Coulomb distortion in the inelastic regime Patricia Solvignon Argonne National Laboratory Work done in collaboration with Dave Gaskell (JLab) and John Arrington (ANL) International Workshop on Positrons at Jefferson Lab JPOS09 March

22 Coulomb distortion and two-photon exchange Incident (scattered) electrons are accelerated (decelerated) in the Coulomb well of the nucleus. e e’e’ Exchange of 2 (hard) photons with a single nucleon TPE Coulomb distortion Opposite effect with positrons p n Exchange of one or more (soft) photons with the nucleus, in addition to the one hard photon exchanged with a nucleon OPE

3 Effective Momentum Approximation (EMA) E → E + V E p → E p + V } 3 How to correct for Coulomb distortion ? _ _ ⇔ Aste and Trautmann, Eur, Phys. J. A26, (2005) 1 st method 2 nd method  Focusing of the electron wave function  Change of the electron momentum DWBA ➫

4  Focusing of the electron wave function  Change of the electron momentum ➫ Effective Momentum Approximation (EMA) E → E + V E p → E p + V } 4 How to correct for Coulomb distortion ? _ _ ⇔ Aste and Trautmann, Eur, Phys. J. A26, (2005) 1 st method 2 nd method DWBA One-parameter model depending only on the effective potential seen by the electron on average.

55 Coulomb distortion measurements in quasi-elastic scattering Aste and Trautmann, Eur, Phys. J. A26, (2005) Gueye et al., PRC60, (1999)

66 Coulomb distortion measurements in quasi-elastic scattering Aste and Trautmann, Eur, Phys. J. A26, (2005) Gueye et al., PRC60, (1999) Coulomb potential established in Quasi-elastic scattering regime !

77 Physics sensitive to Coulomb distortion x>1 experiments L/T experiments EMC effect Color transparency In-medium modification on the nucleon FF x>1 experiments L/T experiments EMC effect Color transparency In-medium modification on the nucleon FF About every experiments that used nuclei with A>12 Coulomb distortion: ➡ Not accounted for in typical radiative corrections ➡ Usually, not a large effect at high energy machines ➡ Important for E p <<E

88 Physics sensitive to Coulomb distortion x>1 experiments L/T experiments EMC effect Color transparency In-medium modification on the nucleon FF x>1 experiments L/T experiments EMC effect Color transparency In-medium modification on the nucleon FF About every experiments that used nuclei with A>12 Coulomb distortion: ➡ Not accounted for in typical radiative corrections ➡ Usually, not a large effect at high energy machines ➡ Important for E p <<E in this talk

99 The EMC effect p n ∗∗ Nucleus at rest (A nucleons = Z protons + N neutrons) e-e- e-e- ≠ ∗∗ ∗∗ Z + N EMC (Cu) BCDMS (Fe) E139 (Fe)  A /  D Effects found in several experiments at CERN, SLAC, DESY x

10 SLAC E139 results on the EMC effect  SLAC E139: –Most complete data set: A=4 to 197 –Most precise at large x – Q 2 -independent – universal shape – magnitude dependent on A E139

11 Effect of Coulomb distortion on JLab E results 50 o 40 o JLab is at lower energy than SLAC but the luminosity is much higher. We obtain similar or larger Q 2 values in many cases by going to larger angles such that E p is smaller. So Coulomb distortion effects are 'doubly' amplified: lower beam energy and lower fractional E p.

12 E heavy target results Preliminary no Coulomb corrections applied

13 E heavy target results Preliminary Coulomb corrections applied

14 Extrapolation to nuclear matter NM Exact calculations of the EMC effect exist for light nuclei and for nuclear matter. SLAC E139&E140 CERN EMC CERN BCDMS CERN NMC No Coulomb corrections applied

15 Extrapolation to nuclear matter NM SLAC E139&E140 CERN EMC CERN BCDMS CERN NMC Coulomb corrections applied Exact calculations of the EMC effect exist for light nuclei and for nuclear matter. Non-negligible effects on SLAC data

16 Extrapolation to nuclear matter NM SLAC E139&E140 CERN EMC CERN BCDMS CERN NMC JLab E prel. Coulomb corrections applied Exact calculations of the EMC effect exist for light nuclei and for nuclear matter.

17 R(x,Q 2 ) Dasu et al., PRD49, 5641(1994) TPE can affect theεdependence (talk of E. Christy on Thursday) Coulomb Distortion could have the same kind of impact as TPE, but gives also a correction that is A- dependent.

18 Meaning of R In a model with: a. spin-1/2 partons: R should be small and decreasing rapidly with Q 2 b. spin-0 partons: R should be large and increasing with Q 2 Dasu et al., PRD49, 5641(1994)

19 Access to nuclear dependence of R Dasu et al., PRD49, 5641(1994) slopes ⇒ R A -R D Nuclear higher twist effects and spin-0 constituents in nuclei: same as in free nucleons ⇐ R A -R D =0

20 Access to nuclear dependence of R A non-trivial effect in R A -R D arises after applying Coulomb corrections Dasu et al., PRD49, 5641(1994) ➫ re-analysized

21 Access to nuclear dependence of R Preliminary New data from JLab E03-103: access to lowerε Coulomb corrections appliedNo Coulomb corrections applied Iron-Copper

22 Access to nuclear dependence of R Preliminary Coulomb corrections appliedNo Coulomb corrections applied Gold New data from JLab E03-103: access to lowerε

23 Access to nuclear dependence of R Preliminary After taking into account the normalization uncertainties from each experiment Hint of an A-dependence in R in Copper-Iron

24 ε dependence of the Coulomb distortion E=11 GeV E=8.8 GeV E=6.6 GeV Theε-dependence of the Coulomb distortion has effect on the extraction of R in nuclei Iron-Copper

25 Summary  At present, corrections for Coulomb distortion in inelastic regime are done using a prescription for quasi-elastic scattering regime ➡ need a measurement of the amplitude of the effect in the inelastic regime ➡ need a prescription in the inelastic regime  Coulomb distortion affects the extrapolation to nuclear matter which is key for comparison with theoretical calculations  Coulomb distortion has a real impact on the A-dependence of R: clearε- dependence ➡ hint of an A-dependence of R: could impact many experiments which used R p or R D for R A ➡ could change our conclusion on the spin-0 constituent contents and higher twist effect in nuclei versus free nucleons.

26 Back-ups

27 Nucleon only model  no EMC effect Smith & Miller, PRC 65, and (2002) “… some effect not contained within the conventional framework is responsible for the EMC effect.” Smith & Miller, PRC 65, (2002)

28 Nucleons and pions model  Pion cloud is enhanced and pions carry an access of plus momentum:  and using is enough to reproduce the EMC effect  But excess of nuclear pions  enhancement of the nuclear sea  But this enhancement was not seen in nuclear Drell-Yan reaction E906 projected E772 Drell-Yan Fig from P. Reimer, Eur.Phys. J A31, 593 (2007)

29 Another class of models  Interaction between nucleons  Model assumption:  nucleon wavefunction is changed by the strong external fields created by the other nucleons Cloet, Bentz, and Thomas, PLB 642, 210 (2006) Model requirements: Momentum sum rule Baryon number conservation Vanishing of the structure function at x A Should describe the DIS and DY data Smith & Miller, PRL 91, (2003)

30 EMC effect in nuclear matter No Coulomb corrections applied

31 EMC effect in nuclear matter Coulomb corrections applied

32 EMC effect in nuclear matter preliminary Coulomb corrections applied

33 World data re-analysis ExperimentsE (GeV)Ax-rangePub. 1 st author CERN-EMC Aubert 12,63, Ashman CERN-BCDMS Bari Benvenuti CERN-NMC2004,12, Amaudruz 2006, Arneodo SLAC-E ,27,65, Stein SLAC-E Bodek SLAC-E Bodek SLAC-E ,9,12,27,40,56,108, Gomez SLAC-E , Dasu DESY-HERMES27.53,14, Airapetian

34 Figs from J. Gomez, PRC49, 4348 (1994)) A or density dependence ? Density calculated assuming a uniform sphere of radius: R e (r=3A/4pR e 3 )

35 The structure of the nucleon ∗∗ e-e- e-e- Deep inelastic scattering: probe the constituents of the nucleon, i.e. the quarks and the gluons 4-momentum transfer squared Invariant mass squared Bjorken variable