EMC effect and short-ranged correlations

Gerald A. Miller University of Washington

RMP with Or Hen, Eli Piasetzky, Larry Weinstein arXiv: 1611.09748 Will focus on 0.3

I NTERNATIONAL JOURNAL OF HIGH-ENERGY PHYSICS CERNCOURIER

V OLUME 53 NUMBER 4 M AY 2013 Higinbotham, Miller, WELCOME CERN Courier – digital edition Welcome to the digital edition of the May 2013 issue of CERN Courier. Hen, Rith Last July, the ATLAS and CMS collaborations announced the discovery of a new particle at the LHC with a mass of 125 GeV. They referred to it as a “Higgs-like boson” because further data were needed to pin down more of its properties. Now, the collaborations have amassed enough evidence to identify the new particle as a Higgs boson, although the question remains of whether CERN Courier 53N4(’13)24 it is precisely the Higgs boson of the Standard Model of particle physics. The Deep in the nucleus: masses of these particles were just as electroweak theory predicted, based on a puzzle revisited other particle interactions continue to provide puzzles in more complex heavy-ion collisions.

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HEAVY IONS ASTROWATCH IT’S A The key to fi nding Planck reveals an out if a collision almost perfect HIGGS BOSON EDITOR: CHRISTINE SUTTON, CERN is head on universe The new particle DIGITAL EDITION CREATED BY JESSE KARJALAINEN/IOP PUBLISHING, UK p31 p12 is identifi ed p21 1

CERNCOURIER WWW. V OLUME 53 NUMBER 4 M AY 2013 Eur. Phys. J. A (2016) 52: 268 Page 57 of 100

Table 5. Key measurements in e +AcollisionsatanEICtoexplorethedynamicsofquarksandgluonsina nucleusinthe non-saturation regime.

Deliverables Observables What we learn 2 Collective Ratios R2 Q evolution: onset of DGLAP violation, beyond DGLAP nuclear effects from inclusive DIS A-dependence of shadowing and antishadowing at intermediate x Initial conditions for small-x evolution Transport Production of light Color neutralization: mass dependence of hadronization coefficients in and heavy hadrons, Multiple scattering and mass dependence of energy loss The EMC EFFECTnuclear matter and jets in SIDIS Medium effect of heavy quarkonium production 3 JLab Q2=3-6 GeV2 Nuclear density Hadron production Transverse momentum broadening of produced hadrons 2 1.2 Because these data are at somewhat lower Q than D and its fluctuation in SIDIS Azimuthal φ-modulation of produced hadrons σ

2 2 / E03103 Norm. (1.6%)

previous high-x results, typically Q =5 or 10 GeV for C

SLAC E139 [2], extensive measurements were made to σ 1.1 SLAC Norm. (1.2%) verify that our result is independent of Q2.Thestruc- ture functions were extracted at several Q2 values and 1.2 fort to study the properties of quarks and gluons and their found to be consistent with scaling violations expected 1 EMC E136 from QCD down to Q2 ≈ 3GeV2 for W 2 ≥ 1.5GeV2, 1.1 dynamics in the nuclear environment both experimentally while the structure functions ratios show no Q2 depen- NMC E665 and theoretically. dence. Figure 1 shows the carbon to deuteron ratio for 0.9 2 2 1 Using the same very successful QCD formulation at the five highest Q settings (the lowest and middle Q 1.2 D D 2 values were measured with a 5 GeV beam energy). There σ / E03103 Norm. (1.7%) the leading power in Q for proton scattering, and using

2 / F is no systematic Q dependence in the EMC ratios, even Be 0.9 σ 1.1 SLAC Norm. (1.2%) Ca the DGLAP evolution for the scale dependence of par- at the largest x values, consistent with the observation 2 of previous measurements [3]. F 0.8 ton momentum distributions, several QCD global analy- 1 ses have been able to fit the observed non-trivial nuclear 1.2 D Q2=4.06 0.7 σ

/ dependence of existing data, attributing all observed nu- 2 C Q =4.50 σ 2 0.9 clear dependences —including its x-dependence and nu- Q =4.83 0.6 EIC 1.1 2 Q =5.33 1.2 D clear atomic weight A-dependence— to a set of nucleus- 2

Q =6.05 σ / E03103 Norm. (1.5%) 0.5 dependent quark and gluon distributions at an input scale

4He 0.0001 0.001 0.01 0.1 1 1 σ 1.1 SLAC Norm. (2.4%) Q0 ! 1GeV[176,178,179].Asanexample,thefittingre- x sult of Eskola et al. is plotted along with the data on the 1 0.9 Fig. 56. The ratio of nuclear over nucleon F2 structure func- ratio of the F2 structure function of calcium divided by tion, R2, as a function of Bjorken x,withdatafromexisting that of deuterium in fig. 56, where the dark blue band 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.9 fixed target DIS experimentsWhite at Q2 > 1GeVPaper2,alongwiththe indicates the uncertainty of the EPS09 fit [176]. The suc- x 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 QCD global fit from EPS09 [176]. Also shown is the expected cess of the QCD global analyses clearly indicates that the kinematic coverage of the inclusive measurements at the EIC. FIG. 1: (Color online) Carbon EMC ratios [10] for the five x response of the nuclear cross-section to the variation of highest Q2 settings (Q2 quoted at x =0.75). Uncertainties The purple error band is the expected systematic uncertainty 12 9 4 the probing momentum scale Q Q0 is insensitive to the are the combined statistical and point-to-point systematic. ForFIG. 2: (Color 0.3neutron structure excess (see text). Closed is modified: (open) circles ror, valence while the statistical quark uncertainty momentum is expected depleted. to be much 2 2 not introduce any nuclear dependence. However, it does For all further results, we show the ratios obtained denote W above (below) 2 GeV .Thesolidcurveisthe smaller. ◦ A-dependent fit to the SLAC data, while the dashed curve Why are ratios independent from the 40 data (filled squares in Fig. 1). While there 12 not answer the fundamental questions: Why are the par- ◦ is the fit to C. Normalization uncertainties are shown in 2 are data at 50 (open circles) for all nuclei, the statis- EFFECTSparentheses for both measurements. ARE SMALL ~15% 2 ton distributions in a nucleus so different from those in a tical precision is noticeably worse, and there are much of Q ? larger corrections for charge symmetric background and free nucleon at the probing scale Q0?Howdothenuclear Coulomb distortion (for heavier nuclei). high-energy proton collisions with a momentum transfer structure and QCD dynamics determine the distributions The EMC ratios for 12C, 9Be, and 4He are shown in data from HERMES. Note that the HERMES 3He data larger than 2 GeV (corresponding to hard scatterings tak- of quarks and gluons in a nucleus? Fig. 2 along with results from previous SLAC extractions. have been renormalized by a factor of 1.009 based on ing place at a distance less than one tenth of a femtome- The 4He and 12Cresultsareingoodagreementwiththe comparisons of their 14NEMCeffect and the NMC 12C The nucleus is a “molecule” in QCD, made of nucleons SLAC results, with much better precision for 4He in the result [11]. We show both the measured cross section ter). —which, in turn, are bound states of quarks and gluons. new results. While the agreement for 9Be does not ap- ratio (squares) and the “isoscalar” ratio (circles), where pear to be as good, the two data sets are in excellent the 3He result is corrected for the proton excess. Previ- Are the quarks and gluons in a nucleus confined within Unlike the molecule in QED, nucleons in the nucleus are agreement if we use the same isoscalar correction as E139 ous high-x EMC measurements used a correction based the individual nucleons? Or does the nuclear environment packed next to each other, and there are many soft gluons (see below) and take into account the normalization un- on an extraction of the F2n/F2p ratio for free nucleons 2 significantly affect their distributions? The EMC experi- inside nucleons when probed at small x.TheDISprobe certainties in the two data sets. In all cases, the new data from high Q measurements of F2d/F2p.Weuseglobal extend to higher x,althoughatlowerW 2 values than the fits [12, 13] to the free proton and neutron cross sections ment at CERN [213] and experiments in the following two has a high resolution in transverse size 1/Q.Butits SLAC ratios. The EMC ratio for 4He is comparable to evaluated at the kinematics of our measurement and then decades clearly revealed that the momentum distribution resolution in the longitudinal direction, which∼ is propor- 12C, suggesting that the modification is dependent on the broadened using the convolution procedure of Ref. [14] to average nuclear density, which is similar for 4He and 12C, yield the neutron-to-proton cross section ratio in nuclei. of quarks in a fast-moving nucleus is not a simple super- tional to 1/xp 1/Q,isnotnecessarilysharpincom- rather than a function of nuclear mass. Using the “smeared” proton and neutron cross section position of their distributions within nucleons. Instead, parison with the∼ Lorentz contracted size of a light-speed Figure 3 shows the EMC ratio for 3He, with the low-x ratios more accurately reflects the correction that should 1/3 the measured ratio of nuclear over nucleon structure func- nucleus, 2RA(m/p), with nuclear radius RA A tions, as defined in eq. (23), follows a non-trivial function and the Lorentz∼ contraction factor m/p and nucleon∝ mass of Bjorken x,significantlydifferent from unity, and shows m. That is, when 1/xp > 2RA(m/p), or at a small the suppression as x decreases, as shown in fig. 56. The ob- x 1/2mRA 0.01, the DIS probe could interact coher- served suppression at x 0.01, which is often referred to ently∼ with quarks∼ and gluons of all nucleons at the same as the phenomenon of nuclear∼ shadowing, is much stronger impact parameter of the largest nucleus moving nearly than what the Fermi motion of nucleons inside a nucleus at the speed of light, p m. The destructive interfer- could account for. This discovery sparked a worldwide ef- ence of the coherent multiple≫ scattering could lead to a Eur. Phys. J. A (2016) 52: 268 Page 57 of 100

Table 5. Key measurements in e +AcollisionsatanEICtoexplorethedynamicsofquarksandgluonsina nucleusinthe non-saturation regime.

Deliverables Observables What we learn 2 Collective Ratios R2 Q evolution: onset of DGLAP violation, beyond DGLAP nuclear effects from inclusive DIS A-dependence of shadowing and antishadowing at intermediate x Initial conditions for small-x evolution Transport Production of light Color neutralization: mass dependence of hadronization coefficients in and heavy hadrons, Multiple scattering and mass dependence of energy loss The EMC EFFECTnuclear matter and jets in SIDIS Medium effect of heavy quarkonium production 3 JLab Q2=3-6 GeV2 Nuclear density Hadron production Transverse momentum broadening of produced hadrons 2 1.2 Because these data are at somewhat lower Q than D and its fluctuation in SIDIS Azimuthal φ-modulation of produced hadrons σ

2 2 / E03103 Norm. (1.6%)

previous high-x results, typically Q =5 or 10 GeV for C

SLAC E139 [2], extensive measurements were made to σ 1.1 SLAC Norm. (1.2%) verify that our result is independent of Q2.Thestruc- ture functions were extracted at several Q2 values and 1.2 fort to study the properties of quarks and gluons and their found to be consistent with scaling violations expected 1 EMC E136 from QCD down to Q2 ≈ 3GeV2 for W 2 ≥ 1.5GeV2, 1.1 dynamics in the nuclear environment both experimentally while the structure functions ratios show no Q2 depen- NMC E665 and theoretically. dence. Figure 1 shows the carbon to deuteron ratio for 0.9 2 2 1 Using the same very successful QCD formulation at the five highest Q settings (the lowest and middle Q 1.2 D D 2 values were measured with a 5 GeV beam energy). There σ / E03103 Norm. (1.7%) the leading power in Q for proton scattering, and using

2 / F is no systematic Q dependence in the EMC ratios, even Be 0.9 σ 1.1 SLAC Norm. (1.2%) Ca the DGLAP evolution for the scale dependence of par- at the largest x values, consistent with the observation 2 of previous measurements [3]. F 0.8 ton momentum distributions, several QCD global analy- 1 ses have been able to fit the observed non-trivial nuclear 1.2 D Q2=4.06 0.7 σ

/ dependence of existing data, attributing all observed nu- 2 C Q =4.50 σ 2 0.9 clear dependences —including its x-dependence and nu- Q =4.83 0.6 EIC 1.1 2 Q =5.33 1.2 D clear atomic weight A-dependence— to a set of nucleus- 2

Q =6.05 σ / E03103 Norm. (1.5%) 0.5 dependent quark and gluon distributions at an input scale

4He 0.0001 0.001 0.01 0.1 1 1 σ 1.1 SLAC Norm. (2.4%) Q0 ! 1GeV[176,178,179].Asanexample,thefittingre- x sult of Eskola et al. is plotted along with the data on the 1 0.9 Fig. 56. The ratio of nuclear over nucleon F2 structure func- ratio of the F2 structure function of calcium divided by tion, R2, as a function of Bjorken x,withdatafromexisting that of deuterium in fig. 56, where the dark blue band 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.9 fixed target DIS experimentsWhite at Q2 > 1GeVPaper2,alongwiththe indicates the uncertainty of the EPS09 fit [176]. The suc- x 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 QCD global fit from EPS09 [176]. Also shown is the expected cess of the QCD global analyses clearly indicates that the kinematic coverage of the inclusive measurements at the EIC. FIG. 1: (Color online) Carbon EMC ratios [10] for the five x response of the nuclear cross-section to the variation of highest Q2 settings (Q2 quoted at x =0.75). Uncertainties The purple error band is the expected systematic uncertainty 12 9 4 the probing momentum scale Q Q0 is insensitive to the are the combined statistical and point-to-point systematic. ForFIG. 2: (Color 0.3 2RA(m/p), or at a small the suppression as x decreases, as shown in fig. 56. The ob- x 1/2mRA 0.01, the DIS probe could interact coher- served suppression at x 0.01, which is often referred to ently∼ with quarks∼ and gluons of all nucleons at the same as the phenomenon of nuclear∼ shadowing, is much stronger impact parameter of the largest nucleus moving nearly than what the Fermi motion of nucleons inside a nucleus at the speed of light, p m. The destructive interfer- could account for. This discovery sparked a worldwide ef- ence of the coherent multiple≫ scattering could lead to a Q2 dependence of nuclear effects - 1

J.J. Aubert et al., Nucl. Phys. B 481 (1996) 23 Klaus Rith J. Gomez et al., PRD 49 (1994) 4348

J. Seely et al., PRL 103 (2009) 202301 EMC SLAC E139 JLAB E03103

Q2 dependence of EMC effect is small 3 K.R. Why? 25 Ideas: ~1000 papers 3 ideas • Proper treatment of known effects: binding, Fermi motion, pionic- NO nuclear modification of internal nucleon/pion quark structure • Quark based- high momentum suppression implies larger confinement volume a• bound nucleon is larger than free one- a mean field effect b• multi-nucleon clusters - beyond the mean field

4 Ideas: ~1000 papers 3 ideas • Proper treatment of known effects: binding, Fermi motion, pionic- NO nuclear modification of internal nucleon/pion quark structure • Quark based- high momentum suppression implies larger confinement volume a• bound nucleon is larger than free one- a mean field effect b• multi-nucleon clusters - beyond the mean field

EMC – “Everyone’s Model is Cool (1985)4’’ Ideas: ~1000 papers 3 ideas • Proper treatment of known effects: binding, Fermi motion, pionic- NO nuclear modification of internal nucleon/pion quark structure • Quark based- high momentum suppression implies larger confinement volume a• bound nucleon is larger than free one- a mean field effect b• multi-nucleon clusters - beyond the mean field

EMC – “Everyone’s Model is Cool (1985)4’’ One thing I learned since ‘85 • Nucleon/pion model is not cool Deep Inelastic scattering from nuclei- nucleons only free structure function • Hugenholz van Hove theorem nuclear stability implies (in rest + - frame) P =P =MA + • P =A(MN - 8 MeV) • average nucleon k+ + k =MN-8 MeV, Not much spread

F2A/A~F2N no EMC effect Momentum sum rule- Binding causes no matrix element of energy EMC effect momentum tensor More on sum rules

• Baryon & momentum sum rules originate from matrix elements of conserved currents in the nucleon wave function-Collins book • The virtual photon -proton system is not the proton • Shadowing and final state interactions are not in the proton, sum rules do not apply to A F2 • Sum rules apply to light front wave functions of the proton

6 Nucleons and pions + + + PA = PN + Pπ =MA + Pπ /MA =.04, explain EMC, sea enhanced try Drell-Yan, Bickerstaff, Birse, Miller 84 proton(x1) nucleus(x2)

x1

x2 Nucleons and pions + + + PA = PN + Pπ =MA + Pπ /MA =.04, explain EMC, sea enhanced try Drell-Yan, Bickerstaff, Birse, Miller 84

proton(x1) nucleus(x2)

x1

x2

DY (Fe) 2 DY ( H)

E772 PRL 69,1726 (92) Nucleons and pions + + + PA = PN + Pπ =MA + Pπ /MA =.04, explain EMC, sea enhanced try Drell-Yan, Bickerstaff, Birse, Miller 84

proton(x1) nucleus(x2)

x1

x2

DY (Fe) 2 DY ( H)

Bertsch, Frankfurt, Strikman“crisis”

E772 PRL 69,1726 (92) Ideas: ~1000 papers 3 ideas • Proper treatment of known effects: binding, Fermi motion, pionic- NO nuclear modification of internal nucleon/pion quark structure • Quark based- high momentum suppression implies larger confinement volume a• bound nucleon is larger than free one- a I don’t see how you can get plateaus mean field effect at large x in a mean field model b• multi-nucleon clusters - beyond the mean field

8 q Nucleon in nucleus p + q ⇤ On mass shell p p2 = M 2 MA 6 Off-mass shell Nucleus A-1 is form factor of a A-1 nucleus is low-lying state “large” proton A- 1 nucleus is 1 fast nucleon +A-2 nucleus b the struck nucleon is part of correlated pair SRC 2 2 If Nucleus A-1 is highly excited, then p M is big

Such large virtuality occurs from two nearby correlated9 nucleons Highly virtually nucleon is not a nucleon- different quark config. q Nucleon in nucleus p + q ⇤ On mass shell p p2 = M 2 MA 6 Off-mass shell Nucleus A-1 is form factor of a A-1 nucleus is low-lying state “large” proton A- 1 nucleus is 1 fast nucleon +A-2 nucleus b the struck nucleon is part of correlated pair SRC 2 2 If Nucleus A-1 is highly excited, then p M is big

Such large virtuality occurs from two nearby correlated9 nucleons Highly virtually nucleon is not a nucleon- different quark config. Free nucleon Suppression of Point Like Configurations Frankfurt Strikman

Schematic + ✏✏ .. two-component . nucleon model . Blob-like config:BLC . Point-like config: PLC Bound nucleon PLC smaller, fewer quarks high x

1 + ✏✏ .. Medium interacts with BLC1 M . energy denominator increases .. PLC Suppressed . ✏M < ✏ U | | | |

A-1

10 Quark structure of nucleon Frankfurt- Schematic Strikman PLC two-component BLC nucleon model: + ✏ .. . Blob-like config:BLC . gives high x . Point-like config: PLC q(x) . PLC does not Cioffi degli Atti ‘07 1 E V Free nucleon : H = B ,V >0 interact with 0 VE U (in MeV)P Ciofi degli Atti et al.nucleus 2007 A U = v(p,E) /2M h i V 3H=e -34.59 N = B + ✏ P , ✏ = E E < 0 e | i | i | i B P 4He -69.40 E U V 12C -82.28 In nucleus (M) : H = B | | Large values from two- VE 16O -79.68  P 40Ca -84.54 56 N M = B + ✏M P , ✏M < ✏ , PLC suppressed, ✏M ✏ > 0 amplitude e↵ect! Fe -82.44 | i | i | i | | | | 208Pb -92.20 p2 m2 N N (✏ ✏) U = Shroedinger eq. nucleon correlations | iM | i/ M / 2M large values from q (x)=q(x)+(✏ ✏)f(x) q(x), df < 0,x 0.3 PLC suppression M M dx two nucleon R = qM ; dR =(✏ ✏) df < 0 Reproduces EMC e↵ect - like every model correlations Simula q dx M dx Why this model??? Large e↵ect if v = p2 m2 is large, it is 11 EFT: Chen et al ‘16 Implications of model

The two state model has a ground state N and an excited state N ⇤ | i | i N = N +(✏ ✏) N ⇤ | iM | i M | i The nucleus contains excited states of the nucleon These configurations are the origin of high x EMC ratios

Previously missing in models of the EMC effect- same model predicts some other effect

12 A(e,e’) at x>1 is the simplest reaction to check dominance of 2N, 3N SRC andA(e,e’) to measure at absolute x>1 shows probability dominance of SRC of 2N SRCNUCLEAR PHYSICS Q22 Define Q x =x =A x goes from 1 to A Close nucle22qMo0m⌫nA encounters x=1 is exact kinematic limit for all Q2 for the scattering off a free nucleon; Jeffersonx=2 (x=3)Lab may is exact have directlykinematic observed limit for short-range all Q2 for the nucleic scattering correlations, off a A=2(A=3) with densities systemsimilar (up to those<1% correction at the heart due of to a nuclear neutron binding) star. Mark Strikman explains. M Strikman Scientists believe that the crushing forces 1 1.5,two before nucleons (left) of and SRC areis tfasthe square of the four momenta trans- during the E2 run, the team measured after (right) absorption4 of the photon. ferred to the nucleus, and q0 is the energy ratios of the cross-sections for electrons transferred to the nucleus.) In addition, scattering with large momentum transfer one needs to restrict Q2 to values of less off medium, and light nuclei in the kine- than a few giga-electron-volts squared; in matic region that is forbidden for low- this case13, nucleons can be treated as par- momentum scattering. Steps in the value tons with structure, since the nucleon of this ratio appear to be the first direct remains intact in the final state due to final observation of the short-range correlations phase-volume restrictions. (SRCs) of two and three nucleons in nuclei, If the virtual photon scatters off a two- with local densities comparable to those in Fig. 2. Scattering of a virtual photon off a nucleon SRC at x > 1, the process goes as the cores of neutron stars. three-nucleon correlation, x > 2, before (left) follows in the target rest frame. First, the SRCs are intimately connected to the and after (right) absorption of the photon. photon is absorbed by a nucleon in the fundamental issue of why nuclei are dilute SRC with momentum opposite to that of bound systems of nucleons. The long-range attraction between nucle- the photon; this nucleon is turned around and two nucleons then fly ons would lead to a collapse of a heavy nucleus into an object the out of the nucleus in the forward direction (figure 1). The inclusive size of a hadron if there were no short-range repulsion. Including a nature of the process ensures that the final-state interaction with repulsive interaction at distances where nucleons come close the rest of the nucleus does not modify the cross-section. Accord- together, ≤0.7 fm, leads to a reasonable prediction of the present ingly, in the region where scattering off two-nucleon SRCs domi- description of the low-energy properties of nuclei, such as binding nates (which for Q2 ≥ 1.4 GeV2 corresponds to x > 1.5), one predicts energy and saturation of nuclear densities. The price is the prediction that the ratio of the cross-section for scattering off a nucleus to that of significant SRCs in nuclei. off a deuteron should exhibit scaling, namely it should be constant For many decades, directly observing SRCs was considered an independent of x and Q2 (Frankfurt and Strikman 1981). In the important, though elusive, task of nuclear physics; the advent of 1980s, data were collected at SLAC for x > 1. However, they were in high-energy electron–nucleus scattering appears to have changed somewhat different kinematic regions for the lightest and heavier all this. The reason is similar to the situation encountered in particle nuclei. Only in 1993 did the sustained efforts of Donal Day and col- physics: though the quark structure of hadrons was conjectured in laborators to interpolate these data to the same kinematics lead to the mid-1960s, it took deep inelastic scattering experiments at SLAC the first evidence for scaling, but the accuracy was not very high. and elsewhere in the mid-1970s to prove directly the presence of The E2 run of the CLAS detector at Jefferson Lab was the first exper- quarks. Similarly, to resolve SRCs, one needs to transfer to the iment to take data on 3He and several heavier nuclei, up to iron, with nucleus energy and momentum ≥1 GeV, which is much larger than identical kinematics, and the collaboration reported their first find- the characteristic energies/momenta involved in the short-distance ings in 2003 (Egiyan et al. 2003). Using the 4.5 GeV continuous nucleon–nucleon interaction. At these higher momentum transfers, electron beam available at the lab’s Continuous Electron Beam one can test two fundamental features of SRCs: first, that the shape Accelerator Facility (CEBAF), they found the expected scaling behav- of the high-momentum component (>300 MeV/c) of the wave func- iour for the cross-section ratios at 1.5 ≤ x ≤ 2 with high precision. tion is independent of the nuclear environment, and second, the The next step was to look for the even more elusive SRC of three balancing of a high-momentum nucleon by, predominantly, just one nucleons. It is practically impossible to observe such correlations in nucleon and not by the nucleus as a whole. intermediate energy processes. However, at high Q2, it is straightfor- An extra trick required is to select kinematics where scattering off ward to suppress scattering off both slow nucleons and two-nucleon ▲

CERN Courier November 2005 1 How/why nucleons in nuclei cluster one pion exchange between n and p

⇡ huge from ( 3)2 =9 1 S. eq. (k) ⇠ k2 300 MeV/c

1

a2

15 Egiyan ‘06 DIS Hen et al 2013

0.4 χ2 / ndf 5.673 / 5 197Au /dx a -0.07004 ± 0.003658

EMC 0.3 56 12 Fe C 9 Linear relation -dR Be 0.2 4 He accident? 0.1 3He

d 0

12345 a2(A/d)

Fomin et al 2012 a2 Seely et al 2009 get slope

16 Common cause of dR/dx and a2(A): large virtuality

p p2-M2 large

Given Q2,x,p ? + 4-momentum conservation determines 2 p ↵ and v = p2 M 2 P + D ⌘ Q2 =2.7 GeV2,p =0 Sees wave function at ↵ 1.2 ? ⇡ |U| is large v is large can only get this from 1 short range correlation M large v is responsible for both dR/dx and a2(A) 17 The word both had been missing from models of EMC effect many models have been ad hoc. The PLC suppression model is not. Implications for nuclear physics • Nucleus modifies nucleon electroweak form factors • Nucleon excited states exist in nuclei • Medium modifications in deuteron influence extracted neutron F2 • spectator tagging • …..

18 Logic/Summary

Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed

Large virtuality

Short-ranged np interactions dominance 19 EMC effect and Logic/Summary large x plateau have same cause Data DIS-large x (e,e’) Plateau large x (e,e’,NN)

Interpret: valence quark 2 baryon clusters momentum decrease in A nucleon wf has QCD BLC,PLC etc PLC -high x PLC suppressed Three phenomena Large virtuality related by common ideas of correlations Short-ranged np related to high virtuality interactions dominance 19 Spares follow

20 17 Summary of Correlations J Ryckebusch pic NN= np -Hen talk

FIG. 16: The relative fraction of np and pp SRC pairs (excluding nn pairs) derived from A(e, e0p) and A(e, e0pp) measurements on a range of nuclei (Hen et al., 2014b).

21 is still dominated by scattering o↵ SRC pairs and ex- tracted the relative fraction of np- and pp-SRC pairs. FIG. 17: A qualitative sketch of the dominant features Fig. 16 shows that SRC pairs are predominantly np-SRC of the nucleon momentum distribution in nuclei. At pairs even in heavy neutron rich nuclei. kkF , the nucleon belongs to a D. Universal Properties of Short Range Correlations in pn-SRC pair and its momentum is balanced by that of Nuclei one other nucleon. The combined results from the inclusive and exclusive measurements described in Sections II.B and II.C lead to SRC pairs will equal 1. This, in turn, implies that in a universal picture of SRC pairs in nuclei. In the conven- neutron rich nuclei, a larger fraction of the protons will tional momentum space picture, the momentum distri- be in an SRC pair (Hen et al., 2014b; Sargsian, 2014a), bution for all nuclei and nuclear matter can be divided i.e., that a minority nucleon (e.g., a proton) has a higher into two regimes, above and below the Fermi-momentum probability of belonging to a high-momentum SRC-pair (see Fig. 17). The region below the Fermi momentum than a majority nucleon (e.g., a neutron). This e↵ect accounts for about 80% of the nucleons in medium and should grow with the nuclear asymmetry and could pos- heavy nuclei (i.e., A 12) and can be described using sibly invert the kinetic energy sharing such that the mi- mean-field approximations. The region with momenta nority nucleons move faster on average then the majority. greater than the Fermi momentum accounts for about This asymmetry could have wide ranging implications 20–25% of the nucleons (see the pie chart in Fig. 12) and for the NuTeV anomaly (Zeller et al., 2002, 2003) (see is dominated by nucleons belonging to NN-SRC, pre- Sects III.D.1,VI.A.5), the nuclear symmetry energy and dominantly pn-SRC. neutron star structure and cooling rates (Hen et al., 2016, The SRC dominance of the high-momentum tail im- 2015c), neutrino-nucleus interactions in Liquid-Argon de- plies that the shape of the momentum distributions of all tectors (Acciarri et al., 2014; Weinstein et al., 2016) and nuclei at high momenta is determined by the short range more. The study of the nuclear asymmetry dependence part of the fundamental NN interaction. The magnitude of the number of SRC pairs and their isospin structure is of the distribution (i.e., the average number of SRC pairs) a important topic that could be studied in future high- comes from the average e↵ects of the nuclear medium. energy radioactive beam facilities. The specific predominance of pn-SRC over pp- and nn-SRC is largely associated with the large contribu- tion of the tensor part of the NN interaction at short- III. Deep Inelastic Scattering (DIS) and the EMC e↵ect distances (Alvioli et al., 2008; Sargsian et al., 2005b; Schi- avilla et al., 2007), implying that the high-momentum Basic models of nuclear physics describe the nucleus as distribution in heavier nuclei is approximately propor- a collection of free nucleons moving non-relativistically tional to the deuteron momentum distribution. Experi- under the influence of two-nucleon and three-nucleon mental and theoretical studies of the latter show that, for forces, which can be treated approximately as a mean 300 k 600 MeV/c, n(k) 1/k4 (Hen et al., 2015a). field. In such a picture, the partonic structure functions   / This specific functional form follows directly from the of bound and free nucleons should be identical. There- dominance of the tensor force acting in second order, see fore, it was generally expected that, except for nucleon Section IX.A for details. motion e↵ects, Deep Inelastic Scattering (DIS) experi- The predominance of np-SRC pairs implies that, even ments which are sensitive to the partonic structure of in asymmetric nuclei, the ratio of protons to neutrons in the nucleon would give the same result for all nuclei. 17 Summary of Correlations J Ryckebusch pic NN= np -Hen talk

FIG. 16: The relative fraction of np and pp SRC pairs (excluding nn pairs) derived from A(e, e0p) and A(e, e0pp) measurements on a range of nuclei (Hen et al., 2014b).

21 is still dominated by scattering o↵ SRC pairs and ex- tracted the relative fraction of np- and pp-SRC pairs. FIG. 17: A qualitative sketch of the dominant features Fig. 16 shows that SRC pairs are predominantly np-SRC of the nucleon momentum distribution in nuclei. At pairs even in heavy neutron rich nuclei. kkF , the nucleon belongs to a D. Universal Properties of Short Range Correlations in pn-SRC pair and its momentum is balanced by that of Nuclei one other nucleon. The combined results from the inclusive and exclusive measurements described in Sections II.B and II.C lead to SRC pairs will equal 1. This, in turn, implies that in a universal picture of SRC pairs in nuclei. In the conven- neutron rich nuclei, a larger fraction of the protons will tional momentum space picture, the momentum distri- be in an SRC pair (Hen et al., 2014b; Sargsian, 2014a), bution for all nuclei and nuclear matter can be divided i.e., that a minority nucleon (e.g., a proton) has a higher into two regimes, above and below the Fermi-momentum probability of belonging to a high-momentum SRC-pair (see Fig. 17). The region below the Fermi momentum than a majority nucleon (e.g., a neutron). This e↵ect accounts for about 80% of the nucleons in medium and should grow with the nuclear asymmetry and could pos- heavy nuclei (i.e., A 12) and can be described using sibly invert the kinetic energy sharing such that the mi- mean-field approximations. The region with momenta nority nucleons move faster on average then the majority. greater than the Fermi momentum accounts for about This asymmetry could have wide ranging implications 20–25% of the nucleons (see the pie chart in Fig. 12) and for the NuTeV anomaly (Zeller et al., 2002, 2003) (see is dominated by nucleons belonging to NN-SRC, pre- Sects III.D.1,VI.A.5), the nuclear symmetry energy and dominantly pn-SRC. neutron star structure and cooling rates (Hen et al., 2016, The SRC dominance of the high-momentum tail im- 2015c), neutrino-nucleus interactions in Liquid-Argon de- plies that the shape of the momentum distributions of all tectors (Acciarri et al., 2014; Weinstein et al., 2016) and nuclei at high momenta is determined by the short range more. The study of the nuclear asymmetry dependence part of the fundamental NN interaction. The magnitude of the number of SRC pairs and their isospin structure is of the distribution (i.e., the average number of SRC pairs) a important topic that could be studied in future high- comes from the average e↵ects of the nuclear medium. energy radioactive beam facilities. The specific predominance of pn-SRC over pp- and nn-SRC is largely associated with the large contribu- tion of the tensor part of the NN interaction at short- III. Deep Inelastic Scattering (DIS) and the EMC e↵ect distances (Alvioli et al., 2008; Sargsian et al., 2005b; Schi- avilla et al., 2007), implying that the high-momentum Basic models of nuclear physics describe the nucleus as distribution in heavier nuclei is approximately propor- a collection of free nucleons moving non-relativistically tional to the deuteron momentum distribution. Experi- under the influence of two-nucleon and three-nucleon mental and theoretical studies of the latter show that, for forces, which can be treated approximately as a mean 300 k 600 MeV/c, n(k) 1/k4 (Hen et al., 2015a). field. In such a picture, the partonic structure functions   / This specific functional form follows directly from the of bound and free nucleons should be identical. There- dominance of the tensor force acting in second order, see fore, it was generally expected that, except for nucleon Section IX.A for details. motion e↵ects, Deep Inelastic Scattering (DIS) experi- The predominance of np-SRC pairs implies that, even ments which are sensitive to the partonic structure of in asymmetric nuclei, the ratio of protons to neutrons in the nucleon would give the same result for all nuclei. Two nucleon correlations 8 n(k) 8 Chen et al ‘16

FIG. 4: The nucleon momentum distributions n0(k) (dashed line) and n(k) (solid line) plotted versus 1 4 12 A momentum in fm for the deuteron, He, C and FIG. 5: Scaled two-body distribution function ⇢2,1(r)/A 56Fe. Figure adapted from (Ciofi degli Atti and Simula, (seeProbability Eq. (81)) for nuclei to withfindA =2, 3, 4. A correlation 1996a). hole is seen for all of these nuclei. The two sets of curves 2 FIG. 4: The nucleon momentum distributions n0(k) nucleonsare obtained with separated the AV18+UIX22 (left) and N LO (dashed line) and n(k) (solid line) plotted versus (right)by r potentials. Figure adapted from (Chen et al., bers of the deuteron (S =1,T = 0), a neutron-proton 2016). The meaning of R0 is discussed in the text. 1 4 12 A momentum in fmsystem. for the deuteron, He, C and FIG. 5: Scaled two-body distribution function ⇢2,1(r)/A 56Fe. Figure adaptedThe two from nucleons (Ciofi in 2N degli-SRC Attihave a andtypical Simula, distance of (see Eq. (81)) for nuclei with A =2, 3, 4. A correlation about 1 fm which means that their local density is a few V18 potential (Wiringa et al., 2014b) the d-wave compo- times higher1996a). than the average. The relative momentum nenthole is due is seen to the for pion all exchange of these tensor nuclei. force. The The com- two sets of curves of the two nucleons in the pair can be a few times the binationare of obtainedd- and s-waves with leads the to AV18+UIX a “broad shoulder” (left) and N2LO Fermi momentum, kF . Therefore the 2N-SRC are tem- in the(right) deuteron potentials. momentum distribution, Figure adapted which extends from (Chen et al., porary local density and momentum fluctuations of size from about 300 to 1400 MeV/c in the AV18 potential. bers of the deuteronequal to (S a few=1 times,T the= mean 0), values. a neutron-proton SRC of more than See Sect.2016). IX for The an explanation. meaning This of R broad0 is shoulder discussed is in the text. two nucleons probably also exist in nuclei, and might also a dominant feature in the tail of the single-nucleon system. have higher density than that of the 2N-SRC. However momentum distributions in A 12 nuclei calculated with The two nucleonstheir in probability 2N-SRC is expected have a to typical be significantly distance smaller of the AV18 potential (Wiringa et al., 2014b), see Fig. 4 about 1 fm whichthan means the probability that their of 2N local-SRC (Bethe, density 1971). is a few V18We can potential also consider (Wiringa the spatialet wave al. function, 2014b) of the the d-wave compo- The 2N-SRC are isospin-dependent fluctuations. For nucleus. The short range part of the NN interaction times higher thanexample, the average. the deuteron The is the relative only bound momentum two-nucleon sys- givesnent a correlation is due to hole the at smallpionNN exchangerelative distances, tensor force. The com- of the two nucleonstem. in We the know pair now that can density be a fluctuations few times involving the seebination Fig. 5. Precise of d definitions- and s are-waves given in leads Sect. IX. to Cal- a “broad shoulder” one neutron and one proton occur more often than those culations with various bare realistic interactions show Fermi momentum,involvingkF . Therefore like-nucleons, see the Sect. 2N IIC.-SRC Therefore are tem- we ex- that,in the apart deuteron from a normalization momentum factor depending distribution, upon which extends porary local densityamine and the deuteron momentum first. fluctuations of size thefrom di↵erent about number 300 of pairs to 1400 in di↵erent MeV/c nuclei, the in rela- the AV18 potential. The simplest nucleus, the deuteron has spin S =1, tive two-nucleon density ⇢rel(r) and its spin-isospin com- equal to a few times the mean values.⇡ + SRC of more than See Sect.N1N2 IX for an explanation. This broad shoulder is isospin T =0, and J =1. The relevant quantity ponents ⇢ST (r) at r 1.5 fm exhibit similar correla- two nucleons probablyfor electron also scattering exist is n in(k) nuclei, which is the and probability might of tionalso holes, a dominant generated by the feature interplay in of the the short-range tail of the single-nucleon have higher densityfinding than a nucleon that of of momentum the 2N between-SRC.k Howeverand k + dk. repulsionmomentum and the distributionsintermediate-range in tensorA attraction12 nuclei of calculated with This function is the sum of two terms, one arising from the NN interaction, with the tensor force governing the their probabilitythe is expectedl =0(s-wave), to and be the significantly other from the smallerl =2(d- overshootingthe AV18 at potentialr 1.0 fm. The (Wiringa correlationet hole al. is, 2014b), uni- see Fig. 4 ' than the probabilitywave). of At 2 momentaN-SRC of (Bethe, interest for 1971). short range correlated versal,We in thatcan it also is almost consider independent the of spatial the mass waveA of function of the pairs (i.e., p significantly greater than p 250 MeV/c, the nucleus (C. Ciofi degli Atti, 2015). The depth of the F ⇡ The 2N-SRC arewhere isospin-dependentpF is the typical Fermi momentum fluctuations. for medium For and correlationnucleus. hole The depends short on the range short-distance part behaviorof of the NN interaction example, the deuteronheavy nuclei), is the the only otherwise-small bound two-nucleond-wave becomes sys- very thegives potential. a correlation The value of R hole0 shown at in small Fig. 5 refersNN torelative distances, important. This is especially true at p 400 MeV/c the cuto↵ on the short distance N2LO nucleon-nucleon tem. We know nowwhere that there is density a minimum fluctuations in the s-wave. In⇡ involving the Argonne potential,see Fig. as 5. defined Precise in (Gezerlis definitionset al., 2014). are A given corre- in Sect. IX. Cal- one neutron and one proton occur more often than those culations with various bare realistic interactions show involving like-nucleons, see Sect. IIC. Therefore we ex- that, apart from a normalization factor depending upon amine the deuteron first. the di↵erent number of pairs in di↵erent nuclei, the rela- The simplest nucleus, the deuteron has spin S =1, tive two-nucleon density ⇢rel(r) and its spin-isospin com- ⇡ + N1N2 isospin T =0, and J =1. The relevant quantity ponents ⇢ST (r) at r 1.5 fm exhibit similar correla- for electron scattering is n(k) which is the probability of tion holes, generated by the interplay of the short-range finding a nucleon of momentum between k and k + dk. repulsion and the intermediate-range tensor attraction of This function is the sum of two terms, one arising from the NN interaction, with the tensor force governing the the l =0(s-wave), and the other from the l =2(d- overshooting at r 1.0 fm. The correlation hole is uni- wave). At momenta of interest for short range correlated versal, in that it is' almost independent of the mass A of pairs (i.e., p significantly greater than p 250 MeV/c, the nucleus (C. Ciofi degli Atti, 2015). The depth of the F ⇡ where pF is the typical Fermi momentum for medium and correlation hole depends on the short-distance behaviorof heavy nuclei), the otherwise-small d-wave becomes very the potential. The value of R0 shown in Fig. 5 refers to important. This is especially true at p 400 MeV/c the cuto↵ on the short distance N2LO nucleon-nucleon where there is a minimum in the s-wave. In⇡ the Argonne potential, as defined in (Gezerlis et al., 2014). A corre- Final summary

• EMC effect is related to NN correlations in two theories. Mechanism: PLC suppression enhanced by correlations • Correlations account for high x plateau seen in several experiments • Correlations are important in nuclear shadowing, important for EIC studies of nuclear gluons

23 2

2 2 Q (Ca) [GeV ] 2 1 the initial scale µ0.Astrongerx-dependence also for Eur.0.2 Phys.2 J. A (2016) 52: 268 large dipoles, such as in the in the GBW or bCGC mod- Page 57 of 100 els, gives a stronger x-dependence of shadowing at fixed 2 0.9 Q .AsshowninFig.1(center),boththeIPsatand p 2 Table 5. Key measurements in e +AcollisionsatanEICtoexplorethedynamicsofquarksandgluonsina2 nucleusinthe non-saturation regime. bCGC models predict strong Q -dependence (at fixed x) /AF

A for shadowing. It is this latter effect which is primar- 2 F Ca, IPsat Deliverables Observablesily responsible for the shadowingWhat effect we seen learn in the NMC Ca, bCGC NMC Sn/C Ca, IPsat A p NMC Ca IPsat Ca, bCGC data. Precision2 measurements of F2 /AF2 would shed C, IPsat CollectivebCGC Pb, IPsatRatios R2 Q evolution: onset of DGLAP violation,2 beyond DGLAP

0.7 0.8 C, bCGC more light on the relative importance of Q and x evolu- NMC C Pb, bCGC nuclear effects from inclusive DIStion in this regime.A-dependence of shadowing and antishadowing -3 -2 -4 -3 10 10 24810 10 We now turn to a discussion of the A and x dependence x at intermediate2 2 x x Initial conditions for small-x evolution Q [GeV ] of the saturation scale. In a simple GBW type model, Transport Production of lightinsertingColor a θ-function neutralization: impact parameter mass dependence dependence of into hadronization FIG. 1: Left: Predictions for shadowing compared to NMC R2 A2/3 coefficientsSn in C and heavy hadrons, Multiple scattering and2 mass1 dependence/3 p 2 of energy loss data. Center: predictions for 12F2 /118F2 compared to Eq. (5) yields the estimate Qs,A ≈ A R2 Qs,p ≈ 2 2 A ShadowingNMC data& at x Anti-shadowing=0.0125.nuclear Right: Likewisematter for Qand=5GeV jets in SIDIS 1/3 2 Medium2 effect of heavy quarkonium1/3 production 0.26A Q for 2πR ≈ 20 mb and RA ≈ 1.1 A fm. as a function of x. s,p p Nuclear density Hadron productionThe smallnessTransverse of Q2 momentum/Q2 ,duetotheconstantfactor broadening of produced hadrons ⇤ ⇤ s,A s,p and its fluctuation in SIDIS ∼ 0.26 has sometimesAzimuthal beenφ-modulation interpreted of[9, produced 15, 16] as hadrons a evolution at high parton densities, combined with a re- weak nuclear enhancement of Qs.Wewillarguehere alistic b-dependence, is better captured in the bCGC that detailed considerations of QCD evolution and the b-dependence of the dipole cross section result in a sig- model [10, 11]. Both1.2 the IPsat model and the bCGC fort to study the properties of quarks and gluons and their nificantly larger nuclear enhancement of Qs. model provide excellent fitsEMC to E136 a wide range of HERA dynamics in the nuclear environment both experimentally 1.1 The effect of QCD evolution on Qs,A in the IPsat nu- data for x ≤ 0.01 [11, 12].NMC We E665 will now discuss the pos- Green sibility that DIS off nuclei can distinguish respectively clear dipole crossand section theoretically. is from the DGLAP-like growth 1 of the gluon distribution.Using The the increase same in very the successfulgluon den- QCD formulation at between theseD “classical CGC” and “quantum CGC” mo- 2 2 tivated models. sity with increasingtheQ leadingand decreasing power in(dominant)Q for proton dipole scattering, and using nucleons / F 0.9 radius r causes Q grow even faster as a function of A. Astraightforwardgeneralizationofthedipoleformal-Ca thes DGLAP evolution for the scale dependence of par- 2

ism to nuclei isF to introduce0.8 the coordinates of the indi- This is seen qualitativelyton momentum for two di distributions,fferent nuclei, A severaland QCD global analy- b B (with A>B), in a “smooth nucleus” approximation vidual nucleons { ⊥i}.OneobtainsintheIPsatmodel, ses have been able to fit the observed non-trivial nuclear A b b 0.7 of Eq. (4) wherebydependencei=1 Tp( of⊥ existing− ⊥i)isreplacedby data, attributing all observed nu- A dσ 2 A b⊥ dip −r F (x,r) P T (b⊥−b⊥ ) ATA( ). We obtain =2 1 − e i=1 p i , EIC(4) clear dependences —including its x-dependence and nu- 2b 0.6 - Frankfurt Strikman and Guzeyd ⊥ 2 2 2 Q A T (bclear⊥) F ( atomicx, Q ) weightA1/3 AF-dependence—(x, Q ) to a set of nucleus- ! " s,A = A s,A ∼ s,A . (6) 0.5 2 bdependent2 quark and1/3 gluon2 distributions at an input scale where F is defined0.0001 in Eq. (3). 0.001 The positions 0.01 of 0.1Qs,B 1 B TB( ⊥) F (x, Qs,B) B F (x, Qs,B) Physics Reports 512 (2012) 255–393 b Q0 1GeV[176,178,179].Asanexample,thefittingre- the nucleons { ⊥i} are distributed accordingx to the ! b⊥ The scaling violationssult of in EskolaF implyet that,al. is as plotted observed along in with the data on the Woods-Saxon distribution TA( i). We denote the 1/3 no parton saturation Fig. 56. The ratio of nuclearb⊥ over nucleon F2 structureRefs. [9, func- 17], theratio growth of of theQs Fis2 fasterstructure than A function.Also, of calcium divided by average of an observable O over { i} by ⟨O⟩N ≡ 2 A because the increase of F with Q is faster for smaller x, dtion,2b⊥ TR2(,b as⊥ ) aO function({b⊥ }). of The Bjorken averagex,withdatafromexisting differen- that of deuterium in fig. 56, where the dark blue band i=1 i A i i 2 2 the A-dependence of Q is stronger for higher energies. In Kowalski Lappi Venugopalantial dipole PRLfixed cross target100, section DIS is 022303 wellexperiments approximated at useQ by[9]> 1GeV CGC,,alongwiththe indicatess the uncertainty of the EPS09 fit [176]. The suc- Contents lists available at SciVerse ScienceDirect# $ QCD global fit from EPS09 [176]. Also shown iscontrast, the expected the dipolecess2 cross of the section QCD in globalthe bCGC analyses model de-clearly indicates that the A A pends only on the “geometrical scaling” combination [26] gluon saturation; many recent paperskinematicdσ coverage & discussion of theT inclusive(b⊥) measurements of detailed at the EIC. modelsresponse of the nuclear cross-section to the variation of dip A p rQ (x)withoutDGLAPscalingviolationsandtherefore 2 2 The purple≈ 2 error1 − band1 − is the expectedσdip systematic(5) uncertaintys Q (Ca) [GeV ] d2b⊥ 2 2 the probing momentum scale Q Q0 is insensitive to the

1 ! % atthe the& EICN initial assuming' scale( aµ0.Astronger2% (a total) * of 4%)x-dependence systematicdoes not have er- also this for particular nuclear enhancement [27]. 0.2 2 ± nuclear structure, since the DGLAP evolution itself does ror,large while dipoles, the statistical such as uncertainty in the in is the expected GBWPrecise to or be bCGCextraction much mod- of the A dependence of Qs will play an where, for large A,theexpressioninparenthesiscanbe important role innot distinguishing introduce between any nuclear “classical” dependence. and However, it does smaller. b⊥ Physics Reports replaced byels, exp gives− ATButA( a stronger) σp nuclear[13].x-dependence All parameters wave of of shadowing functions at fixednot answer the fundamental questions: Why are the par- 2 2 dip “quantum” evolution in the CGC. 0.9 Q .AsshowninFig.1(center),boththeIPsatand p the model come from either fits of the model to ep-data Acarefulevaluationshowsthatbecausethedensityton distributions in a nucleus so different from those in a

2 + , 2 or from the Woods-SaxonbCGC modelsenter distributions; predict in strong noall additional Qapproaches-dependence pa- profile in(at a nucleusfixedfreex is) nucleonmore uniform at the than probing that of scale the pro-Q0?Howdothenuclear

/AF rametershigh-energy are introduced proton for eA collisionscollisions. Thewith same a momentum ex- ton, transferthe saturationstructure scales in and nuclei QCD decrease dynamics more slowly determine the distributions

A for shadowing. It is this latter effect which is primar- journal homepage:2 www.elsevier.com/locate/physrepercise is repeatedlarger than for the 2 GeV bCGC (corresponding model. to hard scatteringswith b than tak- in the proton. The dependence of the satu-

F of quarks and gluons in a nucleus? Ca, IPsat ingily place responsible at a distance for the less shadowing than one tenth effect of seen a femtome- in the NMC Ca, bCGC NMC Sn/C Ca, IPsat In Fig. 1 (left), we compare the prediction of the IP- A rationp scale on the impactThe nucleus parameter is a is “molecule” plotted in Fig. in 2. QCD, made of nucleons NMC Ca IPsat Ca, bCGCsat and bCGCter).data. models Precision with the measurements experimental data of [25]F2 /AFThe2 saturationwould shedscale—which, in gold in nuclei turn, at are the boundmedian impactstates of quarks and gluons. C, IPsat bCGC Pb, IPsat 2 0.7 0.8 C, bCGC on nuclear DISmoreAre from the light thequarks on NMC the and collaboration relative gluons in importance a[14]). nucleus Fig- confined ofparameterQ and within forx evolu- theUnlike total cross the molecule section bmed. inis QED, about nucleons 70% in the nucleus are NMC C Pb, bCGC 2 ure 1 (right)thetion individual shows in thisthat nucleons? theregime.x dependence Or does of the shadow- nuclear environmentof the value at packedb =0;incontrast, next to eachQs other,,p(bmed. and)isonly there are many soft gluons -3 -2 -4 -3 2 10 10 24810 10 ing for fixedsignificantlyQWein now the a IPsatff turnect model their to a discussion is distributions? very flat. of This the The is A EMCand∼ 35%x experi-dependence of the valueinside24 at b nucleons=0. when probed at small x.TheDISprobe x 2 2 x because the best fit to ep-data in DGLAP-based dipole The A dependence of the saturation scale for various Q [GeV ] mentof theat CERN saturation [213] and scale. experiments In a simple in the GBW following type two model,has a high resolution in transverse size 1/Q.Butits models [8, 9] is given by a very weak x-dependence at x is shown in Fig. 3, for the IPsat model on the left and ∼ decadesinserting clearly a θ revealed-function that impact the momentum parameter distribution dependence intoresolution in the longitudinal direction, which is propor- FIG. 1: Left: Predictions for shadowing compared to NMC of quarks in a fast-moving nucleus is not a simpleR2 super-A2/3 tional to 1/xp 1/Q,isnotnecessarilysharpincom- Leading twist nuclear shadowing phenomenaSn C in hard processes2 1/3 p 2 ∼ data. Center: predictions for 12F2 /118F2 compared to positionEq. (5) of yields their distributions the estimate withinQs,A nucleons.≈ A Instead,R2 Qs,pparison≈ with the Lorentz contracted size of a light-speed 2 2 A 1/3 NMC data at x =0.0125. Right: Likewise for Q =5GeV the measured1/3 ratio2 of nuclear2 over nucleon structure func-1/3 nucleus, 2RA(m/p), with nuclear radius RA A 0.26A Qs,p for 2πRp ≈ 20 mb and RA ≈ 1.1 A fm. ∼ ∝ as a function of x. tions, as defined in eq. (23),2 follows2 a non-trivial function and the Lorentz contraction factor m/p and nucleon mass with nuclei The smallness of Q /Qs,p,duetotheconstantfactor of Bjorken x,significantlydis,A fferent from unity, and shows m. That is, when 1/xp > 2RA(m/p), or at a small the∼ suppression0.26 has sometimesas x decreases, been as shown interpreted in fig. 56. [9, The 15, ob- 16] asx a 1/2mR 0.01, the DIS probe could interact coher- ∼ A ∼ evolution at high parton densities, combined with a re- servedweak suppression nuclear enhancement at x 0.01, which of Q iss.Wewillarguehere often referred to ently with quarks and gluons of all nucleons at the same a b, c ∼ L. Frankfurt , V. Guzey ⇤, M. Strikmanalistic b-dependence, is better captured in the bCGC asthat the phenomenon detailed considerations of nuclear shadowing, of QCD is much evolution stronger andimpact the parameter of the largest nucleus moving nearly than what the Fermi motion of nucleons inside a nucleus at the speed of light, p m. The destructive interfer- model [10, 11]. Both the IPsat model and the bCGC b-dependence of the dipole cross section result in a sig- ≫ a could account for. This discovery sparked a worldwide ef- ence of the coherent multiple scattering could lead to a Nuclear Physics Department, School of Physics and Astronomy,model provide Tel Aviv excellent University, fits to a 69978 wide range Tel Aviv, of HERA Israel nificantly larger nuclear enhancement of Qs. data for x ≤ 0.01 [11, 12]. We will now discuss the pos- The effect of QCD evolution on Qs,A in the IPsat nu- b Theory Center, Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA sibility that DIS off nuclei can distinguish respectively clear dipole cross section is from the DGLAP-like growth c Department of Physics, the Pennsylvania State University,between State these College, “classical PA CGC” 16802, and USA “quantum CGC” mo- of the gluon distribution. The increase in the gluon den- 2 tivated models. sity with increasing Q and decreasing (dominant) dipole Astraightforwardgeneralizationofthedipoleformal- radius r causes Qs grow even faster as a function of A. ism to nuclei is to introduce the coordinates of the indi- This is seen qualitatively for two different nuclei, A and b B (with A>B), in a “smooth nucleus” approximation vidual nucleons { ⊥i}.OneobtainsintheIPsatmodel, article info A b b abstract of Eq. (4) whereby i=1 Tp( ⊥ − ⊥i)isreplacedby A dσdip − 2 A b −b ATA(b⊥). We obtain r F (x,r) Pi=1 Tp( ⊥ ⊥i) 2 =2 1 − e , (4) - d b⊥ 2 2 2 Article history: We present and discuss the theory and phenomenologyQ A T (b⊥) F of(x, the Q ) leadingA1/3 F ( twistx, Q ) theory ! " s,A = A s,A ∼ s,A . (6) Accepted 7 December 2011 2 b 2 1/3 2 whereof nuclearF is defined shadowing in Eq. which(3). The is positions based on of theQ combinations,B B TB( ⊥) F of(x, the Qs,B) generalizationB F (x, Qs,B) of the b Available online 8 January 2012 the nucleons { ⊥i} are distributed according to the Gribov–Glauber theory, QCD factorization theorems,The scaling violations and the in F HERAimply that, QCD as analysis observed in of Woods-Saxon distribution T (b⊥ ). We denote the editor: W. Weise A i 1/3 diffraction in lepton–protonb⊥ deep inelastic scatteringRefs. [9, 17], (DIS). the growth We of applyQs is faster this than techniqueA .Also, for average of an observable O over { i} by ⟨O⟩N ≡ 2 A because the increase of F with Q is faster for smaller x, d2b⊥ T (b⊥ )O({b⊥ }). The average differen- thei=1 analysisi A ofi a widei range of hard processesthe withA-dependence nuclei of –Q inclusiveis stronger for DIS higher on energies. deuterons, In tial dipole cross section is well approximated by[9] s #medium-range$ and heavy nuclei, coherent andcontrast, incoherent the dipole diffractive cross section DIS in the with bCGC nuclei, model de- and A b A pends only on the “geometrical scaling” combination [26] hard diffractiondσdip in proton–nucleusTA( ⊥) p scattering – and make predictions for the effect of ≈ 2 1 − 1 − σdip (5) rQs(x)withoutDGLAPscalingviolationsandtherefore nucleard2 shadowingb⊥ in the corresponding2 sea quark and gluon parton distributions. We also % &N ' ( ) * does not have this particular nuclear enhancement [27]. analyze the role of the leading twist nuclear shadowingPrecise extraction in generalized of the A dependence parton of Q distributionss will play an where, for large A,theexpressioninparenthesiscanbe important role in distinguishing between “classical” and in nuclei and inAT certainA(b⊥) p characteristics of final states in nuclear DIS. We discuss the limits replaced by exp − 2 σdip [13]. All parameters of “quantum” evolution in the CGC. theof applicability model come+ from of either the fits leading, of the model twist to approximationep-data Acarefulevaluationshowsthatbecausethedensity for small x scattering off nuclei and the oronset from the of the Woods-Saxon black disk distributions; regime no and additional methods pa- ofprofile detecting in a nucleus it. It iswill more be uniform possible than to that check of the many pro- rametersof our predictions are introduced for ineA thecollisions. near future The same in theex- studieston, the of saturation the ultraperipheral scales in nuclei decrease collisions more slowly at the ercise is repeated for the bCGC model. with b than in the proton. The dependence of the satu- LargeIn Fig. Hadron 1 (left), weCollider compare (LHC). the prediction Further of the checks IP- willration be scale possible on the impact in pA parametercollisions is plotted at the in LHC Fig. and 2. satforward and bCGC hadron models production with the experimental at the Relativistic data [25] The Heavy saturation Ion Collider scale in gold (RHIC). nuclei at Detailed the median tests impact will on nuclear DIS from the NMC collaboration [14]). Fig- parameter for the total cross section bmed. is about 70% be possible at an Electron–Ion Collider (EIC) in the USA and at the Large Hadron–Electron2 ure 1 (right) shows that the x dependence of shadow- of the value at b =0;incontrast,Qs,p(bmed.)isonly ingCollider for fixed (LHeC)Q2 in the at IPsat CERN. model is very flat. This is ∼ 35% of the value at b =0. because the best fit to ep-data in DGLAP-based dipole The ©A dependence2012 Elsevier of the B.V. saturation All rights scale for reserved. various models [8, 9] is given by a very weak x-dependence at x is shown in Fig. 3, for the IPsat model on the left and

Contents

1. Introduction...... 257 2. The Gribov results for nuclear shadowing...... 260 2.1. The Gribov picture of space–time evolution of high-energy processes ...... 260 2.2. Nuclear shadowing in pion–deuteron scattering ...... 260 2.3. Comparison of the Gribov and Glauber results for nuclear shadowing ...... 265 2.4. The AGK cutting rules and nuclear shadowing...... 266 3. Leading twist theory of nuclear shadowing for quark and gluon nuclear parton distribution functions...... 267 3.1. Derivation of the master equation for nuclear parton distribution functions...... 267 3.1.1. Contributions of the interaction with one and two nucleons of the target ...... 267 3.1.2. Contribution to nuclear shadowing of the interactions with N 3 nucleons of the target: the cross section (color) fluctuation formalism...... 272 3.1.3. The color fluctuation approximation within the color fluctuation formalism ...... 275 3.1.4. Eikonal approximation violates constraints due to energy–momentum conservation...... 277

⇤ Corresponding author. Tel.: +1 757 269 7243; fax: +1 757 269 7002. E-mail addresses: [email protected] (L. Frankfurt), [email protected] (V. Guzey), [email protected] (M. Strikman).

0370-1573/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2011.12.002 2

Jastrow method used traditionally, or whether it sup- (spin-independent) two-body density: ports one or more of the approaches introduced recently. + + We also point out that apparent differences between the PF (r) ≡⟨f| δ (r − rab) τa τb |i⟩ , (5) results of UCOM and Brueckner methods are largely fic- a

25 Deep Inelastic Scattering

e Q2 k0 + k3 k+ 2 x = = = Qq ⌫,Q 2P q P 0 + P 3 P + · 19. Structure functions 13 k k+=x P+ Nucleon from PDG 1 1 P NNPDF2.3 (NNLO) g/10 0.9 0.9 xf(x,µ2=10 GeV2) xf(x,µ2=104 GeV2) s 0.8 0.8 g/10 0.7 0.7 d 0.6 0.6 The 1982 EMC effect involves deep u v c 0.5 0.5 uv inelastic scattering from nuclei 0.4 0.4 u dv 0.3 0.3 b d s v EMC= European Muon Collaboration 0.2 0.2 d u 0.1 0.1 c 0 0 -3 -3 10 10-2 10-1 1 10 10-2 10-1 1 26x x Figure 19.4: The bands are x times the unpolarized parton distributions f(x) (where f = uv,dv, u, d, s s,¯ c =¯c, b = ¯b, g) obtained in NNLO NNPDF2.3 global 2≃ 2 2 4 2 2 analysis [45] at scales µ =10GeV and µ =10 GeV ,withαs(MZ)=0.118. The analogous results obtained in the NNLO MSTW analysis [43]canbefoundin Ref. [62].

γ γ γ γ where we have used F2 =2xFT + FL,nottobeconfusedwithF2 of Sec. 19.2. Complete formulae are given, for example, in the comprehensive reviewofRef.80. γ 2 The hadronic photon structure function, F2 ,evolveswithincreasingQ from the ‘hadron-like’ behavior, calculable via the vector-meson-dominance model, to the dominating ‘point-like’ behaviour, calculable in perturbative QCD. Due to the point-like γ 2 coupling, the logarithmic evolution of F2 with Q has a positive slope for all values of x, see Fig. 19.15. The ‘loss’ of quarks at large x due to gluon radiation is over-compensated by the ‘creation’ of quarks via the point-like γ qq¯ coupling. The logarithmic evolution was first predicted in the quark–parton model→ (γ∗γ qq¯)[81,82],andtheninQCDin the limit of large Q2 [83]. The evolution is now known→ to NLO [84–86]. The NLO data analyses to determine the parton densities of the photon can be found in [87–89].

19.5. Diffractive DIS (DDIS) Some 10% of DIS events are diffractive, γ∗p X + p, in which the slightly deflected proton and the cluster X of outgoing hadrons→ are well-separated in rapidity. Besides 2 x and Q , two extra variables are needed to describe a DDIS event: the fraction xIP of the proton’s momentum transferred across the rapidity gapandt,thesquareofthe 4-momentum transfer of the proton. The DDIS data [90,91] are usually analyzed using D two levels of factorization. First, the diffractive structurefunctionF2 satisfies collinear

August 21, 2014 13:18 Implication 1 for EIC?

Why are EMC ratios independent of Q2?

• Is the medium modification for matrix elements yielding higher-twist effects same as for leading twist? M. Strikman • Can EIC add by examining Q2 dependence • Large x is on the kinematic edge, but perhaps

can do during a phase in which energy is 27 ramped up The EMC Effect Cern Courier I NTERNATIONAL JOURNAL OF HIGH-ENERGY PHYSICS Nov. 1982 CERNCOURIER

WELCOME V OLUME 53 NUMBER 4 M AY 2013 CERN Courier – digital edition Welcome to the digital edition of the May 2013 issue of CERN Courier.

Last July, the ATLAS and CMS collaborations announced the discovery of a new particle at the LHC with a mass of 125 GeV. They referred to it as a “Higgs-like boson” because further data were needed to pin down more of its properties. Now, the collaborations have amassed enough evidence to identify the new particle as a Higgs boson, although the question remains of whether it is precisely the Higgs boson of the Standard Model of particle physics. The Deep in the nucleus: masses of these particles were just as electroweak theory predicted, based on a puzzle revisited other particle interactions continue to provide puzzles in more complex heavy-ion collisions.

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HEAVY IONS ASTROWATCH IT’S A The key to fi nding Planck reveals an out if a collision almost perfect HIGGS BOSON EDITOR: CHRISTINE SUTTON, CERN is head on universe The new particle DIGITAL EDITION CREATED BY JESSE KARJALAINEN/IOP PUBLISHING, UK p31 p12 is identifi ed p21

CERNCOURIER WWW. V OLUME 53 NUMBER 4 M AY 2013 Higinbotham, Miller, Hen, Rith CERN Courier 53N4(’13)24 28 The EMC Effect Cern Courier I NTERNATIONAL JOURNAL OF HIGH-ENERGY PHYSICS Nov. 1982 CERNCOURIER

WELCOME V OLUME 53 NUMBER 4 M AY 2013 CERN Courier – digital edition Welcome to the digital edition of the May 2013 issue of CERN Courier.

Last July, the ATLAS and CMS collaborations announced the discovery of a new particle at the LHC with a mass of 125 GeV. They referred to it as a “Higgs-like boson” because further data were needed to pin down more of its properties. Now, the collaborations have amassed enough evidence to identify the new particle as a Higgs boson, although the question remains of whether it is precisely the Higgs boson of the Standard Model of particle physics. The Deep in the nucleus: masses of these particles were just as electroweak theory predicted, based on a puzzle revisited other particle interactions continue to provide puzzles in more complex heavy-ion collisions.

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HEAVY IONS ASTROWATCH IT’S A The key to fi nding Planck reveals an out if a collision almost perfect HIGGS BOSON EDITOR: CHRISTINE SUTTON, CERN is head on universe The new particle DIGITAL EDITION CREATED BY JESSE KARJALAINEN/IOP PUBLISHING, UK p31 p12 is identifi ed p21

• How does thCERNe nucCOURIERleus WWW. V OLUME 53 NUMBER 4 M AY 2013 Higinbotham, Miller, Hen, Rith • emerge from QCD, a theory CERN Courier 53N4(’13)24 • of quarks and gluons? 28