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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 - PowerPoint PPT Presentation
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G. Smirnov INFN, Milano, 15.12.05 1
Relating F2p(x), F2
n(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
G. Smirnov INFN, Milano, 15.12.05 2
Motivation
Due to absence of free neutron targets the d quark distribution is poorely constrained beyond x about 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 F2
n(x) , in particular in the region close to x = 1.
G. Smirnov INFN, Milano, 15.12.05 3
Options for extracting neutron structure functions from deuteron data:
1. Naive assumption: 2F2D = F2
p + 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 theamplitude of modification, but never the form of x dependence
Introduction
G. Smirnov INFN, Milano, 15.12.05 4
EMC effect (BCDMS, EMC, SLAC)
Data: BCDMS, SLAC Blue line: Burov,
Molochkov and Smirnov
G. Smirnov INFN, Milano, 15.12.05 5
Quantitative description of the EMC effect
G. Smirnov INFN, Milano, 15.12.05 6
Evolution of the nucleon structure in two stages
G. Smirnov 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
G. Smirnov INFN, Milano, 15.12.05 8
Bodek-Yang correction is equivalent to assumption of the same internucleon spacing in the deuteron and heavy nuclei, which results in two errors:
(1) Wrong magnitude of the EMC effect
(2) Wrong x-dependence
F2n(x) can not be evaluated from the data collected on medium and
heavy nuclear targets untill the realtion between
F2n(x), F2
p(x) and F2D(x)
Is known.
Lessons from the EMC effect studies
G. Smirnov INFN, Milano, 15.12.05 9
We suggest an approach of extracting F2n(x) from the data collected in
deep inelastic scattering experiments, which relies on relativistic theoretical description of F2
D(x) and well defined assumptions on the high x asymptotics for the ratio F2
n(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
Practical way of finding F2n(x)
G. Smirnov INFN, Milano, 15.12.05 10
Hadronic Tensor ( bound states )
G. Smirnov 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
G. Smirnov INFN, Milano, 15.12.05 12
The covariant Bethe-Salpeter formalism provides the integral equation
relating F2p, F2
n and F2D.
It is solved iteratively by using input structure functions
F2p and F2
D
Additionally, this allows extrapolation of F2D into a wide range of x and Q2
G. Smirnov INFN, Milano, 15.12.05 13
Deuteron structure function
(4)
EMC-effect cannot be explained without changing the nucleon
structure in a nucleus –
4D – radius of a bound nucleon changes
Second term results from the Fermi motion along time axis
G. Smirnov 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.
G. Smirnov INFN, Milano, 15.12.05 15
Structure Functions of Light Nuclei:A = 3
G. Smirnov INFN, Milano, 15.12.05 16
Structure Functions of Light Nuclei:A = 4
G. Smirnov INFN, Milano, 15.12.05 17
Nuclear effects in 4He
The ratio of the helium to deuteron structure functions as callculated by
Burov, Molochkov and Smirnov is shown by the solid line
« log » scale « lin» scale
G. Smirnov INFN, Milano, 15.12.05 18
Missing Data on the Structure Functions :
A = 3
3H and 3He
G. Smirnov INFN, Milano, 15.12.05 19
Relating F2p , F2
n and F2d
Use of SMC fit for F2p and its modification
Modification suggested by BMST ( x 1 ) : 2 2 + (3 – 2 ) x15
Remember about derivative !
G. Smirnov INFN, Milano, 15.12.05 20
Assumptions
Main assumption: F2p(x) is known in the range 3.5 10– 5 < x < 0.85
G. Smirnov 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 »
G. Smirnov 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 »
G. Smirnov 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.
G. Smirnov INFN, Milano, 15.12.05 24
Comparison with the naive approximation for the F2
n(x) evaluation
Naive approach:
F2n = 2 F2
D – 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
G. Smirnov 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) / F2
p(x) at x = 1
G. Smirnov INFN, Milano, 15.12.05 26
Conclusions
Theoretically justified and fully consistent procedure for extracting F2n(x) in
the kinematic range 10 –3 < x < 1 under three different assumptions on F2
n(x) / F2p(x) at x = 1 is proposed.
Increase in experimental accuracy in measurements of F2p(x) and F2
D(x) in the range 0.6 < x < 0.8 by factor of two will be sufficient for verification of models suggested for the evaluation of the d/u ratio at x = 1 .
Technique relies on a good approximation of F2D(x) which is not sensitive to
different high x limits of the neutron structure function.
This also means that F2D(x) measured by already completed DIS experiments
( x < 0.9 ) can be described without introducing nonbaryonic degrees of freedom. The interval which remains unmeasured can in principle accommodate dibaryon states or some other exotica.