The nuclear EMC effect in the deep-inelastic and the resonance - - PowerPoint PPT Presentation

The nuclear EMC effect in the deep-inelastic and the resonance region

Sergey Kulagin

Institute for Nuclear Research of the Russian Academy of Sciences, Moscow Talk at the

XVth International Seminar on Electromagnetic Interactions of Nuclei EMIN-2018 Moscow, Russia October 8, 2018

Outline

◮ Data overview on the nuclear EMC effect in deep-inelastic scattering region. ◮ Understanding and modelling nuclear corrections

◮ Sketch of basic mechanisms of nuclear DIS in different kinematic regions. ◮ Brief review of our efforts to build a quantitative model of nuclear structure

functions.

◮ Nucleon and nuclear structure functions and nuclear ratios in the resonance

and transition region and comparison with JLab data on D/(p + n) BONuS,

2015 and 3He/D and 3He/(D + p) Hall C, 2009 ◮ Summary/Conclusions

Kulagin (INR) 2 / 37

Data summary on nuclear effects on the parton level

◮ Nuclear ratios ℛ(A/B) = σA(x, Q2)/σB(x, Q2) or F A 2 /F B 2 from DIS

experiments

◮ Data for nuclear targets from 2H to 208Pb

◮ Fixed-target experiments with e/µ: ◮ Muon beam at CERN (EMC, BCDMS, NMC) and FNAL (E665). ◮ Electron beam at SLAC (E139, E140), HERA (HERMES), JLab (E03-103). ◮ Kinematics and statistics:

Data covers the region 10−4 < x < 1.5 and 0 < Q2 < 150 GeV2. About 800 data points for the nuclear ratios ℛ(A/B) with Q2 > 1 GeV2.

◮ Nuclear effects for antiquarks have been probed by Drell-Yan experiments at

FNAL (E772, E866).

◮ Nuclear cross sections from high-energy measurements with neutrino BEBC

(2H and 20Ne), NOMAD (12C and 56Fe) CDHS, CCFR and NuTeV (56Fe) CHORUS (207Pb). Nuclear cross section ratios Fe/CH and Fe/CH from MINERvA in the region of low Q2.

Kulagin (INR) 3 / 37

Nuclear ratios from DIS experiments

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 4 2He

F2(A)/F2(D)

SLAC E139 CERN NMC JLab E03103 7 3Li 9 4Be SLAC E139 (Be) CERN NMC (Li) JLab E03103 (Be) 12 6C 14 7N SLAC E139 (C) CERN NMC (C) FNAL E665 (C) DESY HERMES (N) JLab E03103 (C) 27 13Al SLAC E139 CERN NMC (Al/C)*(C/D) 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 10-4 10-3 10-2 0.1 0.3 0.5 0.7 0.9 40 20Ca

F2(A)/F2(D)

Bjorken x SLAC E139 CERN NMC FNAL E665 10-3 10-2 0.1 0.3 0.5 0.7 0.9 56 26Fe 63 29Cu 84 36Kr Bjorken x SLAC E139 (Fe) CERN EMC (Cu) CERN BCDMS (Fe) DESY HERMES (Kr) 10-3 10-2 0.1 0.3 0.5 0.7 0.9 108 47Ag 119 50Sn 131 54Xe Bjorken x SLAC E139 (Ag) CERN NMC (Sn/C)*(C/D) FNAL E665 (Xe) 10-3 10-2 0.1 0.3 0.5 0.7 0.9 1 197 79Au 208 82Pb Bjorken x SLAC E139 (Au) CERN NMC (Pb/C)*(C/D) FNAL E665 (Pb)

Kulagin (INR) 4 / 37

HERMES and JLab measurements on 3He

0.8 1 1.2 1.4 1.6 1.8 0.2 0.4 0.6 0.8 1 W < 1.8 GeV Cross section ratio Bjorken x JLab E03-103 3He/(2H+p) [D.Gaskell, private communication] JLab E03-103 3Heis/2H [PRL103(2009)202301] DESY HERMES 3Heis/2H [PLB475(2000)386;567(2003)339(E)]

0.94 0.96 0.98 1 1.02 0.2 0.25 0.3 0.35 0.4 0.45 0.5

3% HERMES-JLab data offset

Kulagin (INR) 5 / 37

SLAC E139 and JLab BONUS results on 2H

0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 F2D / (F2p + F2n) Bjorken x JLab BONuS, W > 1.8 GeV JLab BONuS, 1.2<W<1.8 GeV SLAC E139 0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.3 0.4 0.5 0.6 0.7 0.8 F2n/F2D Bjorken x BONuS data W > 1.8 GeV BONuS data 1.4 < W < 1.8 GeV

◮ SLAC E139 [PRD49(1994)4348] obtains RD = F D

2 /(F p 2 + F n 2 ) by extrapolating data

• n RA = F A

2 /F D 2

with A ≥ 4 assuming RA − 1 scales as nuclear density.

◮ BONuS [PRC92(2015)015211] obtains RD from a direct measurement of F n

2 /F D 2

[PRC89(2014)045206] using world data on F D

2 /F p 2 .

Kulagin (INR) 6 / 37

Understanding and modelling the nuclear corrections

Kulagin (INR) 7 / 37

Why nuclear corrections survive at DIS?

Space-time scales in DIS Wµν = ∫︂ d4x exp(iq · x)⟨p|[Jµ(x), Jν(0)]|p⟩ q · x = q0t − |q|z = q0t − √︂ q2

0 + Q2z ≃ q0(t − z) − Q2

2q0 z

◮ DIS proceeds near the light cone: |t − z| ∼ 1/q0 and t2 − z2 ∼ Q−2. ◮ In the TARGET REST frame the characteristic time and longitudinal distance are

NOT small at all: t ∼ z ∼ 2q0/Q2 = 1/MxBj. DIS proceeds at the distance ∼ 1 Fm at xBj ∼ 0.2 and at the distance ∼ 20 Fm at xBj ∼ 0.01.

◮ Two different regions in nuclei from comparison of coherence length (Ioffe time)

L = 1/MxBj with average distance between bound nucleons rNN:

◮ L < rNN (or x > 0.2) ⇒ Nuclear DIS ≈ incoherent sum of contributions

from bound nucleons. Nuclear corrections ∼ EL and ∼ |p|2L2 where E(p) typical energy (momentum) in the nuclear ground state.

◮ L ≫ rNN (or x ≪ 0.2) ⇒ Coherent effects of interactions with a few

nucleons are important.

Kulagin (INR) 8 / 37

Incoherent nuclear scattering

A good starting point is incoherent scattering off bound protons and neutrons F A

2 =

∫︂ d4p K (𝒬pF p

2 + 𝒬nF n 2 )

◮ The four-momentum of the bound proton (neutron) p = (M + ε, p) ◮ 𝒬p,n(ε, p) the proton (neutron) nuclear spectral function, which is normalized to

the nucleon number ∫︁ dεdp𝒬p = Z and describes probability to find a bound nucleon with momentum p and energy p0 = M + ε.

◮ The bound nucleon structure functions depend on 3 independent variables

F p,n

2

= F p,n

2

(x′, p2, Q2), x′ = Q2/2p · q is the Bjorken variable of a nucleon with four-momentum p. Note the nucleon virtuality p2 is additional variable for off-shell nucleon.

◮ Kinematical factor K = (1 + pz/M)

(︁ 1 + 𝒫(p2/|q|2) )︁ .

Kulagin (INR) 9 / 37

Nuclear spectral function

The nuclear spectral function describes probability to find a bound nucleon with momentum p and energy p0 = M + ε: 𝒬(ε, p) = ∫︂ dt e−iεt⟨ψ†(p, t)ψ(p, 0)⟩ = ∑︂

i

|⟨(A − 1)i, −p|ψ(0)|A⟩|2 2πδ (︁ ε + EA−1

i

(p) − EA )︁

◮ The sum runs over all possible states of the spectrum of A − 1 residual

system.

◮ The nuclear spectral function determines the rate of nucleon removal

reactions such as (e, e′p). For low separation energies and momenta, |ε| < 50 MeV, p < 250 MeV/c, the observed spectrum is dominated by bound states A − 1 similar predicted by the mean-field model.

Kulagin (INR) 10 / 37

Sketch of the mean-field picture

In the the mean-field model the bound states of A − 1 nucleus are described by the one-particle wave functions φλ of the energy levels λ. The spectral function is given by the sum over the occupied levels with the occupied number nλ: 𝒬MF(ε, p) = ∑︂

λ<λF

nλ|φλ(p)|2δ(ε − ελ)

◮ Due to interaction effects the δ-peaks corresponding to the single-particle

levels acquire a finite width (fragmentation of deep-hole states).

◮ High-energy and high-momentum components of nuclear spectrum can not

be described in the mean-field model and driven by short-range nucleon-nucleon correlation effects in the nuclear ground state as witnessed by numerous studies.

Kulagin (INR) 11 / 37

High-momentum part

◮ As nuclear excitation energy becomes higher the mean-field model becomes

less accurate. High-energy and high-momentum components of nuclear spectrum can not be described in the mean-field model and driven by correlation effects in nuclear ground state as witnessed by numerous studies.

◮ The corresponding contribution to the spectral function is driven by (A − 1)*

excited states with one or more nucleons in the continuum. Assuming the dominance of configurations with a correlated nucleon-nucleon pair and remaining A−2 nucleons moving with low center-of-mass momentum we have |A−1, −p⟩ ≈ ψ†(p1)|(A−2)*, p2⟩δ(p1 + p2 + p).

Kulagin (INR) 12 / 37

The matrix element can thus be given in terms of the wave function of the nucleon-nucleon pair embeded into nuclear environment. We assume factorization into relative and center-of-mass motion of the pair ⟨(A−2)*, p2 |ψ(p1)ψ(p)| A⟩ ≈ C2ψrel(k)ψA−2

CM (pCM)δ(p1 + p2 + p),

where ψrel is the wave function of the relative motion in the nucleon-nucleon pair with relative momentum k = (p − p1)/2 and ψCM is the wave function of center-of-mass (CM) motion of the pair in the field of A−2 nucleons, pCM = p1 + p. The factor C2 describes the weight of the two-nucleon correlated part in the full spectral function. 𝒬cor(ε, p) ≈ ncor(p) ⟨ δ (︃ ε + (p + pA−2)2 2M + EA−2 − EA )︃⟩

A−2

Kulagin (INR) 13 / 37

The two-component model of the spectral function

In what follows we combine the mean-field together with SRC contributions and consider a two-component model Ciofi degli Atti & Simula, 1995 S.K. & Sidorov, 2000 S.K. &

Petti, 2004

𝒬 = 𝒬MF + 𝒬cor We assume that the normalization is shared between the MF and the correlated parts as 0.8 to 0.2 for the nuclei A ≥ 4 [for 208Pb 0.75 to 0.25] following the

• bservations on occupation of deeply-bound proton levels NIKHEF 1990s, 2001.

Kulagin (INR) 14 / 37

Average separation and kinetic energies

Average separation ⟨ε⟩ and kinetic ⟨T⟩ energies are related by the Koltun sum rule (exact relation for nonrelativistic system with two-body forces) ⟨ε⟩ + ⟨T⟩ = 2εB, where εB = EA

0 /A is nuclear binding energy per bound nucleon

⟨ε⟩ = A−1 ∫︂ [dp]𝒬(ε, p)ε, ⟨T⟩ = A−1 ∫︂ [dp]𝒬(ε, p) p2 2M .

Kulagin (INR) 15 / 37

Nuclear binding, separation and kinetic energies

10 20 30 40 50 60 70 1 10 100 MeV A Nuclear energies B E T

Kulagin (INR) 16 / 37

EMC effect in impulse approximation

◮ Impulse approximation: F2(x′, Q2, p2) = F2(x′, Q2, M 2) ◮ Fermi motion leads to a rise at

large Bjorken x

◮ Nuclear binding correction is

important and results in a “dip” at x ∼ 0.6 − 0.7

Akulinichev,Vagradov & S.K., 1984. ◮ However, even realistic nuclear

spectral function fails to accurately explain the slope and the position of the

• minimum. Therefore, the

impulse approximation should be corrected for a number of effects.

0.8 0.9 1 1.1 1.2 1.3 1.4 0.1 0.3 0.5 0.7 0.9 (F2A/A) / (F2D/2) Bjorken x

56Fe SLAC E139 56Fe CERN BCDMS 63Cu CERN EMC

Fermi gas model, no binding Q2=10 GeV2 Mean-field model Mean field + SRC Mean field + SRC+OS Mean field + SRC+OS+MEC

Kulagin (INR) 17 / 37

Nucleon off-shell effect

Bound nucleons are off-mass-shell, p2 < M 2. The treatment of p2 dependence can greatly be simplified in the vicinity of the mass shell. If the virtuality parameter v = (p2 − M 2)/M 2 is small (e.g. average virtuality v ∼ −0.15 for 56Fe) then expand q(x, Q2, p2) in series in v F N

2 (x, Q2, p2) ≈ F N 2 (x, Q2)

(︁ 1 + δf(x, Q2) v )︁

◮ δf(x, Q2) is a special structure function describing the modification of the

• ff-shell nucleon PDFs in the vicinity of the mass shell.

◮ Off-shell correction is closely related to modification of the nucleon size in

nuclear environment S.K. & R.Petti, 2004.

Kulagin (INR) 18 / 37

Nuclear meson-exchange current effect (MEC)

Leptons can scatter on nuclear meson field which mediate interaction between bound nucleons. This process generate a MEC correction to nuclear sea quark distribution δF MEC

2

(x, Q2) = ∫︂

x

dyfπ/A(y)F π

2 (x

y , Q2)

◮ Contribution from nuclear pions (mesons) is important to balance nuclear

light-cone momentum ⟨y⟩π + ⟨y⟩N = 1.

◮ The nuclear pion distribution function is localized in a region

y < pF /M ∼ 0.3. For this reason the MEC correction to nuclear (anti)quark distributions is localized at x < 0.3.

◮ The magnitude of the correction is driven by average number of “nuclear pion

excess” nπ = ∫︁ dy fπ/A(y) and nπ/A ∼ 0.1 for a heavy nucleus like 56Fe.

Kulagin (INR) 19 / 37

Nuclear shadowing

Coherent nuclear correction is due to propagation of intermediate state γ* → h in nuclear environment, which can be described in the multiple scattering theory

Glauber, Gribov 1970s.

δF coh

2A

F2N = Im δ𝒝 Im a δ𝒝 = δ𝒝(2) + δ𝒝(3) + . . . δ𝒝(2) = ia2 ∫︂

z1<z2

d2b dz1dz2 ρ(b, z1)ρ(b, z2) ei z1−z2

L

◮ ρ(r) is the nuclear number density,

∫︁ d3rρ(r) = A

◮ a = σ 2 (i + α) is the (effective) forward scattering amplitude of intermediate

state h off the nucleon

◮ L is the coherence length of intermediate state which accounts finite life time

• f intermediate state, 1/L = Mx(1 + m2

h/Q2). Its presence suppresses the

coherence effect in the region of large x.

Kulagin (INR) 20 / 37

Modelling the nuclear corrections

Assemble everything together and confront model to data

S.K. & R.Petti, NPA765(2006)126; PRC82(2010)054614; PRC90(2014)045204

F A

2 = Z ⟨F p 2 ⟩ + N ⟨F n 2 ⟩ + δF MEC 2

+ δF coh

2

Strategy of the analysis:

◮ Compute the proton and neutron structure functions in terms of free proton

PDF with relevant perturbative QCD corrections, TMC, as well as HT correction.

◮ Using F p,n 2

compute nuclear structure functions/cross sections with accurate treatment of nuclear spectral function effects (Fermi-motion and nuclear binding), MEC and nuclear shadowing correction.

◮ Treat the off-shell function δf(x) and effective amplitude a as unknown and

parametrize them. Study the data on the nuclear DIS in terms of the ratios F A

2 /F B 2 and determine δf(x) together with the amplitude a from data. ◮ Use the normalization conditions and the DIS sum rules (GLS, Adler) to

determine the amplitude a (responsible for nuclear shadowing) in the region

• f high Q2, which is not constrained by data.

◮ Verify the model by comparing the calculations with data not used in analysis.

Kulagin (INR) 21 / 37

Results

◮ The x, Q2 and A dependencies of the nuclear ratios are reproduced for all

studied nuclei (4He to 208Pb) in a 4-parameter fit with χ2/d.o.f. = 459/556.

◮ Parameters of the off-shell function δf and effective amplitude aT are

determined with a good accuracy. For detailed discussion see S.K. & R. Petti, Nucl.Phys.A765(2006)126.

Kulagin (INR) 22 / 37

Determination of the off-shell function δf(x)

◮ Analysis of heavy target to deuterium

ratios with a model δf(x) = CN(x−x1)(x−x0)(1+x0−x) (gray area)

◮ Global QCD analysis using deuteron

data and a model δf(x) = Ax2 + Bx + C (red) Alekhin,

S.K., Petti, 2017. Results are consistent

with S.K. & R.Petti, 2006.

◮ The function δf(x) provides a measure of the modification of the quark

distributions in a bound nucleon.

◮ The slope of δf(x) in a single-scale nucleon model is related to the change of the

radius of the nucleon in the nuclear environment S.K. & R.Petti, 2006. The observed slope suggests an increase in the bound nucleon radius in the iron by about 10% and in the deuteron by about 2%.

Kulagin (INR) 23 / 37

Determination of effective cross section

◮ The monopole form σ = σ0/(1 + Q2/Q2

0) for the

effective cross section of C-even q + ¯ q combination provides a good fit to data on DIS nuclear shadowing for Q2 < 15 GeV2 with σ0 = 27 mb and Q2

0 = 1.43 ± 0.06 ± 0.195 GeV2.

Note σ0 is fixed from Q2 → 0 limit by the vector meson dominance model. Also we assume Re a/ Im a for C-even amplitude to be given by VMD at all energies.

0.1 1 10 1 10 100 Cross section, mb Q2, GeV2

• Phen. cross section
• Eff. cross section

◮ Nuclear shadowing correction for the C-odd valence distribution q − ¯

q is also driven by same cross section σ. Note, however, important interference effect between the phases of C-even and C-odd effective amplitude.

◮ The cross section at high Q2 > 15 GeV2 is not constrained by data. It is possible to

evaluate σ in this region using the the normalization condition. Requiring exact cancellation between the off-shell and the shadowing correction in the normalization we have: ∫︂ 1 dx (︂ ⟨v⟩ qval(x, Q2)δf(x) + δqcoh

val (x, Q2)

)︂ = 0 with ⟨v⟩ = ⟨︁ p2 − M2⟩︁ /M2 the average nucleon virtuality. Numeric solution to this equation is shown by dotted curve.

Kulagin (INR) 24 / 37

Summary of results on the nuclear ratios F A

2 /F D 2

0.7 0.8 0.9 1 1.1 1.2 1.3 F2

is(A)/F2(D)

4 2He

SLAC E139 CERN NMC KP model

7 3Li 9 4Be

SLAC E139 CERN NMC (7

3Li)

KP model 0.7 0.8 0.9 1 1.1 1.2 1.3 0.0001 0.001 0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 F2

is(A)/F2(D)

Bjorken x

12 6C

SLAC E139 CERN NMC FNAL E665 KP model 0.0001 0.001 0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Bjorken x

27 13Al

SLAC E139 CERN NMC (Al/C)*(C/D) KP model

Kulagin (INR) 25 / 37

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 F2

is(A)/F2(D)

40 20Ca

SLAC E139 CERN NMC FNAL E665 KP model

56 26Fe 63 29Cu

SLAC E139 CERN EMC (63

29Cu)

CERN BCDMS KP model 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0.001 0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 F2

is(A)/F2(D)

Bjorken x

108 47Ag 119 50Sn 131 54Xe

SLAC E139 CERN NMC (119

50Sn/C)*(C/D)

FNAL E665 (131

54Xe)

KP model 0.001 0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Bjorken x

197 79Au 208 82Pb

SLAC E139 CERN NMC (Pb/C)*(C/D) FNAL E665 (208

82Pb)

KP model

Kulagin (INR) 26 / 37

Verification with recent JLab data (not a fit)

0.9 1 1.1 1.2

σ12C/σ2H

KP model

0.9 1 1.1 1.2

σ9Be/σ2H

KP model (IA)

0.8 0.9 1 1.1 1.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

σ4He/σ2H

JLab E03103 scaled by 0.98

Bjorken x

◮ Very good agreement of our predictions S.K. & R.Petti, PRC82(2010)054614 with

JLab E03-103 for all nuclear targets: χ2/d.o.f. = 26.3/60 for W 2 > 2 GeV2.

◮ Nuclear corrections at large x is driven

by nuclear spectral function, the

• ff-shell function δf(x) was fixed from

previous studies.

◮ A comparison with the Impulse

Approximation (shown in blue) demonstrates that the off-shell correction is crucial to describe the data leading to both the modification

• f the slope and the position of the

minimum of the ratios.

Kulagin (INR) 27 / 37

Verification with HERMES data (not a fit)

0.8 0.85 0.9 0.95 1 1.05 1.1

σ14N/σ2H

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 10

• 2

10

• 1

σ84Kr/σ2H

HERMES NMC 12C/2H

Bjorken x

KP model

◮ A good agreement of our predictions S.K. & R.Petti, PRC82(2010)054614 with

HERMES data for 14N/D and 84Kr/D with χ2/d.o.f. = 14.7/24

◮ A comparison with CERN NMC data

for 12C/D shows a notable Q2 dependence at small x in the shadowing region related to the Q2 dependence of effective cross-section. The model correctly describes the

• bserved x and Q2 dependence.

Kulagin (INR) 28 / 37

Nuclear effects in the resonance and DIS transition region

Kulagin (INR) 29 / 37

Comparison between the resonance and the DIS fit

0.1 0.2 0.3 Proton F2 Q2 = 1 GeV2 Neutron F2 Christy-Bosted (RES) Alekhin (DIS) Deuteron F2 0.1 0.2 0.3 Q2 = 2 GeV2 0.1 0.2 0.3 1 10 Q2 = 4 GeV2 W2 (GeV2) 1 10 W2 (GeV2) 1 10 W2 (GeV2) Kulagin (INR) 30 / 37

Duality

DIS and RES structure functions are dual in the integral sense Bloom & Gilman, 1970: ∫︂ W 2

W 2

th

dW 2 F DIS

2

(W 2, Q2) = ∫︂ W 2

W 2

th

dW 2 F RES

2

(W 2, Q2) Wth = Mp + mπ the pion production threshold energy and W0 = 2 GeV the boundary of the resonance region. Comparing Christy-Bosted (RES) and Alekhin (DIS) analyses we observe:

◮ For the proton the error of the duality relation < 5% for 1 ≤ Q2 < 10 GeV2. ◮ For the neutron the error is larger ∼ 5 − 10%. This could be related to a

different treatment of the deuteron correction in Alekhin and CB fits.

Kulagin (INR) 31 / 37

Predictions for proton and deuteron vs. data

0.2 0.4 0.6 0.8 1 1 10 0.895 0.478 0.247 0.101 0.051 W2 (GeV2) F2 Bjorken x CLAS proton Q2 = 1.025 GeV2 CLAS deuteron Q2 = 1.025 GeV2 SLAC proton Q2 = 1.025 GeV2 +- 3% SLAC deuteron Q2 = 1.025 GeV2 +- 3% 0.2 0.4 0.6 0.8 1 1 10 0.914 0.532 0.290 0.123 0.063 W2 (GeV2) F2 Bjorken x CLAS proton Q2 = 1.275 GeV2 CLAS deuteron Q2 = 1.275 GeV2 SLAC proton Q2 = 1.275 GeV2 +- 3% SLAC deuteron Q2 = 1.275 GeV2 +- 3% NMC deuteron Q2 = 1.25 GeV2 0.2 0.4 0.6 0.8 1 1 10 0.955 0.693 0.447 0.217 0.117 W2 (GeV2) F2 Bjorken x CLAS proton Q2 = 2.525 GeV2 CLAS deuteron Q2 = 2.525 GeV2 SLAC proton Q2 = 2.525 GeV2 +- 3% SLAC deuteron Q2 = 2.525 GeV2 +- 3% NMC deuteron Q2 = 2.5 GeV2 0.2 0.4 0.6 0.8 1 1 10 0.967 0.759 0.531 0.279 0.156 W2 (GeV2) F2 Bjorken x CLAS proton Q2 = 3.525 GeV2 CLAS deuteron Q2 = 3.525 GeV2 SLAC proton Q2 = 3.525 GeV2 +- 3% SLAC deuteron Q2 = 3.525 GeV2 +- 3% NMC deuteron Q2 = 3.5 GeV2

Proton and deuteron F2 computed at Q2 = 1.025, 1.275, 2.525, 3.525 GeV2 in a combined RES-DIS

• model. Data from SLAC Whitlow,1991 and JLab-CLAS Osipenko,2003,2005 and NMC,1997.

Kulagin (INR) 32 / 37

The ratio (F p

2 + F n 2 )/F D 2 in the RES model

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(F2

p + F2 n)/F2 D

Bjorken x RES Q2 = 2 GeV2 RES Q2 = 4 GeV2 RES Q2 = 8 GeV2 DIS Q2 = 8 GeV2

Kulagin (INR) 33 / 37

Comparison with JLab BONuS Deuteron

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 0.2 0.3 0.4 0.5 0.6 0.7 0.8

F2

D/(F2 p + F2 n)

x

BONuS data W > 1.4 GeV DIS model at xavr, Q2

avr

RES model at xavr, Q2

avr

RES xbin avr RES xbin avr & Q2 +- 15%

Griffioen et al,2015 measurement of F D

2 /(F p 2 + F n 2 )

compared with model predictions. The dashed (dotted-blue) line shows the DIS (RES) results at average x and Q2 for each x-bin. The dash-dotted green line is the result of averaging over x within each x-bin. The solid line is the result of additional smearing over Q2.

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8

F2

n/F2 D

x

BONuS data W > 1.4 GeV DIS model at xavr, Q2

avr

RES model at xavr, Q2

avr

RES xbin avr RES xbin avr & Q2 +- 15%

Tkachenko et al,2014 measurement of

F n

2 /F D 2

compared with model

• predictions. The notations are

similar to those of left panel.

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Comparison with JLab E03103 3He

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (F23He/3) / (F2D/2) Bjorken x JLab E03-103 * 1.03 DESY HERMES DIS model DIS+RES model

Data on F 3He

2

/F D

2

from JLab Hall C Seely et

al, 2009 and DESY HERMES measurement

(both corrected for the proton excess) compared with model predictions. The dashed line is DIS model, the solid line is a combined DIS+RES model.

0.8 1 1.2 1.4 1.6 1.8 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 F23He / (F2D + F2p) Bjorken x JLab E03-103 * 1.025 DIS model DIS+RES model

The isoscalar ratio F 3He

2

/(F D

2 + F p 2 ) from

Seely et al, 2009 (D.Gaskell, private communication)

compared with our predictions. The notations are similar to those of the left panel.

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Using F n

2 /F p 2 as a consistency test of nuclear data

0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 F2(Neutron)/F2(Proton) Bjorken x Extraction from NMC 2H/1H data Extraction from E03103 3He/2H data Alekhin08 SLAC E139 model

Extraction of F n

2 /F p 2

from F p

2 /F D 2

(NMC) and F

3He

2

/F D

2

(JLab) with account of nuclear effect (full symbols) and also with no nuclear effects (open symbols).

◮ Significant mismatch in F n 2 /F p 2 extracted from different experiments. At

x ∼ 0.35, where nuclear corrections are negligible, the ratio F n

2 /F p 2 from

JLab E03-103 is 15% bigger than that from NMC.

◮ Normalization of F n 2 /F p 2 is directly related to the normalization of 3He/D.

Requiring F n

2 /F p 2 from JLab to match NMC, we obtain a renormalization

factor of 1.03+0.006

−0.008 for the central values of JLab 3He/D measurement.

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Summary

◮ The data on the ratio of nuclear structure functions F A 2 /F B 2 (nuclear EMC

effect) show nontrivial oscillating shape spanning different kinematical regions

• f Bjorken x.

◮ The data in the DIS region can be understood if we address a number of

corrections including nuclear momentum distribution and binding effects,

• ff-shell correction, meson-exchange currents as well as the matter

propagation effects of hadronic component of virtual photon. Those nuclear effects result in the corrections relevant in different regions of x.

◮ In the resonance region (low Q2 and/or large x) we find a strong combined

Q2 and x dependence of nuclear ratios for light nuclei (2H, 3He and 3H). Current data can be understood in terms of smearing of the resonance structures with nuclear spectral function (the wave function in the deuteron case).

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