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Deep-Inelastic Scattering on the Tri-Nucleons

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Deep-Inelastic Scattering on the Tri-Nucleons Three-body dynamics in hadron structure & hadronic systems: A symposium in celebration of Iraj Afnan’s 70th birthday Jefferson Lab, July 24, 2009 Deep-inelastic scattering on the tri-nucleons Wally Melnitchouk Outline Motivation: neutron structure at large x d/u ratio, duality in the neutron Status of large-x quark distributions nuclear corrections new global analysis of inclusive DIS data (CTEQx) DIS from A=3 nuclei model-independent extraction of neutron F2 plans for helium-3/tritium experiments Quark distributions at large x Parton distributions functions (PDFs) provide basic information on structure of hadronic systems needed to understand backgrounds in searches for new physics beyond the Standard Model in high-energy colliders, neutrino oscillation experiments, ... DGLAP evolution feeds low x, high Q2 from high x, low Q 2 1 dq(x, t) αs(t) dy x x = Pqq q(y, t)+Pqg g(y, t) dt 2π x y y y ! " # $ # $ % 2 2 t = log Q /ΛQCD Ratio of d to u quark distributions at large x particularly sensitiveHigher to twistsquark dynamics in nucleon SU(6) spin-flavor symmetry (a) (b) (c) proton wave function ↑ 1 ↑ √2 ↓ p = d (uu)1 d (uu)1 −3 − 3 Higher twists √2 ↑ 1 ↓ 1 ↑ + u (ud)1 u (ud)1 + u (ud)0 τ = 2 6 τ >− 23 √2 (τ = 2) (a) (b) (c) diquark spin single quark interactingqq and qg corquarkrelationsspectator scattering diquark τ = 2 τ > 2 single quark qq and qg scattering correlations Ratio of d to u quark distributions at large x particularly sensitive to quark dynamics in nucleon SU(6) spin-flavor symmetry proton wave function ↑ 1 ↑ √2 ↓ p = d (uu)1 d (uu)1 −3 − 3 √2 ↑ 1 ↓ 1 ↑ + u (ud)1 u (ud)1 + u (ud)0 6 − 3 √2 u(x)=2d(x) for all x n F2 2 p = F2 3 scalar diquark dominance M∆ >MN =⇒ (qq)1 has larger energy than (qq)0 . =⇒ scalar diquark dominant in x → 1 limit . since only u quarks couple to scalar diquarks . =⇒ . d → 0 u n F2 1 p → F2 4 Feynman 1972, Close 1973, Close/Thomas 1988 hard gluon exchange at large x, helicity of struck quark = helicity of hadron q↑ ! q↓ =⇒ . =⇒ helicity-zero diquark dominant in x → 1 limit . d 1 → u 5 n F2 3 p → F2 7 Farrar, Jackson 1975 At large x, valence u and d distributions extracted from p and n structure functions 4 1 F p ≈ u + d 2 9 v 9 v 4 1 F n ≈ d + u 2 9 v 9 v u quark distribution well determined from p data d quark distribution requires n structure function 4 − n p d ≈ F2 /F2 n p u 4F2 /F2 − 1 Duality in the neutron? Bloom-Gilman duality well established for the proton W. Melnitchouk et al. / Physics Reports 406 (2005)156 127–301 W. Melnitc155houk et al. / Physics Reports 406 (2005) 127–301 0.4 Q2 = 1.5 GeV2 ∆ 0.3 0.3 0.2 0.1 0.2 0 0.1 Q2 = 2.5 GeV2 0.2 p p 2 2 0 F F 0.4 0.1 S11 LT Separated Data 0.3 0 0.2 Q2 = 3.5 GeV2 0.2 0.15 0.1 SLAC 0.1 0.05 MRST (NNLO) + TM CTEQ6 (DIS) + TM 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 X p 2 Fig. 13. Proton F2 structure function in the !Niculescu(top) and S11 et(bottom) al., PRLresonance 85 (2000)Fig.regions14. Proton1182,from Jef F1185ferson2 structureLab HallfunctionC, comparedin the resonance region for several valuesChristyof Q ,eta sal.indicated. (2005)Data from Jefferson Lab with the scaling curve from Ref. [7]. The resonances move to higher " with increasing Q2, which ranges from 0.5 GeV2 2 Hall C [65,66] are compared with∼ some recent parameterizations of the deep inelastic data at the same Q values (see text). (smallest " values) to 4.5 GeV2 (largest " values). ∼ higher Q2 values. It is difficult to evaluate precisely the equivalence ofComparisonthe two if Qof2 eresonancevolution [60]reisgionnotdata with PDF-based global fits allows the resonance–scaling com- taken into account. Furthermore, the resonance data and scaling curvparisones, althoughto be madeat the sameat the" orsame#", arevalues of (x,Q2), making the experimental signature of duality less at different x and sensitive therefore to different parton distributions.ambiguous.A more stringentSuch a testcomparisonof the scalingis presented in Fig. 14 for F p data from Jefferson Lab experiment E94- behavior of the resonances would compare the resonance data with fundamental scaling predictions for 2 110 [65,66], with the data bin-centered to the values Q2 1.5, 2.5 and 3.5 GeV2 indicated. These F p the same low-Q2, high-x values as the data. = 2 Such predictions are now commonly available from several groupsdata arearoundfrom antheewxperimentorld, for instance,capable of performing longitudinal/transverse cross section separations, and the Coordinated Theoretical-Experimental Project on QCD (CTEQ)so are[61]e;vMartin,en moreRoberts,preciseStirling,than thoseand shown in Figs. 11–13. Thorne (MRST) [62]; Gluck, Reya, and Vogt (GRV) [63]; and BlümleinTheandsmoothBöttchercurv[64]es,tinonFig.ameaf14eware. the perturbative QCD fits from the MRST [67] and CTEQ [68] These groups provide results from global QCD fits to a full range ofcollaborations,hard scatteringeprocesses—includingvaluated at the same Q2 values as the data. The data are shown with target mass (TM) lepton–nucleon deep inelastic scattering, prompt photon production,corrections,Drell–Yawhichn measurements,are calculatedjet pro-according to the prescription of Barbieri et al. [16]. The SLAC curve duction, etc.—to extract quark and gluon distribution functions (PDFs)is a fitforto thedeepproton.inelasticThe ideascatteringof suchdata [69], which implicitly includes target mass effects inherent in global fitting efforts is to adjust the fundamental PDFs to bring thetheoryactualand data.experimentThe tarintogetagreementmass corrected pQCD curves appear to describe, on average, the resonance for a wide range of processes. These PDF-based analyses include strengthpQCD radiatiat eachve correctionsQ2 value.whichMoreogivever, this is true for all of the Q2 values shown, indicating that the 2 rise to logarithmic Q dependence of the structure function. In thisresonancereport, weauseveragesparameterizationsmust be follofromwing the same perturbative Q2 evolution [60] which governs the pQCD all of these groups, choosing in each case the most straightforwardparameterizationsimplementation for(MRSTour needs.and CTEQ).It is This demonstrates even more emphatically the striking duality not expected that this choice affects any of the results presented here. between the nominally highly nonperturbative resonance region and the perturbative scaling behavior. An alternate approach to quantifying the observation that the resonances average to the scaling curve has been used recently by Alekhin [70]. Here the differences between the resonance structure func- p tion values and those of the scaling curve, !F2 , are used to demonstrate duality, as shown in Fig. 15, p F2 resonance spectrum * * JLab Hall C Psaker, WM, Christy, Keppel, Phys. Rev. C 78 (2008) 025206 how much of this region is leading twist ? Higher twists 1/Q 2 expansion of structure function moments 1 (4) (6) 2 n−2 2 (2) An An Mn(Q )= dx x F2(x, Q ) = An + + + ··· !0 Q2 Q4 matrix elements of operators with specific “twist” (= dimension - spin) twist > 2 reveals long-range q-g correlations phenomenologically important at low Q 2 and large x parametrize x dependence by C(x) F (x, Q2)=F LT (x, Q2) 1+ 2 2 Q2 ! " larger S 11 HT small ∆ HT Psaker, WM, Christy, Keppel, Phys. Rev. C 78 (2008) 025206 higher twists < 10-15% for Q2 > 1 GeV2 Is duality in the proton a coincidence? consider symmetric nucleon wave function 2 cat’s ears diagram (4-fermion higher twist ~ 1 /Q ) 2 e e e2 e2 ∝ i j ∼ i − i i=j i i !! " ! # ! coherent incoherent 4 1 proton HT 1 2 + = 0 ! ∼ − × 9 9 ! " 4 1 neutron HT 0 +2 =0 ∼ − 9 × 9 $ ! " need to test duality in the neutron! No FREE neutron targets (neutron half-life ~ 12 mins) use deuteron as ‘‘effective” neutron target d p n BUT deuteron is a nucleus, and F2 != F2 + F2 nuclear effects (nuclear binding, Fermi motion, shadowing) obscure neutron structure information need to correct for “nuclear EMC effect” Nuclear effects in the deuteron nuclear “impulse approximation’’ incoherent scattering from individual nucleons in d (good approx. at x >> 0) 896 G. PILLER, W. MELNITCHOUK, AND A. W. THOMAS 54 N=p+n 2 2 2 ∗ A␮␯␣͑k,q͒ϭi͑q ⑀␮␯k␣ϩ͑k Ϫm ͒⑀␮␯q␣ γ d 2 N 2 Ϫ2͑k␮⑀kq␣␯Ϫk␯⑀kq␣␮͒͒, ͑8c͒ F2 (x, Q )= dy f(y,γ) F2 (x/y, Q ) 2 x A␮␯␣␤͑k,q͒ϭϪim͑q g␮␣g␯␤ϩ2q␣͑k␮g␯␤Ϫk␯g␮␤͒͒. ͑8d͒ ! (off) d N + δ F2 Here k is the interacting quark four-momentum, and m is its ␣ ␤ mass. We use the notation ⑀␮␯kqϵ⑀␮␯␣␤k q . ͑The com- plete forward scattering amplitude would also contain a crossed photon process which we do not consider here, since d in the subsequent model calculations we focus on valence quark distributions.͒ The function (k,p) represents the soft FIG. 1. DIS from a polarized nucleus in the impulse approxima- quark-nucleon interaction. SinceHone is calculating the tion. The nucleus, virtual nucleon, and photon momenta are denoted imaginary part of the forward scattering amplitude, the inte- by P, p, and q, respectively, and S stands for the nuclear spin vector. The upper blob represents the truncated antisymmetric gration over the quark momentum k is constrained by ␦ ˆ functions which put both the scattered quark and the nonin- nucleon tensor G␮␯ , while the lower one corresponds to the polar- ˆ teracting spectator system on-mass-shell: ized nucleon-nucleus amplitude A.
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