EMC Effect, Short-Range Correlations in Nuclei and Neutron Stars

EMC Effect, Short-Range Correlations in nuclei and Neutron Stars

Mark Strikman, Penn State University

PANIC 11, July 28, 2011 Key questions relevant for high density cold nuclear matter in neutron stars: • Are nucleons good nuclear quasiparticles? Do nucleon momentum distributions make sense for k > mπ? yes - at least up to momenta ~ 500 MeV/c • Probability and structure of the short-range/ high momentum correlations in nuclei 20% in medium and heavy nuclei - mostly tensor pn correlations. I=1 << I=0 • What are the most important non-nucleonic degrees of freedom in nuclei? EMC effect - deﬁnite signal - but probes admixture on the scale ≤ 1% • Microscopic origin of intermediate and short-range nuclear forces Meson exchange models - serious problem with lack of enhancement of antiquarks in nuclei

2 Probability and structure of SRC in nuclei Questions: ☛ Probability of SRC? ☛ Isotopic structure ☛ Non-nucleonic components

Dominant contribution for large k; 2N SRC: k1 ~k |p1| kF k ~-k momentum dependence - singular V(k) |p2|

Two nucleon SRC

2N SRC ρ 5ρ0 ∼ Connections to neutron stars:

m n f a) I=1 nn correlations, 2

Short-range NN correlations . p 1 n b) admixture of protons in neutron (SRC) have densities ÷ p 1.7 fm 1 stars → I=0 sensitivity comparable to the density in ∼ p n the center of a nucleon - n c) multi-nucleon correlations drops of cold dense nuclear

matter 3 ρ .17fm− 0 ∼

3 A(e,e’) at x>1 is the simplest reaction to check dominance of 2N, 3N SRC and to measure absolute probability of SRC NUCLEAR PHYSICS Q2 Deﬁne x = A Close nucle2qo0mnA 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 toto those<1% correction at the heart due of to a nuclear neutron binding) star. Mark Strikman explains.

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 case, 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 L

CERN Courier November 2005 1 20

FIG. 2.9: A typical conﬁguration for the j-nucleon correlation.

1 3 j 0.15 We c0a.22lculated the r0a.27diative correction factors for xB < aj(A) d rρ (r), a2 A(2); a3 A ; a4 A (2.40) ∝ A A ∼ 2 us∼ing Sargsian’s∼cross sections [19] andforthe fA>orm 12alism of ! N in the range A = 12 207. Thus ρA(α, k ) should beMaopracticallyand Tsaiuniv[20]ersal. Thfunctionese factoofrsα,akre ainlmaowidest inαd,ekpenrange.dent where ρA(r) is the nuclear density−. Eq. 2 predicts a⊥faster ⊥ ⊥ In momentum space ρj(α, k ) corresponds to the conotributionf xB forof1j<-nucleonxB < configuration,2 for all nucleiwhereused.theSincelarge momenthere tumare increase with Aofothef hifastghernrucleonelativeiscbalancedo2rre⊥latiobnys,theleadothering t(oj 1)n2onucleonstheoretoficathisl crconfigurationoss section c(seealcufig.latio2.9).ns foTher x momen> 2,tumwe σA1 (j 1 1.4 3(Zσep + Nσen) A ( He) (GeV/c)2 one expects [6, 9] that the ratio R(A, 3He) = 5 Y 2 3σA(Q ,xB ) where Z and N are the number of protons and neutrons 2 o15f inclusive electron scattering from nucleus Aσ3He(Q ,xB) We thank Prof. V.A. Khodel for the explanation, how these formulae can be obtained within the Fermi liquid theory. Similar expression 3 for a was discussed b2y Erikssons [157]. This estimate is ratherin nrough,ucleussinceAgas, σapproeN iximations the elisecnottrogono-dnuifclargeleonhardcrocoress seeffcectstioaren, A and He is indep2endent of Q and xB (ie: it scales). 2 present. is the normalized yield in a given (Q ,xB ) bin [32] and This scale factor is related to the relative probability of Y A Crad is the ratio of the radiative correction factors for A 2-nucleon SRC those nuclei. In our previous work [10] we and 3He (CA = 0.95 and 0.92 12C and 56Fe respec- directly measured these ratios for the first time and es- radA tively). In our Q2 range, the elementary cross section tablished that they indeed scale, confirming findings [9] correction factor A(2σep+σen ) is 1.14 0.02 for C and which reported scaling based on the comparison of the 3(Zσep+Nσen) ± data for A 3 [11–13] and A = 2 [14] obtained in some- 4He and 1.18 0.02 for Fe. Fig. 1 shows the resulting what differ≥ent kinematic conditions. In this work, we ratios integrat±ed over Q2 > 1.4 GeV2. repeat our previous measurement with higher statistics. These cross section ratios a) scale the first time for 3 Moreover we can use the ratio R(A, He) to search 1.5 < xB < 2, which indicates that 2-nucleon SRCs dom- for the even more elusive 3-nucleon SRC: correlations inate in this region (see Ref. [10]), b) increase with xB which originate from both short-range NN interactions for 2 < xB < 2.25, which can be explained by scattering and three-nucleon forces. As 3-nucleon SRC are very off nucleons involved in moving 2-nucleon SRCs, and c) low-probability, we need to suppress 2-nucleon SRC by scale a second time at 2.25 xB 2.8, which indicates 2 ≤ ≤ choosing xB > 2 so that ν k /2mN . This analysis was that 3-nucleon SRCs dominate in this region. designed to probe for 3-nu$cleon correlations by looking Assuming that the scaling regions indicate the kine- for scaling in the region 2 xB 3. matical domain where the corresponding SRCs dominate, Two sets of measurem≤ents w≤ere performed at the the ratio of the per-nucleon SRC probabilities in nucleus 3 3 3 Thomas Jefferson National Accelerator Facility in 1999 A relative to He, a2(A/ He) and a3(A/ He), are just and 2002. The 1999 measurements used 4.461 GeV elec- the values of the ratio r in the appropriate scaling region. 4 12 3 3 trons incident on liquid He and solid C targets. The a2(A/ He) is evaluated at 1.5 < xB < 2 and a3(A/ He) 20

FIG. 2.9: A typical conﬁguration for the j-nucleon correlation.

In relativistic theory the answer is more complicated. It seems fruitful for the theoretical analysis of hard phenomena to define formally the notion of j-nucleon correlation. Look at a subsystem of j nucleons in the ground state having invariant mass jmN, where nucleons obtain large relative momenta due to hard short-range interactions between all j nucleons. Typical example of the three-nucleon correlation is shown in fig. 2.8. Before a hard interaction the j N nucleons are in the average configuration (αi αj 1), j-nucleon correlation contribute to ρA(α, k ) in the region 3 α < j only due to momentum conservation. In∼the non-relativistic∼ Schrödinger equation this kinematic⊥ decomposition N of j-nucleon correlations is not evident. Therefore one cannot relate simply n(k) to ρA(α, k ) for α 2. will depend only on the ratio aj(A)/aj(A!). This ‘scal- 2002Nmeasurements used 4.471 G⊥ eV electrons incident on Though at α A A-nucleon correlation should dominate ρA(α, k ), in the region 1 < α A relative contributions → 56⊥ ing’ of theofraditiffoerenwillt bconfigurationse strong evidearencedeterminedfor the dombiynathencecompaetitionsolid of Ftweotafactors:rget andthe4.7smallGeVprobabilitelectronys ainj ctoidefindnt oan a of scattercorrelationing from awithj-nuclargeleonjSandRC.theNotenhancemene that mottioofn ohigherf liquidcorrelations3He tdueargetot. a Tslohwe er12decreaseC and 5of6Fetheirdatcona wtributionere taken N the SRC towilρlAc(hαa, nkge) atthelargevaluαe (seeof theq.e r(2.43)).atio, buThereforet not theit seemswithnaturalan emtoptyexpliqectuidthat-targatetleastcell.in the region of not too ⊥ scaling itselflarge[7α, 8].3 (which is probed until now) few-nucleon correlationsScatte(FNC)red eldominate.ectrons weThreus,dethetectneucleond in tdensithe CLyAmatrixS spec- N ρA(α, k ) can be effectively expanded over the contribution of j-nucleon correlations ρj(α, k ): Final state int⊥eractions (FSI) also can affect the inclu- trometer [15]. The lead-scin⊥tillator electromagnetic sive cross section and must be taken into account . In caAlorimeter provided the electron trigger and was used to 1 N SRC studies, FSI consists of two components: inρterA(αac-, k ) =identaijfρyj(eαle,cktr)o.ns in the analysis. Vertex cuts we(2.38)re used A ⊥ ⊥ tion of the struck nucleon (i) with other nucleons in the toj=2eliminate the target walls. The estimated remaining j-nucleon SRC and (ii) with nucleons in the A j residual contribution from the two Al 15 µ target cell windows nucleus. DueMoretoaccuratethe smatreatmenller distat ncesis requiredand smato −lleraccounrelat tforivethe c.m.is lessmotionthanof0the.1%j.-nucleonSoftwaconfigurationre fiducial cinutsthewmeanere usedfield to of the nucleus. It is expected that this effect should lead to small corrections except near the edge of the j-nucleon momenta of nucleons in the SRC, the first component of correlation. This is because the scale of the repulsive peotenxclutialde isreconsiderablygions of nonlarger-unifothanrm dthatetectforor rtheesplong-rangeonse. Kine- FSI dominpaotentestial.[9, 21]. This means that FSI are localized matic corrections were applied to compensate for drift mainly withThein SaRjC’ssin, heq.ence(2.38)the FcanSI bcaenestimatedmodify σon(j)thebubasist ofchtheambnon-relativisticer misalignmeScnthr¨s aodingernd magequationnetic fieforld unnuclearcertaiWFnties. not aj(A)since(ratitheyos) iaren thdeterminedScalinge decom ofpo bthesyittheio ratiosn meanof Eq ofin. (tern 1(e,e’)) ucleon crossdistances. sectionsWe uThesedwtellhe knoGEwnANfactT-bthatasedtheCLnAucleonS simudensitlatioyn,inGtheSIM, Since thcene terproofbathebilitniucleuses of jis-nlargerucleonthanSRCneararetheexsurfacepectedleadstoto determinea certain deptendencehe electronof aj onacctheeptatomicance cnoumrrebcer.tioThisn fac- to drop rdepapiendencedly withcanj b(e sestimatedince the innutheclegasus iappros a dximationilute where15 for j A Qualitative idea - to absorb a large Q for j> x>j-1 atto leastrs, t aj knucleonsinginto shouldaccoun tcome“bad close” or “together.dead” h a rdware bound system of nucleons) one expects the cross section channels in various components of CLAS. The mea- For each configuration wave function is determined by local propertiesj 3 and hence universal. For ratios of heavy and light nuclei for j < x < j +aj1 to(1/A)sur[ρeAd(ar)]ccedprt.ance-corrected, normalized inclusive e(2.39)lectron B ∼ suchA! x,aj (scatteringA) off j+1 nucleons is a small correction. 3 4 12 56 equal . Moreover one expects that the relative yields on He, He, C and Fe at 1 < xB < 2 agree A aj (A!) ·Here ρ (r) is the nucleon density in the coordinate spacewnormalizedith Sargsiaaccordingn’s radiatoted ρcr(ors)ds 3srec=tiAon. sThe[16calculation] that were probabilities of Aj-nucleon SRC 2should grow witahj(AA()for 2 A 2 using the convσeneAtional(x, Qfits)ofx>ρA1(=r), obtainedA in electronσj(x,andtuned Q proton) on scatteringSLAC datdataa [1[158,7] and159]descrleadsibtoedarrathereasonasimilarbly well A 12) as [4] j σj(x>j,Q )=0 ≥ A dependence of aj, which can be roughlyj=2 approximatedtashe Jefferson Lab Hall C [18] data. 1 3 j 0.15 W0.22e calculated t0h.27e radiafortive A>co r12rection factors for xB < aj(A) d rρA(r), a2 A ; (2) a3 A ; a4 A (2.40) ∝ A ∼ ∼2 using Sargsia∼n’s cross sections [19] and the formalism of ! N Mo and Tsai [20]. These factors are almost independent in the range A = 12 207. Thus ρA(α, k ) should be a practically universal function of α, k in a wide α, k range. where ρA(r) is the nuclear de−nsity. E2q. 2 predic⊥ts a faster 2 ⊥ ⊥ In momentum space ρj(α, k ) corresponds to the contributionof xBoffojr-n1ucleon< xBconfiguration,< 2 for all nwhereuclei uthesed.largeSincemomenthertume are increasσe Aw1it(hjA of1hitum2, we an expectation of steps in the ratio of σ(A) for heavy a−nd dependence of ρ2 is expected toσb(Ae!similar) to that of the useddeuteron,the 1since< xtheB 1.4 3(Zσep + Nσen) A ( He) (GeVOnly/c)2 o nfinale exp stateects [6 ,interaction9] that the r a(fsi)tio R within(A, 3He) correlation= survives in this limit forY σtot. 2 3σA(SinceQ ,xB ) the local structure of WFs is universal wher- thesee Z a localnd N fsiare shouldthe num beber alsoof pr ouniversal.tons and neutrons Aσ (Q2,x ) of inclusive electron scattering from nucleus 3He 15BWe thank Prof. V.A. Khodel for the explanation, how these formulae can be obtained within the Fermi liquid theory. Similar expression 3 2 in nucleus A, σeN is the electron-nucleon cross section, A and Heforis ai2nwdasepdiscussedendent boyfErikssonsQ and[157].xB This(ie: estimateit scales).is rather rough, since gas approximation is not good if large 2hard core effects are 6 is the normalized yield in a given (Q ,xB ) bin [32] and This scale fpresenactort. is related to the relative probability of Y A Crad is the ratio of the radiative correction factors for A 2-nucleon SRC those nuclei. In our previous work [10] we and 3He (CA = 0.95 and 0.92 12C and 56Fe respec- directly measured these ratios for the first time and es- radA tively). In our Q2 range, the elementary cross section tablished that they indeed scale, confirming findings [9] correction factor A(2σep+σen ) is 1.14 0.02 for C and which reported scaling based on the comparison of the 3(Zσep+Nσen) ± data for A 3 [11–13] and A = 2 [14] obtained in some- 4He and 1.18 0.02 for Fe. Fig. 1 shows the resulting what differ≥ent kinematic conditions. In this work, we ratios integrat±ed over Q2 > 1.4 GeV2. repeat our previous measurement with higher statistics. These cross section ratios a) scale the first time for 3 Moreover we can use the ratio R(A, He) to search 1.5 < xB < 2, which indicates that 2-nucleon SRCs dom- for the even more elusive 3-nucleon SRC: correlations inate in this region (see Ref. [10]), b) increase with xB which originate from both short-range NN interactions for 2 < xB < 2.25, which can be explained by scattering and three-nucleon forces. As 3-nucleon SRC are very off nucleons involved in moving 2-nucleon SRCs, and c) low-probability, we need to suppress 2-nucleon SRC by scale a second time at 2.25 xB 2.8, which indicates 2 ≤ ≤ choosing xB > 2 so that ν k /2mN . This analysis was that 3-nucleon SRCs dominate in this region. designed to probe for 3-nu$cleon correlations by looking Assuming that the scaling regions indicate the kine- for scaling in the region 2 xB 3. matical domain where the corresponding SRCs dominate, Two sets of measurem≤ents w≤ere performed at the the ratio of the per-nucleon SRC probabilities in nucleus 3 3 3 Thomas Jefferson National Accelerator Facility in 1999 A relative to He, a2(A/ He) and a3(A/ He), are just and 2002. The 1999 measurements used 4.461 GeV elec- the values of the ratio r in the appropriate scaling region. 4 12 3 3 trons incident on liquid He and solid C targets. The a2(A/ He) is evaluated at 1.5 < xB < 2 and a3(A/ He) 3

at large x, where scattering from nucleons below the initial energy and momentum of the struck nucleon, and Fermi momentum is forbidden. If these high-momentum so is not directly measured in inclusive scattering. Thus, components are related to two-nucleon correlations (2N- the plateau region is typically examined as a function of SRCs), then they should yield the same high-momentum x or α2n, which corresponds to αi under the approxi- tail whether in a heavy nucleus or a deuteron. mation that the photon is absorbed by a single nucleon The first detailed study of SRCs in inclusive scattering from a pair of nucleons with zero net momentum [12]. We combined data from several measurements at SLAC [12], take the A/D ratio for xmin deuterium; only A/3He ratios were The last column is the ratio at 18 after the subtraction of available. Finally, JLab Hall C data at 4 GeV [15, 16] the estimated inelastic contribution (with a systematic uncer- tainty of 100% of the subtraction). measured scattering from nuclei and deuterium at larger ◦ ◦ ◦ 2 A θ=18 θ=22 θ=26 Inel.sub Q values than the previous measurements, but the deu- 3 terium cross sections had limited x coverage. Thus, while He 2.14±0.04 2.28±0.06 2.33±0.10 2.13±0.04 4He 3.66±0.07 3.94±0.09 3.89±0.13 3.60±0.10 there is significant evidence for the presence of SRCs Be 4.00±0.08 4.21±0.09 4.28±0.14 3.91±0.12 ✺ Universality of 2N SRC is confirmed by Jlabin experiments inclusive scattering, clean and precise ratio measure- C 4.88±0.10 5.28±0.12 5.14±0.17 4.75±0.16 ments for a range of nuclei are lacking. Cu 5.37±0.11 5.79±0.13 5.71±0.19 5.21±0.20 E2-019 -2011 Au 5.34±0.11 5.70±0.14 5.76±0.20 5.16±0.22 ●E2-019 -2011 !Q2" 2.7 GeV2 3.8 GeV2 4.8 GeV2 6 6 Frankfurt et al 1993 3 12 xmin 1.5 1.45 1.4 (A) ● He C 2 ● ● 3 a ● 5 ● ● ● 0 At these high Q2 values, there is some inelastic contri-

/2) 6 D 4 63 bution to the cross section, even at these large x values.

! He Cu 4 ● Our cross section models predicts that this is approxi-

/A)/( 3 ◦

● A mately a 1–3% contribution at 18 ,butcanbe5–10%at ! ● ( 0 the larger angles. This provides a qualitative explanation 3 2 6 for the systematic 5–7% diﬀerence between the lowest Q 9Be 197Au data set and the higher Q2 values. Thus, we use only the ◦ 2 ● 3 18 data, corrected for our estimated inelastic contribution, in extracting the contribution of SRCs. ● 0 0.8 1 1.2 1.4 1.6 1.8 1 1.2 1.4 1.6 1.8 2 The typical assumption for this kinematic regime is x x that the FSIs in the high-x region come only from rescat-

◦ tering between the nucleons in the initial-state correla- FIG.Per 2: nucleon Per-nucleon cross cross section section ratio ratios vsat xQat2=2.7θ=18 GeV. 2 tion, and so the FSIs cancel out in taking the ratios [1– Probability of the high momentum component in nuclei per nucleon, 3, 12]. However, it has been argued that while the ratios normalized to the deuteron wave function Figure 2 shows the A/D cross section ratios for the are a signature of SRCs, they cannot be used to provide ◦ E02-019 data at a scattering angle of 18 .Forx>1.5, a quantitative measurement since different targets may Amazingly good agreement between the data show the expected near-constant behavior, al- have different FSIs [17]. With the higher Q2 reach of though the point at x =1.95 is always high because the these data, we see little Q2 dependence, which appears the three (e,e’) analyses for a2 (A) 7 2 H cross section approaches zero as x → MD/Mp ≈ 2. to be consistent with inelastic contributions, supporting This was not observed before, as the previous SLAC ra- the assumption of cancellation of FSIs in the ratios. Up- tios had much wider x bins and larger statistical uncer- dated calculations for both deuterium and heavier nuclei tainties, while the CLAS took ratios to 3He. are underway to further examine the question of FSI con- Table I shows the ratio in the plateau region for a range tributions to the ratios [18]. of nuclei at all Q2 values where there was sufficient large- Assuming the high-momentum contribution comes en- x data. We apply a cut in x to isolate the plateau region, tirely from quasielastic scattering from a nucleon in an although the onset of scaling in x varies somewhat with n–p SRC at rest, the cross section ratio σA/σD yields Q2. The start of the plateau corresponds to a fixed value the number of nucleons in high-relative momentum pairs of the light-cone momentum fraction of the struck nu- relative to the deuteron and r(A, D) represents the rela- cleon, αi [1, 12]. However, αi requires knowledge of the tive probability for a nucleon in nucleus A to be in such Superscaling of the ratios FS88

Compare the ratios for different Q2 at x corresponding to the same momentum of nucleon in nuclei (including effect of excitation of the residual system - best done in the light-cone formalism) Remark for people with a QCD 2 2 q +2m W 4mN background: This variable is αtn =2 − 1+ − rather close to Nachtmann − 2mN W 2 2 2 variable for massive quarks where q = q0 q3,W =4mN +4q0mN Q − − −

2 αtn (Q → ∞)=x

2 αtn vs x for Q =1, 4, 10, 50, ∞.

8 reminder - local FSI interaction, a (A ) ⇒ = 2 1 up to a factor of 2 for σ(e,e’), a2(A2) 1.6>α 1.3 | ≥ cancels in the ratio of σ’s ρ- Light-cone density

W − MD ≤ 50 MeV

Masses of NN system produced in the process are small - strong suppression of kmin=0.3 GeV isobar, 6q degrees of freedom. Frankfurt et al, 93 kmin=0.25 GeV

Right momenta for onset of scaling !!! 9 To observe SRC directly consider semi-exclusive processes e(p) +A → e(p) + p + “ nucleon from decay” +(A-2) since it measures both momentum of struck nucleon and decay of the nucleus → k2

→ k1 Prediction of back to back correlations FS77 81 qualitatively different from mean ﬁeld picture

kp~q

removal of a nucleon residual nucleus in ground or excited state of the shell model Hamiltonian - decay products practically do not remember

10 direction of momentum of struck proton BNL data of 94-98 - pC→ppn (A-2)

p .The correlation between pn and its γ direction γ relative to pi. The momenta on the labels are the beam momenta. The dotted vertical line corresponds to kF=220 MeV/c.

SRC appear to dominate at momenta k> 250 MeV/c - very close to kF. A bit of surprise - we expected dominance for k> 300 - 350 MeV/c. Naive inspection of the realistic model predictions for nA(k) clearly shows dominance only for k > 350 MeV/c. Important to check a.s.p. - easy task for CLAS data mining?

11 Directional correlation: back to back smeared by motion of the pair

12C(e,e’pp)

MCEEP Simulation with pair CM motion σCM=136 MeV/c

p BG (off peak) p γ

12 Theoretical analysis of the (p,ppn), (e,e’pN) data: Very strong correlation - removal of proton with k > 250 MeV/c - in 90% cases neutron is emitted, in 10% - proton. ✺ Combined analysis of (e,e’) and knockout data Structure of 2N correlations - probability ~ 20% for A>12 → dominant term in kinetic energy) 90% pn + 10% pp < 10% exotics ⇒ probability of exotics < 2%

2 2 EVA BNL 5.9 GeV protons (p,2p)n -t= 5 GeV ; t=(pin-pﬁn)

(e,e’ pp), (e,e’pn) Jlab Q2= 2GeV2

Different probes, different kinematics - the same pattern of very strong correlation - Universality is the answer to a question: “How to we know that (e,e’pN) is not due to meson exchange currents?”

13 ✺ EMC effect - recent developments

2 F (x ,Q2) 2 2A A 2 EMC effect - RA(x, Q )= 2 where xA=AQ /2mAq0 , deviates from one A F22H (x2H ,Q ) signal for presence of non-nucleonic degrees of freedom

Many nucleon approximation: dα Light cone nuclear nucleon F (x ,Q2)= ρN (α,p )F (x /α) d2p density (light cone projection of 2A A A t 2N A α t the nuclear spectral function N dα 2 ρ (α,pt) d pt = A baryon charge sum rule A α fraction of nucleus momentum 1 N dα 2 αρ (α,pt) d pt =1 λA NOT carried by nucleons A A α −

14 2 2 λAxFN (x, Q ) Fermi motion RA(x, Q )=1 2 x≡xA − FN (x, Q ) 2 2 2 xF2N (x, Q )+(x /2)F2N (x, Q ) 2(TA T2H ) + 2 − F2N (x, Q ) · 3mN

n 2 λAnx xn [x(n + 1) 2] (TA T2H ) F (1 x) ,n 3 RA(x, Q )=1 + − − 2N ∝ − ≈ − 1 x (1 x)2 · 3m − − N small negative for x <0.5 > 0 and rapidly growing for x >0.5

One of the ﬁrst models of the EMC effect - extra pions - λπ ~ 3% _ _ Prediction q¯Ca(x)/q¯N =1.1 1.2 x=0.05 0.1 ÷ | ÷ Drell-Yan experiments: qA/qN ~ 0.97

meson A-dependence of antiquark distribution, data are model 2 2 from FNAL nuclear Drell-Yan experiment, curves - Q = 15 GeV expectation 1.10 pQCD analysis of Frankfurt, Liuti, MS 90. Similar conclusions Eskola et al 93-07 analyses N

¯ 1.00 q

/ 0.90 A ¯ q 2 2 Q = 2 GeV x 15 Usually all EMC effect is considered as due to modiﬁcation of nucleons in nuclei, extra mesonic, 6q,... decreases of freedom. Two effects were missed (FS2010)

☛ In the fast frame (high energy processes) Coulomb photons are dynamical degree of freedom - implicit in the Fermi calculation of e.m interactions of fast particles. For large Z photons carry a signiﬁcant fraction of the nucleus momentum - 1.5 % for A=200

2 2 ☛ Experimentalists used xp=Q /2mpq0 instead of Bj’s xA=AQ /2mAq0

16 L. FRANKFURT AND M. STRIKMAN PHYSICAL REVIEW C 82,065203(2010)

2 nuclear parton distribution functions (PDF’s). Our conclusions Here ν 2(pq) Q /xA, kt is the transverse momentum of = = 2 are presented in Sec. VI. the photon, and F2A(ν,Q )isthenucleusstructurefunction which does not include the photon field. In the above formulas II. PHOTON DISTRIBUTION IN HEAVY NUCLEI. we neglected the small contribution of the longitudinally polarized photons (F A).The calculation of the photon structure Anucleusischaracterizedbyquark,gluon,photondis- L function accounting for the nucleus excitations is essentially tributions within a nucleus. To suppress particle production the same as for the QCD evolution of the gluon distribution, by hard probe from vacuum, the gauge condition A 0is + cf. [14]. The analogous expression for the photon distribution chosen, where A is the operator of the photon field. In= this µ in protons and neutrons is given in [6]. gauge photon distribution has a form familiar from the parton Account of the photon degrees of freedom requires mod- model; compare Fig. 1.Thephotonpartondistributioncanbe ification of the QCD evolution equation by including x P written as the matrix element of the product of the operators; A A in addition to x G ,x V ,x S .Thepresenceofthephoton compare [14]: A A A i A i component in the nuclear light-cone wave function leads to 2 1 ∞ the modification of the momentum sum rule as follows: PA(xA,Q ) (2πxAp+)− dy− exp ( ixAp+y−)1/2 = − 1 !−∞ 2 2 2 µ, [xAVA(xA,Q ) xASA(xA,Q ) xAGA(xA,Q ) A [Fµ+(0,y−, 0),F +(0)] A A+ 0. 0 + + × $ | | % = ! µ 2 " xAPA(xA,Q )] dxA 1. (3) (1) + = To remove the kinematic effects it is convenient to redefine the Here Fµ, is the operator of the strengths of the photon field variables by introducing + 2 with transverse component µ and xA Q /2(pAq)isthe Bjorken x for the nuclear target, which= is the fraction of x AxA, (4) = the nucleus momentum carried by a parton (we will later leading to rescale it by a factor of A to match it more closely to the A case of the nucleon target). 2 2 2 (1/A)[xVA(x,Q ) xSA(x,Q ) xGA(x,Q ) A large group of hard processes will probe high-energy + + !0 processes off the nucleus Coulomb field in the ultraperipheral 2 xPA(x,Q )] dx 1. (5) processes at the LHC [15]. One example of ultraperipheral pro- + = cesses is high-energy photon scattering off nucleus (nucleon) We will show that in the case of heavy nuclei the photon Coulomb field with diffractive production of massive lepton distribution in a nucleus cannot be neglected in the evaluation pairs γ A L+ L− A.Anotherprocessinvolving of the EMC effect. photon distribution+ → is+ the+ exclusive meson photoproduction The model for the evaluation of impact of the internucleon off the Coulomb field of the nucleus (the Primakoff effect). electromagnetic interactions (which contribute to the nuclear 2 To simplify the calculations it is convenient to represent binding energy term Z /RA)intothemomentumsumrule inel coherent ∝ PA as the sum of two contributions PA P PA .The for the heavy nucleus target has been suggested in Ref. [16]. first term includes nucleus excitations—we= will+ refer to it The model suggested a relation between the nucleus Coulomb as the inelastic term. The second term is the contribution of binding energy and the momentum sum rule through the equivalent photons. We will refer to it as the coherent term. application of the virial theorem in the nucleus rest frame. So Let us start with a brief discussion of the inelastic far there exists no model independent derivation of the con- contribution. Previously we defined it exactly the same way nection between rest frame Coulomb energy and the momen- as other parton densities, cf. Eq. (1). This definition allows tum sum rule. Their model estimates differ from the well- the calculation of PA by evaluating corresponding Feynman established equivalent photon approximation employed in this The photondiagrams; parton cf. Fig. 1 :distribution can be written paper.as the Our numericalmatrix results element are also different. of the product of the operators ν inel 2 αem 2 dν' 2xAPA (xA,Q ) + 1d kt ∞ + + µ,+ = π ν + PA(xA,Q )=(2πxAp )!− !νmin dy' − exp ( ixApIII.y THE−)1 CONTRIBUTION/2 A =0 . 2 − kt 2 µ −∞ F2A ν',kt . (2) Here we will calculate the coherent contribution to the par- × 2 2 2 Here we use A+=0kt gauge,Q ν'/ν and Fμ+ photon field strength + ton nucleus distribution that dominates the photon distribution # $ in a nucleus in the leading order in Z.Thiscontributionto h # $ h 2 PA(x,Q )arisesfromtheinteractionofahardprobewitha photon coherently emitted by the target nucleus. The coherent H Diagramcontribution for to the the photon interaction structure function of is unambiguouslyphoton of calculablethe nucleus in terms of with the electromagnetic a hard probe form factors h of the nucleus target. In the calculation we neglect by the small A A contribution of the magnetic form factor of the nucleons, which 2 is concentrated at large kt . FIG. 1. Diagram for the interaction of photon of the nucleus with We calculate the field of equivalent photons due to the a hard probe h. Lorentz transformation of the familiar nucleus rest frame 2 2 2 2 2 α Z F065203-2(k + x m ) xP coherent(x, Q2)= em k2d2k A t N A π A t t (k2 + x2m2 )2 t N fraction of fast nucleus momentum carried by the coherent photon field 1 2 2 coh Z 2 2 2 Z √3 λγ =2αem dx ln(√3/xmN RA)exp( RAmN x /3) αem A − ≈ A mN RA 0 Z 1 λ = − λcoh excess momentum carried by photons in nucleus γ Z γ 17 10

One can see from Fig.3 that deviation of the data from the dashed curves grows with increase of10x for x 0.6 indicating increasing importance of the ”hadronic EMC effect”. This is consistent with the One≥ can see from Fig.3 that deviation of the data from the dashed curves grows with increase of x expectation that suppression of the EMC ratio due to the effect of the suppression of the point-like for x 0.6 indicating increasing importance of the ”hadronic EMC effect”. This is consistent with the configurations≥ in bound nucleons should be maximal for quarks that carry a fraction of the light - cone expectation that suppression of the EMC ratio due to the effect of the suppression of the point-like momentum of the bound nucleons close to 1 [9]. Since the Fermi motion effect is TA for 0.5

A Signiﬁcant correction to 2 2 2 2 (1/A)(xVA(x, Q )+xSA(x, Q )+xGA(x, Q )) + xPA(x, Q ) dx =1 the momentum sum rule 0 x< 0.6 0.5 Bj x + Coulomb 12 9Be C

/dx +Fermi motion

) 0.4 x ( 4

A 0.3 He

dR 0.2 3He Bj x + Coulomb

0.1

0 0 0.2 0.4 0.6 0.8 1 100 (( 2 )/m + λ (A)) · A − H N γ Large hadronic effect only for x>0.5 - natural in the color screening model of F&S 85

FIG. 3. The solid curve is the contribution to the EMC ration of the nucleus field of equivalent photons and effect of proper definition of x calculated using Eq.22 which is applicable for x 0.7 only. The dashed curves ≤ FIG.include 3. also The the solid eff curveect of is the the Fermi contribution motion estimated to the EMC using ration Eq. of 24. the The nucleus data field are from of equivalent [19, 20]. photons Open circles and ecorrespondffect of proper to W< definition2GeV. of x calculated using Eq.22 which is applicable for x 0.7 only. The dashed curves ≤ include also the effect of the Fermi motion estimated using Eq. 24. The data are from [19, 20]. Open circles correspond to W<2GeV. Theoretical expectation LF & MS85 hadronic effect ∝ nucleon virtuality ∝ Contribution of nucleon modification to the a2(A) EMC effect - weak function of A for A≥12 Example - magic point x=0.5 - no Fermi motion

∝a2(A)

Coulomb + x-scale + (hadronic EMC effect ∝ a2(A))

Signiﬁcant hadronic EMC effect at x > 0.55 - momentum, proportional to which is mostly due to SRCs. . Probability for a quark to have x> 0.5, ~ 0.02 Probability of exotic component hadronic EMC effect at x ~ 0.5, ~ 0.02 relevant for the large x EMC effect~ 2 10-3

Nuclei are build of nucleons with accuracy ~ 99%, with large high momentum 2N SRC component (high density drops) 19 These observations match recent ﬁnding of a heavy neutron star M≈ 2 M⊙ - models where nonnucleonic degrees of freedom are easily excited cannot reach this mass range.

due to SRCs is dominant > 80% contribution to

Extrapolation from properties of nuclei with Z ~ N to Z<

20 Some implications for neutron stars

✻ Our focus is on the outer core where nucleon density is close to nuclear one: 3 ρ ~ (2 ÷ 3) ρ0; ρ0 ≈0.16 nucleon/fm and x=p/n ~ 1/10 k (p)/k (n)=(N /N )1/3 x1/3 1 F F p n ≡

Fermi liquid Neutron gas heats proton n(k) gas due to large pn SRC n(k)

practical disappearance of ➠ the proton Fermi surface kF(p) kF(n) k kF(p) kF(n) k FS08

21 High momentum tail of proton, neutron distributions are directly calculable.

2 2 In the leading order in kF /k the occupation numbers for protons and neutrons with momenta above Fermi surface are

V (k) 2 V (k) 2 f (k, T = 0) (ρ )2 ( nn +2x pn ) n ≈ n k2/m k2/m N N

V (k) 2 V (k) 2 f (k, T = 0) (ρ )2 (x2 pp +2x pn ) p ≈ n k2/m k2/m N N

Here ρi is the density of constituent i

Equal number of “p” and “n” above Fermi surface, but since x<< 1, effect is much larger for protons

22 Internucleon interaction tends to equilibrate momenta of protons and neutrons -strong departure from the ideal gas approximation. Migdal jump in proton momentum distribution almost disappears in this limit. Neutron gas heats proton gas.

Suppression of proton Fermi surface leads to the suppression of proton superconductivity. Superﬂuidity of neutrons and proton-neutron pairs is not excluded.

Large enhancement of neutrino cooling of the neutron stars at ﬁnite temperatures

The enhancement (factor of R as compared to URCA process) is due to presence of proton holes in the proton Fermi sea. For example taking x =0.1, neutron density ~ ρ0, we ﬁnd for T<< 1 MeV

R ≈ 0.1 (MeV/kT) 3/2 R = ∞ for x<< 0.1

kT(neutron star ) for t > 1 year < 0.01 MeV ⇒ large enhancement 47

23 Conclusions

☛ Impressive experimental progress of the last few years - discovery of strong short range correlations in nuclei with strong dominance of I=0 SRC - conﬁrmed a series of our predictions of 80‘s & has proven validity of general strategy of using hard nuclear reactions. It provides solid basis for further studies. Several experiments are under way and several are been planned for 12 GeV.

☛ Hadronic EMC effect is much smaller for x ≤ 0.5 than previously, but kicks in very fast at x ~ 0.6

☛ Nucleons remain nearly intact up to local densities comparable to neutron star densities - consistent with stiff equation of state for neutron stars

☛ Direct observation of 3N SRCs, nonnucleonic degrees of freedom in nuclei which are of direct relevance for neutron stars core dynamics are one of the aims of our data mining program at Jlab, Jlab 12. Complementary experiments with hadron beams (FEAR, J-PARC,...) are highly desirable.

24 Supplementary slides Color coherence mechanism of the nucleon polarization Frankfurt & MS 85 nucleon in PLC have a weaker attraction to other nucleon

PLC’s are suppressed in bound nucleons

˜ Vij ψA(i) 1 + ψA(i) ∆E mN mN 600 800 MeV ≈  ∆E  ∗ j=i ∼ − ∼ − average excitation energy in the energy denominator.  

2 p2 − 2 ε PLC’s suppression in deuteron/two 2m − D δD(p)=1 +  nucleon short-range correlation ΔED     Qualitative consideration - consider dependence of deformation for the process e + A → e + (A-1)* +X [X=p, inclusive] 2 2 2 2 on virtuality of the interacting nucleon pint ≡ (pA- p(A-1)*) . Analytically continue to pint = mN expect no EMC effect. Natural to have deviations from the free nucleon case to be proportional in the lowest order to

2 2 2 A p (pA- p(A-1)*) - mN 2m + MA 1 + mN MA ≈ A 1 2m − − − N

Cioﬁ, Frankfurt, Kaptari, MS 07 performed detailed analysis including effects of nuclear excitations. Find the expression which is valid for all A 2 p2 m2 − δ(p, E )= 1 int − exc − 2m ∆E N

Expect small conﬁgurations at small x - natural for hadronic effect to kick in at x >0.5 Enhancement of neutrino cooling of the neutron stars at ﬁnite temperatures

Common wisdom: dominant process of neutrino cooling of neutron stars at finite temperature is URCA process: n p + e +¯ν ,e+ p n + ν . → e → e URCA is allowed by the energy-momentum conservation law if the proton concentration exceeds (11 − 15)% (Lattimer et al). If proton concentration is below threshold or direct URCA process is suppressed. Due to nucleon superfluidity neutrino cooling proceeds through the less rapid modified URCA processes:

n +(n, p) p +(n, p)+e +¯ν , and e + p +(n, p) n +(n, p)+ν → e → e in which additional nucleon enables momentum conservation.

28 Neutrino luminosity, εURCA in the Fermi liquid approach.

Usual starting point - Fermi distribution for constituents. Analysis for x> 1/8 of Lattimer et al uses 1 fi,bare(k, T)= E µ 1 + exp i− i kT

It corresponds to the Pauli blocking 1 - fe(k,T), 1 - fp(k,T) = c(kT )6θ(k (e)+k (p) k (n)) URCA F F − F

c(x ≥ 0.1) is expressed through the square of the electroweak coupling constant relevant for low energy weak interactions and the phase volume factors

29 Account for the high momentum proton component leads to more rapid neutrino cooling-larger neutrino luminosity:

ε URCA = c(kT)6 R

where enhancement factor R is f (k, T = 0)θ(k (e)k (p) k (n)d3k R p F F − F p ≈ (1 f (k, T)θ(k (e)k (p) k (n)d3k − bare F F − F p Here we neglect small corrections to to electron holes, take small T so that we can neglect deviation of the proton distribution in the interacting nuclear media from T=0.

The enhancement is due to presence of proton holes in the proton Fermi sea. For example taking x =0.1, neutron density ~ ρ0, we ﬁnd for T<< 1 MeV

R ≈ 0.1 (MeV/kT) 3/2 R = ∞ for x<< 0.1

kT(neutron star ) for t > 1 year < 0.01 MeV ⇒ large enhancement 30 Perspectives of studies of short-range nuclear structure

Jlab plans ☛ Quantifying and extending recent studies (several of the current numbers have 20% errors)

☛ Data from (e,e’), (e,e’NN) experiments at 6 GeV is currently been analyzed; data mining initiative CLAS is ﬁnally approved by DOE, x> 1 for 12 GeV,... Discovering new phenomena

☀ Direct observation of 3N SRC

☀ Direct observation of non-nucleonic degrees of freedom in nuclei

31 ☺ What can be done at GSI at FAIR? Example: PANDA detector will be able to collect in one year of running (3 months with protons) > 103 higher statistics than the one collected by EVA BNL (p,2pn) experiment. Very interesting to compare antiproton and proton induced reactions - for example J/ψ production off bound nucleons - will be sensitive to nucleon gluon ﬁeld modiﬁcation in nuclei.

☻ Look for effects of SRCs including 3N correlations - comparison on pn, pp channels,... ++ ☻ non-nucleonic degrees of freedom - discover Δ’s? Large angle pA ∆ + p +(A 1)∗ → − ☻ Color & chiral transparency effects, ... _ The simplest doable experiment: p(p)A →pNN +(A-1)*

o Need large -t. For 90 c.m. -t=TpmN. Hence (anti) proton beams starting with Tp=4 GeV are ﬁne.

Studies of SRC ar FAIR can nicely complement Jlab 12 program