EMC effect - constrains & and future directions of study Can account of Fermi motion describe the EMC effect? A ( α , p t ) d α Z F 2 N ( x/ α , Q 2 ) ρ N F 2 A ( x, Q 2 ) = α d 2 p t = A YES If one violates baryon charge conservation or momentum conservation or both Many nucleon approximation: A ( α , p t ) d α Z α d 2 p t = A baryon charge sum rule ρ N fraction of nucleus 1 A ( α , p t ) d α Z αρ N α d 2 p t = 1 − λ A momentum =0 in many nucl. approx. A NOT carried by nucleons 1
◉ ◉ ◉ ◉ Generic models of the EMC effect extra pions - λ π ~ 4% -actually for fitting Jlab and SLAC data ~ 6% R A ( x, Q 2 ) = 1 − λ A nx α π ~ 0.15 + enhancement from scattering off pion field with 1 − x 6 quark configurations in nuclei with P 6q ~ 20-30% Nucleon swelling - radius of the nucleus is 20--15% larger in nuclei. Color is significantly delocalized in nuclei Larger size → fewer fast quarks - possible mechanism: gluon radiation starting at lower Q 2 (1 /A ) F 2 A ( x, Q 2 ) = F 2 D ( x, Q 2 ξ A ( Q 2 )) / 2 Mini delocalization ( color screening model) - small swelling - enhancement of deformation at large x due to suppression of small size configurations in bound nucleons + valence quark antishadowing with effect roughly ∝ !k nucl2 2
PHYSICAL REVIEW LETTERS 1 OCTOBER 1990 VOLUME 65, NUMBER 14 Rs(x, Q ) — I=S~(x, Q )/ that the fraction carried that which assume momentum the difference find we by AS~(x, Q ) — at x =0. 05, increases in a nucleus the same as in a free nu- by a sea quarks remains 1, evaluated Q =3 and 25 GeV . In are consistent factor of 2 as Q cleon, hardly with deep-inelastic and varies between Drell- Yan data. if QCD aligned-jet the model particular, we use is a QCD extension of Let us brieAy (QAJM) of Refs. 4 and 5 (which consider ideas that may be dynamical of the logic of Bjorken) to calculate consistent the small-x with picture emerging the well-known parton (x ~ 0. 1) parton Ca, Rg(x=0. 04, of nuclei. Rs(x, Q ), we in the case of structure In the nucleus rest find, frame the x =0. 1 region corresponds Q =3 GeV ) =0. 9 and Rs(x=0. 04, Q =25 GeV ) to a possibility for =0. 97. to interact the virtual two nucleons The agreement photon with which last number with is in good I fm [cf. Eq. (I)]. But at these (see Fig. 2). Thus, are at distances of about that Drell-Yan data we conclude in Ref. distances of different nu- for S~ observed and distributions 3 for quark gluon the small shadowing x=0. 04 & 16 GeV2 cleons may overlap. So, in analogy with the pion model to corresponds a much and Q for Q =Qo. of the European Muon Collaboration effect, the natural larger shadowing at x =0. 04 of the observed of gluon interpretation enhancement and in the sea-quark distribution Shadowing [Rs(x=0. 04, Q =3 GeV ) =0. 9), combined in- valence-quark distributions is that intermediate-range the with forces are a result of interchange F2 (x, Q )/AF2 (x, Q ) of quarks ternucleon at the data for experimental value of x [F2 (x, Q )/AFi (x, Q ) & I], unambi- such a model, screening of the color and gluons. Within same of quarks i. e. , Rv(x, Q ): of the valence charge and would prevent sig- gluons quarks, any an enhancement implies guously — of the meson V~(x, Q )/AV~(x, Q ) & 1. For nificant enhancement field in nuclei. Such Ca, GeV ) = 1. 1, Rv(x =0. 04-0. 1, a picture of internucleon con- forces does not necessarily for whereas 3 Q we find Rv(x =0. 04-0. 1, Q =3 the experience of nuclear tradict in the Really, physics. matter, nuclear infinite GeV ) ~ 1. 2. degrees of processes where and gluon low-energy quark the baryon-charge sum rule By applying of quarks excited, freedom cannot be the exchange [Eq. (2)], we conclude data that require experimental between nucleons the at small (gluons) equivalent, within of shadowing is for valence quarks the presence of x [i. e. , Rv(x, Q ) & 1 for x, h &0. 01-0. 03]. representation over the transfer, dispersion momentum values for Rv(x, Q ) is of a group of a few mesons. to the exchange Another of shadowing the amount Moreover, for as the shadowing about the same (somewhat larger) (see Fig. 3). The overall change the sea-quark channel at of the momentum and sea quarks carried by valence Q'= I GeV' is vs Prediction yv(Qo) =1. 3%, )s(Qo) = — Drell-Yan experiments: q Ca ( x ) / ¯ ¯ q N = 1 . 1 ÷ 1 . 2 | x =0 . 05 ÷ 0 . 1 4. 6%. 1. 10I— 1989 the present data are consistent with the To summarize, q Ca / ¯ q N ≈ 0 . 97 ¯ in Ref. 7: All par- scenario 6rst suggested parton-fusion meson model . 00 at small x, while at larger are shadowed ton distributions CL are en- distributions x, only valence-quark and gluon expectation 0. 90 At the same time, other scenarios inspired hanced. by (see, e. g. , Ref. 8) idea of parton fusion, the now popular q Ca ( x ) / ¯ ¯ q N = 1 . 1 ÷ 1 . 2 | x =0 . 05 ÷ 0 . 1 0, 80 Q2 = 15 GeV2 x 1. 30 1 0 Ca/D R(x, gj) (2/3)F" (x, gf)/FP(x, g$) 1. 20 FIG. 3. Ratios R=Rv(x, gS) -(2/A) Vq(x, gf)/Vo(x, QS) (dashed line), = Rs(x, g/) =(2/A)S~(x, g/)/SD(x, g/) and R— line), (solid Ca. (dot-dashed line) All curves have been obtained at in A-dependence of antiquark Q) =2 GeV . The Iow-x behavior (x ~ x, h) corresponds q N to the q Ca / ¯ distribution, data are from FNAL of the QA3M of Refs. 4 and 5; the antishadowing predictions nuclear Drell-Yan experiment, (i. e. , a enhancement the valence channel pattern 10/o in to a less than 5% no enhancement in the sea, leading whereas curves - pQCD analysis of ¯ increase of F~q at x =0. 1-0. 2) has been evaluated within the Frankfurt, Liuti, MS 90. Similar rules (2) and (3) are that sum present approach by requiring data are from Ref. 1 (diamonds) and satisfied. Experimental conclusions by Eskola et al 93-07 Ref. 3 (squares), the latter representing the sea-quark ratio Rg data analyses (cf. Fig. 2). The theoretical curves are located below the data FIG. 2. Ratio R =(2/A)ug(x, g')/uD(x, g') plotted values of g~: (g ) at small x, due to the vs x, experimental high 1 and (Q ) =16 GeV2 in Ref. 3, respec- =14. 5 GeV~ in Ref. Q2 = 2 GeV2 values of Q . Notations as in Fig. 1. Experimen- for diff'erent tal data from Ref. 3. tively. 3 1727
Combined analysis of (e,e’) and knockout data ✺ Structure of 2N correlations - probability ~ 20% for A>12 → dominant but not the only term in kinetic energy 90% pn + 10% pp < 10% exotics ⇒ probability of exotics < 2% Analysis of (e,e’) SLAC data at x=1 -- tests Q 2 dependence of the ✺ nucleon form factor for nucleon momenta k N < 150 MeV/c and Q 2 > 1 GeV 2 : ☛ /r free r bound < 1 . 036 N N Similar conclusions from combined analysis of (e,e’p) and (e,e’) JLab data — 1~ ~ 0.04. Analysis of elastic pA scattering This inequality is relevant for Problem for the nucleon swelling models of the EMC effect with 20% swelling 4
First five commandments Remember baryon conservation law Honour momentum conservation law Thou shalt not introduce dynamic pions into nuclei Thou shalt not introduce large deformations of low momentum nucleons However large admixture of nonnucleonic degrees of freedom (20-- 30 %) strange but was not initially ruled out. Qualitative change due to direct observation of short-range NN correlations at JLab and BNL Honour existence of large predominantly nucleonic short-range correlations Thou shalt not introduce large exotic component in nuclei - 20 % 6q, Δ ’s 5
Thou shalt take into account leading twist shadowing andrelated leading twist antishadowing Leading twist nuclear shadowing phenomena in hard processes with nuclei L. Frankfurt a , V. Guzey b, ∗ , M. Strikman c Physics Reports 512 (2012) 255–393 2 2 2 2 Im + Re Im − Re γ∗ γ∗ γ∗ γ∗ H H H H Theory of the leading twist shadowing based on the Gribov unitarity relations and j j j QCD factorization theorem for hard j diffraction. Predictions for LHC, EIC,... CMS Preliminary 10 / dy [mb] P P P P N1 Pb+Pb Pb+Pb+J/ s = 2.76 TeV → ψ 9 NN -1 L = 159 b µ CMS Α Α int N2 ALICE p p p p 8 coh AB-MSTW08 A − 2 AB-HKN07 σ 7 d STARLIGHT Leading twist contribution Hard diffraction GSZ-LTA 6 AB-EPS09 off parton "j" to the nuclear shadowing for AB-EPS08 5 structure function fj (x,Q 2 ) 4 3 Cross section of coherent J/ ψ production in 2 γ + Α → J/ ψ + Α ultraperipheral collisions. 1 Yellow band is our prediction - large (~ 0.6 ) gluon 0 shadowing is observed -1 0 1 2 3 4 y y x=10 -3 6 χ
Two minor effects to be included in a precision analysis of the EMC ratio requires a) correction for the definition of x= AQ 2 /2q 0 mA b) 1% of heavy nucleus LC momentum carried by Weizs ̈ acker-William photons
Very few models of the EMC effect survive when constraints due to the observations of the SRC are included & lack of enhancement of antiquarks and Q 2 dependence of the quasielastic (e,e’) at x=1 It appears that essentially one generic scenario survives - strong deformation of rare configurations in bound nucleons increasing with nucleon momentum and with most of the effect due to the SRCs . 8
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