Hadron Propagation in the Medium

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ICTP Workshop, Trieste, Italy 23 May, 2006. Hadron Propagation in the Medium. The Exclusive Process A(e,ep)B in few-nucleon systems . H. Morita for. < Perugia-Dubna-Sapporo Collab. >. C. Ciofi degli Atti , M. Alvioli , V. Palli, I. Chiara, Univ. of Perugia - PowerPoint PPT Presentation

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  • Hadron Propagation in the Medium H. Morita forICTP Workshop, Trieste, Italy 23 May, 2006 The Exclusive Process A(e,ep)B in few-nucleon systems < Perugia-Dubna-Sapporo Collab. >C. Ciofi degli Atti, M. Alvioli , V. Palli, I. Chiara, Univ. of PerugiaL.P. Kaptari, BLTP JINP, DubnaH. Morita, Sapporo Gakuin Univ., Sapporo

  • A(e,ep)B Reactionkeq,ek=k1+qp B=(A-1)keep1(k)k1Apm1. IntroductionFSI

  • Outline of my talkIntroductionFramework of the calculation for the A(e,ep)B Reaction -Generalized Eikonal Approximation-Results of 3He(e,ep)2H(pn) Reaction Results of 4He(e,ep)3H ReactionFinite Formation Time Effect on 4He(e,ep)3H Reaction -at higher Q2 region-Summary

  • 2.Framework of the Calculation for the A(e,ep)B Reactionnuclear distorted spectral functione-N cross sectionIf B(recoil system) is bound state We use Factorization Ansatz.nucleon distorted momentum distributiondistorted by FSI(here only unpolarized cross section will be discussed)< Cross Section of A(e,ep)B >

  • Nuclear Distorted Spectral Function in 3He(e,ep)2H(pn) process3He(e,ep)2H3He(e,ep)pnSG: Glauber operatorC. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. C71, 024005 (2005)

  • Glauber Operator SG 1st nucleon Struck proton tot Particle Data Group (http://pdg.lbl.gov/) Partial-Wave Analysis Facility (http://lux2.phys.va.gwu.edu/)Usual Parameterizationnot q !!

  • Generalized Eikonal Approximation Frozen ApproximationL.L.Frankfurt et al., Phys. Rev. C56, 1124(1997) and M.M. Sargsian et al, Phys. Rev. C71 044614(2005)C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. C71, 024005 (2005)Conventional Glauber ApproximationGeneralized Eikonal ApproximationConsider the Fermi motionPPnq,

  • Diagramatic representation of the process 3He(e,ep)2H(pn)++

  • Single Rescattering Amplitude sd

  • Single Rescattering Amplitude sd (cont.)Using the coordinate space representation of the propagatorFinally we get GEA Operator

  • Double Rescattering Case Finally we get the distorted spectral functionRef) L.L.Frankfurt et al., Phys. Rev. C56, 1124(1997)In the following calculation, we putfor the double rescattering

  • 3.Results of 3He(e,ep) 2H(pn) ReactionC. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005)Q21.55(GeV/c)2, x=1Data: JLab E89044M.M. Rvachev et al., Phys. Rev. Lett. 94(2005) 192302GEA(GA) Calculation reproduces the data almost perfectly.

  • Multiple Scattering ContributionsC. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005)d(pm) has different (three) slopes

  • Results of 3He(e,ep) pn C. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. Lett. 95, 052502 (2005)Q21.55(GeV/c)2, x=1Data: JLab E89044F. Benmokhtav et al., Phys. Rev. Lett. 94(2005) 082325GEA(GA) Calculation reproduces the data quite well.

  • 4. Results of 4He(e,ep)3H ReactionATMS method M. Sakai et al., Prog.Theor.Phys.Suppl.56(1974)108. H. Morita et al., Prog.Theor.Phys.78(1987)1117. Variational wave functionWe extend the same calculation as 3He-case to 4He(e,ep)3H reactionBut, for the realistic wave function we adopted the ATMS method< Extension to 4He(e,ep)3H Reaction >< Experimental Data >JLab E97-111: B. Reitz et al., Eur. Phys. J. A S19(2004) 165 Py2 KinematicsParallel Kinematics CQ2 KinematicsPerpendicular Kinematics

  • Results at Py2-Kinem.slightly underestimate agreement is reasonably well.Parallel Kinem.Preliminary0.58 Q2 0.90 (GeV/c)2

  • Effect of the GEA on GAGEA effect is small at this (parallel) kinematicsM.S.

  • Results at CQ-Kinem.agreement is quite good.Perpendicular Kinem.Q2=1.78(GeV/c) =0.525(GeV)

  • Effect of the GEA on GA30%effect on conventional Glauber

  • Multiple Scattering ContributionsRef: GEA Effect at higher pm

  • Comment on the choice of Z-axiscorrect choice of z-axis is important!

  • 5. Finite Formation Time Effect on 4He(e,ep)3H Reactionat High Q2 regionM.A.Braun et al.Phys. Rev. C62, 034606(2000)One must take into account the effect of p*Finite Formation Time (FFT) effect

  • Effect of the FFTFFT effect is small at this regionQ2=1.78(GeV/c)2

  • FFT effect becomes sizablePara. Kinem. at Q2=5(GeV/c)2 ,x=1

  • dip appears!Q2-dep. -Parallel Kinem.-at Q2=10(GeV/c)2

  • Glauber + FFTFFT effect is prominent!large Q2-dep.Q2-dep. -Parallel Kinem.-Glauber +FFT

  • Q2-dep. -Parallel Kinem.-Glauber Glauberlittle Q2-dep

  • Pab-dep. of tottot almost const. at high PLab

  • 6. SummaryWithout any free parameter, the data of 3He(e,ep)2H(pn) and 4He(e,ep)3H were well reproduced by the Glauber/GEA calculation.This means that in the energy-momentum range covered by the data, FSI (propagation of knocked out proton in medium) can be described within the GA/GEA.In the case of 3He(e,ep)2H(pn), the effect of GEA on GA (conventional Glauber approximaion) is rather small at considered kinematics. In the 4He(e,ep)3H reaction it gives 30 % effect at (JLab E97-111) CQ2 kinematics.1. Ability of the GA/GEA to describe the FSI

  • Summary -2In the 3He(e,ep)2H reaction, the pm-dep. of dexp exhibits different slopes (pm800(MeV/c) .

    2. Multiple Scattering Feature of the GA/GEA

  • Summary -3FFT effects are small at JLab E97-111 CQ2 Kinematics (Q2=1.78(GeV/c)2)We extend theoretical calculation to higher Q2 region and found..FSI is almost diminished by FFT effect at aroundQ210(GeV/c)2 region.FFT effect will be appeared as a prominent Q2-dep. of nD(pm) around dip region (pm 2.2(fm-1)).

    3. FFT Effect on 4He(e,ep)3H

  • Future DevelopmentsCalculations without factorization are now in progress.Under such calculation we will derive each nuclear response functions: RL,RT,RTT,RTL Then we will calculate ATL(left-right asymmetry) , which is consider to be sensitive to the theoretical prescription.

  • Results of 3He(e,ep) pnC. Ciofi degli Atti, L.P. Kaptari, Phys. Rev. C71, 024005 (2005)C. Marchand et al., Phys. Rev. Lett. 60(1988) 1703

  • ATMS Few-body Wave FunctionATMS method M. Sakai et al., Prog.Theor.Phys.Suppl.56(1974)108. H. Morita et al., Prog.Theor.Phys.78(1987)1117. w(ij): on-shell correlation functionu(ij) : off-shell correlation function

  • Introduction of the State dependence ^ ^ ^ ^ w(ij)=1wS(ij)P1E(ij)+ 3wS(ij)P3E(ij) + 3wD(ij)SijP3E(ij)

    Euler-Lagrange eq. u[ - E ] = 0 u:performed respect to {w,u}

    The radial form of {w(r),.u(r)} are directly determined from Euler-Lagrange eq. Results VNN(r): Reid Soft core V8 model potential =-21.2 MeV, 1/2=1.57 fm PS=87.94%, PS=0.24%, PD=11.82%

  • Experimental Data JLab E97-111 B. Reitz et al., Eur. Phys. J. A S19(2004) 165 Py2 KinematicsParallel Kinematics CQ2 KinematicsPerpendicular Kinematics

    Kinem.Ee(GeV)(GeV)q(Gev/c)Q2(GeV/c)2pm(MeV/c)CQ23.9520.5251.431.78395CQ23.9520.5251.431.78446CQ23.9520.5251.431.78495PY2a3.170.5371.090.90824PY2b3.170.6531.140.868124PY2c3.170.7981.210.818223PY2d3.170.9851.310.753323PY2e3.171.2391.480.666423PY2f3.171.4811.670.582493

  • Multiple Scattering ContributionsSingle rescattering contribution is dominant!Double starts to contribute!

  • Multiple Scattering Contributions 2

  • Note: Choice of z-axisq = p1 + pmMomentum transferMom. of ejected protonMissing Mom.However, in the Glauber theory z-axis should be the direction of the incident particle p1 directionIn many cases q-direction is taken to be z-axis assuming q >> pmThe deviation by will make some different results especially at perpendicular kinematics (q pm)

  • GEA Effect at higher PmDiscussion data 1

  • GEA Effect on the Single Rescatt.Discussion data 2

  • GEA Effect on the Double Rescatt.Discussion data 3

  • GEA Effect on the Triple Rescatt.Discussion data 4Full Calculation

  • 5. Formulation of FFT effectM.A.Braun et al.Phys. Rev. C62, 034606(2000).Virtuality of particle 1m:Nucleon MassBjorken variable

  • Scattering Amplitudef :on-shall AmplitudeF(v)F.F. for Vertuality dep.F(0)=1Scattering MatrixVertuality dep.J(z) (Virtuality dep. Factor)

  • Here if we take

    thenFormation lengthIn the following calculation(Braun et al.)M2Average Virtuality

  • z-axis effects Ref) 2H(e,ep)n caseCalculation by L.Kaptari

  • Para. Kinem. at Q2=2(GeV/c)2 ,x=1Dip masked by FSI

  • dip apparent!Q2-dep. -Parallel Kinem.-at Q2=20(GeV/c)2

  • ATL within Factorization Calc.Factorization calculation can not reproduce these structures.Calculations with no factorization are now in progress.M.M. Rvachev et al., Phys.Rev.Lett. 94 (2005) 192302Data