On Nuclear Modification of Bound Nucleons On Nuclear Modification of Bound Nucleons G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru Contents.
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On Nuclear Modification of Bound On Nuclear Modification of Bound NucleonsNucleons
G. Musulmanbekov JINR, Dubna, Russiae-mail:genis@jinr.ru
Contents•Introduction•Strongly Correlated Quark Model•Quark Arrangement inside Nuclei•EMC – effect •Color Transparency•Conclusions
Introduction
1. EMC – effect F₂A(x)/F₂D(x)
Regions of the effect * Shadowing * Antishadowing * EMC – effect * Fermi motion
Introduction
2. Color Transparency Quasielastic scattering
p+A pp+X at θcm=900
Observable:
T = σA/(Z σN)
4 6 8 10 12 14 160,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Tra
nspa
renc
y
Beam Momentum, GeV/c
Introduction
2. Color Transparency
Exclusive electroproduction of ρ0 in µA scattering
Observable: T = σA/(Aσ0)
Fit for specified Q2 region: σA = σ0Aα
Then T = Aα-1
Introduction
QCDQCD
Hadrons
Nuclei
Constituent Quarks Current Quarks
Chiral Symmetry BreakingChiral Symmetry Breaking
Quark ModelsQuark Models
Strongly Correlated Quark ModelG.Musulmanbekov, 1995
What is Chiral Symmetry and its Breaking?
• Chiral Symmetry
SU(3)L × SU(3)R for ψL,R = u, d, s
• The order parameter for symmetry breaking is quark or chiral condensate:
<ψψ> - (250 MeV)³, ψ = ≃ u,d,s.
• As a consequence massless valence quarks (u, d, s) acquie dynamical masses which we call constituent quarks
MC ≈ 350 – 400 MeV
Strongly Correlated Quark Model
(SCQM)
Attractive Force
Attractive Force
Vacuum polarization around single quark
Quark and Gluon Condensate
Vacuum fluctuations(radiation) pressure
Vacuum fluctuations(radiation) pressure
(x)
Interplay Between Current and Constituent Quarks Chiral Symmetry Breaking and Restoration Dynamical Constituent Mass Generation
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.64
t = 0
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.20
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.05
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.05
t = T/4
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.64 t = T/2
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.20
The Strongly Correlated Quark Model
Hamiltonian of the Quark – AntiQuark System
)2()1()1( 2/122/12 xV
mmH
qqq
q
q
q
, are the current masses of quarks, = (x) – the velocity of the quark (antiquark), is the quark–antiquark potential.
qm qm
qqV
)(
)1()(
)1( 2/122/12 xUm
xUm
Hq
q
q
q
)2(2
1)( xVxU
qq is the potential energy of the
quark.
Conjecture:
),(2),()(2 xMrxxdydzdxU Q
where is the dynamical mass of the constituent quark and
)()(
xMQQ
),,(),,(
),(),(
zyxxzyxxC
rxCrx
For simplicity
XAXA
rT
exp)(det
)(2/3
2/1
Generalization to the 3 – quark system (baryons)
ColorSU )3(
3 RGB,
_ 3 CMY
qq 1 33-
qqq 3 3
3
3
3
31- -
-
_ ( 3)Color
SCQM Chiral Symmerty Breaking
Consituent Current Quarks Consituent Quarks Asymptotic Freedom Quarks
t = 0x = xmax
t = T/4x = 0
t = T/2x = xmax
During the valence quarks oscillations:
...321332123211 gqqqcqqqqqcqqqcB
SCQM The Local Gauge
Invariance Principle
Destructive Interference of color fields Phase rotation of the quark w.f. in color space:
Colorxig
Color xex )()( )(
Phase rotation in color space dressing (undressing) of the quark the gauge transformation );()()( xxAxA here
)0,0,0,( A
Parameters of SCQM for Proton
tot pp_
2.Amplitude of VQs oscillations : xmax=0.64 fm,
3.Constituent quark sizes (parameters of gaussian distribution): x,y=0.24 fm, z =0.12 fm
,36023
1)( max)(
MeVmm
xM NQQ
Parameters 2 and 3 are derived from the calculations of Inelastic Overlap Function (IOF) and in and pp – collisions.
1.Mass of Consituent Quark
Constituent Quarks – Solitons SCQM Breather Solution of Sine- Gordon
equation 0),(sin),( txtx
Breather – oscillating soliton-antisoliton pair, the periodic solution of SG:
2
21
1/cosh
1/sinhtan4),(
uxu
uuttx ass
The evolution of density profile of the soliton-antisoliton pair (breather)
x
txtx ass
ass
),(),(
is identical to that one of our quark-antiquark system.
Breather (soliton –antisoliton) solution of SG equation
Soliton – antisoliton potential
)(tanh2)( 2 mxMxV
Here M is the soliton mass
Summary on Quarks in Hadrons
• Quarks and gluons inside hadrons are strongly correlated;
• Hadronic matter distribution inside hadrons is fluctuating quantity;
• There are no strings stretching between quarks inside hadrons;
• Strong interactions between quarks are nonlocal: they emerge as the vacuum response on violation of vacuum homogeneity by embedded quarks;
• Maximal displacement of quarks in hadrons x 0.64f
• Sizes of the constituent quark: x,y 0.24f, z
0.12f
• Constituent quarks are identical to solitons.
Quark Arrangement inside Nuclei
QCDQCD
Hadrons Nuclei
Nuclear Models
Shell Models
Liquid Drop Model
Crystalline Models of Nuclei
Cluster Models
The closed shell n = 0, nucleus 4He
pp
n
d
d uu
u
u
d u
d
1
2 3
3He
4 5
6
n
u
d d
1
2 3
n
3He + neutron or 3H + proton
p n
n
u
du
u
u d
u
d
u
udd
12
3
6 5
4
pd
pd
u
ud
du
u
u
d u
d
u
5
6
2
13
dn
p
n
Connections 1 1 2 2 3 3
Binding Energy and Sizes of Nuclei
Nucleus EB, MeV < r2 >1/2, fm
deuteron 2.22 2.4
3H 8.48 1.7
3He 7.72 1.88
4He 28.29 1.67
6He 29.27
Hidden Color in Nuclei
Deuteron|6q> = c1|SS> + c2|CC>
c1 c2
deuteron
(6q)
15% 85%
triton
(9q)
9% 91%
4He
(12q)
2% 98%
Face – Centered – Cubic Lattice
n - value j - value m - value
s - value i - value - clusters
40Ca
n=(x + y +z – 3)/2 =(r sincos + r sin sin + r cos - 3) / 2
j = l + s = (x + y – 1) / 2 = (r sincos + r sin sin
m = x / 2 = (r sincos
Conjecture: Current quark states in bound nucleons are suppressed
...321332123211* gqqqcqqqqqcqqqcN
)(/)()(/)( 22 xdxdxFxF DADA
Bound Nucleon, N*
suppressed
),(/)()(/)(**
22 xdxdxFxF NNNN
Bound Nucleon, N*
sxxM 212
Heisenberg inequality:
2. Calculation of cross sectons
Inelastic Overlap Function:
b2),(112)( dbsGs intot
Parameters of SCQM
Free Nucleon
Amplitude of VQs oscillations: xmax= 0.64 fm
Bound (distorted) nucleon:
Reduced amplitude of VQs oscillations
Displacement of the origin of VQs oscillations to the nucleon perephery
Adjusted values:xmin= 0.32 fm, xmax= 0.64 fm
Comparison with experiments
2. Color Transparency “Breaking” in quasielastic scattering
p+A pp+X at θcm=900
Observable:
T = σA/(Z σN)
Conclusions
• EMC effect could be explained by valence quark momentum distribution reaggangements.
• Quasielastic proton – proton and lepton – proton scattering at high Q2 are not adequate reactions to observe Color Transparency
• Favorable reaction for CT observation is the Vector meson production in lepton – nucleus scattering at Q2
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