short range correlations (hard nuclear processes) · 1. outstanding problems in src studies -...

Short Range Correlations� (Hard Nuclear Processes)�

3. Probing the deuteron at small distances�

4. Probing multi-nucleon SRCs in medium to heavy nuclei�

I. Short Range Correlation Studies�1. Outstanding Problems in SRC studies �

2. Choosing the probe reaction �

3. Extracting J/Psi-N interaction near the threshold �

II. Hard Photodisintegration of few-body systems�1. Probing the mechanism of hard QCD hadronic interaction �

2. Probing Non-nucleonic degrees of freedom/hidden color�

1. Outstanding Problems in SRC studies �

- Nuclear Forces at Short Distances: �NN repulsive core

-  Direct Observation of the dominance of high momentum � protons in neutron rich heavy nuclei �

-  Direct Observation of 3N SRCs�

-  Non-Nucleonic Content of 2N SRCs�

- Nuclear Forces at Short Distances: � NN repulsive core

Jastrow 1951 assumed the existence of the hard core to explain the angular distribution of pp cross section at 340 MeV (r0=0.6fm)�

r0 = 0.4fm

Stability Theorem: Nuclei will Collapse without �Repulsive interaction 1950s Weisskopf, Blatt �

V 2N = V 2NEM

+ V 2N! + V 2N

R

V 2NR

= V c + V l2L2 + V tS12 + V lsL · S + vls2(L · S)2

V i = Vint,R + Vcore

Vcore =

!

1 + er!r0

a

"

!1

60’s

Modern NN Potentials�

0.2 0.4 0.6 0.8

5000

10 000

15 000

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0

V C(r) [MeV]

r [fm]

-50

0

50

100

0.0 0.5 1.0 1.5 2.0

1S03S1OPEP

Lattice Calculations�

0.2 0.4 0.6 0.8

5000

10 000

15 000

Pauli Blocking

Contradicts Neutron Star Observations: �will predict masses not more than 0.1 - 0.6 Solar mass �

QCD

0.2 0.4 0.6 0.8

5000

10 000

15 000

Perturbative QCD �

Hidden Color�

Intrinsic strangeness/charm�

r

Vc, MeV

~80% hidden color Brodsky,Ji, Lepage, PRL 83

Probing the Deuteron at Short Distances�

d = pn + �� + NN⇤ + hc · · ·

hc = Nc,Nc

The NN core can be due to the orthogonality of �

h Nc,Nc | N,N i = 0

O.Hen et al Phys. ReV .C 2014

10-4

10-3

10-2

10-1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1p , GeV/c

Deut

erum

wav

e fun

ction

fm3/2

10-4

10-3

10-2

10-1

1

10

10 2

10 3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1p , GeV/c

n(p)

GeV

-3

Probing Polarized Structure of the Deuteron at x > 1 �

- Tensor Polarized Deuteron = Compact Deuteron �

10-4

10-3

10-2

10-1

1

10

10 2

10 3

10 4

0 50 100 150 200 250 300 350 400 450 500

pnt Mev/C

Gev-3

(l11+l1-1+l10)/3

(l11+l1-1-2l10)/3@ ParisBonn A

pnz=0

Fig.6

for large k > kFermi nA(k) ⇡ aNN (A)nNN (k)

E. Piasetzky, MS, L. Frankfurt, M. Strikman,J.Watson PRL , 2006

TheoreTcal analysis of BNL Data

Direct Measurement at JLab R.Subdei, et al Science , 2008

Missing Momentum [GeV/c]0.3 0.4 0.5 0.6

SRC P

air Fr

action

(%)

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 [

pn

pp

Factor of 20�

Expected 4�(Wigner counting)�

Ppn/px

= 0.92+0.08�0.18

-  Direct Observation of the dominance of high momentum � protons in neutron rich heavy nuclei �

p+A ! p+ p+ n+X

e+A ! e0 + p+ (p/n) +X

�(1)(k1, · · · , kc, · · · ,�kc, · · · , kA) ⇡UNN (kc)

k2cFA(k1, · · ·0 · · ·0 , · · · , kA)

nA(k) ⇡ aNN (A)nNN (k)

VT

Vc

-150

-100

-50

0

50

100

150

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5r,fm

V, MeV

Theoretical Interpretation

VNN (r) � Vc(r) + Vt(r) · S12(r) + VLS · �L�S

S12 = 3(�1 · r̂)(�2 · r̂)� �1�2 S12|pp� = 0

S12|nn� = 0

S12|pn⇥ �= 0

Isospin 1 states

Isospin 0 states

S12|pn� = 0

3He

Explana'on lies in the dominance of the tensor part in the NN interac'on

M.S, Abrahamyan, Frankfurt,Strikman PRC,2005

VNN (r) � Vc(r) + Vt(r) · S12(r) + VLS · �L�S

S12 = 3(�1 · r̂)(�2 · r̂)� �1�2 S12|pp� = 0

S12|nn� = 0

S12|pn⇥ �= 0

Isospin 1 states

Isospin 0 states

S12|pn� = 0Sciavilla, Wiringa, Pieper, Carlson PRL,2007

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

10-1

100

101

102

103

104

105

l NN(q

,Q=0

) (fm

6 )

AV18/UIX 4HeAV6’ 4HeAV4’ 4HeAV18 2H

Explana'on lies in the dominance of the tensor part in the NN interac'on

- Dominance of pn short range correlations� as compared to pp and nn SRCS �-  Dominance of NN Tensor as compared � to the NN Central Forces at <= 1fm �

-  Two New Properties of High Momentum Component�

- Energetic Protons in Neutron Rich Nuclei �

2006-2008s�

at p > kF

nA(p) ⇠ aNN (A) · nNN (p)

-- Dominance of pn Correlations � (neglecting pp and nn SRCs) nNN (p) ⇡ npn(p) ⇡ n(d)(p)

(1)

(2)

a2(A) ⌘ aNN (A) ⇡ apn(A)

nA(p) ⇠ apn(A) · nd(p)

- Define momentum distribution of proton & neutron nA(p) =

Z

AnAp (p) +

A� Z

AnAn (p)RnAp/n(p)d

3p = 1

(3)

- Define Ip =

Z

A

600Z

kF

nAp (p)d

3p In =A� Z

A

600Z

kF

nAn (p)d

3p

- and observe that in the limit of no pp and nn SRCs Ip = In

- Neglecting CM motion of SRCs Z

AnAp (p) ⇡

A� Z

AnAn (p)

First Property: Approximate Scaling Relation

- for ⇠ kF � 600 MeV/c region:

xp · nAp (p) ⇡ xn · nA

n (p)

where xp = ZA and xn = A�Z

A .

-‐if contribuTons by pp and nn SRCs are neglected and the pn SRC is assumed at rest MS,arXiv:1210.3280

Phys. Rev. C 2014

Realistic 3He Wave Function: Faddeev Equation

10-4

10-3

10-2

10-1

11010 210 3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1p , GeV/c

x n(p)

, GeV

-3

00.20.40.60.8

11.21.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1p , GeV/c

Ratio

xpnp

xnnn

1/2 nd

.

MS,PRC 2014

Be9 Variational Monte Carlo Calculation: � Robert Wiringa 2013

0 1 2 3 4 5 6 7 8 9 1010-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

k (fm-1)

l(k)

9Be(c) - AV18/UIX

lp

ln

hap://www.phy.anl.gov/theory/research/momenta/

0 2 4 6 8 1010-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

k (fm-1)

l(k)

10Be - AV18/UIX

lp

ln

B10 Variational Monte Carlo Calculation: � Robert Wiringa

Second Property:

xp · nAp (p) ⇡ xn · nA

n (p)

Using DefiniTon:

where y = |1� 2xp| = |xn � xp|- aNN (A, 0) corresponds to the probability of pn SRC in symmetric nuclei

- aNN (A, 1) = 0 according to our approximation of neglecting pp/nn SRCs

nA(p) =Z

AnAp (p) +

A� Z

AnAn (p)

ApproximaTons: nA(p) ⇠ aNN (A) · nNN (p)

nNN (p) ⇡ npn(p) ⇡ n(d)(p)

One Obtains: ⇡ 1

2aNN (A, y)nd(p)

MS,arXiv:1210.3280 Phys. Rev. C 2014

And: Ip = In Ip + In = 2IN = apn(A)

600Z

0

nd(p)d3p

Second Property: Fractional Dependence of � High Momentum Component

aNN (A, y) ⇡ aNN (A, 0) · f(y) with f(0) = 1 and f(1) = 0

f(|xp

� x

n

|) = 1�nP

j=1b

i

|xp

� x

x

|i withnP

j=1b

i

= 0

In the limit nP

j=1b

i

|xp

� x

x

|i ⌧ 1 Momentum distribuTons of p & n are inverse proporTonal to their fracTons

nA

p/n

(p) ⇡ 12xp/n

a2(A, y) · nd

(p)

xp/n = Z/NA

Observations: High Momentum Fractions

Pp/n

(A, y) = 12xp/n

a2(A, y)1R

kF

nd

(p)d3p

A Pp(%) Pn(%) 12 20 20 27 23 22 56 27 23 197 31 20

O. Hen, M.S. L. Weinstein, et.al. Science, 2014

Requires dominance of pn SRCs in heavy neutron reach nuclei


Is the total kinetic energy inversion possible?

Checking for He3 �

Epkin = 14 MeV (p= 157 MeV/c)

Enkin = 19 MeV (p= 182 MeV/c)

Energetic Neutron �Energetic Neutron �(Neff & Horiuchi) �Ep

kin = 13.97 MeV

Enkin = 18.74 MeV

VMC Estimates: Robert Wiringa Table 1: Kinetic energies (in MeV) of proton and neutron

A y Epkin En

kin Epkin � En

kin8He 0.50 30.13 18.60 11.536He 0.33 27.66 19.06 8.609Li 0.33 31.39 24.91 6.483He 0.33 14.71 19.35 -4.643H 0.33 19.61 14.96 4.658Li 0.25 28.95 23.98 4.9710Be 0.2 30.20 25.95 4.257Li 0.14 26.88 24.54 2.349Be 0.11 29.82 27.09 2.7311B 0.09 33.40 31.75 1.65


Heavy Nuclei ?

- Three Nucleon Short Range Correlations: �

Factorization of 2N SRC distribution in nuclei�

0

3

6 3He

0

3

6 4He

(mA/A

)/(m D

/2)

0

3

6

0.8 1 1.2 1.4 1.6 1.8x

9Be

12C

63Cu

1 1.2 1.4 1.6 1.8 2x

197Au

Egiyan, et al PRC 2004 Fomin et al PRL 2011


Subedi et al Science 2006

pm

rp 3r2p

pmr2p rp 3

q q(a) (b)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55pn(GeV/c)

cosa

5.9 GeV/c, 988.0 GeV/c, 989.0 GeV/c, 985.9 GeV/c, 947.5 GeV/c, 94

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

!cos -1.00 -0.98 -0.96 -0.94 -0.92 -0.90

Co

un

ts

0

10

20

30

40

!p

p

Tang et al PRL 2002

p+A ! p+ p+ n+X e+A ! e0 + pf + pb +X


Factorization of 3N SRC distribution in nuclei?�

Egiyan, et al PRL 2006 Fomin et al PRL 2011

For 2 < x < 3 R ⇡ a3(A1)a3(A2)

0

1

2

3

4

5

1 1.5 2 2.5 3x

(mHe

4/4)/(m H

e3/3)

R(4He/3He)

CLASE02-019

- Three Nucleon Short Range Correlations: � New Signatures of 3N SRCs�

r2pr2p

q q

rp

p

rp

p

3

3

mm(a) (b)

20406080100120140160180 200

400

600

10-5

10-4

10-3

10-2

10-1

11010 2

20406080100120140160180 200

400

600

10-4

10-3

10-2

10-1

1

10

D(p

i,ER

,pR

), G

eV-5

D(p

i,ER

,pR

), G

eV-5

Or, Deg.

Or, Deg.

E R, M

eV

E R, M

eV

2N-I

3N-I

3N-II

3N-I

2N-I3N-I

3N-II3N-I

(a)

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

100 150 200 250 300 350 400 450 500ER, MeV

pp/pn

-  Non-Nucleonic Content of 2N SRCs�

- The relative momenta in the NN system which will be sensitive to the core dynamics can be estimated based on the threshold of inelastic N-Delta transition �

- No non-nuclonic component is observed for pn system up to 650 MeV/c�

pM2

N + p2 �MN > M� �MN

p � 800 MeV/c

3. Deuteron > 800 MeV/c (core physics)�

4.Observation and systematic studies of 3N SRCs�

- Outstanding Problems in SRC studies�1. Deuteron 500 - 800 MeV/c �

2. Protons in neutron rich nuclei�

2. Choosing the probe�

� +A ! Nf + ⇡ +Nr +X

� +Ni ! Nf + ⇡at fixed and large ✓cm ⇠ 90

0

d�dt ⇠ f(✓cm)

s7 for E� > 1 GeV

si = s0 · ↵i Reaction chooses ↵i < 1!

Frankfurt, Liu, Strikman, Farrar PRL 1989

↵i =Ei�pz

iMN

-  External probe selects a bound nucleon � moving in the probes direction �

� +A ! n+ ⇡+ +Nr +X

� +A ! p+ ⇡� +Nr +X

� +A ! p+ ⇡0 +Nr +X

Probing proton

Probing neutron

Probing proton

Maria Patsyuk’s talk

3. Probing the Deuteron at Small Distances��

� �

⇡

⇡ ⇡

NN

N N

3. Probing multi-nucleon SRCs in medium to heavy� nuclei��

Maria Patsyuk’s talk

II. Hard Photodisintegration of few-body systems�1. Probing the mechanism of hard QCD hadronic interaction �

N

N

N

N

qqq- g g g

-Can be Studied in Hard Exclusive NN Scattering Reactions

-Last Experiments were done at early 90’s at AGS, BNL

N

N

N

N

q qqq- g g g

s = (k! + pd)2 = 2MdE! + M2

d

t = (k! ! pN )2 = [cos!cm ! 1]s ! M2

d

2

E! = 2 GeV, s = 12 GeV2, t |900" !4 GeV2, Mx = 2 GeV

E! = 12 GeV, s = 41 GeV2, t |900" !18.7 GeV2, Mx = 4.4 GeV

Mx! N

ND

Brodsky, Chertock, 1976

Holt, 1990

Gilman, Gross, 2002

! D, 3He(pp, n)

N,�, ...R

N,�, ...R

(⇤)

A

B

C

D

f(t

s)

1

s

A ! F (t

s)

1

snA+nB+nC+nD

2!2

d!

dt!

|A|2

s2= F

2(t

s)

1

snA+nB+nC+nD!2

Brodsky, Farrar 1975Matveev, Muradyan, Takhvelidze, 1975

1

s

additional

Exclusive large-momentum-transferscattering

•Dimensional counting rule:

)f( S st)2-n(N- A DCB nnn

CDABdtd +++=

→

∝σ

N = 1 + 6 + 3 + 3 – 2 = 11

) ( ) ( tt phighnphighpd +→γFor

Notice:

410 GeV/c) 4( / GeV/c) 1( ≈== γγ

σσ EdtdE

dtd

scaling

!d ! pn

0

5

1 0

1 5

2 0

0 1 2 3 4 5

x=0x=0.5x=1.0x=1.5x=2.0

i = Ea = Q2/2mx

W2 < m d2

17

13

86

66

52

50

NNN6

(GeV)

(GeV

2 )

Mx!N

ND

Gilman & Gross 2002

!

k + qpdp

p

p

p2

1

B

q

A

k 2

k 1

1

Mx

Mx

N

N

N

N

Mmax=w > 2 GeV

w !

!

2E!mN

E! ! 2.5 GeV

NN -amplitude

pQCD

Frankfurt, Miller, MS, Striman Phys. Rev. Lea. 2000

0.10.20.30.40.50.60.70.80.9

1

2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5Ea , GeV

s11dm

/dt (

kb-G

eV20

)

00.20.40.60.8

11.21.41.61.8

2

20 40 60 80 100 120 140Ocm , deg

dm/d1

cm(n

b/sr

)

a + d A p + n

a + d A p + n, Ea=2.4 GeV

10-3

10-2

10-1

1

10

0 20 40 60 80 100 120 140 160 180

�c.m.

s10d�/dt

pn ! pn

� + d ! p+ n

Break up of pn from the deuteron Break up of pp from Helium 3

d2p

n

p

n

p

n

p

p

He3

p

Brodsky, Frankfurt, Gilman, Hiller, Miller Piasetzky, M.S., Strikman Phys. Lea. B 2004

Frankfurt,Miller,M.S. Strikman Phys. Lea. Let. 2000

Break up of pp from Helium 3�

p

n

p

p

He3

p

pp

p

n

p

n

! s!13 ! s

!11

(GeV)aE0 1 2 3 4 50.00

0.05

0.10 ,pp)naHe(3

c.m.°90

X 1/5

X 1/200

b.

)20/dt

(kb Ge

Vmd11 s

0.0

0.2

0.4

0.6

0.8

1.0MainzSLAC NE17SLAC NE8JLab E89-012This workQGSRNAHRM

,p)nad( c.m.°90

)2s (GeV4 6 8 10 12 14 16 18 20 22

a.

s11 d�dt

C. Grandos,MS, Phys. Rev. C 2009

Photodisintegration of 3He:

56

� +3 He ! p+ d

D. Maheswari,MS, 2017 Phys. Rev. C in press

I.Pomerantz , et al Phys. Rev. Lea. 2013

What’s Next:

1. Studying Hard Hadronic Processes

Break – up reactions to the deuteron break-up of other 2Baryons

Extraction of hard Baryonic Helicity Amplitudes from Polarized measurement

2. Probing or component of the nucleon

! D, 3He(pp, n)

N,�, ...R

N,�, ...R

(⇤)

� + d ! �+� M. S., and C.GranadosPhys. Rev. C 2011

(ss̄) (cc̄)

Studying cc component in the deuteron

� + d� p + �+c + D�c

d2

p

n

p

d2p

n

p

�+c �+

c

D�c

D�c

Intrinsic Produced

Outlook- (JLAB 4-6 GeV) : Experimentally established adequacy of QCD degrees of freedom in hard break-up of light nuclei - (JLAB 4-6 GeV) : Hard Rescattering Mechanism consistent with major observations of the break-up reaction

- (JLAB 12 GeV ) : Studying Hard Rescattering Mechanism of break up of light nuclei into baryonic resonances (including strangeness production)

III. Extracting J/Psi-N interaction near the threshold �-Vector meson photoproduction can be used to extract VN scattering cross section �- Experience from coherent vector meson photoproduction� � + d ! V + d0

10-1

1

10

10 2

10 3

10 4

10 5

0 0.2 0.4 0.6 0.8 1 1.2 1.4-t [GeV2]

dm/d

t [n

b/(G

eV)2 ]

Figure 2

10-1

1

10

-2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0t (GeV2/c2)

dm/dt

[nb/(

GeV2 /c2 )]

�⇢N = 25mb

III. Extracting J/Psi-N interaction near the threshold �

v

vv

vv

v

v

vv

v

v

vv

v

v

� + d ! J/ + p+ n Adam Freese, MS, PRC 2013

Outlook �

-  Vector Meson Production with deuteron break-up is an � effective tools for extracting VN scattering cross section�

short range correlations (hard nuclear processes) · 1. outstanding problems in src studies -...

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