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On Nuclear Modification of Bound On Nuclear Modification of Bound NucleonsNucleons
G. Musulmanbekov JINR, Dubna, Russiae-mail:[email protected]
Contents•Introduction•Strongly Correlated Quark Model•Quark Arrangement inside Nuclei•EMC – effect •Color Transparency•Conclusions
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Introduction
1. EMC – effect F₂A(x)/F₂D(x)
Regions of the effect * Shadowing * Antishadowing * EMC – effect * Fermi motion
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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
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Introduction
2. Color Transparency Quasielastic scattering
e+A e`p+X
Observable:
T = σA/ σPWIA
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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
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Introduction
QCDQCD
Hadrons
Nuclei
Constituent Quarks Current Quarks
Chiral Symmetry BreakingChiral Symmetry Breaking
Quark ModelsQuark Models
Strongly Correlated Quark ModelG.Musulmanbekov, 1995
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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
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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)
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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
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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.
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Conjecture:
),(2),()(2 xMrxxdydzdxU Q
where is the dynamical mass of the constituent quark and
)()(
xMQQ
),,(),,(
),(),(
zyxxzyxxC
rxCrx
QQ
QQ
For simplicity
XAXA
rT
exp)(det
)(2/3
2/1
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Quark Potential
I
II
U(x) > I – constituent quarksU(x) < II – current(relativistic) quarks
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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
qq
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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
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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
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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
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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.
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Breather (soliton –antisoliton) solution of SG equation
Soliton – antisoliton potential
)(tanh2)( 2 mxMxV
Here M is the soliton mass
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Quark PotentialQuark Potential
Uq xUq = 0.36tanh2(m0x)
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Structure Function of Valence Quark in Proton
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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.
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Quark Arrangement inside Nuclei
QCDQCD
Hadrons Nuclei
Nuclear Models
Shell Models
Liquid Drop Model
Crystalline Models of Nuclei
Cluster Models
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Two Nucleon System in SCQM
Quark Potential Inside Nuclei
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Deutron
Spin Flip l = 2
qcNcNcD 622 3*
21
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Three Nucleon Systems in SCQM
3H
3He
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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
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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
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Hidden Color in Nuclei
Deuteron|6q> = c1|SS> + c2|CC>
c1 c2
deuteron
(6q)
15% 85%
triton
(9q)
9% 91%
4He
(12q)
2% 98%
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The closed shell n = 1, 16O
6
1
3He
ndd
u
pd
u
up
u d
u
3He
p
d
uu
pu
u
d
u
nd d
n
d
dup
u d
u
n
d
du
3H
54
32
d un
d
up
d
u
n
d
du
3H
1
32
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The closed shell n = 1, 16O
3
6
5
2
4
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Face – Centered – Cubic Lattice Model (FCC) (N. Cook, 1987)
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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
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Conjecture: Current quark states in bound nucleons are suppressed
...321332123211* gqqqcqqqqqcqqqcN
)(/)()(/)( 22 xdxdxFxF DADA
Bound Nucleon, N*
suppressed
),(/)()(/)(**
22 xdxdxFxF NNNN
Bound Nucleon, N*
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Method: Monte–Carlo Simulation
1. The Model of DIS: SCQM + VDM
Xpqqp
22 1
Qr qq
p
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sxxM 212
Heisenberg inequality:
2. Calculation of cross sectons
Inelastic Overlap Function:
b2),(112)( dbsGs intot
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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
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Comparison with experiments
1. EMC – effect
)(/)( 22 xFxF DA
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Comparison with experiments
2. Color Transparency “Breaking” in quasielastic scattering
p+A pp+X at θcm=900
Observable:
T = σA/(Z σN)
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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