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G. Smirnov

Relating F 2 p ( x ), F 2 n ( x ) and F 2 D ( x ) Using a Relativistic Description of the Deuteron Structure. G. Smirnov Joint Institute for Nuclear Research, Dubna, Russia and

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G. Smirnov

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  1. Relating F2p(x), F2n(x) and F2D(x) Using a Relativistic Description of the Deuteron Structure G. Smirnov Joint Institute for Nuclear Research, Dubna, Russia and Université Blaise Pascal, Clermont-Ferrand, France ITEMS: 1. Changes of the nucleon structure in nuclei as a function of A 2. 4D structure of bound states (lightest nuclei: D,3H, 3He and 4He) 3. Determination of the neutron structure function from experiments INFN, Milano, 15.12.05

  2. Motivation Due to absence of free neutron targets the d quark distribution is poorely constrained beyond xabout 0.6. The isoscalar and mirror nuclei have to be used as the « neutron target ». Also an advantage owing to the access to higher x. Discussions of the « nuclear effects » in evaluating F2n(x) from nuclear targets data often result in compromises and simplifications that distort considerably F2n(x) , in particular in the region close to x = 1. INFN, Milano, 15.12.05

  3. Introduction • Options for extracting neutron structure functions from deuteron data: • Naive assumption: 2F2D = F2p + F2n • 2. Theoretical models • 3. Extrapolation of the EMC effect from heavy nuclei to A = 2 • (Bodek - Yang correction) Most dangerous is option (3) : one can approximately esimate the amplitude of modification, but never the form of x dependence INFN, Milano, 15.12.05

  4. EMC effect (BCDMS, EMC, SLAC) • Data: BCDMS, SLAC • Blue line: Burov, Molochkov and Smirnov INFN, Milano, 15.12.05

  5. Quantitative description of the EMC effect INFN, Milano, 15.12.05

  6. Evolution of the nucleon structure in two stages INFN, Milano, 15.12.05

  7. Topology of the interaction ( 1 – x3 )~mean spacing of nucleons inside a nucleus A 6 : • Distributions of quarks are not sensitive to a nuclear structure • 3 nucleons only can be seen by virtual photon in the nucleus « in one shot »  3He (3H) topology x3 INFN, Milano, 15.12.05

  8. Lessons from the EMC effect studies F2n(x) can not be evaluated from the data collected on medium and heavy nuclear targets untill the realtion between F2n(x), F2p(x) and F2D(x) Is known. • Bodek-Yang correction is equivalent to assumption of the same internucleon spacing in the deuteron and heavy nuclei, which results in two errors: • Wrong magnitude of the EMC effect • Wrong x-dependence INFN, Milano, 15.12.05

  9. Practical way of findingF2n(x) We suggest an approach of extracting F2n(x) from the data collected in deep inelastic scattering experiments, which relies on relativistic theoretical description of F2D(x) and well defined assumptions on the high x asymptotics for the ratio F2n(x) / F2p(x). It is based on the covariant Bethe-Salpeter formalism and allows to express the hadronic part of the nuclear deep inelastic amplitude W in terms of the off-mass-shell nucleon and antinucleon amplitudes. Work in collaboration with V.V. Burov, A.V Molochkov and H. Toki INFN, Milano, 15.12.05

  10. Hadronic Tensor ( bound states ) INFN, Milano, 15.12.05

  11. Diagrams involved in evaluating of the forward Compton amplitude TA W A(P,q) = 1/2 ImT A(P,q) Impulse approximation Interaction correction to G 4   contribution of 2-nucleon propagators INFN, Milano, 15.12.05

  12. The covariant Bethe-Salpeter formalism provides the integral equation relating F2p, F2n and F2D. It is solved iteratively by using input structure functions F2p and F2D Additionally, this allows extrapolation of F2D into a wide range of x and Q2 INFN, Milano, 15.12.05

  13. Deuteron structure function (4) Second term results from the Fermi motion alongtime axis EMC-effect cannot be explained without changing the nucleon structure in a nucleus – 4D – radius of a bound nucleon changes INFN, Milano, 15.12.05

  14. Application of the Bethe-Salpeter formalism to the DIS of leptons on the lightest nuclei • BS amplitude for Compton scattering on the deuteron: • V.V. Burov, A.V. Molochkov, G.I. Smirnov and H. Toki: Phys. Lett. B587 (2004) 175. • V.V.Burov and A.V.Molochkov: Nucl. Phys. A637 (1998) 31. • BS amplitude for Compton scattering on 3H, 3He and 4He: • V.V. Burov, A.V. Molochkov and G.I. Smirnov: Phys. Lett. B466 (1999) 1. • S.G. Bondarenko, V.V. Burov, A.V. Molochkov, G.I. Smirnov and H. Toki : J. Prog. Part. Nucl. Phys. 48 (2002) 449—535. INFN, Milano, 15.12.05

  15. Structure Functions of Light Nuclei:A = 3 INFN, Milano, 15.12.05

  16. Structure Functions of Light Nuclei:A = 4 INFN, Milano, 15.12.05

  17. Nuclear effects in 4He « log » scale « lin» scale The ratio of the helium to deuteron structure functions as callculated by Burov, Molochkov and Smirnov is shown by the solid line INFN, Milano, 15.12.05

  18. Missing Data on the Structure Functions :A = 33Hand3He INFN, Milano, 15.12.05

  19. Relating F2p , F2n and F2dUse of SMC fit for F2p and its modification Remember about derivative ! Modification suggested by BMST ( x  1 ) : 22 + (3 – 2 ) x15 INFN, Milano, 15.12.05

  20. Assumptions Main assumption:F2p(x)is known in the range 3.5 10– 5 < x < 0.85 INFN, Milano, 15.12.05

  21. Deuteron structure function compared with data from SLAC and NMC experiments (low x region) Bjorken x Q 2 (GeV 2 ) F2D(x) approximated with Eq. (4) in the range 10-3 < x < 0.6 with constraints listed in « Assumptions » INFN, Milano, 15.12.05

  22. Deuteron structure function compared with data from SLAC and NMC experiments (high x region) Bjorken x Q 2 (GeV 2 ) F2D(x) approximated with Eq. (4) in the range 10-3 < x < 0.6 with constraints listed in « Assumptions » INFN, Milano, 15.12.05

  23. Results representing ratios of structure functionsversus Bjorken x Squares and triangles — results of NMC and SLAC, respectively, obtained in naive approach. Squares and triangles — results of NMC and SLAC, respectively. INFN, Milano, 15.12.05

  24. Comparison with the naive approximation for the F2n(x) evaluation Naive approach: F2n = 2 F2D – F2p The ratio is virtually 1.0 below x = 0.7 due to cancellation of contributions from 3D Fermi motion and the Fermi motion along time axis INFN, Milano, 15.12.05

  25. Ratio of the neutron and proton structure functions Three values of a2 correspond to three different assumptions on F2n(x) / F2p(x) at x = 1 INFN, Milano, 15.12.05

  26. Conclusions Theoretically justified and fully consistentprocedure for extracting F2n(x)in thekinematic range 10 –3 < x < 1 under three different assumptionson F2n(x)/F2p(x)at x = 1 is proposed. Increase in experimentalaccuracy in measurements of F2p(x) and F2D(x) in therange 0.6 < x <0.8 by factor of twowill be sufficient forverification of models suggested for the evaluation of the d/uratio at x=1 . Technique relies ona good approximation of F2D(x) which isnot sensitive to different high x limits of the neutronstructure function. This also means that F2D(x) measuredby already completed DIS experiments ( x < 0.9 ) can bedescribed without introducing nonbaryonic degrees of freedom.The interval which remains unmeasured can in principle accommodatedibaryon states or some other exotica. INFN, Milano, 15.12.05

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