Transcript Change of nucleon primodial distribution inside medium
The Nucleon Structure and the EOS of Nuclear Matter
Jacek Rozynek INS Warsaw
Nuclear Physics Workshop KAZIMIERZ DOLNY 2006
Summary
• EMC effect • Relativistic Mean Field Problems • Hadron with quark primodial distributions • Pion contributions • Nuclear Bjorken Limit - M N (x) • Higher densities & EOS • Conclusions
EMC effect
Historically ratio R(x) = F
2 A
(x)/ F
2 N
(x)
Pion excess
x Three approaches to its description:
Three approaches to EMC effect
in term of nucleon degrees of freedom through the nuclear spectral function. (nonrelativistic off shell effects) G.A.Miller&J. Smith, O. Benhar, I. Sick, Pandaripande,E Oset
in terms of quark meson coupling model
modification of quark propagation by direct coupling of quarks to nuclear envirovment A.Thomas+Adelaide/Japan group, Mineo, Bentz, Ishii, Thomas, Yazaki (2004)
by the direct change of the partonic primodial distribution.
S.Kinm, R.Close
Sea quarks from pion cloud.
G.Wilk+J.R.,
D I S
Q 2 , n
j e p
r(emnant)
Hit quark has momentum j
+
= x p
+
Experimentaly x =
Q 2 / 2M
n and is iterpreted as fraction of longitudinal nucleon momentum carried by parton(quark) for n 2 > Q 2 -> oo
On light cone Bjorken x is defined as x = j
+
/p
+
where p
+
=p
0
+ p
z
Deep inelastic scattering
d
W
n
l
n
W
x
n
(
p
W
n
W
n
q
-
r
)
p J
( 0 )
X X J
n
( 0 )
d
4
e iq
-
(
g
n -
p q
q v J
(
)
J
n
( 0 )
p
/
q
2 )
W
1 (
q
2 ,
n
)
1 /
M
2
p
(
p
(
n -
(
Mv
/
q
2 )
q
)(
p
n
/
M
)
n
lim
W
2 (
q
2 ,
n
)
-
(
M
n
/
q
2 )
q
n
)
W
2 (
q
2 ,
n
)
F
2 (
x T
)
Bjorken Scaling q
(
n
, 0 , 0 ,
-
v
2
Q
2 ),
Q
2
-
q
2
q
(
n
, 0 , 0 ,
n -
Mx
)
x T
Q
2 / 2
M
n
fixed
Light cone coordinates
W
n
d
4
e iq
q
(
n
, 0 , 0 ,
-
p J
(
)
J
n
( 0 )
v
2
Q
2 ),
p Q
2
-
q
2
Q
2
with x q
(
n
, 0 , 0 ,
n -
Mx
)
fixed
(
Q
2
x
Q
2 /
n
2 ) / 2
M
n
0
fixed q
1 / 2 (
q
0
q
3 ) in Bjorken limit so
q
-
if
q
but q
-
q
-
Mx
/
q
then 2
0 but |
-
|
2 /
Mx
|
0 |
1 /
Mx
and |
3 |
1 /
Mx
Relativistic Mean Field Problems
In standard RMF electrons will be scattered on nucleons in average scalar and vector potential: [a
p
+ b( M+U S ) - ( e -U V )]y0 where U S =-g S /m S r S U V =-g V /m V r U S = 300MeV r/ r 0 U V = 300MeV r/r 0
Relativistic Mean Field Problems
In standard RMF electrons will be scattered on nucleons in average scalar and vector potential: Gives the nuclear distribution f(y) of longitudinal nucleon momenta p + =y A M A [a
p
+ b( M+U S ) - ( e -U V )]y0 where U S =-g S /m S r S U V =-g V /m V r r
A
(
y A
)
4
r
d
4 ( 2
p
) 4
S N
(
p
0 , p )
1
p
3
E
(
p
)
y
-
(
p
0
p
3 )
U S = -400MeV r/ r 0 S N () - spectral fun. - nucleon chemical pot.
U V = 300MeV r/r 0
Relativistic Mean Field Problems
connected with Helmholz-van Hove theorem - e(p F )=M e In standard RMF electrons will be scattered on nucleons in average scalar and vector potential: Gives the nuclear distribution f(y) of longitudinal nucleon momenta p + =y A M A [a
p
+ b( M+U S ) - ( e -U V )]y0 where U S =-g S /m S r S U V =-g V /m V r r
A
(
y A
)
4
r
d
4 ( 2
p
) 4
S N
(
p
0 , p )
1
p
3
E
(
p
)
y
-
(
p
0
p
3 )
U S = -400MeV r/ r 0 S N () - spectral fun. - nucleon chemical pot.
U V = 300MeV r/r 0 r
A
(
y A
)
3
v A
2 4
-
(
y A v
3
A
-
1 ) 2 ,
v A
p F
/
E F
*
Strong vector-scalar cancelation
Hadrons with quark primodial distributions based on Heinserberg uncertainty relation •
Gaussian distribution of quark (u and d ) momenta j
Hadrons with quark primodial distributions based on Heinserberg uncertainty relation • •
Gaussian distribution of quark momenta j
Monte Carlo simulations
0 < (j+q) < W 0 < r < W ’
W - invariant mass
• Proton • Width - .18GeV
Hadrons with quark primodial distributions based on Heinserberg uncertainty relation • •
Gaussian distribution of quark momenta j
Monte Carlo simulations
0 < (j+q) < W 0 < r < W '
W - invariant mass
• Proton • Width - .18GeV
• • • Pion width -.18MeV
Hadron with quark primodial distributions Good description - Edin, Ingelman Phys. Let. B432 (1999) • •
Gaussian distribution of quark momenta j
Monte Carlo simulations
0 < (j+q) < W 0 < r < W ’
W - invariant mass
• Proton • Width - .18GeV
• • • • Pion Component width =52MeV N =7.7 %
f N
(
x
;
Q
0 2 )
dy y f
(
y
;
Q
0 2 )
f pion
(
x
/
y
;
Q
0 2 ) Sea parton distribution is given by the pionic (fock) component of the nucleon
Change of nucleon primodial distribution inside medium • •
Gaussian distribution of quark momenta j
Monte Carlo simulations
in medium
0 < (j+q) < W m 0 < r < W’ m
W - invariant mass
• pion cloud (mass) renormalization momentum sum rule • • Proton • Width - .18GeV
• Pion width - 52MeV • N =7.7 % IN MEDIUM • Proton • Width - .165GeV • Pion width =52MeV • N =7.7 %
Primodial Distributios and Monte –Carlo Simulations for NM • Calculations for the realistic nuclear distributions The Change of the primodial disribution in medium
N
0 .
172
GeV
0 .
050
GeV N ex
12 %
N
(
p
)
N mf
N tail
(
p
)
A
1 3
N tail
(
p
)
N C e
b
p for p
>
p C
__________ __________ __________ __
Zabolitsk y Ei Phys
.
Lett
.
76
B N C
b 0 .
021
Afm
3 1 .
5
fm p C
2
fm
1
Results
Results
with G. Wilk Phys.Lett.
B473
, (2000), 167
N O S H A D O W I N G
Today - Convolution model for x <0.15
1
x A F
2
A
(
x A
)
A
dy A dx
x
(
x A
-
y A x
)
r
A
(
y A
)
F
2
N
(
x
)
• We will show that in deep inelastic scattering the magnitude of the nuclear Fermi motion is sensitive to residual interaction between partons influencing both Structure Function the Nucleon • Relativistic Mean Field problems • Primodial parton distributions
F 2 N
(x)
• • and nucleon mass in th
NM M B (x)
• Bjorken x scaling in nuclear medium
Nuclear Deep Inelastic limit
1
A
nA i
1
j Ai
M A A
M N
e
d
3
p M B
p
2
M B
M N
e -
e Fermi
Nuclear Deep Inelastic limit
1
A
nA i
1
j Ai
M A A
M N
e
d
3
p M B
p
2
M B
M N
e -
e Fermi
Nuclear Deep Inelastic limit
1
A
nA i
1
j Ai
M A A
M N
e
d
3
p M B
p
2
M B
M N
e -
e Fermi
To much pions
RMF failure & Where the nuclear pions are • • M Birse PLB 299(1985), JR IJMP(2000), G Miller J Smith PR (2001) GE Brown, M Buballa, Li, Wambach , Bertsch, Frankfurt, Strikman
TTwo resolutions scales in deep inelastic scattering
1 1/ Q 2 virtuality of connected with probe .
(A-P evolution equation -
well known)
1/Mx = z distance how far can propagate the quark in the medium.
(Final state quark interaction -
not known
) z=9fm
For x=0.05 z=4
fm
Nuclear final state interaction
r N - av. NN distance r C - nucleon radius • if z(x) > r N M(x) = M N if z(x) < r C M(x) = M B
z(x)
Effective nucleon Mass M(x)=M( z(x) , r C ,r N ) J.R. Nucl.Phys.A in print
Nuclear deep inelastic limit revisited x dependent nucleon „rest” mass in NM F 2
N
(
x
)
f
(
x
)
F
2 2
N
(
x
)
( 1
-
f
(
x
))
F
2
N
f(x) - probability that struck quark originated from correlated nucleon
M x
M N
1
-
f
2 (
x
)
V N
> •
Momentum Sum Rule violation 1
A
F
2
A
(
x A
)
dx A
F
2
N
(
x
)
dx
1
C[f
]
V N M
>
( 1
e
)
M(x) & in RMF solution the nuclear pions almost disappear Because of Momentum Sum Rule in DIS Nuclear sea is slightly enhanced in nuclear medium - pions have bigger mass according to chiral restoration scenario
BUT also change sea quark contribution to nucleon SF
rather then additional (nuclear) pions appears The pions play role rather on large distances?
Results
Results
Fermi Smearing
Results
Fermi Smearing Constant effective nucleon mass
Results
“no” free paramerers
Fermi Smearing Constant effective nucleon mass x dependent effective nucleon mass with G. Wilk Phys.Rev.
C71
(2005)
Drell Yan Calculations
Good description due to the x dependence of nucleon mass (no nuclear pions in Sum Rules)
Effective Mass in RMF
• W - Nucleon bare mass in the Walecka mean field approach • ZM constructed by changing of covariant derivative in W model. Langrangian describes the motion of baryons with effective mass and the density dependent scalar (vector) coupling constant.
ZM - Zimanyi Moszkowski
Relativistic Mean Field & EOS
quark condensate < qq> m in the medium 0
q q q q
> > r
1
r
m
2
eff f
2
q q q q
> >
m
1
-
m
2
N f
2
(
-
1
m g
2
g
2
a
2
m
2 ( )
M g
r
2
2
N m
2
M
-
M N N
* )
(
M N
-
M N
* ) 2
• Delfino, Coelho, Malheiro
< qq > m
0 for a1 (ZM models)
Condensates
Results
“no” free paramerers
Fermi Smearing Constant effective nucleon mass x dependent effective nucleon mass with G. Wilk Phys.Rev.
C71
(2005)
Results
“no” free paramerers
Fermi Smearing Constant effective nucleon mass x dependent effective nucleon mass Soft EOS density- .6 fm -3
EOS in NJL
EMC effect
• pion mass in the medium in chiral symmetry restoration • Nucleon mass in the medium ?
Bernard,Meissner,Zahed PRC (1987)
Estimate of Chiral Stability
f
2
2
i
2
92
MeV
H.Kleinert, B. Vanden Bossche Phys. Lett. B474 (2000)
i
2
>
3
2 / 16
2
>
f
2
• For such pionic cutoff Λ fluctuation of pion field pola shift the ground state out of magic circle to <σ 2 >=0 . • In our model : Λ>700MeV for ρ=5ρ 0 (chiral symmetry restoration) • For NJL Chiral Restoration occures when Λ >0.8 Λ q..
where Λ q cutoff for quark momenta • In our model : Λ >0.8 Λ q for ρ=(4-5)ρ 0 .
Conclusions
• Good fit to data for Bjorken x>0.1 by modfying the nucleon mass in the medium (~24 MeV depletion) will correct the EOS for NM.
Although such subtle changes of nucleons mass is difficult to measure inside nuclear medium due to final state interaction this reduction of nucleon mass is compatible with recent observation of similar reduction in Delta invariant mass in the decay spectrum to (N+Pion) T.Matulewicz Eur. Phys. J A9 (2000) • MORE momentum is carried (~ 1% only) by sea quarks ( nuclear pions) due to x dependent effective nucleon mass supported by Drell-Yan nuclear experiments .
• Increase of the „additional nuclear pion mass” 5% means that nuclear density is about 2 times smaller than critical .
k
2
T
> • for higher density SF strongly depend from EOS
x dependent nucleon effective mass
• it is possible to show that in DIS
k T
2
Medium
/
k T
2
In the x>0.6 limit (no NN interaction)
X-N Wang Phys. Rev.C (2000)
Dependence from initial in p-A collision k T
2
Miller, Smith, Phys. Rev. Lett. 2003
Chiral solitons in nuclei
L
y _ (
i
( 0 ) -
Me i
5 (
nr
) (
r
) y ( ) 0 r
s q
(
r
) y y > 0 r
s v
(
r
)
d
3
r
' r (
r
-
r
' ) r
s v
(
r
' )
M N
N C E v
E
r
s N
4
k F
d
3
k k
2
M N
( r
s v
)
M N
(
q s v
) (
r
) arctan r
q ps
(
r
) r
s q
(
r
)
E A
4 r
B
(
k F
)
k F
d
( 2 3
k
) 3
k
2
M N
(
k F
) 2
g v
2
m v
2 r
B
(
k F
)
Chiral Quark Soliton Model
Petrov- Diakonov
q
(
x
)
N C M N
n
y _
n
(| 1 0 3 ) (
E n
p
3 -
xM N
) | y
n
> So far effect to strong
Nuclear Vector Potential in DIS
• Free Nucleon 4
W
n
d
4
e iq
P
| [
J
( ),
J
n ( 0 )] |
P
>
c J
( ) y _ ( )
Q
y ( )
W
n ( -
g
n
q
q
n )
F
1
q
2 [(
P
n
q
2
q
)(
P
n n
q
2
q
n )]
F
2 / n
F
1 (
x
)
d
-
e
-
iMx
/ 2
P
| y ( )
Q
2
P
y ( 0 ) y ( 0 )
Q
2
P
y ( ) |
P
> 0 , 0
Quark inside nucleus
( -
i
m
(
r
))
q n
( ) (
E n
-
V
0 )
q n
( ) QMC model ~
F
1 (
x
)
d
-
e
-
iMx
/ 2
P
|
e
-
iV
y ( )
Q
2
P
y ( 0 )
e iV
y ( 0 )
Q
2
P
y ( ) |
P
> 0 , 0 ~
F
1 (
x
)
d
-
e
-
iMx
/ 2
P
|
e
-
iV
y 0 ( )
Q
2
P
y 0 ( 0 )
e iV
y 0 ( 0 )
Q
2
P
y 0 ( ) |
P
> 0 , 0