (S. Mueller talk)

We included f p+ p- decay in our calculation, by looking to the channel f p 0 p 0 (similar to H. Czyz et al. hep-ph/0412239) d. BR/dm x 108 (Me. V-1) We use the Achasov 4 quark parametrization with the parameters of the model taken from the fit of the KLOE data f p 0 p 0. (f + - g is related to f 0 0 g by isospin symmetry) CAVEAT: For the moment we consider only the contribution of f 0 (no s meson). This could be too crude for low Q 2 ! mpp(Me. V)

dspp /d. Q 2 (nb/Ge. V 2) (Analytical) Comparisons (at s=mf 2): 0 o<qp< 180 o 0 o<q < 180 o = FSRs. QED+Df = f p+ p- resonant cont. = FSRs. QED Since MFSR*Mf |Mf|2 at low Q 2 Df can be relevant only for destructive interference (we will consider only this case in the following) = Df Q 2(Ge. V 2) What happens for s<mf 2 ?

dspp /d. Q 2 (nb/Ge. V 2) The comparison at s=1 Ge. V 2 (off f peak): = FSRs. QED+Df = 100·f p+ p- resonant cont. = FSRs. QED 0 o<qp< 180 o 0 o<q < 180 o Multiplied by a factor 100 = Df 1/|Df( s)|2 Q 2(Ge. V 2) 1 Ge. V s 1. 04 Ge. V In this case the interference MFSR*Mf is expected to be >>|Mf|2 ÞWe could not neglect the interference contribution (i. e. f contr. ), but the work off the resonance region is attractive (3 p background is much less)

ds/d. Q 2 (nb/Ge. V 2) Numerical results: differential cross section… s=mf 2 50 o<qp< 130 o 50 o<q < 130 o ds. TOT/dss. QED+f/dss. QED = ISR+FSRs. QED + f ds. TOT/dss. QED+f = ISR+FSRCHPT + f Q 2(Ge. V 2) Effect al low Q 2…however the contribution of f is not much accurate (no interference with s has been taken into account)

ds/d. Q 2 (nb/Ge. V 2) A closer look at the threshold region: ds. TOT/dss. QED+f/dss. QED = ISR+FSRs. QED + f ds. TOT/dss. QED+f = ISR+FSRCHPT + f 0. 35 Q 2(Ge. V 2) Up to 30% of contribution beyond s. QED at the threshold. Results are sensitive to FSR model

And asymmetry… = ISR+FSRs. QED = ISR+FSRCHPT + f = ISR+FSRs. QED + f -25% Q 2(Ge. V 2)

Conclusions and outlook • First MC results on a generalization of FSR using Ch. PT with and a 1 mesons have been presented. • A sizeable effect can be seen on the cross section (at low Q 2 only). • The situation on the asymmetry is more complicate. Üthe 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 Q 2): to consider the phi decay in Ch. PT • try to take into account and ' mesons contribution in Ch. PT • 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 s. QED!!!

BACKUP SLIDES

Asymmetry ISR+FSRs. QED + f ISR+FSRs. QED Q 2(Ge. V)