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Nuclear EMC Effect for Electron and Neutrino Scattering

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Nuclear EMC Effect for Electron and Neutrino Scattering Nuclear EMC Effect for Electron and Neutrino Scattering Sergey Kulagin Institute for Nuclear Research, Moscow Talk at the workshop Neutrino-Nucleus Interactions for Current and Next Generation Neutrino Oscillation Experiments Seattle, December 9, 2013 Outline Overview of data on nuclear effects in lepton deep inelastic scattering (DIS). Overview of a model of nuclear DIS Sketch of basic physics mechanisms of nuclear corrections in different kinematic regions Trying to put those mechanisms together in a model Discuss performance and predictions of the model New data (JLab E03-103, HERMES) and model predictions Predictions for DY data (E772 and E866 experiments). Predictions for neutrino DIS S.Kulagin (INR) Nuclear DIS 2 / 61 Data on nuclear effects in DIS Data on nuclear effects in DIS are available in the form of the ratio 2 2 A B R(A/B)= σA(x,Q )/σB(x,Q ) or F2 /F2 . 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. Additional information on nuclear effects for antiquarks comes from Drell-Yan production from fixed-target experiments at FNAL (E772, E866). Neutrino data on DIS cross sections on nuclear targets 2H, 20Ne, 12C, 56Fe, 207Pb from CERN (BEBC, CDHS, CHORUS, NOMAD) and FNAL (CCFR, NuTeV). Upcoming measurement of the nuclear ratios from MINERvA in a shallow inelastic region. S.Kulagin (INR) Nuclear DIS 3 / 61 A D µ Data on the EMC ratios show pronounced 1.3 Data on F2 /F2 from /e DIS A dependence of the ratios R(A/D) and a 1.2 BCDMS (Fe/D) weak Q2 dependence of nuclear effects. SLAC-E139 (Fe/D) 1.1 NMC (Cu/D) Characteristic nuclear effects vs. the Bjorken x – neutrino structure function 1 strength oscillation 0.9 0.8 Suppression (shadowing) at small x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (x< 0.05). Bjorken x 1.1 Enhancement (antishadowing) at 1 0.1 <x< 0.25. 0.9 A well with a minimum at 0.8 x ∼ 0.6 ÷ 0.75 (EMC effect). 0.7 0.6 NMC (C/D) NMC (Ca/D) Enhancement at large values of E665 (Pb/D) 0.5 x> 0.75 ÷ 0.8 (Fermi motion region). 0.0001 0.001 0.01 0.1 Bjorken x S.Kulagin (INR) Nuclear DIS 4 / 61 Recent data from JLAB E03-103 experiment at Jlab J.Seely et.al., PRL103,202301,2009: Nuclear target ratios: 12C/2H, 9Be/2H, 4He/2H, 3He/2H. Kinematics: Beam energy E = 5.011 and 5.766 GeV. Scattering angles are 32, 36, 40, 46, 50 grad. About 150 data points were reported in the region 0.3 <x< 0.9 and 2.8 <Q2 < 7 GeV2. Statistics of E03-103 at large x is significantly higher than that from previous measurements. S.Kulagin (INR) Nuclear DIS 5 / 61 1.3 SLAC E139 1.3 SLAC E139 JLAB E03103 JLAB E03103 1.2 1.2 D D σ σ / 1.1 / 1.1 9Be 12C σ σ 1 1 0.9 0.9 0.8 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Bjorken x Bjorken x 1.3 SLAC E139 1.3 Raw data JLAB E03103 Iso corrected 1.2 1.2 D D σ σ / 1.1 / 1.1 4He 3He σ 1 σ 1 0.9 0.9 0.8 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Bjorken x Bjorken x S.Kulagin (INR) Nuclear DIS 6 / 61 Consistency of different experiments 1.05 2H σ Shapes of all nuclear cross-section / 1 JLab E03103 12C ratios are consistent σ 0.95 Evaluate χ2 for each pair of 0.9 HERMES 14N/2H experiments in coarse x-bins within the 1.05 2H overlap region of the data sets σ / 1 SLAC E139 9Be σ Consistent overall normalization for 0.95 SLAC E139, NMC and HERMES data 0.9 sets 1.05 2H σ The new JLab E03-103 data is / 1 NMC 4He systematically above previous σ 0.95 measurements resulting in a 0.9 χ2/d.o.f. = 42.7/12 with respect to 1.1 SLAC E139 data on the same targets 12C σ / 1.05 An overall normalization factor 0.98 for 9Be σ 1 all JLab E03-103 points improves the 0.95 statistical consistency with SLAC E139 2 0.9 data to χ /d.o.f. =8.8/12 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Bjorken x S.Kulagin (INR) Nuclear DIS 7 / 61 DIS space-time scales The analysis of characteristic space-time scales involved into DIS helps to approach the nuclear physics of the process. Typical DIS space-time regions in the target rest frame as derived from uncertainty principle 2 2 −2 −1 DIS proceeds near the light cone: t − z ∼ Q and r⊥ ∼ Q . Characteristic DIS time and longitudinal distance t ∼ z ∼ L =(Mx)−1 NOT small in hadronic scale (in the target rest frame) ⇒ the reason for nuclear effects to survive even at high Q2. L has to be compared with average distance between bound nucleons d = (3/4πρ)1/3 ∼ 1.2 Fm (ρ is the nucleon number density in central region of heavy nuclei). This suggests two different kinematical regions: LI <d (x> 0.2) ⇒ Nuclear DIS ≈ incoherent sum of contributions from bound nucleons. LI ≫ d (x ≪ 0.2) ⇒ Coherent effects of interactions with a few nucleons are important. S.Kulagin (INR) Nuclear DIS 8 / 61 Impulse approximation A 4 τ τ Wµν (PA,q)= d p Tr Wµν (p,q)A (p; A) , τ=p,n X Z h i τ 3 ip0t−ip·rc τ τ Aαβ(p; A)= dtd re hA|Ψβ(t, r)Ψα(0)|Ai Z τ •Ψα(t, r) the nucleon Dirac field operator. •The off-shell nucleon tensor Wµν (p,q) is the matrix in the Dirac space. 2 2 On the mass shell p = M , averaging Wµν (p,q) over the nucleon polarizations we obtain the nucleon tensor givenc in terms of 2 structure functions 1 c W τ (p,q)= Tr (6 p + M)Wτ (p,q) = g F + p p F /p · q µν 2 µν µν 1 µ ν 2 h i How many structure function do we have off-mass-shell p2 6= M 2? Expand in the c e e e Dirac basis: n Wµν = Wµν Γn n Xα αβ α cΓn = I,γ ,σ ,γ γ5,γ5 S.Kulagin (INR) Nuclear DIS 9 / 61 Require the symmetry under P and T transformations AND keeping ONLY current-conserving terms (qµWµν = 0) we have 7 independent structure functions. (0) (1) (2) sym f1 f1 6p f1 6q 2 Wµν (p,q) = − gµν + 2 + M M p · q ! c (0) (1) (2) (3) epµpν f2 f2 6p f2 6q f2 α + + 2 + + p{µgν}αγ , p · q M M p · q ! p · q e e Contribution of each of these structure functions is goverened by correspondinge e matrix element hΨΓnΨi. On the mass shell p2 = M 2 we only have 2 independent structure functions (0) (1) (2) F1 = f1 + f1 + f1 , (0) (1) (2) (3) F2 = f2 + f2 + f2 + f2 S.Kulagin (INR) Nuclear DIS 10 / 61 Weak binding approximation Assume the ground state to be nonrelativistic: • |p| ≪ M, kp0 − M| ≪ M • No strong scalar and vector fields in nuclei Reduce the four-component relativistic field Ψ to a two-component nonrelativistic operator ψ ψ(p,t) p2 Ψ(p,t)= e−iMtZ , Z = 1 − (σ · p/2M) ψ(p,t) 8M 2 The renormalization operator Z provides a correct normalization of the nonrelativistic two-component nucleon field ψ: d3pΨ†Ψ= d3pψ†ψ to order p2/M 2. Separate the nucleon mass M from the energy p , p =(M + ε, p). Examine and R R 0 reduce all the Lorentz–Dirac structures of Wµν . The result to order ε/M and p2/M 2 can be summarized as c S.Kulagin (INR) Nuclear DIS 11 / 61 1 1 Tr A(p; A) Wµν (p,q) = P(ε, p) Wµν (p,q), MA M + ε c P(ε, p)= dte−iεthψ†(p,t)ψ(p, 0)i Z A 4 W (PA,q) d p µν = Pτ (ε, p)W τ (p,q), M M + ε µν A τ=p,n X Z p2 − M 2 p2 F (x,Q2,p2)= f (0) 1+ + f (1) + f (2), 1 1 2M 2 1 M 2 1 p2 − M 2 p2 F (x,Q2,p2)= f (0) 1+ + f (1) + f (2) + f (3) 2 2 2M 2 2 M 2 2 2 S.Kulagin (INR) Nuclear DIS 12 / 61 Comments: In the nonrelativistic limit to order p2/M 2 ∼ ε/M we have a factorization of the high-energy amplitude Wµν from the nuclear spectral function P which describes the low-energy part of the problem.
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