2N and 3N Correlations in Few Body Systems at x > 1faculty.fiu.edu/~sargsian/talks/Day.pdf · 2N...

2N and 3N Correlations in Few Body Systems at x > 1

Next generation nuclear physics with JLab12 and EIC

Donal DayUniversity of Virginia

1

Searching for 3N Correlations at x > 1

Outline

2

• Accepted Notions on SRCs• NN potential

responsible• Implications

• Some examples• Two nucleon correlations

in inclusive data• Examples• Implications

• Searching for 3N correlations• Data in depth

• 4He/3He• 12C/4He etc

• Finish• Wish List

Mark Strikman, John Arrington, Eli Piasetsky, Or Hen, Erez Cohen, Nadia Fomin, Doug Higinbotham, Patricia Solvignon, Elena Long

Independent particle states of a uniform potential - a mean field.

Independent Particle Shell Model

S(⌅p, E) =X

�

| ��(p) |2 ⇥(E + ⇤�)

• Enormous strong force acting• So many nucleons to collide with• How can nucleons possibly complete whole orbits (1021/s) without interacting?

Wood-Saxon

• The single-particle energies ξα and wave function Φα are the basic quantities - can be accessed in knockout reactions

• The spectral function should exhibit a structure at fixed energies with momentum distributions characteristic of the shell (orbit).

• Long mean free paths • No two-body interactions• Absence of correlations in

ground-state wave function. They do interact and they interact violently

4

VNN

r

correlated wf

uncorrelated wf

• The nucleon-nucleon (NN) interaction is singularly repulsive at short distances• Difficult to find two nucleons close to each other.

• Loss in configuration space components signals an increase of high-momentum components

• Both the correlation hole and the high-k components are absent in IPMs

• Taken together the loss of configuration space and the strengthening of high of momentum components are “correlations”.

• The NN tensor force also provides high-momentum components; required to obtain the quadrupole moment of the deuteron and predicts a isospin dependence of SRCs.

Case for Correlations

High enough to modify nucleon structure?

Densely packed - at small distances multiples of NM

10 CHAPTER 1. INTRODUCTION AND OVERVIEW

-2 -1 0 1 20.0

0.5

1.0

1.5

2.0

ρ ch

(fm-3

)

d = 1 fm

-2 -1 0 1 20.0

0.5

1.0

1.5

2.0

ρ ch

(fm-3

)

1.5 fm

-2 -1 0 1 20.0

0.5

1.0

1.5

2.0

z (fm)

ρ ch

(fm-3

)

2 fm

Figure 1.3: The scalar charge densities of two nucleons 1, 1.5 and 2 fm apart.

(BCC) solid, the particles have eight first neighbors at a distancep

3 a/2, where a is thelength of the cube side, (a3/2) is the volume of the unit cell, and (a3/2)Ω0 = 1. At nuclearmatter density this distance is

BCC nearest neighbor distance =

s

3

4

√

2

Ω0

!1/3

' 2 fm . (1.14)

On the other hand, particles in uncorrelated gases have a nearest neighbor at a distanceª r0. The mean nearest-neighbor distance in nuclei and nuclear matter is in between theselimits. It is of the order 1/mº ª 1.4 fm.

The radius of the proton distribution in a nucleus, denoted by RA,prms, can be obtained

from the charge radius of that nucleus by correcting for the proton and neutron sizes. When

z (fm)

-2 2-1 10

Pand

haripa

nde, P

iepe

r an

d Sc

hiav

illa

Evidence of SRC

pm [MeV/c]1 10 100

mass number A0

102030405060708090

100

rela

tive s

pect

rosc

opic

fact

or (%

) 3He 4He 6Li

7Li 12C 16O

30Si31P

32S

40Ca

48Ca

51V 208Pb90Zr

(e,e’p) at NIKHEF

Occupation numbersscaled down by a factor ∼0.65.

5

Central density is saturated - nucleons can be packed only so close together: pch * (A/Z) = constant

Ciofi/Simula

What many calculations indicate is that the tail of n(k) for different nuclei has a similar shape - reflecting that the NN interaction, common to all nuclei, is the source of these dynamical correlations. Suggests isospin dependence - similar to deuteron k > 250 MeV/c

20% of nucleons60% of KE

k < 250 MeV/c80% of nucleons40% of KE

Theory suggests a common feature for all nuclei

Isolate short range interactions (and SRC’s) by probing at high pm: (e,e’p) and (e,e’)

10Friday, May 31, 13

6

n(k) is A dependent at k < kf yet has a universal shape at large k, reflecting the details of the NN interaction. The cross sections mirror this universal behavior at x > 1.5.

Momentum distributions and cross sectionsInclusive scattering at large x

➡ Motion of nucleon in the nucleus broadens the peak.➡ little strength from QE above x ≈ 1.3.

High momentum tails accessible AND should yield constant ratio if seeing SRC

A(e,e’) E02019 Fomin et. al., 5.766, 18o

e

e’

Nucleus A

€

θ

At x ≈ 1

QE

Large x

€

θ

11Friday, May 31, 13

In the region where correlations should dominate, large x,

)2A

�

A

(x, Q2)�

D

(x, Q2)= a2(A)

áàààÜ1<x2

3A

�

A

(x, Q2)�

A=3(x, Q2)= a3(A)

áàààÜ2<x3

7

CS Ratios and SRC

aj(A) is proportional to probability of finding a j-nucleon correlation

FSDS

, Phy

s.Rev

.C48

:245

1-24

61,19

93

αtn = 2 −

q− + 2m

2m

!

1 +

√

W2− 4m2

W

"

SLAC data

2222

Simple SRC Model:• 2N, 3N dominate at x ≤ 1, 2• 2N, 3N configurations “at rest”• Isospin independent

N. Fomin,et al., PRL 108 (2012) 092052

Experimental observations:• Clear evidence for 2N-SRC at x>1.5 • Suggestion of 3N-SRC plateau(?)• Isospin dependence ?

K. Egiyan et al, PRL96, 082501 (2006)8

CS Ratios from Jlab

6

1

2

3

1

2

3

4

A(e,e/), 1.4<Q

2<2.6

r(4H

e,3

He

)

4He

r(1

2C

,3H

e)

12C

xB

r(5

6F

e,3

He

)

56Fe

2

4

6

1 1.25 1.5 1.75 2 2.25 2.5 2.75

FIG. 4: Cross section (A/3He) ratios at large x as measured in CLAS.

state interactions, due to the different mix of nn, np, and pp correlations in non-isoscalar nuclei.However, there are calculations indicating that there are significant final state interactions that donot vanish rapidly as Q2 increases, and which do not cancel in the target ratios [19] (i.e. do not comefrom short range configurations that are identical in all nuclei). This calculation indicates that theFSI (when including inelastic channels) has a very weak Q2 dependence and will persist, challengingour interpretation of the impulse approximation analysis. In addition, it predicts that the FSI effectswill increase the x > 1.5 cross section in iron by approximately a factor of ten, and that even in theratio of iron to deuterium, there is a factor of five effect from these FSIs. An important portion ofthe proposed measurement is the ability to test these precisions of FSIs by extracting absolute crosssections for x > 1.5 on a variety of few-body (and heavy) nuclei over a range of Q2.

For the deuteron, which is dominated by the simple two-body breakup assumed in an impulseapproximation analysis, we can extract the nucleon momentum distribution from the inclusive datawithout the complications caused by neglecting the separation energy of the full spectral function.The momentum distribution for the deuteron as extracted from experiment E89-008 is shown inFig. 5 [3]. The normalization of the extracted momentum distribution is consistent with unity,and the high momentum components are in good agreement with calculations based on moderntwo-body nucleon–nucleon potentials. This sets limits on the impact of FSI, even in the regiondominated by short range correlations, indicating that the scattering is consistent with the impulseapproximation and that final state interactions much smaller than those observed in coincidenceA(e,e’p) measurements, or those predicted in some calculations. In the proposed measurements, wewill extract absolute cross sections for 2H, 3He, and 4He, not available for the CLAS results, whichwill allow us to set limits on the size (and A dependence) of final state interactions.

The extension of these ratio measurements to higher Q2 will allow us to better test the x and Q2

Connection between SRCs and EMC effect: Importance of two-body correlations?

L. Weinstein, et al., PRL 106, 052301 (2011)O. Hen, et al, PRC 85, 047301 (2012)

J. Seely, et al., PRL103, 202301 (2009) N. Fomin, et al., PRL 108, 092052 (2012)J. Arrington, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86 (2012) 065204

Virtuality or Local density

Many body calculations connecting SRC and EMC are lacking

Q2 = 1.5

Q2 = 1.5

Integration limits over spectral functionQES

DIS

The limits on the integrals are determined by the kinematics. Specific (x, Q2) select specific pieces of the spectral function.

|Å

}

d

2�

d⌦d⌫/Zd

~

k

ZdE�

ei

S

i

(k, E)|Å}Spectral function

�()

d

2�

d⌦d⌫/Zd

~

k

ZdE W

(p,n)1,2 S

i

(k, E)|Å}Spectral function

Given the fact that EMC and SRC integrate over very different parts of the spectral function needs close examination

11

Theory and experiment display isospin dependence

Data show large asymmetry between np, pp pairs:Qualitative agreement with calculations; effect of tensor force. Huge violation of often assumed isospin symmetry

Missing Momentum [GeV/c]0.3 0.4 0.5 0.6

SRC

Pai

r Fra

ctio

n (%

)

10

210

C(e,e’p) ] /212C(e,e’pp) /12pp/2N from [

C(e,e’p)12C(e,e’pn) /12np/2N from

C(p,2p)12C(p,2pn) /12np/2N from

C(e,e’pn) ] /212C(e,e’pp) /12pp/np from [

R. Subedi et al, Science 320, 1476(2008)

Two-nucleon knock-out experiment

Tensor Forces and the Ground-State Structure of Nuclei

R. Schiavilla,1,2 R. B. Wiringa,3 Steven C. Pieper,3 and J. Carlson4

1Jefferson Laboratory, Newport News, Virginia 23606, USA2Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA3Physics Division, Argonne National Laboratory, Argonne, Illinois 61801, USA

4Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA(Received 10 November 2006; published 27 March 2007)

Two-nucleon momentum distributions are calculated for the ground states of nuclei with mass numberA ! 8, using variational Monte Carlo wave functions derived from a realistic Hamiltonian with two- andthree-nucleon potentials. The momentum distribution of np pairs is found to be much larger than that ofpp pairs for values of the relative momentum in the range "300–600# MeV=c and vanishing total mo-mentum. This order of magnitude difference is seen in all nuclei considered and has a universal characteroriginating from the tensor components present in any realistic nucleon-nucleon potential. The correla-tions induced by the tensor force strongly influence the structure of np pairs, which are predominantly indeuteronlike states, while they are ineffective for pp pairs, which are mostly in 1S0 states. These featuresshould be easily observable in two-nucleon knockout processes, such as A"e; e0np# and A"e; e0pp#.

DOI: 10.1103/PhysRevLett.98.132501 PACS numbers: 21.30.Fe, 21.60.$n, 25.30.$c, 27.10.+h

The two preeminent features of the nucleon-nucleon(NN) interaction are its short-range repulsion and inter-mediate- to long-range tensor character. These inducestrong spatial-spin-isospin NN correlations, which leavetheir imprint on the structure of ground- and excited-statewave functions. Several nuclear properties reflect the pres-ence of these features. For example, the two-nucleon den-sity distributions !MS

TS "r# in states with pair spin S % 1 andisospin T % 0 are very small at small internucleon separa-tion r and exhibit strong anisotropies depending on the spinprojection MS [1]. Nucleon momentum distributions N"k#[2,3] and spectral functions S"k; E# [4] have large high-momentum and, in the case of S"k; E#, high-energy com-ponents, which are produced by short-range and tensorcorrelations. The latter also influence the distribution ofstrength in response functions R"k;!#, which characterizethe response of the nucleus to a spin-isospin disturbanceinjecting momentum k and energy! into the system [5,6].Lastly, calculations of low-energy spectra in light nuclei(up to mass number A % 10) have demonstrated that tensorforces play a crucial role in reproducing the observed

ordering of the levels and, in particular, the observedabsence of stable A % 8 nuclei [7].

In the present study we show that tensor correlations alsoimpact strongly the momentum distributions of NN pairsin the ground state of a nucleus and, in particular, that theylead to large differences in the np versus pp distributionsat moderate values of the relative momentum in the pair.These differences should be observable in two-nucleonknockout processes, such as A"e; e0np# and A"e; e0pp#reactions. This work goes beyond that of Ref. [7], whichdid not address the momentum dependence of the ten-sor force and induced correlations, by showing importanteffects at relative momenta greater than 1:5 fm$1. Theseeffects, associated with small total and large relativemomenta in the NN pair, cannot be computed within thevlow k framework [8] directly, but require the inclusion ofadditional many-body, nonlocal, spin-isospin dependentoperators.

The probability of finding two nucleons with relativemomentum q and total momentum Q in isospin state TMTin the ground state of a nucleus is proportional to thedensity

!TMT"q;Q# % A"A$ 1#

2"2J& 1#XMJ

Zdr1dr2dr3 ' ' ' drAdr01dr02

yJMJ"r01; r02; r3; . . . ; rA#e$iq'"r12$r012#e$iQ'"R12$R012#

( PTMT"12# JMJ

"r1; r2; r3; . . . ; rA#; (1)

where r12 ) r1 $ r2, R12 ) "r1 & r2#=2, and similarly forr012 and R012. PTMT

"12# is the isospin projection operator,and JMJ

denotes the nuclear wave function in spin andspin-projection state JMJ. The normalization is

Z dq"2"#3

dQ"2"#3 !TMT

"q;Q# % NTMT; (2)

where NTMTis the number of NN pairs in state TMT .

Obviously, integrating !TMT"q;Q# over only Q gives the

probability of finding two nucleons with relative momen-tum q, regardless of their pair momentum Q (and viceversa).

The present study of two-nucleon momentum distribu-tions in light nuclei (up to A % 8) is based on variationalMonte Carlo (VMC) wave functions, derived from a real-istic Hamiltonian consisting of the Argonne v18 two-

PRL 98, 132501 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending30 MARCH 2007

0031-9007=07=98(13)=132501(4) 132501-1 © 2007 The American Physical Society

0 1 2 3 4 5q (fm-1)

10-1

100

101

102

103

104

105

ρ NN(q,

Q=0)

(fm6 )

AV18/UIX 4HeAV18 2H

D-wave

S-wave

Scaled momentumdistribution of the deuteron

nppp

2626

Isospin structure of 2N-SRCs in inclusive scattering

■ 40% difference between full isosinglet dominance and isospin independence in 3He/3H ratio in 2N-SRC region

■ Few body calculations [M. Sargisan, Wiringa/Peiper (GFMC)] predict n-p dominance, with sizeable contribution from T=1 pairs

■ Goal is to measure ratio 1.5% precision■ Extract R(T=1/T=0) with uncertainty of 3.8%

3He/3H is simple/straightforward case:E12-11-112: x>1 measurements of correlations

Patricia Solvignon

12

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

n/p

Avg densitygenerated on 2013-07-16 by Donal Day

world setproposedincluded

n/p

Average Density

Seek out ranges of n/p ratios for isospin dependence studies

Other targets

To also be addressed in E12-06-105

Onset of scaling for 2<x<3 at which pmiss ?

(a)

(b)

1

1

2

2

3

3

p3 = p1+p2

p1 = p2 = p3

extremely large momentum

“Star-configuration”

13

3N Correlations2N SRC (3N SRC)

• p > kF i.e. its momentum exceeds characteristic nuclear Fermi momentum, (kF ≳ 250 MeV/c)

• balanced by the momentum of a (two) correlated nucleon(s)• In both cases the center of mass momentum of the SRC, pcm < kF

A(e,e’) cross section ratios and SRC

K. S. Egiyan et al., Phys. Rev. Lett. 96, 082501 (2006)

Hall B Hall CN. Fomin et al., Phys. Rev. Lett. 108, 092502 (2012)

examined the high-momentum tail of the deuteron momen-tum distribution and used target ratios at x > 1 to examinethe A and Q2 dependence of the contribution of 2N-SRCs.The SRC contributions are extracted with improved statis-tical and systematic uncertainties and with new correctionsthat account for isoscalar dominance and the motion of thepair in the nucleus. The 9Be data show a significant devia-tion from predictions that the 2N-SRC contribution shouldscale with density, presumably due to strong clusteringeffects. At x > 2, where 3N-SRCs are expected to domi-nate, our A=3He ratios are significantly higher than theCLAS data and suggest that contributions from 3N-SRCsin heavy nuclei are larger than previously believed.

We thank the JLab technical staff and accelerator divi-sion for their contributions. This work supported by theNSF and DOE, including contract DE-AC02-06CH11357and contract DE-AC05-06OR23177 under which JSA,LLC operates JLab, and the South African NRF.

*Deceased.[1] J. Vary, Proc. Sci. LC2010 (2010), 001.[2] R. Schiavilla, R. B. Wiringa, S. C. Pieper, and J. Carlson,

Phys. Rev. Lett. 98, 132501 (2007).[3] L. L. Frankfurt and M. I. Strikman, Phys. Rep. 76, 215

(1981).[4] D. B. Day, J. S. McCarthy, T.W. Donnelly, and I. Sick,

Annu. Rev. Nucl. Part. Sci. 40, 357 (1990).

[5] J. Arrington, D. Higinbotham, G. Rosner, and M. Sargsian,arXiv:1104.1196.

[6] N. Fomin et al., Phys. Rev. Lett. 105, 212502 (2010).[7] N. Fomin, Ph.D. thesis, University of Virginia, 2007,

arXiv:0812.2144.[8] A. Aste, C. von Arx, and D. Trautmann, Eur. Phys. J. A 26,

167 (2005).[9] E. Pace and G. Salme, Phys. Lett. B 110, 411 (1982).[10] D. B. Day et al., Phys. Rev. Lett. 59, 427 (1987).[11] J. Arrington et al., Phys. Rev. Lett. 82, 2056 (1999).[12] T. DeForest, Nucl. Phys. A392, 232 (1983).[13] J. J. Kelly, Phys. Rev. C 70, 068202 (2004).[14] J. Arrington, W. Melnitchouk, and J. A. Tjon, Phys. Rev. C

76, 035205 (2007).[15] R. Arnold et al., Phys. Rev. Lett. 61, 806 (1988).[16] C. Ciofi degli Atti, L. P. Kaptari, and D. Treleani, Phys.

Rev. C 63, 044601 (2001).[17] K. Kim and L. Wright, Phys. Rev. C 76, 044613

(2007).[18] A. Bussiere et al., Nucl. Phys. A 365, 349 (1981).[19] C. Ciofi degli Atti and C. B. Mezzetti, Phys. Rev. C 79,

051302 (2009).[20] X.-D. Ji and J. Engel, Phys. Rev. C 40, R497 (1989).[21] C. Ciofi degli Atti and G. B. West, arXiv:nucl-th/9702009.[22] J. Arrington, arXiv:nucl-ex/0306016.[23] J. Arrington, arXiv:nucl-ex/0602007.[24] C. Ciofi degli Atti and G. B. West, Phys. Lett. B 458, 447

(1999).[25] C. Ciofi degli Atti, E. Pace, and G. Salme, Phys. Rev. C

43, 1155 (1991).[26] L. L. Frankfurt, M. I. Strikman, D. B. Day, and M.

Sargsian, Phys. Rev. C 48, 2451 (1993).[27] K. S. Egiyan et al., Phys. Rev. C 68, 014313 (2003).[28] K. S. Egiyan et al., Phys. Rev. Lett. 96, 082501 (2006).[29] J. Arrington et al., Phys. Rev. C 64, 014602 (2001).[30] O. Benhar et al., Phys. Lett. B 343, 47 (1995).[31] L. L. Frankfurt and M. I. Strikman, Phys. Rep. 160, 235

(1988).[32] C. C. degli Atti and S. Simula, Phys. Lett. B 325, 276

(1994).[33] C. C. degli Atti and S. Simula, Phys. Rev. C 53, 1689

(1996).[34] C. B. Mezzetti, arXiv:1003.3650.[35] C. B. Mezzetti, arXiv:1112.3185.[36] R. Subedi et al., Science 320, 1476 (2008).[37] J. Seely et al., Phys. Rev. Lett. 103, 202301 (2009).[38] J. Arrington et al., Jefferson Lab Experiment E08-014

(2008), http://www.jlab.org/exp_prog/proposals/08/PR-08-014.pdf.

[39] V. Stoks, R. Klomp, C. Terheggen, and J. de Swart, Phys.Rev. C 49, 2950 (1994).

[40] M. Lacombe et al., Phys. Lett. B 101, 139 (1981).[41] R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev.

C 51, 38 (1995).

0

1

2

3

4

5

1 1.5 2 2.5 3x

(σH

e4/4

)/(σ

He3

/3)

R(4He/3He)

CLASE02-019

FIG. 3 (color online). The 4He=3He ratios from E02-019(Q2 ! 2:9 GeV2) and CLAS (hQ2i ! 1:6 GeV2); errors arecombined statistical and systematic uncertainties. For x > 2:2,the uncertainties in the 3He cross section are large enough that aone-sigma variation of these results yields an asymmetric errorband in the ratio. The error bars shown for this region representthe central 68% confidence level region.

PRL 108, 092502 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

2 MARCH 2012

092502-5

Good agreement in the 2N-SRC region

14


but potential difference in the 3N-SRC region

15


CLAS 4He/3He

Step?

16


CLAS 4He/3HeE02019 4He/3He

O. Hen and D. Higinbotham, bin drift

17


CLAS 4He/3HeE08014 (Z. Ye) 4He/3HePrelim

18


CLAS 4He/3HeSLAC E121 4He/3He

Rock et al, PRC 26, 1593 (1982)

19


CLAS 4He/3HeE02019 4He/3HeE08014 (Z. Ye) 4He/3HeSLAC E121 4He/3He

Cross section model shows a rapid falloff of the 3He cross section starting near x approaching 2.5.

20


CLAS 4He/3HeE02019 12C/4HeE02019 12C/3He

Rise in 12C/4He very gradual compared to 12C/3He Step?

21

Fe/3He (CLAS) Fe/4He (NE3)


Step?

22

9Be/4He (E02019)


Step?

23


Ratio of 9Be, 12C, Cu, Au to 4He @ Q2 = 2.5

From E02019, Fomin thesis data

Ratio

to 4He

x

2N SRC

3N SRC ??

Step?

24


64Cu/12C

25

Benhar calculation, with folded FSI


26

Evidence for 3N correlation in ratios to 3He?

Naive SRC model, where 2N- and 3N-SRCs are at rest, the rise in the ratio as x → 3 as coming from the difference between stationary 3N-SRC in 3He and moving SRCs in heavier nuclei.

CM motion has to play a role that must be modeled in inclusive

Violation of naive scaling picture, which predicts a plateau

This violation is also seen in ratios to 2H 2N-SRC region.

It different as the motion of the 2N- SRC yields mainly a small enhancement of the plateau, with modest distortion until x > 1.9, where the deuteron cross section falls sharply from its exponential falloff with x

For 3N-SRCs, motion of the correlations would yield a sharp rise further from the kinematic limit at x = 3 due to the earlier onset of the rapid cross section falloff

27

Some indication of a step but rise as x grows above is obvious.What should we expect in magnitude and shape?CMM is poorly understood and clearly must beHigh quality data from medium heavy to light (A = > 4) data

Evidence for 3N correlations in ratios to 4He?

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

n/p

Avg densitygenerated on 2013-07-16 by Donal Day

world setproposedincluded

n/p

Average Density

Seek out ranges of n/p ratios for isospin dependence studiesZ N Sym A26 22 Ti 48 30 28 Ni 58 36 28 Ni 64 52 44 Ru 96 58 46 Pd 10460 47 Ag 107146 92 U 238138 90 Th 228

Beam time is finite, we have to select

carefully

F2 versus xσ vs energy loss

Heavier nuclei QEP is averaged

out - duality

F2(x, Q2) =

x

2

⇠

2r

3F

02 (⇠, Q

2)

+6M2

x

3

Q

2r

4h2(⇠, Q

2) +12M4

x

4

Q

4r

5g2(⇠, Q

2)

SFs at x > 1 sensitive to SRC. The bulk of the strength for x ≥ 1.1–1.2 come from the high momentum nucleons generated by SRCs. See slide 10.

Fomin et. al., Phys.Rev.Lett. 105 (2010) 212502

⇠ = 2x/(1 +p1 + 4M2

x

2/Q

2)F2 versus ξ

Large Q2, large x additionally sensitive to small admixtures of exotic components - e.g. 5% 6q cluster in D leads to dramatic effect on large x pdfs: Mulders and Thomas

In OPE F20 (not F2) should be independent Q2 in absence of QCD evolution and higher twists.

Correlations in DIS at x > 1

E12-06-105

What’s planned? XEMC part 2HM

S|Å

}

HMS

|Å}

SHMS

SHMS|Å} SRC, n(k), σ FSI

EMC|Å}super-fast quarksquark distribution functionsmedium modifications

29

E12-06-105

30

11 GeV

24 GeV JLAB

6 GeV4 GeV

What is possible in the future

31

Summary

• 2N SRC and their isospin dependence (anticipated by our understanding of the NN interaction) is now firmly established in multiple observables, experiments projectiles, final states and nuclei

• Relation of SRC to EMC established - only lacking are calculations that exposes the underlying connection

• Refined theory and calculation are needed incorporating SRC, FSI, and off-shell behavior will advance understanding

• SRC demand high densities (momenta, virtuality) and, if these rare fluctuations can be captured, they should expose, potentially large, medium modifications

• Evidence for 3N SRC are as yet elusive - some sleuthing underway• Approved experiments across labs with different focuses over next

5-7 years will reveal much• Next big opportunity in inclusive scattering (in my view) is the

transition from QES to DIS at x > 1 at very large momenta transfer

SRC Wish List 2N-SRC

1. For the 2N-SRC pair, what is the CM , relative momentum and the correlation between them as a function of all relevant parameters

a) What are the most important parameters ? momentum, different nuclei.b) How to best compare data with theoretical calculations?

2. Can we identify and quantify the amount of 2N-SRC at X ≤ 1 ?3. How to characterize the transition between mean field and 2N-SRC dominant regions ?4. What is the number and isospin structure of 2N-SRC in very asymmetric nuclei (N≠Z) ?

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2N-SRC

5. Can we identify and quantify the decay of 2N-SRC to non - 2 nucleon final states?6. Can we identify and quantify signature for exotica (intermediate hidden color state or non-nucleonic DOF) in the 2N-SRC?7. How to extrapolate the 2N-SRC (and the EMC) to infinite symmetric nuclear matter?8. How to extrapolate the 2N-SRC (and the EMC) to high density (n star)?9. Are 2N-SRC relevant to the neutrino nuclear problems?

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SRC Wish List

3N-SRC

1.What is the amount of 3N-SRC as a function of relevant parameters (what are the relevant parameters?: momentum, nuclei….2. Can we identify the structure of 3N-SRC ? Coplanar, star configuration…?3. Can we study the isospin structure of 3N-SRC and the relation between it and the geometry of the 3N-SRC ?4. What determines the transition between 2N-SRC and 3N-SRC dominant regions ?5.What is the number and isospin structure of 3N-SRC in very asymmetric nuclei (N≠Z).6.What and how can we learn about 3N forces from 3N-SRC ?

SRC Wish List

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2N and 3N Correlations in Few Body Systems at x > 1faculty.fiu.edu/~sargsian/talks/Day.pdf · 2N...

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Transcript of 2N and 3N Correlations in Few Body Systems at x > 1faculty.fiu.edu/~sargsian/talks/Day.pdf · 2N...