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G. Smirnov INFN, Milano, 15.12.05 1 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 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, 3 H, 3 He and 4 He) 3. Determination of the neutron structure function from experiments

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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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Page 1: G. Smirnov

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

Page 2: G. Smirnov

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.

Page 3: G. Smirnov

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

Page 4: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 4

EMC effect (BCDMS, EMC, SLAC)

Data: BCDMS, SLAC Blue line: Burov,

Molochkov and Smirnov

Page 5: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 5

Quantitative description of the EMC effect

Page 6: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 6

Evolution of the nucleon structure in two stages

Page 7: G. Smirnov

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

Page 8: G. Smirnov

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

Page 9: G. Smirnov

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)

Page 10: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 10

Hadronic Tensor ( bound states )

Page 11: G. Smirnov

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

Page 12: G. Smirnov

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

Page 13: G. Smirnov

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

Page 14: G. Smirnov

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.

Page 15: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 15

Structure Functions of Light Nuclei:A = 3

Page 16: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 16

Structure Functions of Light Nuclei:A = 4

Page 17: G. Smirnov

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

Page 18: G. Smirnov

G. Smirnov INFN, Milano, 15.12.05 18

Missing Data on the Structure Functions :

A = 3

3H and 3He

Page 19: G. Smirnov

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 !

Page 20: G. Smirnov

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

Page 21: G. Smirnov

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 »

Page 22: G. Smirnov

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 »

Page 23: G. Smirnov

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.

Page 24: G. Smirnov

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

Page 25: G. Smirnov

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

Page 26: G. Smirnov

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.