Superfast Quarks in the Nuclear Medium

Misak Sargsian

Florida International University

Kim Egiyan Memorial workshop SRC2006 JLab, Newport News 20-21-October, 2006

GE =1

(1+ q2

R2

0

)2ρ(r) = R

3

0

8πe−R0r

ρ0 = 0.17fm−3

R0 ≈ 4.27fm−1

Rc ≈ 0.3fm Rc ≈1

R0

Nuclear Matter

Electromagnetic Interaction

Strong Interaction

rN ≈ 0.86fm

ρ(r) = R3

0

8πe−R0r

R0 ≈ 4.27fm−1

ρ(r=0)ρ0

= 18.2

ρ(r=0.3fm)ρ0

= 5.1

ρ(r=0.68fm)ρ0

= 1

Quark Degrees of Freedom

Neutron Stars

r ≤ ∼ 0.3

ρ ≥ ∼ 10ρ0

1

50

100

150

200

250

early universe

LHC

RHIC

SPS

AGS

SIS

atomicnuclei neutron stars

chemical freeze out

thermal freeze out

hadron gas

quark gluon

plasma

deconfinement

chiral restoration

JLAB12

2 50.3

ρ/ρ

8

tem

per

atu

re T

(M

eV)

0

ρ(r=0)ρ0

= 18.2

RBH ≤ 4km

How to get nucleons close together

Probing at large relative momenta

0

0.1

0.2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.02

0.04

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.005

0.01

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.005

0.01

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

!d(r

)2r

2

0

0.002

0.004

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.05

0.1

x 10-3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

r, Fm

k = 100 MeV/c , rrms

= 2.36 Fm

k = 200 MeV/c , rrms

= 2.21 Fm

k = 300 MeV/c , rrms

= 1.72 Fm

k = 500 MeV/c , rrms

= 1.07 Fm

k = 700 MeV/c , rrms

= 1.65 Fm

k = 1000 MeV/c , rrms

= 2.12 Fm

r ∼1

k

P3

P2

fPP1

He3P

He3! NNN

! N

r3

r2

q"#

+ P

P

!NN

!p1 = !pf − !q

Em = q0 − Tf − TA−1

Quasi-Elastic Reaction

α ≥ x

α ≈ 1 +p

z

1

m

pz

1 ≈ m(1 − x)

Xb=Q2/2M!

|Pmmin|, Gev/c

0.5

1.0

1.5

2.0

2.5

3.0

4.0

Q2

"

(2N)(e,e/), Quasielastic

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

P3

P2

fPP1

He3P

He3! NNN

! N

r3

r2

q"#

+ P

P

!NN

Signatures

R =A2σ[A1(e,e′)X]A1σ[A2(e,e′)X]

For 1 < x < 2 R ≈a2(A1)a2(A2)

For 2 < x < 3 R ≈a3(A1)a3(A2)

r(4He,3 He)

a)

r(12 C,3 He)

b)

xB

r(56 Fe,3He) c)

1

2

3

1

2

3

4

2

4

6

1 1.25 1.5 1.75 2 2.25 2.5 2.75

0

0.5

1

1.5

2

2.5

3

3.5

4

0.8 1 1.2 1.4 1.6 1.8 2

A(e,e/)

Xb=Q2/2M!

3"C/12"He3

Q2<1.30

a)

Xb=Q2/2M!

3"C/12"He3

Q2>1.40

b)

0

0.5

1

1.5

2

2.5

3

3.5

4

0.8 1 1.2 1.4 1.6 1.8 2

Egiyan, et al PRL 2006 Egiyan, et al PRC 2004

Frankfurt, Strikman, Phys.Rep 1988

A(e,e/)

Xb=Q2/2mp!

3"C12/12"

He3

Q2=1.5

Q2=2.5

a)

Xb=Q2/2mp!

3"Fe56/56"

He3

Q2=1.5

Q2=2.5

b)

PRELIM

INARY

0

0.5

1

1.5

2

2.5

3

0.8 1 1.2 1.4 1.6 1.8 2

0

0.5

1

1.5

2

2.5

3

0.8 1 1.2 1.4 1.6 1.8 2

Day,Frankfurt, MS, Strikman, PRC 1993

Egiyan, et al PRC 2004

Calculations

Data

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60

A(e,e/)

A

R AHe3

a)

b)

A

a 2,A

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60

Deep Inelastic Scattering at x>1

P3

P2

fPP1

He3P

He3! NNN

! N

r3

r2

q"#

+ P

P

!NN

X

Two processes driving nucleons close together

First: Kinematics

pz1 = m(1 − x − x

[W 2

N−m2

Q2

])

W [GeV]1 1.5 2 2.5 3

[GeV

/c]

initi

alp

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

-0 , x=12 = 10 (GeV/c)2Q, x=1.52 = 10 (GeV/c)2Q

, x=12 = 15 (GeV/c)2Q, x=1.52 = 15 (GeV/c)2Q

WN

Second: Dynamics

Consider: Deuteron

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x

F 2p

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.5 1 1.5 2 2.5 3x

F 2A/A

Q2 = 1GeV 2Q2 = 1GeV 2

Q2 = 10GeV 2Q2 = 10GeV 2

Convolution Model

F2d =2∫

x

ρNd

(α, pt)F2N ( x

α, Q2)d

2α

αd2pt

F2N → Fmod2N

d

X

N

γ∗

Quark-Cluster - 6q - Model

F2D = F2,(6q) ∼ (1 −x2 )10

d

γ∗

Carlson, Lassila, Sukhatme, PLB 1988,1991

++++T

TT

TT

- F2 ∼ (1 − x)2N−3+2|∆λ|

Gunion, Nason, Blankenbecler, PRD 1984

Hard Gluon-Exchange Model

F2d = W++· ν

(mN

pd+

)2

W++=

14πmd

∫|M+|2dQ

Mµ =

∫Ψd(α, pt)

(1 − α)

dα

α

d2pt

2(2π)3×

u(kf )[eqγµ]uζ′(kf − q)

1

(kf − q)2 − m2q

uζ′(kf − q)[gT aγν1 ]uζ(k1)ψN (y1, k1t)

y1

uη′(kf2)[gT bγν2 ]uη(k2)ψN (y2, k2t)

y2

dν1,ν2δab

(k2 − kf2)2

(1)

d

γ∗

kf

kf2

γL

γR

γ+

y1, k1t

y2, k2tx2, rt

x, − rt

γR,L = γx ± γy

γ± = γ0 ± γz

kernel =√

xx2(1 − α)α(1 −x

y1 + y2

)8pd+

((1 − α)y1 + αy2)r2t

F2D ≈ N

[∫ψd(α, pt)α

dα

α

d2pt

2(2π)3

]2

×

×

1∫0

1∫0

(1 −

x

y1 + y2

)2

θ(y1 + y2 − x)f1(y1)f2(y2)dy2dy1

(1)

q+ = 0Reference Frame

q = (0, 2νmd

pd+,√

Q2)

pd = (pd+,m2

d

pd+, 0)

.

-This softening of x distribution

-This may be unique to DIS

-May not happen to QE scattering

d

γ∗

d

γ∗

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

0.4 0.6 0.8 1 1.2 1.4 1.6x

F 2d/2

6q

hgex

Convolution

Q2= 20GeV 2

6q cluster

HG model2N SRCs+F2-Mod

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

0 2 4 6 8 10 12 14 16 18 20Q2, GeV2

F 2d /A

d(e,e/ )X

x = 1

x = 1.5

x

(2F 2A

)/(A

F2d

)

x

(2F 2A

)/(A

F2d

)

Q2 =3.0GeV25.0GeV27.0GeV210.0GeV2

15.0GeV2

20.0GeV2

A/d Ratios with Parton Evalution

2N models only

2N+3N models

x0

x

x0 > x

Summary

- QE scatterings show a sizable 2N and finite 3N SRCs in Nuclei

- DIS reactions at x>1 may allow to probe the content of the nuclear core

- They allow to study the hadron-quark transition at short space time separation in nuclei

- Our study shows that within fast quark picturenuclear core is more accessible than within

standard hadronic picture