The EMC Effect - Front page | ECT* · 2015-06-30 · The EMC Effect CERNCOURIER 1 VOLUME 53 NUMBER 4 MAY 2013 ... by the ‘creation’ of quarks via the point-like γ → q¯q coupling.

The EMC Effect

1CERNCOURIERV O L U M E 5 3 N U M B E R 4 M A Y 2 0 1 3

V O L U M E 5 3 N U M B E R 4 M A Y 2 0 1 3

CERNCOURIERI N T E R N A T I O N A L J O U R N A L O F H I G H - E N E R G Y P H Y S I C S

Deep in the nucleus:a puzzle revisited

ASTROWATCHPlanck reveals analmost perfectuniverse p12

IT’S AHIGGS BOSON

The new particleis identifi ed p21

The key to fi ndingout if a collisionis head on p31

HEAVY IONS

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 GLVFRYHU\�EULQJV�WKH�ÀQDO�WRXFKHV�WR�D�SLFWXUH�WKDW�FDPH�LQWR�IRFXV��\HDUV�DJR��ZKHQ�H[SHULPHQWV�DW�&(51�ÀUVW�REVHUYHG�WKH�:�DQG�=�ERVRQV��7KH�masses of these particles were just as electroweak theory predicted, based on WKHLU�LQWHUDFWLRQV�ZLWK�D�K\SRWKHVL]HG�+LJJV�ÀHOG�DQG�LWV�ERVRQ��0HDQZKLOH��other particle interactions continue to provide puzzles in more complex V\VWHPV��IURP�UHODWLYHO\�VLPSOH�QXFOHL�WR�WKH�KRW��GHQVH�ÀUHEDOO�FUHDWHG�LQ�heavy-ion collisions. To sign up to the new issue alert, please visit: http://cerncourier.com/cws/sign-up.

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ED ITOR: CHR IST INE SUTTON, CERNDIG ITAL ED IT ION CREATED BY JESSE KARJALA INEN/ IOP PUBL ISH ING, UK

Gerald A. Miller, Univ. of Washington

What is the EMC effect? What does it mean? What are the consequences?Higinbotham, Miller, Hen

CERN Courier 53N4(’13)24

EMC Effect -Outline• Basic issues -what is the EMC effect, why

important? • Simple ideas • What is Drell-Yan pair production, why

relevant? • Why nucleon structure must be modified for

nucleons in nuclei • Simple models and examples of tests • Two-nucleon effects are important • Necessities for future progress

2

Fundamental questions of Nuclear Physics

• Is the nucleus made only of nucleons and mesons?

• How does the nucleus emerge from QCD, a theory of quarks and gluons?

• Why is the nucleon-meson picture of nuclei so accurate?

• Is the gluonic content of the nucleus the same as for nucleons in free space?

• Is there a non-perturbative sea in the nucleon?

3No one asked such questions before the EMC effect was discovered

Electron loses energy and is scattered by some angle: two variables: ⌫, Q

2

Large ⌫, Q

2scattering on elementary quark. Four-momentum conservation !

dynamics depend on x =

Q2

2M⌫

x ratio of quark p

+to proton momentum P

+(P

± ⌘ P

0 ± P

3)

Primer- Deep Inelastic Scattering- large

4

e

P

Q

x P+

The EMC effect involves deep inelastic scattering from nuclei

⌫, Q2

EMC= European Muon Collaboration

19. Structure functions 13

x-310 -210 -110 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

g/10

vu

vd

d

c

s

u

NNPDF2.3 (NNLO))2=10 GeV2µxf(x,

x-310 -210 -110 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

g/10

vu

vd

d

u

s

c

b

)2 GeV4=102µxf(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 globalanalysis [45] at scales µ2 = 10 GeV2 and µ2 = 104 GeV2, with αs(M2

Z) = 0.118.The analogous results obtained in the NNLO MSTW analysis [43] can be found inRef. [62].

where we have used F γ2 = 2xF γ

T + F γL , not to be confused with F γ

2 of Sec. 19.2. Completeformulae are given, for example, in the comprehensive review of Ref. 80.

The hadronic photon structure function, F γ2 , evolves with increasing Q2 from

the ‘hadron-like’ behavior, calculable via the vector-meson-dominance model, to thedominating ‘point-like’ behaviour, calculable in perturbative QCD. Due to the point-likecoupling, the logarithmic evolution of F γ

2 with Q2 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-compensatedby the ‘creation’ of quarks via the point-like γ → qq coupling. The logarithmic evolutionwas first predicted in the quark–parton model (γ∗γ → qq) [81,82], and then in QCD inthe limit of large Q2 [83]. The evolution is now known to NLO [84–86]. The NLO dataanalyses 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 deflectedproton and the cluster X of outgoing hadrons are well-separated in rapidity. Besidesx and Q2, two extra variables are needed to describe a DDIS event: the fraction xIPof the proton’s momentum transferred across the rapidity gap and t, the square of the4-momentum transfer of the proton. The DDIS data [90,91] are usually analyzed usingtwo levels of factorization. First, the diffractive structure function FD

2 satisfies collinear

August 21, 2014 13:18

Nucleon from PDG

The EMC EFFECT

5

Fig. 1: Image of the EMC data as it appeared in the November 1982 issue of the CERN Courier. This image nearly derailed the highly cited refereed publication (Aubert et al., 1983), as the editor argued that the data had already been published.

Fig. 2: The image shows the ratio of deep-inelastic cross sections of Ca to D from NMC (solid circles) and SLAC (open circles). The downward slope from 0.3 < x < 0.7 and subsequent rise from xB > 0.7 is a universal characteristic of EMC data and has became known as the EMC effect. The reduction of the ratio at lower values of xB, where valence quarks should no longer be playing a significant role, is known as the shadowing region.

Nucleon structure is modified: valence quark momentum depleted. How do quarks work in a nucleus?

BUT EFFECTS ARE SMALL ~15%

Valence quark momentum is reduced

The EMC EFFECT

5

Fig. 1: Image of the EMC data as it appeared in the November 1982 issue of the CERN Courier. This image nearly derailed the highly cited refereed publication (Aubert et al., 1983), as the editor argued that the data had already been published.

Fig. 2: The image shows the ratio of deep-inelastic cross sections of Ca to D from NMC (solid circles) and SLAC (open circles). The downward slope from 0.3 < x < 0.7 and subsequent rise from xB > 0.7 is a universal characteristic of EMC data and has became known as the EMC effect. The reduction of the ratio at lower values of xB, where valence quarks should no longer be playing a significant role, is known as the shadowing region.

Nucleon structure is modified: valence quark momentum depleted. How do quarks work in a nucleus?

BUT EFFECTS ARE SMALL ~15%

Valence quark momentum is reduced

Simple models of reduction of valence quark momentum

• quarks in nuclei move through a larger confinement volume (uncertainty principle)

• bound nucleons are larger than free ones • nucleons in nuclei move in 6, 9 or 3A

quark bags • nuclear binding, Fermi motion, pionic

effects

6

Simple models of reduction of valence quark momentum

• quarks in nuclei move through a larger confinement volume (uncertainty principle)

• bound nucleons are larger than free ones • nucleons in nuclei move in 6, 9 or 3A

quark bags • nuclear binding, Fermi motion, pionic

effects

6

EMC – “Everyone’s Model is Cool (1985)’’

One thing I learned since ‘85

One thing I learned since ‘85

• One model is not cool- • unmodified nucleon -free

structure function

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

Pb

Binding causes no EMC effect

SLAC-E139

Smith Miller ‘02

Phys.Rev. C65 (2002) 015211, Phys.Rev. C66 (2002) 049903 Phys.Rev. C65 (2002) 055206

Smith & Miller

Nucleons and pionsPA

+ = PN+ + Pπ+ =MA

Pπ+ /MA =.04, explain EMC try Drell-Yan, Bickerstaff, Birse, Miller 84

proton(x1) nucleus(x2)

Phys.Rev.D33:3228,1986 Phys.Rev.Lett.53:2532,1984.

x1

x2


+ = PN+ + Pπ+ =MA

Pπ+ /MA =.04, explain EMC Drell-Yan, E772

π fails

No one’s model is cool

PRL 69,1726 (92)


+ = PN+ + Pπ+ =MA

Pπ+ /MA =.04, explain EMC Drell-Yan, E772

π fails

No one’s model is coolBertsch, Frankfurt, Strikman “crisis in nuclear theory” conventional physics does not work

PRL 69,1726 (92)

Nucleons, pions, shadowing, universal nucleon modification

• A model containing all of these aspects does account for DIS and DY-Kulagin Petti

• No underlying dynamics-can’t predict other phenomena

11

⇡�

Single nucleon modification by nuclei

• Does it make sense? It is inevitable. Pion cloud modified by nucleus, W cloud too

• Neutron in nucleus is modified, lifetime changed from 15 minutes to forever

• Binding changes energy denominator, suppresses component

• Change energy denominator change wave fun • Also Strong fields polarize nucleons- analog of

Stark effect

peν

np

(Ef , ~p + ~q)

Inevitability of medium modifications-(e,e’p)

13

MAp

(Es,�~p)

(⌫, ~q)

Form factor modified because p2 6= M2

Nucleus A-1Problem: conventional nuclear wave function involves on-mass shell nucleons

1

�⇤

Single nucleon in a nucleus

14

R

1947 Shell Model

R

1968 SLAC-MIT nucleon not a point: !quarks don’t interact

1982 EMC

?

1

?

1

?

1

?

1

or

1985 PLC Suppression Frankfurt Strikman 1995 BLC Frank Jennings Miller

15

?

1

?

1

?

1

?

1

+✏

Nucleon has large blob-like configuration BLC and small point like configuration PLC!BLC is affected by nucleus PLC, not affected . Result PLC suppressed/BLC enhanced

Nucl.Phys. B250 (1985) 143-

Phys.Rev. C54 (1996) 920-

Nuclear matter

External fields

Nucleon in medium- 5 models1. QMC- quarks in nucleons

(MIT bag) exchange mesons with nuclear medium, quark mass

2. Use NJL instead of bag 3. CQSM- quarks in

nucleons (soliton) exchange infinite pairs of pions, vector mesons with nuclear medium, mq

4. Suppression of point-like-configurations,

5. Enhancement of blob-like configurations polarization

Cloet

• g1n , g1p in nuclei

!• other way to

enhance EMC?

Bentz, Cloet, Thomas

Spin

Spin experiments-NJL in medium

ratio of g1 medium to free

Kuhn talk

Chiral Quark Soliton Model –Diakonov, Petrov, Polykov, quarks couple to vacuum instantons

• Vacuum dominated by instantons

• quarks with spontaneously generated masses interact with pions !!

• Nucleon is soliton in pion field

• M=420 MeV • good nucleon properties,

DIS and magnetic moments

Negele et al hep-lat/9810053

topological charge density

Chiral Quark Soliton Model of Nucleus- Smith, Miller

2 π exchange – attraction ω (vector meson) exchange - repulsion

Double self consistency profile function and kf

Phys.Rev. C72 (2005) 022203

Phys.Rev. C70 (2004) 065205Phys.Rev.Lett. 91 (2003) 212301, Phys.Rev.Lett. 98 (2007) 099902

Results Smith & Miller ’03,04,05

sea is not much modified

EMC ratio

Nuclear Drell Yan

g1 ratio

full

valence only

About same as DIS, not larger contrasts QMC Kuhn talk

21

Models Predict Form-Factor Medium Modifications

CQS: J.R. Smith and G.A. Miller, Phys. Rev. C 70, 065205 (2004)QMC: D.H. Lu et al., Phys. Lett. B 417, 217 (1998)NJL: I.C. Cloet, W. Bentz, and A.W. Thomas (to be published)

ρ = 0.5 ρ0ρ = 1.0 ρ0ρ = 1.5 ρ0

7

• Changes in the internal structure of bound nucleons result also in bound nucleon form factors.

• Observable effects predicted:

Chiral Quark Soliton (CQS), Quark Meson Coupling (QMC), Skyrme, Nambu-Jona-Lasinio (NJL), GPD Models.

• Model predictions:

‣ are density and Q2 dependent,‣ show similar behavior,‣ consistent with experimental

data (within large uncertainties).

CQS QMC

Another medium effect: form factors

S Strauch slide

22

Strong Medium Effects Observed in 4He Polarization-Transfer Double Ratios

12

2H: B. Hu et al., PRC 73, 064004 (2006). 4He: S. Dieterich et al., PLB 500, 47 (2001); S. S., et al., PRL 91, 052301 (2003); M. Paolone, et al., PRL 105, 0722001 (2010); S. Malace et al., PRL 106, 052501 (2011)

• 2H and 1H polarization-transfer data are similar

• 4He data are significantly different than 2H, 1H data

≈ 10%Effect

low pm data

S. Strauch ratio of GE/GM

Enhancement of Blob-like Configurations- Frank,Jennings, Miller

place in medium:

normal size components attracted energy goes down

PLC does not interact- color screening-FS

BLC is enhanced

quarks lose momentum in medium

free

PRC 54, 920

1995 Frank, Jennings, Miller

Enhancement of Blob-Like Configurations

energy denominator increased

FS-PLC has NO int. with medium

EMC ratio Frank,Jennings Miller ‘95 evaluated as QCD Stark, not modified energy denominator

More data

26

29

corresponds to elastic scattering from a free deuteron.) Quasielastic scattering corresponds to scattering from a single bound nucleon. At large xB (xB > 1.5) this is sensitive to high-momentum nucleons and to nucleon-nucleon short-range correlations (SRC) in the nucleus. We find nuclear modifications of these distributions in the comparison of both deep inelastic and quasielastic nuclear cross sections to those of deuterium. Figure 4.1 displays the ratios of nuclear to deuterium cross sections (per nucleon) over a wide range of xB and nuclei. These ratios are very different from the naively expected value of unity.

4a.1 Short-range structure of nuclei

The short-range repulsive core is a critical component of the NN force. It leads to the saturation necessary for stable nuclei and causes substantial shell occupations at energies and momenta well above the Fermi sea. However its QCD origin remains unclear and little is known about the relative NN wave function at short distances.

Nucleons acquire high-momentum via short-range interactions, rather than by the influence of the nuclear mean-field. Thus, for momenta above the Fermi sea, the shape of the momentum distribution should be universal. This is shown by the plateaus (regions of constant cross section ratio) observed at xB > 1.5 (see Figure 4.1c). The values of the ratio at these plateaus, a2(A/d), are closely related to the probability of finding a nucleon belonging to a short-range correlated pair in nucleus A relative to deuterium.

Experiments at 12 GeV will study the deuteron to better understand the simplest nuclear system [4-18]. Other experiments will extend the SRC studies described above to a much greater range of xB, momentum transfers, and nuclei (including 3H and 3He) to study two and three nucleon correlations (including their isospin character), with higher nucleon momenta [4-19, 4-20]. The highest Q2 data from the xB > 1 measurements will probe the distribution of superfast quarks in nuclei, greatly extending our understanding of nucleons at short distances.

(a) (b) (c)

Figure 4.1: The electron scattering cross section ratios (per-nucleon) of various nuclei to deuterium. (a) Ratios for 0.2 < xB < 0.9 [4-1]; (b) Ratios for 12C for 0.3 < xB < 2 [4-1, 4-2]; (c) Ratios for 0.8 < xB < 1.8 [4-2].

30

4a.2 Nucleon properties in nuclei

Another outstanding question is whether the nuclear medium alters the structure of bound nucleons and, if so, how? The neutron lifetime in nuclei is certainly different. The first evidence for nucleon structure modification was the EMC effect [4-3], in which deep-inelastic scattering from nuclear quarks is significantly different than from quarks inside a “free” nucleon (see Figure 4.1a). The per-nucleon DIS cross section ratio of nucleus A to deuterium decreases approximately linearly for 0.3 < xB < 0.7. The slope of this ratio in this region increases with A but does not scale simply with average nuclear density (see Figure 4.2). Despite a world-wide effort in experiment and theory, the origins of the EMC effect remain unclear. The 12 GeV experimental program will measure the EMC effect in a wide range of nuclei to help unravel the mystery [4-24, 4-25].

Recent phenomenological comparisons [4-4] (see Figure 4.2) show that the strength of the EMC effect in different nuclei is linearly related to the short range correlations scale factor, 𝑎2(A/d). This linear relation indicates, but does not prove, that the EMC effect is caused by local modifications of nucleon structure occurring when two would-be nucleons make a close encounter and briefly comprise a system of density high enough to be comparable to that of neutron stars. This relationship will be tested and refined at 12 GeV by a series of EMC and SRC experiments covering a wide range of nuclei [4-19, 4-20, 4-24, 4-25]. The deuteron experiment mentioned above [4-18] will increase our understanding of the two-nucleon system that we use as a baseline for both the EMC and SRC measurements.

Figure 4.2: (left) The strength of the EMC effect (the EMC slope) plotted versus the average nuclear density [4-1]. (right) The strength of the EMC effect plotted versus the SRC scale factors [4-4]. The drawing in the upper left shows deep inelastic electron scattering from a quark in a nucleon. The drawing in the lower right shows electron scattering from a correlated NN pair. (Figure credit: Anna Shneor).

This linear relationship suggests a fertile field of research at 12 GeV: exploring the local nature of the EMC effect by measuring electron deep inelastic scattering in coincidence with low-energy spectator nucleons or target fragments. This technique has been pioneered at Jefferson Lab by detecting recoiled protons with low-momentum (relative to the nuclear Fermi momentum), that “tag” scattering events on nearly on-shell neutrons in a deuteron target [4-5] and detecting high-momentum recoil protons to study off-shell neutrons [4-6]. If the EMC effect

60

[3-67] A. Prokudin, Private communication

[3-68] A. Gasparian et al., Jefferson Lab Experiment E12-11-106

[3-69] S. Bueltmann et al., Jefferson Lab Experiment E12-06-113

[3-70] G.G. Petratos et al., Jefferson Lab Experiment E12-10-103 [3-71] P.A. Souder et al., The SoLID Experiment, Jefferson Lab Experiment E12-10-007

[3-72] A. Accardi et al., Phys. Rev. D 84, 014008 (2011)

[3-73] G.D. Cates, C.W. de Jager, S. Riodan and B. Wojtsekhowski, Phys. Rev Lett. 106 (2011) 252003

[3-74] C.D. Roberts et al., Eur. Phys. J. ST 140, 53 (2007); I.C. Clöet et al., Few-Body Systems 46, 1 (2009)

[3-75] I.C. Clöet and G.A. Miller, PRC 86, 015208 (2012)

[3-76] M. Guidal, M. V. Polyakov, A. V. Radyushkin, and M. Vanderhaeghen Phys. Rev. D 72, 054013 (2005)

[3-77] P.Maris and P.Tandy, Phys. Rev. C 62, 055204 (2000)

[3-78] V.A. Nesterenko and A.V. Radyushkin, Phys. Lett. B115, 410(1982)

[3-79] C-W. Hwang, Phys.Rev.D 64(2001)n034001

[4-1] J. Seely et al., Phys. Rev. Lett. 103, (2009) 202301

[4-2] N. Fomin, et al., Phys. Rev. Lett. 108, 092502 (2012)

[4-3] J.J. Aubert et al., Phys. Lett. 123B (1983) 275

[4-4] L.B. Weinstein et al., Phys. Rev. Lett. 106, 052301 (2011)

[4-5] N. Baillie et al., Phys. Rev. Lett. 108, 142001 (2012)

[4-6] A.V. Klimenko et al., Phys. Rev. C 73, 035212 (2006)

[4-7] S. Bueltmann et al., “The Structure of the Free Neutron at Large x-Bjorken”, Jefferson Lab Experiment E12-06-113.

[4-8] O. Hen et al., “In Medium Nucleon Structure Functions, SRC, and the EMC effect”, Jefferson Lab Expt E12-11-107.

[4-9] W. Melnitchouk, M. Sargsian, and M.I. Strikman, Z. Phys. A359, 99 (1997)

[4-10] L. El Fassi, et al., Phys. Lett. B712, 326 (2012)

[4-11] L. Frankfurt, G.A. Miller and M.Strikman, Phys. Rev. C 78, 015208 (2008)

[4-12] K. Hafidi et al., “Study of Color Transparency in Exclusive Vector Meson Electroproduction off Nuclei”, Jefferson Lab Experiment E12-06-106.

[4-13] E.M. Aitala et al. [E791 Collaboration], Phys. Rev. Lett. 86, 4773 (2001)

[4-14] L. Frankfurt, G.A. Miller and M. Strikman, Phys. Lett. B304, 1 (1993)

[4-15] B. Clasie, et al., Phys. Rev. Lett. 99, 242502 (2007)

60




























More data

26

29

corresponds to elastic scattering from a free deuteron.) Quasielastic scattering corresponds to scattering from a single bound nucleon. At large xB (xB > 1.5) this is sensitive to high-momentum nucleons and to nucleon-nucleon short-range correlations (SRC) in the nucleus. We find nuclear modifications of these distributions in the comparison of both deep inelastic and quasielastic nuclear cross sections to those of deuterium. Figure 4.1 displays the ratios of nuclear to deuterium cross sections (per nucleon) over a wide range of xB and nuclei. These ratios are very different from the naively expected value of unity.

4a.1 Short-range structure of nuclei

The short-range repulsive core is a critical component of the NN force. It leads to the saturation necessary for stable nuclei and causes substantial shell occupations at energies and momenta well above the Fermi sea. However its QCD origin remains unclear and little is known about the relative NN wave function at short distances.

Nucleons acquire high-momentum via short-range interactions, rather than by the influence of the nuclear mean-field. Thus, for momenta above the Fermi sea, the shape of the momentum distribution should be universal. This is shown by the plateaus (regions of constant cross section ratio) observed at xB > 1.5 (see Figure 4.1c). The values of the ratio at these plateaus, a2(A/d), are closely related to the probability of finding a nucleon belonging to a short-range correlated pair in nucleus A relative to deuterium.

Experiments at 12 GeV will study the deuteron to better understand the simplest nuclear system [4-18]. Other experiments will extend the SRC studies described above to a much greater range of xB, momentum transfers, and nuclei (including 3H and 3He) to study two and three nucleon correlations (including their isospin character), with higher nucleon momenta [4-19, 4-20]. The highest Q2 data from the xB > 1 measurements will probe the distribution of superfast quarks in nuclei, greatly extending our understanding of nucleons at short distances.

(a) (b) (c)

Figure 4.1: The electron scattering cross section ratios (per-nucleon) of various nuclei to deuterium. (a) Ratios for 0.2 < xB < 0.9 [4-1]; (b) Ratios for 12C for 0.3 < xB < 2 [4-1, 4-2]; (c) Ratios for 0.8 < xB < 1.8 [4-2].

30

4a.2 Nucleon properties in nuclei

Another outstanding question is whether the nuclear medium alters the structure of bound nucleons and, if so, how? The neutron lifetime in nuclei is certainly different. The first evidence for nucleon structure modification was the EMC effect [4-3], in which deep-inelastic scattering from nuclear quarks is significantly different than from quarks inside a “free” nucleon (see Figure 4.1a). The per-nucleon DIS cross section ratio of nucleus A to deuterium decreases approximately linearly for 0.3 < xB < 0.7. The slope of this ratio in this region increases with A but does not scale simply with average nuclear density (see Figure 4.2). Despite a world-wide effort in experiment and theory, the origins of the EMC effect remain unclear. The 12 GeV experimental program will measure the EMC effect in a wide range of nuclei to help unravel the mystery [4-24, 4-25].

Recent phenomenological comparisons [4-4] (see Figure 4.2) show that the strength of the EMC effect in different nuclei is linearly related to the short range correlations scale factor, 𝑎2(A/d). This linear relation indicates, but does not prove, that the EMC effect is caused by local modifications of nucleon structure occurring when two would-be nucleons make a close encounter and briefly comprise a system of density high enough to be comparable to that of neutron stars. This relationship will be tested and refined at 12 GeV by a series of EMC and SRC experiments covering a wide range of nuclei [4-19, 4-20, 4-24, 4-25]. The deuteron experiment mentioned above [4-18] will increase our understanding of the two-nucleon system that we use as a baseline for both the EMC and SRC measurements.

Figure 4.2: (left) The strength of the EMC effect (the EMC slope) plotted versus the average nuclear density [4-1]. (right) The strength of the EMC effect plotted versus the SRC scale factors [4-4]. The drawing in the upper left shows deep inelastic electron scattering from a quark in a nucleon. The drawing in the lower right shows electron scattering from a correlated NN pair. (Figure credit: Anna Shneor).

This linear relationship suggests a fertile field of research at 12 GeV: exploring the local nature of the EMC effect by measuring electron deep inelastic scattering in coincidence with low-energy spectator nucleons or target fragments. This technique has been pioneered at Jefferson Lab by detecting recoiled protons with low-momentum (relative to the nuclear Fermi momentum), that “tag” scattering events on nearly on-shell neutrons in a deuteron target [4-5] and detecting high-momentum recoil protons to study off-shell neutrons [4-6]. If the EMC effect

60




























60




























Coincidence?

Inclusive A(e,e�) measurements

!  At high nucleon momentum, distributions are similar in shape for light and heavy nuclei: SCALING.

!  Short distance two-nucleon relative wave function same in all nuclei .

!  One can get the probability of 2N-SRC in any nucleus, from the scaling factor.

)()( knCkn DAA ⋅=

Adapted from Ciofi degli Atti

27

high k

Piasetzky talk

Implications of data

• Previous models need to be extended to a larger range of x

• Detailed nuclear dependence must be explained (Dutta talk)

• Challenge: is EMC effect best described as being on single nucleon or a correlated pair of nucleons?

28

Are nucleons in the SRC modified?

• Need to start with a nuclear model of SRC and compute resulting EMC effect caused by modified structure function

• Medium modification due to mean field (previously discussed models) alternate hypothesis

29

Phenomenology Hen et al Int. J. Mod. Phys.E22, (’13)1330017

• Ciofi degli Atti & Simula, PRC53,1689 (96)-nuclear model- Spectral function has two terms - low momentum, mean-field MF part 80%, high momentum short-ranged correlations SRC 20%

• Strikman & Frankurt: relate nuclear DIS to nucleon structure function using spectral function PLB 183, 254 (87)

• Modification of nucleon structure function is

associated with MF or with SRC- two models

30

31

April 11, 2013 0:17 WSPC/INSTRUCTION FILE EMC˙reviewMar15b

The EMC Effect and High Momentum Nucleons in Nuclei 21

Fig. 9: The ratios of free to bound structure functions for various nuclei, extractedin the nucleus reference frame as detailed in Eq. 9. The dashed line is the result ofa linear fit to the data. The solid red line is the result of the medium-modificationfit, assuming an A-independent modification to SRC nucleons.

Universal modification to nucleon in SRC


The EMC Effect and High Momentum Nucleons in Nuclei 23

Fig. 11: Same as Fig. 9, assuming universal modification to Mean-Field nucleons.It is assumed that deuterium has no Mean-Field component, see text for details.

Universal modification to nucleon in MF

Which gives a better fit?

Int. J. Mod. Phys.E22, (’13)1330017

32


20 O. Hen et al.

x0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

N 2 /

FN 2F

∆

0.05

0.1

0.15

0.2

0.25

0.3

([1]* (x-[0])+[2]*(x-[0]) 2)/((1./56)*(5./9)*1.094*sqrt(x )*(26* 2* (1-x) 3+30*(9./8)* (1-x) 4)+(11./9)* 0.1857*(1-x)^ 7)

Fig. 8: The ratio of the modification term, ∆FN2 to the free nucleon structure

function, FN2 .

We next proceed by assuming that nucleons in high energy excited states (cor-related nucleons) have a different structure function !F2N (x) than free ones F2N (x).Thus we make the replacements

I1(A)F2 → I(0)1 (A)FN2 + I(1)1 (A) !FN

2 = I(0+1)1 (A)FN

2 + I(1)1 (A)∆F2N , etc, (19)

where

∆FN2 (xA) = !FN

2 (xA)− FN2 (xA). (20)

An alternate version in which the medium modification is associated with the mean-field components of the density can be obtained by using

I1(A)FN2 → I(0)1 (A) !FN

2 + I(1)1 (A) = I1(A)FN2 + I(0)1 (A)∆FN

2 , etc. (21)

A condition on ∆FN2 derived from the baryon sum rule is that

" 20 dxA

∆FN2

(xA)xA

= 0.This means that ∆FN

2 must pass through 0 at some value of xA.The analysis proceeds by calculating Eq. 13 with the supplement of Eq. 19

(Eq. 21 for the case of Mean-Field modification), assuming ∆FN2 (xA) is a second

order polynomial in xA. The parameters of ∆FN2 (xA) are fitted to the xA corrected

EMC data (see Appendix A) for all nuclei for which momentum distributions areavailable (i.e., 4He, 12C, 40Ca, 56Fe, and 197Au). Note that the functional form of∆FN

2 (xA) is assumed to be independent of A.The results of the fits for individual nuclei are shown in Fig. 9 (Fig. 11 for the

case of Mean-Field modification). The description of the data is very good for all

Modified Structure Function (SRC)


22 O. Hen et al.

nuclei with a χ2 per degree of freedom of ≈ 1 for both the SRC and Mean-Field fits.These results were obtained using the parametrization of Ref.21 for the free-nucleonstructure function, FN

2 . The modified-to-free structure function ratio is shown inFig. 8 (Fig. 10 for the case of Mean-Field modification).

The present results show that a model incorporating either universal modifica-tion of Mean-Field nucleons or modification of nucleons in SRC pairs can explainthe EMC effect. As expected, the required medium modification of Mean-Field nu-cleons is on the order of a few percent while that of SRC nucleons is a few tensof percent. This model does not prove or disprove that the underlying cause ofthe EMC effect is the unique association with short ranged correlations. Note that9Be was not included in the model calculations since a 9Be spectral function wasnot available. Note also that this model does not separate valence and sea quarkdistributions and therefore can’t make predictions about the Drell-Yan data.

Further experiments are needed to determine whether the Mean-Field or SRCnucleons are modified by the nuclear medium. For example, quasi-elastic electronscattering would be sensitive to the former but not the latter.

x0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

N 2 /

FN 2F

∆

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

([1]* (x-[0])+[2]*(x- [0]) 2)/((1./56)*(5./9)*1.094*sqrt(x )*(26* 2* (1-x) 3+30*(9./8)*(1-x) 4)+(11./9)* 0.1857*(1-x)^ 7)

Fig. 10: Same as Fig. 8, assuming universal modification to Mean-Field nucleons.It is assumed that deuterium has no Mean-Field component, see text for details

5. Summary

We have reviewed recent data showing that the detailed A dependence of the EMCeffect provides important hints in understanding the origin of that effect. The EMC

Modified Structure Function MF

MoModified Structure Functions

Is the EMC effect due to nucleons in SRC pairs or to nucleons moving in the mean field?

32


20 O. Hen et al.

x0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

N 2 /

FN 2F

∆

0.05

0.1

0.15

0.2

0.25

0.3

([1]* (x-[0])+[2]*(x-[0]) 2)/((1./56)*(5./9)*1.094*sqrt(x )*(26* 2* (1-x) 3+30*(9./8)* (1-x) 4)+(11./9)* 0.1857*(1-x)^ 7)

Fig. 8: The ratio of the modification term, ∆FN2 to the free nucleon structure

function, FN2 .

We next proceed by assuming that nucleons in high energy excited states (cor-related nucleons) have a different structure function !F2N (x) than free ones F2N (x).Thus we make the replacements

I1(A)F2 → I(0)1 (A)FN2 + I(1)1 (A) !FN

2 = I(0+1)1 (A)FN

2 + I(1)1 (A)∆F2N , etc, (19)

where

∆FN2 (xA) = !FN

2 (xA)− FN2 (xA). (20)

An alternate version in which the medium modification is associated with the mean-field components of the density can be obtained by using

I1(A)FN2 → I(0)1 (A) !FN

2 + I(1)1 (A) = I1(A)FN2 + I(0)1 (A)∆FN

2 , etc. (21)

A condition on ∆FN2 derived from the baryon sum rule is that

" 20 dxA

∆FN2

(xA)xA

= 0.This means that ∆FN

2 must pass through 0 at some value of xA.The analysis proceeds by calculating Eq. 13 with the supplement of Eq. 19

(Eq. 21 for the case of Mean-Field modification), assuming ∆FN2 (xA) is a second

order polynomial in xA. The parameters of ∆FN2 (xA) are fitted to the xA corrected

EMC data (see Appendix A) for all nuclei for which momentum distributions areavailable (i.e., 4He, 12C, 40Ca, 56Fe, and 197Au). Note that the functional form of∆FN

2 (xA) is assumed to be independent of A.The results of the fits for individual nuclei are shown in Fig. 9 (Fig. 11 for the

case of Mean-Field modification). The description of the data is very good for all

Modified Structure Function (SRC)


22 O. Hen et al.

nuclei with a χ2 per degree of freedom of ≈ 1 for both the SRC and Mean-Field fits.These results were obtained using the parametrization of Ref.21 for the free-nucleonstructure function, FN

2 . The modified-to-free structure function ratio is shown inFig. 8 (Fig. 10 for the case of Mean-Field modification).

The present results show that a model incorporating either universal modifica-tion of Mean-Field nucleons or modification of nucleons in SRC pairs can explainthe EMC effect. As expected, the required medium modification of Mean-Field nu-cleons is on the order of a few percent while that of SRC nucleons is a few tensof percent. This model does not prove or disprove that the underlying cause ofthe EMC effect is the unique association with short ranged correlations. Note that9Be was not included in the model calculations since a 9Be spectral function wasnot available. Note also that this model does not separate valence and sea quarkdistributions and therefore can’t make predictions about the Drell-Yan data.

Further experiments are needed to determine whether the Mean-Field or SRCnucleons are modified by the nuclear medium. For example, quasi-elastic electronscattering would be sensitive to the former but not the latter.

x0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

N 2 /

FN 2F

∆

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

([1]* (x-[0])+[2]*(x- [0]) 2)/((1./56)*(5./9)*1.094*sqrt(x )*(26* 2* (1-x) 3+30*(9./8)*(1-x) 4)+(11./9)* 0.1857*(1-x)^ 7)

Fig. 10: Same as Fig. 8, assuming universal modification to Mean-Field nucleons.It is assumed that deuterium has no Mean-Field component, see text for details

5. Summary

We have reviewed recent data showing that the detailed A dependence of the EMCeffect provides important hints in understanding the origin of that effect. The EMC

Modified Structure Function MF

MoModified Structure Functions

Is the EMC effect due to nucleons in SRC pairs or to nucleons moving in the mean field?

YES

Requirements & Goals

• Model the free distributions • Good support • Consistency with nuclear properties • Describe deep inelastic and di-muon

production data- valence plus sea • describe detailed A (N,Z)

dependence • Predict new phenomena

Ways to search for medium modification of nucleon structure• Quasi-elastic scattering, Coulomb sum rule

form factors of bound nucleons • Quasi-elastic, recoil polarization- • DIS on deuteron, detect spectator • A dependence • Parity violating DIS

34

GE/GM

Summary• nucleon structure is modified by nucleus • minimum model requirements- EMC, DY,

nuclear saturation, A-dependence • predict new phenomena • needed –better evaluations of models • experimental tests –form factors in medium, ( ) spectator tag, PVDIS

nuclear gluon distribution?? • new experiments Jlab and others to

find out how quarks work in a nucleus

eA! e0XN

Where do we stand after 33 years?

36

Where do we stand after 33 years?

36

The EMC Effect - Front page | ECT* · 2015-06-30 · The EMC Effect CERNCOURIER 1 VOLUME 53 NUMBER 4 MAY 2013 ... by the ‘creation’ of quarks via the point-like γ → q¯q coupling.

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