Measurement of Nucleon Form Factors with DAFNE2 Marco Mirazita INFN-LNF LNF SCIENTIFIC COMMITTEE November Introduction Form Factors in the space-like region Form Factors in the time-like region Measurement of Nucleon FFs with DAFNE2 –Angular distribution measurements –Polarization measurements Conclusion

The DAFNE2 opportunity Letter of Intent by 80 physicist from 24 institution in 7 countries: Very positive feedback from the international community at the Workshop on Nucleon Form Factors, October 2005, Frascati The DAFNE energy upgrade offer the opportunity to make a detailed study of the nucleon Form Factors, providing: accurate measurement of pp and nn cross section  model-independent extraction of proton and neutron FFs first measurement of outgoing nucleon polarization  relative phase between G E and G M First measurement of  baryon production (including polarization)  strange baryon FF Study of angular asymmetry in pp (nn) distributions  look for 2-photon contribution Measurement of e + e - → hadrons and other exclusive multipion processes  sub-threshold NN resonance … and many others

Nucleon Form Factors – general properties FFs are analytic complex functions of q 2 = (p – p’) 2 T-invariance in the space-like region implies real FFs Dispersion relations connect the Space-Like (q 2 > 0) and Time-Like (q 2 < 0) regions Two FFs in the one-photon-exchange approximation: Pauli-Dirac (F 1 and F 2 ) or Sachs (G E and G M ) G M (q 2 ) = F 1 (q 2 ) + F 2 (q 2 ) G E (q 2 ) = F 1 (q 2 ) +  F 2 (q 2 )  =q 2 /4M 2 In the Breit reference system, Sachs FFs are the Fourier transform of the charge and magnetization distributions FFs are connected with GPDs (  quark angular momentum contributions)

Space-like FFs in the XX century - 1 Before 2000, the picture was well established and understood: - Proton electric and magnetic SL FFs scaling: G M p   p G E p  charge and magnetization have the same distribution - Neutron electric SL FF G E n  0 within errors - All 3 non-zero FFs are well described by the dipole formula corresponding to the  and  meson resonances in the time-like region and to exponential distribution in the coordinate space No substantial deviations from this picture were expected

Space-like FFs in the XX century - 2 PROTON NEUTRON

Time-like FFs in the XX century Proton data Assuming |G E | = |G M |  no |G E | Early pQCD scaling |G M | ~ Q -4 Time-like FF larger than space-like Steep behaviour close threshold Neutron data Assuming |G E | = 0 neutron ~4 times the proton extrapolation pQCD scaling?

Space-Like FFs in the XXI century - 1 Accuracy of form-factor measurements significantly improved by measuring the interference term G E G M through the beam helicity asymmetry with a polarized target or with recoil polarimetry Recoil polarization measurements proposed more than 40 years ago as the best way to reach high accuracy in the FF measurement Akhiezer et al., Sov. Phys. Jept. 6, 588 (1958) Arnold, Carlson, Gross, PR C23, 363 (1981) had to wait over 30 years for development of - polarized beam with high intensity (~100 µA) and high polarization (>70 %) - beam polarimeters with 1-3 % absolute accuracy - polarized targets with a high polarization or - ejectile polarimeters with large analyzing powers JLab new generation of beams and detectors

polarization Rosenbluth Space-Like FFs in the XXI century The new data imply a completely different picture of the proton Fourier transform of G M and G E : charge and magnetization distributions Quark angular momentum contribution? Second “spin crisis” of the proton

Why a new measurement of time-like FFs in the XXI century? Time-like data can discriminate between models that fit equally well the space-like region Space-like data could perhaps be reconciled with 2-photon exchange contributions. What in the time-like region? Jlab measurements showed that |G E | = |G M | in the space-like region is no more a valid assumption for the proton. Why should be valid in the time-like? The inconsistencies between data and pQCD expectations could be just a consequence of the basic wrong assumption |G E | = |G M | Neutron need a much more careful investigation Phases of time-like FFs never measured Time-like FFS are basically unknown

Electric to magnetic FF ratio Different hypothesis on G E /G M strongly affect the G M extraction, mainly in the low energy region DR analysis Tentative extraction of FF ratio from angular distributions Very suitable energy window DAFNE2

1 m FINUDA well suitable Feasible with minimal modifications interaction region (only one) vacuum chambers dipoles (normal conducting) control system diagnostics Injection at 510 MeV keeping the present injection system ramp up time ~ minutes beam life time ~ hours Experimental requirements Beam requirements: beam energy 1.2 GeV high luminosity ~10 32 cm -2 s -1 (cross section ~ nb) beam polarization not required (but could help) Detector requirements: high detection acceptance for charged and neutral particles identification of exclusive final state - protons  momentum+TOF - high neutron efficiency - detection of antinucleons  converter installation of a polarimeter - carbon analyzer + 2 tracking systems Good p-resolution Adequate n-detection Easy implementation of a polarimeter Possibility to improve n-detection - more converters - new array of scintillators just before the end-cap - n-polarimeter

Minimal changes required in FINUDA 1 cm vertex region OSIM nuclear targets TOFino ISIM 10 cm drift chambers TOFone straw tubes Add Scintillator slabs antineutron converter polarimeter or carbon cylinder remove nuclear targets

e + e -  nn with FINUDA -  s = 1890 MeV, B = 0.2 T 1.5 cm carbon converter A. Filippi, INFN Torino

 s = 1890 MeV, B = 0.2 T e+e-  pp with FINUDA: typical topology

Proton angular distributions Projected data assuming |G E | = |G M | (black) or |G E |/|G M | from DR (red) Integrated luminosity L =100 pb -1 Constant detection efficiency  =80% fit of angular distributions in the FINUDA coverage F(  )=A(1+cos 2  )+Bsin 2  |G E ||G M | FINUDA Max sensitivity to |G E |

Neutron angular distributions Projected data assuming |G E | = |G M | (black) or |G E | = 0 (red) Integrated luminosity L =100 pb -1 Constant detection efficiency  =15% fit of angular distributions in the FINUDA coverage F(  )=A(1+cos 2  )+Bsin 2  FINUDA |G E ||G M |

FF measurement: projected accuracy Integrated luminosity  pb -1 KLOE in last 12 months: 1800 pb -1 at  protonneutron Statistical error of the order of few percent for all the 4 nucleon FFs in the whole explored region

Induced polarization non negligible polarization P y maximal at 45° and 135° high discriminating power between theories extraction of FF relative phase Polarization normal to the scattering plane No beam polarization z x y B B e+e-

Polarization measurement The polarization is measured through secondary scattering in a strong interaction process The spin-orbit coupling causes an azimuthal asymmetry in the scattering tracking system  analyzer pp ss e+e+ e-e- p p P PCPC z’ drift chambers straw tubes TOFone Vertex region OSIM Analysing power

Polarization measurement Polarization is extracted by measuring asymmetries      For P y pol (  cos  ) Averaged analysing power ~ 50 % Polarization ~ 15% max (pQCD model) Expected effect of the order of few % at E BEAM = 1.2 GeV For Δ R/R  30 %: total luminosity  2500 pb -1 (1 year with average cm -2 s -1 )

Integrated luminosity protonneutron s [GeV 2 ]E beam [MeV] L [pb -1 ] cross (100)section (100) (100) (100) polarization

Possible improvements of the detector Neutron polarization measurement - Use scintillator slabs as analyzer  carbon for protons and hydrogen for neutrons - The scintillators can be used to increase neutron detection efficiency Improve nn detection capability - Double converter  increase antineutron efficiency - A second layer of scintillators  double neutron efficiency - Extend angular coverage of TOFone barrel

Time-like FF measurement competitors  s (GeV) MNMN proton neutron DAFNE2 VEPP2000 max. energy ~ 1 GeV per beam, luminosity ~ cm -2 s -1 measure pp and nn final state start run ~ 2007 BEPC energy ~ GeV, luminosity ~ cm -2 s -1 measure pp final state only start run ~ 2007 PAX inverse reaction pp → e + e - (no neutron measurement) single and double polarization measurements start run >2013

Conclusions DAFNE2 at 1.2 GeV provides a very interesting energy region for an accurate determination of nucleon (and hyperon) form factors in the time-like sector. The FINUDA detector with minor modifications is well suitable for the measurements. An integrated luminosity between 100 and 300 pb -1 per beam energy allows measurements of |G M | and |G E | at the few percent level for the proton and below 10% for the neutron. Measurement of the nucleon polarization is feasible, providing the first determination of the relative phase between the electric and magnetic FFs. Other interesting measurements are also possible

Wavelength of the probe can be tuned by selecting momentum transfer Q 2 < 0.1 GeV 2 integral quantities (charge radius,…) GeV 2 internal structure of nucleon > 20 GeV 2 pQCD scaling Stern (1932) measured the proton magnetic moment µ p ~ 2.5µ Dirac indicating that the proton was not a point-like particle Hofstadter (1950’s) provided the first measurement of the proton’s radius through elastic electron scattering (Nobel Prize in 1961) Subsequent Space-Like (SL) data (≤1993) were based on Rosenbluth separation with limited accuracy for G E p at Q 2 >1 GeV 2 Early interpretation based on Vector-Meson Dominance Good description with phenomenological dipole form factor Early studies of nucleon FFs

Space-Like FFs: Experimental techniques Rosenbluth separation Based on cross section measurement Q 2  q 2   * polarization  = Q 2 / 4M 2 Polarization observables For example, electron-to-proton polarization transfer Recoil polarization measurements have been proposed more than 40 years ago as the best way to reach high accuracy in the FF measurement Akhiezer et al., Sov. Phys. Jept. 6, 588 (1958) Arnold, Carlson, Gross, PR C23, 363 (1981) JLab Had to wait for the new generation of beams and detectors Measures d σ /d Ω vs  at constant Q 2 intercept gives G M, slope gives G E

Afanasev et al. hep-ph/ photon exchange -complex space-like FFs -correction to the cross section are of the same order as electric contribution -corrections to polarization observables are expected to be much smaller Rosenbluth and polarization data could be reconciled? Calculations have simple parametrization of 2-  exchange Some authors found negligible contributions to the cross section

Time-Like FFs measurements FF measurements are based on total cross section, under some theoretical assumption on their ratio |G M | can be more easily extracted, but it’s model-dependent |G E | remains unmeasured |G M | = |G E | at the physical threshold s = 4M 2  isotropic distributions G M dominates the cross section for s >> 4M 2 FF extraction from cross section measurements in e + e -  N N  = s/ 4M 2 Up to now, no independent extraction of both TL FFs has been performed (   1 nb)

Total cross section Full lines

e + e -  pp with FINUDA: Preliminary MC study E=1.0 GeV E=1.1 GeV E=1.2 GeV B=10 kgauss proton efficiency For comparison in real data: - Muons in K+ →  +  /p<1% for P  =235 MeV/c

Proton polarimeter Multiple scattering cut Angular cut  5° is required MAIN BACKGROUND SOURCE: multiple scattering at small angles Mainz polarimeter data E p ~ 1.1 ÷ 1.2 GeV scatterer thickness: 7 cm Moliere radius:  m 1.5 o

Fits of exp. data T=60 MeV T=100 MeV T=260 MeV Carbon analysing power A c known from few tenths of MeV up to some GeV Average values  =5°-20° Multiple scattering cut

Hyperon Form Factors Hyperons can also be produced in e + e - interactions ( , , …) energy threshold: √s ~ 2 M  ~ 2.23 GeV 2 From u-spin invariance: G M n ~ 2 G M  Smaller cross section as for nucleon production  TOT ~ 0.1 nbarn Production rates comparable with N N are expected Y Y final state could be identified by detecting the decay of one hyperon Angular distributions  moduli of FF For weakly decaying hyperons ( ,  ± (1189)) the polarization measurement does not require a polarimeter

angular distribution of the proton Weak decay does not conserve parity A  A S + A P P-wave, parity conserving S-wave, parity non conserving  polarization To measure normal  polarization: asymmetry of proton angle with respect to the normal to the scattering plane high efficiency is expected (~ 50 %)

Other measurements made possible by the DA  NE energy upgrade Study of angular asymmetry in pp (nn) distributions  look for 2-photon contribution Measurement of the total cross section e + e - →hadrons to get the hadronic contribution to g  -2 and  (M 2 z ) DA  NE and VEPP2M have measured the hadronic total cross section up to 1 GeV 2 at a percent level (even if there are discrepancies at about ±5% level). A measurement at a few percent level at higher c.m. energies is welcome. The search and study of narrow vector mesons in the GeV mass range BaBar and photoproduction experiments have shown several evidences of narrow (  <100 MeV), unespected structures like for istance in e + e - →3  + 3  -, e + e - →2  + 2  - 2  0, e + e - →  +  - 2  0, e + e - →2  + 2  - and the corresponding channels in diffractive photoproduction, most of them near the NNbar threshold A precision measurement of  →  cross section via e + e - → e + e -  in the mass range from 2m  up to 1 GeV. Actually the measurement of these cross sections has been done by the LEP experiments, but in the case of  +  - detection efficiency and background did not allow for  masses below ~800 MeV and in the case of  0  0 the collected statistics was quite limited.

Anomalous behavior in total cross section BaBar found steps in total cross section at  s =2.2 and 2.9 GeV

Resonance below ppbar threshold? Some anomaly found close to the physical threshold multihadronic cross section Proton FF Combined fit M=1870±10 MeV  =10±5 MeV

6  production DM2 experiment Anomaly close to NN threshold e + e - → 3  + 3  - Same structure in diffractive pion photoproduction FNAL M = ± ± GeV  = 29 ± 11 ± 4 MeV J PC = 1 -- I G = 1 +  p → p 3  + 3  - Mass and width consistent with  (mhad) and proton FF fit Results confirmed by BaBar (unpublished yet) new vector meson? NN bound state?

DA F NE2 parameters for 1.2 GeV operation