Single Spin Asymmetry in Correlated Quark Model G. Musulmanbekov JINR, Dubna e-mail:[email protected]
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Transcript of Single Spin Asymmetry in Correlated Quark Model G. Musulmanbekov JINR, Dubna e-mail:[email protected]
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Single Spin Asymmetry in Single Spin Asymmetry in Correlated Quark Model Correlated Quark Model
G. Musulmanbekov JINR, Dubna
e-mail:[email protected]
Contents
•Introduction•Strongly Correlated Quark Model (SCQM)•Single Spin Asymmetry in hadronic reactions
–Collins Effect–Sivers Effect
•Conclusions
SPIN2006
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IntroductionWhere does the Proton Spin come from?
Spin "Crisis“:DIS experiments: ΔΣ=Δu+Δd+Δs 1≪
SU(6) 1
Sum rule for the nucleon spin:1/2 =(1/2)ΔΣ(Q²)+Δg(Q²)+L(Q2)q+g
gqqLs
SCQM: Total nucleon spin comes from circulating around each of three valence quarks gluon and quark-antiquark condensate.
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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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Constituent Quarks – Solitons
0),(sin),( txtx
2
21
1/cosh
1/sinhtan4),(
uxu
uuttx ass
x
txtx ass
ass
),(),(
Sine- Gordon (SG) equation
Breather – oscillating soliton-antisoliton pair, the periodic solution of SG:
The density profile of the breather:
)(tanh2)( 2 mxMxU
Breather solution of SG is Lorenz – invariant.
Effective soliton – antisoliton potential
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Breather (soliton –antisoliton) solution of SG equation
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Hamiltonian of the Quark – AntiQuark System
)2()1()1( 2/122/12 xV
mmH qq
q
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
For simplicity
XAXA
rT
exp)(det
)(2/3
2/1
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I
II
U(x) > I – constituent quarksU(x) < II – current(relativistic) quarks
Quark Potential inside Light Hadons
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Quark Potential inside Light Quark Potential inside Light HadronsHadrons
Uq = 0.36tanh2(m0x) Uq x
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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
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The Proton
3
1
)()(i
iiColor cxax
One–Quark color wave function
ic
ijji cc
Where are orthonormal states with i = R,G,B
Nucleon color wave function
kjijk
iijkColor cccex 6
1)(
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Considering each quark separately
SU(3)Color U(1)
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 chiral symmetry breaking (restoration)
);()()( xxAxA
here
)0,0,0,( A
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Spin in SCQM
a
rd )((...) 3chchgQ BErLs
1. Now we accept that
Sch = c²Ech× Bch .
3. Total angular momentum created by this Pointing’s vector
is associated with the total spin angular momentum of the constituent quark.
A},{ A
and intersecting Ech and Bch create around VQ
circulating flow of energy, color analog of the Pointing’s vector
Classical analog of electron spin – F.Belinfante 1939; R. Feynman 1964; H.Ohanian 1986; J. Higbie 1988.
2. Circulating flow of energy carrying along with it hadronic matter is associated with hadronic matter current.
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Analogue from hydrodynamicsHelmholtz laws for velocity field
((∂ξ)/(∂t))+ ×(∇ ξ×v)=0,
ξ= ×∇ v,∇⋅v=0,
const.s rv d
σξ
r/1v
5. Quark spins are perpendicular to the plane of oscillation.
6. Quark spin module is conserved during oscillation:
4. Quark oscillations lead to changing of the values of Ech and Bch : at the origin of oscillations they are concentrated in a small space region around VQ. As a result hadronic current is concentrated on a narrow shell with small radius.
lead to
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Parameters of SCQM
in pp_
2.Maximal Displacement of Quarks: xmax=0.64 fm,
3.Constituent quark sizes (parameters of gaussian distribution): x,y=0.24 fm, z =0.12 fm
,36023
1)( max)( MeV
mmxM N
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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Structure Function of Valence Quarks in Proton
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Summary on SCQM
• Quarks and gluons inside hadrons are strongly correlated;
• Constituent quarks are identical to vortical solitons.
• Hadronic matter distribution inside hadrons is fluctuating quantity resulting in interplay between constituent and current quarks.
• Hadronic matter distribution inside the nucleon is deformed;
it is oblate in relation to the spin direction.
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Single Spin Asymmetry in proton – proton collisions
• In the factorized parton model
'' // qqqqp Df
)(),,(
),,(cos
)(),(
3/
2
//2
3
hkzphzPDhddz
d
Pddd
yfdykxfkddxpd
d
qqh
q
prpq
Xpp
0
pq
pqpq
pq
pqq
f
ff
f
fP
/
//
/
/
where
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Determination of PDFs
'' // qqqqp Df
)(),,(
),,(cos
)(),(
3/
2
//2
3
hkzphzPDhddz
d
Pddd
yfdykxfkddxpd
d
qqh
q
prpq
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Geometrical view of possible quark
configurations inside colliding protons at the instant of collision
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Geometrical view of possible quark
configurations inside colliding protons at the instant of collision
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Determination of cross sections
'' // qqqqp Df
)(),,(
),,(cos
),(),(
3/
2
/2
/2
3
hkzphzPDhddz
d
Pddd
ryfrddykxfkddxpd
d
qqh
q
prpq
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Calculation of cross section with the use of Inelastic Overlap Fuction
23
21
)()(4
mdMM
sxxM
jijjii pqppqq
X
rrrr '
+ energy – momentum conservation
Monte-Carlo simulation of inelastic eventsusing modified Heisenberg picture:
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)()()()1(4
1
)(),(
2
/2
,
2
33
kkpxzxkfPP
zDkxfkdkddzdx
pd
d
pd
d
Fqqq
qqduq
qp leading
Calculationsof Collins Effect
Pure Collins Effect: leading quark is a spectator
)exp(1
)(
k
kfq
Chqh zCczD )1)(1()(/
22
)(2
k
kzkPq
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Collins Effect in SSA
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Inclusion of “Sivers” Effect
'' // qqqqp Df
)(),,(
),,(cos
),(),(
3/
2
/2
/2
3
hkzphzPDhddz
d
Pddd
ryfrddykxfkddxpd
d
qqh
q
prpq
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“Sivers” Effect in SSA
Single Spin Asymmetries
Spin-up polarized quark - vortex
Chou & Yang 1976Hadronic matter current distributions insidepolarized hadrons and nuclei
)1(
),,(
zineff
zyxeff
vPP
bbbPOpaqueness
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Collins & “Sivers” Effect in SSA
Single Spin Asymmetries
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Experiments with Polarized Protons
Anti-parallel Spins
Double Spin Asymmetries
Parallel Spins
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Experiments with Polarized Protons