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 - MN(x)
Higher densities & EOS
Conclusions
P
A
R
T
O
N
S
I
N
D
I
S
EMC effect
Historically ratio
Pion
excess
R(x) = F2A(x)/ F2N(x)
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.,
DIS
Q,n
e
2
p
r(emnant)
Hit quark has momentum
Experimentaly x =
j
j+=x p+
Q /2M n
2
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
where p+ =p0 + pz
x = j+ /p+
Light cone coordinates
W n   d 4e iq p J  ( )J n (0) p
q  (n ,0,0,- v 2  Q 2 ),
Q 2  -q 2
Q 2   with x fixed (Q 2 /n )  0
2
q  (n ,0,0,-n - Mx)
q  1/
x  Q 2 / 2 Mn  fixed
2 ( q 0  q 3 ) i n B jork e nl i m i t
q -   but q   - Mx /
2
i f q  q   -  q -  th e n
 0
bu t
|  - |
2 / Mx
s o |  0 | 1 / Mx an d |  3 | 1 / Mx
Relativistic Mean Field Problems
In standard RMF electrons will be
scattered on nucleons in average
scalar and vector potential:
[ap + b(M+US) - (e -UV)]y0
where US=-gS /mSrS UV =-gV /mVr
US = 300MeVr/ r0
UV = 300MeVr/r0
Relativistic Mean Field Problems
In standard RMF electrons will be
scattered on nucleons in average
scalar and vector potential:
[ap + b(M+US) - (e -UV)]y0
where US=-gS /mSrS UV =-gV /mVr
US = -400MeVr/ r0
UV = 300MeVr/r0
Gives the nuclear distribution f(y)
of longitudinal nucleon momenta
p+=yAMA
p 3   ( p0  p 3 ) 

4 d4 p
0
r ( yA )  
S
(
p
,
p
)
1

N
 E ( p)   y r (2 ) 4
 

 
A
SN() - spectral fun.  - nucleon chemical pot.
Relativistic Mean Field Problems
connected with Helmholz-van Hove theorem - e(pF)=M-e
In standard RMF electrons will be
scattered on nucleons in average
scalar and vector potential:
[ap + b(M+US) - (e -UV)]y0
where US=-gS /mSrS UV =-gV /mVr
US = -400MeVr/ r0
UV = 300MeVr/r0
2
2
v
(
y
1
)
3
*
A
r A( yA )  A
,
v

p
/
E
A
F
F
4
v A3
Strong vector-scalar cancelation
Gives the nuclear distribution f(y)
of longitudinal nucleon momenta
p+=yAMA
p 3   ( p0  p 3 ) 

4 d4 p
0
r ( yA )  
S
(
p
,
p
)
1

N
 E ( p)   y r (2 ) 4
 

 
A
SN() - spectral fun.  - nucleon chemical pot.
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 %
Sea parton distribution
dy
2
2
f N ( x; Q )   f ( y; Q0 ) f pion ( x / y; Q0 ) is given by the pionic
y
(fock) component of
2
0
the nucleon
Change of nucleon primodial distribution
inside medium
• Gaussian distribution of
quark momenta j
• Monte Carlo
simulations in medium
0 < (j+q) < Wm
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 The Change of the primodial
nuclear distributions
disribution in medium
 N  0.1 7 2GeV
   0.0 5 0GeV
N ex  1 2%
N ( p )  N mf
( p )  N tail ( p )
  A
N tail ( p )  N C e - bp
1
3
fo r
p > pC
_ _ _ _ _ _ _ _ __
__ _ _ _ _ _ _ __
__ _ _ _ _ _ _ __
__
Za b o litsky Ei
Ph ys.Lett.7 6B
N C  0.0 2 1Afm3
b  1.5 fm
pC  2 fm -1
Results
Results
with G. Wilk Phys.Lett. B473, (2000), 167
N O SHAD OWI NG
Today - Convolution model for x <0.15
1 A
dx
F2 ( x A )  A dyA  ( x A - y A x ) r A ( y A )F2N ( x )
xA
x
• Relativistic Mean
• We will show that in deep inelastic
Field problems
scattering the magnitude of the
nuclear Fermi motion is sensitive to
residual interaction between partons • Primodial parton
influencing both the Nucleon
distributions
Structure Function
F2N(x)
• and nucleon mass in th NM
•
MB (x)
• Bjorken x scaling in
nuclear medium
Nuclear Deep Inelastic limit
2
MA
1 nA 
3
 j Ai  A  M N  e   d p M B  p
A i 1
M B  M N  e - e Fermi
Nuclear Deep Inelastic limit
2
MA
1 nA 
3
 j Ai  A  M N  e   d p M B  p
A i 1
M B  M N  e - e Fermi
Nuclear Deep Inelastic limit
2
MA
1 nA 
3
 j Ai  A  M N  e   d p M B  p
A i 1
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
 connected with
virtuality of  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=4fm
rN - av. NN distance
Nuclear final state interaction
rC - nucleon radius
if z(x) > rN
•
M(x) = MN
if z(x) < rC
M(x) = MB
z(x)
Effective nucleon Mass M(x)=M( z(x) , rC ,rN )
J.R. Nucl.Phys.A in print
Nuclear deep inelastic limit revisited
x dependent nucleon „rest” mass in NM
F2N ( x )  f ( x )F22 N ( x )  (1 - f ( x ))F2N
f(x) - probability that struck quark originated from correlated nucleon
Mx  MN
1 - f ( x)

 VN >
2
• Momentum Sum Rule violation
1
A
F
2 ( x A )dx A

 VN > 

A
  1  C[f ]
(1  e )
N
M
F
(
x
)
dx


2

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
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)
The QCD vacuum
is the vaccum state of quark & gluon system. It is an
example of a non-perturbative vacuum state, characterized
by many non-vanishing condensates such as
the gluon <gg> & quark <qq>
condensates.
These condensates characterize the normal phase or the
confined phase of quark matter.
Unsolved problems in physics: QCD in the nonperturbative regime: confinement The equations of QCD
remain unsolved at energy scale relevant for describing
atomic nuclei. How does QCD give rise to the physics of
nuclei and nuclear constituents?
In vacuum
In nuclear medium
Phys.Rev.C45 1881
Derivative Coupling for scalars RMF Models ZM
A. Delfino, CT Coelho and M. Malheiro, Phys. Rev. C51, 2188 (1995).
{Tensor coupling vector (Bender, Rufa)}
Review J. R. Stone, P.-G. Reinhard nucl-th/0607002 (2006).
M. Baldo, Nuclear Methods and the Nuclear Equation of State
(World Scientific, 1999)
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
 qq >r  1 - r 
 qq >
m f
eff
2
2

 2

m
 

(
*) 
 2 MN MN

g




2

 qq >m  1 -  N (1  a ) m (
2
- M *)
2
2
M
2
N
N 

 qq >
f
g
m  

 MN


2
 g

2

- 2 r

 m




• Delfino, Coelho, Malheiro
<qq>m 0
for a1 (ZM models)
Condensate Ratios in RMF
SF - Evolution in Density
“no” free parameters
Saturation density
SF - Evolution in Density
“no” free parameters
Saturation density
Walecka ( density- 6 fm-3)
Stiff EOS
SF - Evolution in Density
“no” free parameters
Soft EOS (density- .6 fm-3)
pions take 5% of nuclear
longitudinal momenta
Chiral instability
Saturation density
Walecka ( density- 6 fm-3)
Stiff EOS
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
2
f  
2




2
i
H.Kleinert, B. Vanden Bossche
Phys. Lett. B474 (2000)
 92MeV
2
i
>  3 / 16
2
2
>
2
f
• For such pionic cutoff Λ fluctuation of pion field pola shift the
ground state out of magic circle to <σ2>=0 .
• In our model : Λ>700MeV for ρ=5ρ0 (chiral symmetry restoration)
• For NJL Chiral Restoration occures when Λ >0.8 Λq..
where Λq cutoff for quark momenta
• In our model : Λ >0.8 Λq for ρ=(4-5)ρ0 .
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)
• (~ 1% only) of nuclear momentum is carried by sea quarks
nuclear pions) due to x dependent effective nucleon mass
supported by Drell-Yan nuclear experiments for higher densities
increase for soft EOS towards chiral phase transition.
• Increase of the „additional nuclear pion mass” 5% means that
nuclear density is about 2 times smaller than
critical .
2
 kT >
• x – dependent correction to the
distribution
• for higher density SF strongly depend from EOS
• correction to effective NN interaction for high density?
x dependent nucleon effective mass
• it is possible to show that in DIS <kT2> M2
Bartelski Acta Phys.Pol.B9 (1978)
k 
2
T Medium
/k 
2
T
In the x>0.6 limit
(no NN interaction)
<kT2> Nuclear= <kT2> Nukleon
X-N Wang Phys. Rev.C (2000)
Dependence from initial
in p-A collision
kT
2
Miller, Smith, Phys. Rev. Lett. 2003
Chiral solitons in nuclei
_
L  y (i - Me
(0)  -
i 5 ( nr )  ( r )
y
-
r (r )  y y > 0  r sv (r )   d 3 r ' r (r - r ' ) r sv (r ' )
q
s
(  )  0
kF
r  4d k
N
s
M N  NC E  E
v
( r )  arctan
r (r )
q
ps
r sq ( r )
3
E
4

A r B (k F )
M N ( r sv )
k 2  M N (q sv )
kF
2
gv
d 3k
2
2
k

M
(
k
)

r B (k F )
N
F
 (2 ) 3
mv2
_
q( x)  N C M N   y n |(1   0  3 ) ( En  p3 - xM N ) | y n >
n
Chiral Quark Soliton Model
Petrov- Diakonov
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 ( )  Qy ( )
W n  (- g n
F1 ( x)   d e
-
-iMx - / 2
q  qn
n
n
 2 ) F1  [(P  - 2 q  )(Pn - 2 qn )]F2 /n
q
q
q
 2
 2
 P | y ( )  Q Py (0)  y (0)  Q Py ( - ) | P > 

-

  0 ,

0
Quark inside nucleus
(-i    m(r ))qn ( )  (En - V 0 )qn ( )
~
F1 ( x)   d - e -iMx
-
/ 2
 2
 -
 P | e -iV  y  ( - )  Q Py (0) 
 2
 -
e iV  y  (0)  Q Py ( - ) | P > 
~
F1 ( x)   d e
-
 -
QMC model
-iMx - / 2

 P|e
-iV  -

  0 ,

0
 2
y 0 ( )  Q Py 0 (0) 
-
 2
e iV  y 0 (0)  Q Py 0 ( - ) | P > 
  0 ,

0
Deep inelastic scattering
d  l n W
W n 
n
 ( p  q - r)
p J  ( 0) X X J n ( 0) p
x
W n 
4
iq
d

e
p J  ( )J n ( 0) p

W n  -( g n - q  q v / q 2 )W1 ( q 2 ,n )  1 / M 2
( p  - ( Mv / q 2 )q  )( pn - ( Mn / q 2 )qn )W 2 (q 2 ,n )
(n / M ) l i mW 2 ( q 2 ,n )  F2 ( x T )  Bjorken Scaling
n
q  (n ,0,0,- v 2  Q 2 ),
q  (n ,0,0,-n - Mx)
Q 2  -q 2  
x T  Q 2 / 2 Mn  fixed