Probing Quark Correlations in Hard Hadronic...

Misak Sargsian Florida International University, Miami

Probing Quark Correlations in Hard Hadronic Processes

Hadron Physics With High Momentum Hadron Beams @J-PARC

KEK, March 13-16, 2015

Saturday, March 14, 15

Subject: NN Interaction at Short Distances

Main Motivation: Nuclear Forces at Short Distances

Method: Comparative Studies of pp and pn hard Scattering


Some Outstanding Issues of NN Interaction at Short Distances

- NN Repulsive Core

r0 = 0.4fm

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

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


0.2 0.4 0.6 0.8

5000

10 000

15 000

Vc, MeV

r

Perturbative QCD

Hidden Color

Intrinsic strangeness/charm

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

Modern NN - Potential



- Persistence of Nucleonic Degrees of Freedom

- Recent observations of large neutron star masses indicate the existence of rather unreasonably stiff equation of state for the nuclear matter with predominantly nucleonic degrees of freedom.

⇠ 2MSun

Demorest et al, Nature, 2010

- The analysis of the recent results on Short-Range NN correlations innuclei demonstrates that for relative distances correlations almostcompletely are defined by nucleon degrees of freedom

1Fm

Frankfurt, M.S. Strikman, IJMP 2008

- These indicate our poor understanding of the nuclear forces at short distances for bound nucleons



Hard Elastic NN Scattering

0.01

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0.04

0.05

0.06

0.07

0.08

0.09

10 20 30 40s (Gev

2)

(s/1

0)1

0d

!/d

t (

mb

/ G

eV8)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

10 20 30 40 50s (Gev

2)

d!

/dt

(m

b/

GeV

2)

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

10 20 30 40s (Gev

2)

(s/1

0)1

0d

!/d

t (

mb

/ G

eV8)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

10 20 30 40 50s (Gev

2)

d!

/dt

(m

b/

GeV

2)

"CM= 90 deg

pp # pp pp # pp(a) (b)

pn # pn pn # pn(c) (d)

Dimensional or quark-counting rule predicts

d�ab!cd

dt = s�(na+nb+nc+nd�2)F (✓cm)

d�NN

dt = s�10F (✓cm)

Matveev, Muradyan, Takhvelidze Nuovo Cim. 1973, Brodsky & Farrar, PRL 1973

Brodsky & De Teramond PRL 1988

Ralston & Pire, PRL 1982

J = 1, S = 1, L = 1

Resonance

Interference of hard and soft amplitudes

Only to explainpp data at 90deg

- Oscillatory Energy Dependence



- Oscillatory Energy Dependence of Hard Elastic NN Scattering

0.020.040.060.08

10 15 20 25 30 35 40 45s (GeV2)

0.10.20.30.40.50.6

10 15 20 25 30 35 40 45s (GeV2)

ec.m.= 90o

ec.m.= 60o

(s/1

0)10

dm/d

t (m

b/ G

eV8 )

pp A pp

00.010.020.030.040.050.06

6 8 10 12 14 16 18 20 22 24 26s (GeV2)

00.10.20.30.40.50.6

6 8 10 12 14 16 18 20 22 24 26s (GeV2)

ec.m.= 90o

ec.m.= 60o

(s/1

0)10

dm/d

t( m

b/ G

eV8 )

pn A pn



- Anomalous Polarization Asymmetries in Hard pp Scattering

0

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0.7

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0.9

3 4 5 6 7 8 9 10 11 12

-t, (GeV2/c

2)

An

n (

%)

!CM= 90 deg

pQCD QIM

plab = 11.75 GeV/c

�"" ⇡ 4�"#

Crabb et al PRL 1978, Crosbie et al, PRD 1981



- Color Transparency in Hard pA Scattering

Mardor et al, PRL 1998Aclander et al PRC 2004

0

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4 6 8 10 12 14 16

pLab, (GeV/c)

Tp

p

!CM= 90 deg

p + 12

C " p+p+X p+A ! p+ p+X

p+ pbound

! p+ p at ✓cm

= 900

Conventional Absorption


Some Outstanding Issues of NN Interaction at Short Distances- Oscillations Superimposed

0

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0.6

5 10 15 20 25 30 35 40 45

Tpp

0

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5 10 15 20 25 30 35 40 45

Ann

(%)

0.02

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0.1

5 10 15 20 25 30 35 40 45

s (Gev2)

s10d!

/dt

"CM= 90 deg

p + 12

C # p+p+X

p + p # p+p

p + p # p+p

(c)

(b)

(a)

pQCD QIM


Comparative Studies pp and pn Scatterings

0.020.040.060.08

10 15 20 25 30 35 40 45s (GeV2)

0.10.20.30.40.50.6

10 15 20 25 30 35 40 45s (GeV2)

ec.m.= 90o

ec.m.= 60o

(s/1

0)10

dm/d

t (m

b/ G

eV8 )

pp A pp

00.010.020.030.040.050.06

6 8 10 12 14 16 18 20 22 24 26s (GeV2)

00.10.20.30.40.50.6

6 8 10 12 14 16 18 20 22 24 26s (GeV2)

ec.m.= 90o

ec.m.= 60o

(s/1

0)10

dm/d

t( m

b/ G

eV8 )

pn A pn


Comparative Studies pp and pn High Energy Scatterings

First time (1968, Bevatron,LBNL) by M.L. Perl et al using technique of producing high energy neutrons (3-7)GeV/c in initial pA scattering

Second time (1977, Argonne) by Chanowski et al using technique of producing high energy neutrons (5-12)GeV/c in initial pA scattering

Akerlof et al, PR1967(Argonne) up to 13 GeV/cAllaby et al PLB1968)(BNL) up to 21GeV/c

pp elastic scattering

np elastic scattering


Comparative Studies pp and pn High Energy Scatterings

h++ | M I(⇡ � ✓) | ++i = �(�1)Ih++ | M I(✓) | ++ih�� | M I(⇡ � ✓) | ++i = �(�1)Ih�� | M I(✓) | ++ih�+ | M I(⇡ � ✓) | ++i = (�1)Ih+� | M I(✓) | ++ih�+ | M I(⇡ � ✓) | +�i = (�1)Ih+� | M I(✓) | +�i

�I1 ⌘ h++ | M I | ++i = h�� | M I | ��i

�I2 ⌘ h++ | M I | ��i = h�� | M I | ++i

�I3 ⌘ h+� | M I | +�i = h�+ | M I | �+i

�I4 ⌘ h+� | M I | �+i = h�+ | M I | +�i

�I5 ⌘ h++ | M I | +�i = h�+ | M I | ��i = h�� | M I | +�i = h�+ | M I | ++i =�h�� | M I | �+i = �h+� | M I | ++i = �h++ | M I | �+i = �h+� | M I | ��i,

Parity Conservation Time Reversal Invariance Pauli Principle

Generalized Pauli Principled�

dt

pp

=1

16⇡

1

s(s� 4m2)

1

4

X|M I=1|2

d�

dt

np

=1

16⇡

1

s(s� 4m2)

1

4

X 1

4|M I=1 +M I=0|2

preQCD studies - hard processes become central S=0 dominated


Comparative Studies pp and pn Scatterings, in QCD

(a) (b) (c)

Phenomenology: that for at least up to p=10 GeV/c quark-interchange mechanisms dominates

White et al PRC 1993

�p̄p

�pp⇡ 1.7

�p̄p

�pp⇡ 1

40


Comparative Studies pp and pn Scatterings in QCD

~ 1 / s

(a) (b)

d�dt ⇠ 1

s2 |M |2 ⇠ s�10F (✓cm)

M ⇠ s�4�(✓cm)

- SU(6) symmetry was assumed

Sivers, Brodsky, Blankenbeckler Phys.Rep. 1976

Farrar, Gottlieb, Sivers, Thomas PRD 1979

Brodsky, Carlson, Lipkin, PRD 1979


Comparative Studies pp and pn Scatterings

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3 4 5 6 7 8 9 10 11 12

-t, (GeV2/c

2)

An

n (

%)

!CM= 90 deg

pQCD QIM

✓cm = 900

00.10.20.30.40.50.60.70.80.91

0 5 10 15 20 25 30s(GeV2)

R(pn/pp)


Comparative Studies pp and pn Scatterings in QCDAngular Dependence

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1

10

10 2

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1cos(Ocm)

(s/1

0)10

dm/d

t, m

b/G

eV2

PLAB=6GeV/cPLAB=8GeV/cPLAB=11GeV/c

10-3

10-2

10-1

1

10

-1 -0.75-0.5-0.25 0 0.25 0.5 0.75 1cos(ec.m.)

(s/1

0)10

dm/d

t (m

b/G

eV2 )

PLAB=7GeV/cPLAB=8GeV/cPLAB=9GeV/cPLAB=10GeV/cPLAB=11GeV/c

Granados, M.S. PRL 2009


Comparative Studies pp and pn Scatterings in QCD Angular Dependence

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1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1cos(ec.m.)

A90o

PLAB=6GeV/cPLAB=7GeV/cPLAB=8GeV/cPLAB=9GeV/cPLAB=10GeV/cPLAB=11GeV/cPLAB=12GeV/c

A900(✓) =�(✓)� �(⇡ � ✓)

�(✓) + �(⇡ � ✓)

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0

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1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1cos(ec.m.)

A90o


SU(6)

Farrar, et al PRD 1979

Brodsky, Carlson, Lipkin, PRD 1979


Comparative Studies pp and pn Scatterings in QCD Angular Dependence Granados, M.S. PRL 2009

b d

caN

N

N

N

hcd | T | abi =X

↵,�,�

h †c | ↵0

2,�01, �

01ih

†d | ↵0

1,�02, �

02i ⇥

h↵02,�

02, �

02,↵

01�

01�

01 | H | ↵1,�1, �1,↵2�2�2i · h↵1,�1, �1 | aih↵2,�2, �2 | bi

where (↵i,↵0i), (�i,�0

i) and (�i, �0i) describe the spin-flavor quark states of minimal-

Fock component of nucleon wave function before and after the hard scattering

Cj↵,�,� ⌘ h↵,�, � | ji


- Nucleon wave function in the helicity-flavor basis of the valence quarks.

i3N ,hN =1p2

n

�0,0(k1, k2, k3)(�(23)0,0 �

(1)12 ,hN

) · (⌧ (23)0,0 ⌧ (1)12 ,i

3N) + �1,1(k1, k2, k3)⇥

1X

i323=�1

1X

h323=�1

h1, h23;1

2, hN � h23 | 1

2, hN ih1, i323;

1

2, i3N � i323 | 1

2, i3N i ⇥

(�(23)1,h23

�(1)12 ,hN�h23

) · (⌧ (23)1,i323

⌧ (1)12 ,i

3N�i323

)o

where j3N and hN are the isospin component and the helicity of the nucleon.

�j,h and ⌧I,i3 are helicity and isospin wave functions

hj1,m1; j2,m2 | j,mi - Clebsch-Gordan coe�cients

�I,J - the momentum dependent part of the wave function for (I = 0, J = 0)

and (I = 1, J = 1) two-quark spectator states respectively.

⇢ =h�1,1ih�0,0i

(⇢ = 1 - SU(6)) and (⇢ = 0 - good (scalar) diquark configuration)

(⇢ otherwise is unknown quantity)


H ⇡ �↵1↵01�↵2↵0

2��1,�10��1,�0

1��2,�20��2,�0

2

F (✓)

s4

hcd | T | abi = Tr(MacM bd) M i,j↵,↵0 = Ci

↵,��Cj↵0,�� + Ci

�↵,�Cj�↵0,� + Ci

��↵Cj��↵0

pp ! pp

np ! np

�1 = C(s) [(3 + y)F (✓) + (3 + y)F (⇡ � ✓)]

�3 = C(s) [(2� y)F (✓) + (1 + 2y)F (⇡ � ✓)]

�4 = �C(s) [(1 + 2y)F (✓) + (2� y)F (⇡ � ✓)]

�1 = C(s) [(2� y)F (✓) + (1 + 2y)F (⇡ � ✓)]

�3 = C(s) [(2 + y)F (✓) + (1 + 4y)F (⇡ � ✓)]

�4 = C(s) [2yF (✓) + 2yF (⇡ � ✓)]

C(s) = Ns4

y = x(x+ 1) with x =2⇢

3(1 + ⇢

2)


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0 5 10 15 20 25 30

s(GeV2)

!p

n/!

pp

SU(6), "=1

Diquark, "=0


A900(✓) =�(✓)� �(⇡ � ✓)

�(✓) + �(⇡ � ✓)

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-0.5

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1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1cos(ec.m.)

A90o


Scalar diquarks⇢ = 0


A900(✓) =�(✓)� �(⇡ � ✓)

�(✓) + �(⇡ � ✓)

-1

-0.5

0

0.5

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1cos(ec.m.)

A90o

PLAB=6GeV/cPLAB=7GeV/cPLAB=8GeV/cPLAB=9GeV/cPLAB=10GeV/cPLAB=11GeV/cPLAB=12GeV/c-1

-0.5

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0.5

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1cos(ec.m.)

A90o


⇢ = 0

⇢ = 0.3± 0.2


Ann Asymmetry

Appnn =

1

�0Re

h�pp,†1 �pp

3 � �pp,†2 �pp

4

i

pp ! pp

�1 = C(s) [(3 + y)F (✓) + (3 + y)F (⇡ � ✓)]

�3 = C(s) [(2� y)F (✓) + (1 + 2y)F (⇡ � ✓)]

�4 = �C(s) [(1 + 2y)F (✓) + (2� y)F (⇡ � ✓)]

�1 = C(s)2(3 + y)F (90)

�3 = C(s)(3 + y)F (90)

�4 = �C(s)(3 + y)F (90)

�0 =1

2(|�1|2 + |�2|2 + |�3|2 + |�4|2 + 4|�5|2)

Ann = 13 independent of ⇢


What it means ? ⇢ ⇡ �0.3± 0.2

- Consistent with 10% probabilities of bad diquarks

Selem, Wilczek. 2006

- possible to check in Lattice Calculations?

Implications

- Nucleon For Factors

- DIS structure functions at

- Negative sign? In Quantum Mechanics it may indicate di↵erent (attrac-

tion/repulsion) in (quark scalar-diquark) and (quark vector-diquark) channels

x ! 1


Conclusions

- Experiments on hard pp elastic scattering will fill in to the gaps into existing data clarifying situation with energy oscillations

0.020.040.060.08

10 15 20 25 30 35 40 45s (GeV2)

0.10.20.30.40.50.6

10 15 20 25 30 35 40 45s (GeV2)

ec.m.= 90o

ec.m.= 60o

(s/1

0)10

dm/d

t (m

b/ G

eV8 )

pp A pp


Conclusions

- Hard np elastic scattering experiments will break new ground in hard exclusive studies

00.010.020.030.040.050.06

6 8 10 12 14 16 18 20 22 24 26s (GeV2)

00.10.20.30.40.50.6

6 8 10 12 14 16 18 20 22 24 26s (GeV2)

ec.m.= 90o

ec.m.= 60o

(s/1

0)10

dm/d

t( m

b/ G

eV8 )

pn A pn


Conclusions

- Comparative studies of pp and pn scatterings will allow to gain new access in measuring the symmetries of valence quark wave function of nucleon

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1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1cos(ec.m.)

A90o



Conclusions

- More generally these studies will be essential for studying nuclear forces

at short distances


Comparative Studies pp and pn Scatterings in QCDAngular Dependence

10-1

1

10

10 2

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1cos(Ocm)

(s/1

0)10

dm/d

t, m

b/G

eV2

PLAB=6GeV/cPLAB=8GeV/cPLAB=11GeV/c

10-3

10-2

10-1

1

10

-1 -0.75-0.5-0.25 0 0.25 0.5 0.75 1cos(ec.m.)

(s/1

0)10

dm/d

t (m

b/G

eV2 )

PLAB=7GeV/cPLAB=8GeV/cPLAB=9GeV/cPLAB=10GeV/cPLAB=11GeV/c

Mardor et al, PRL 1998Aclander et al PRC 2004


Probing Quark Correlations in Hard Hadronic...

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