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
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