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The Rule Of Orbital Angular Momentum And Polarized Valon Model

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perturbative dressing of the valence quark in QCD. ... polarized Valence quark almost remain constant with increasing Q. Gluon increase rapidly... – PowerPoint PPT presentation

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Title: The Rule Of Orbital Angular Momentum And Polarized Valon Model


1
The Rule Of Orbital Angular Momentum And
Polarized Valon Model
  • Fatemeh Taghavi Shahri
  • IUST( Iran University Of Science Technology)
  • Firooz Arash
  • Tafresh University

MENU 2007 Conference, September
10-14,Julich,Germany
2
Outline
  • Study of Nucleon Structure function in Valon
    model.
  • Spin Crisis and Polarized valon model.
  • Calculation of PPDFs and Polarized Proton
    structure function in valon model.
  • Behavior of first moment of PPDFs in valon and
    proton and extracting the orbital angular
    momentum rule.
  • Conclusion

3
These results based on our new paper polarized
structure of nucleon in the valon
representation Firooz Arash and Fatemeh Taghavi
Shahri JHEP07(2007)071
4
Study of Nucleon Structure function in Valon
model
Proton
  • Valon valence quark and
  • its associated sea quarks and gluons.
  • The structure of a valon arises from the
  • perturbative dressing of the valence quark in
    QCD.
  • The valons carry all the momentum of nucleon and
    the
  • quantum number of valon is the quantum number
  • of its valence quark.
  • They play a role in scattering problems as
  • the constituent quarks do in bound-state
    problems.
  • At sufficiently low value of Q2 the internal
    structure
  • of a valon cannot be resolved.

U
uv
U
q-qbar gluon
q-qbar gluon
D
uv
q-qbar gluon
dv
The existence of the valon can be inferred from
the measurement of the Natchmann moments of the
proton structure functions at Jefferson
laboratory. They point to the existence of a new
scaling that can be interpreted as a constituent
form factor consistent with the elastic nucleon
data. They suggest that there exist extended
objects inside the proton and the size of these
constituents are 0.2-0.3 fm.(hep-ph/0301206v2)
5
The structure function of a hadron is convolution
of two distributions
  • valon distributions in proton.
  • Structure function of a valon.
  • In an unpolarized situation we can write

Structure function of a v valon. It depends on Q2
and the nature of the probe.
Proton structure function
Summation is over the three valons
Describes the valon distribution in a proton. It
independs on Q2.
6
If you know PDF in a valon, you can get PDF in
proton as
Proton
U
uv
U
q-qbar gluon
q-qbar gluon
D
uv
q-qbar gluon
dv
PDF in a valon. It comes from solving GLAP.eq in
a valon
PDF in proton
Valon distribution in proton
Un-polarized structure of nucleon in the
framework of valon model had been studied in
Firooz Arash Ali.N.Khorramian-Physical Review
C 67,045201 (2003)
7
Spin Crisis and Polarized valon model
How can we construct the spin of proton?
New experiments try to find out each component of
the spin precisely
8
N
N
Where
Probability to find parton with spin
aligned/anti-aligned to proton spin
The first moment is a measure for the quark
contribution to the proton spin.
Analogy with un polarized case
9
Polarized Nucleon Structure in valon framework
PPDF in valon model
PPDF in proton
Valon helicity distribution in proton
Summation is over the three valons
PPDF in a valon. It comes from solving the DGLAP
eq.
Polarized hadron structure in valon model
Polarized structure function of a v valon. It
depends on Q2 and the nature of the probe.
Polarized structure function of proton
Valon helicity distribution in proton
10
Mellin transformation
Spin physics and polarized structure
function/Reya Lampe(hep-ph/9810270)
DGlAP eq. in mellin space at NLO approximation
gives ppdf in a valon
???
gives Valence quark distribution
gives Valence sea quark distribution
11
Initial input densities to solve the DGLAP
equations in valon framework
At the initial scale of Q02 proton behaves as a
bound state of three valence quarks. After
that, other partonic contributions can be
resolved in the proton. So the initial input
densities that have a good agreement with the
valon concept are
Our choice is in the range of GRSV group choice
Q020.4 Gev2
12
Valon helicity distribution
Un-polarized valon distribution
We fitted with GRSV distribution
Now we can calculate PPDFs
13
The HERMES Collaboration (2004)
hep-ex/0307064 hep-ex/0407032
In this work ,we neglect from sea quark
polarization .We work with valon concept and
DGLAP eq. as a result of perturbative QCD. In
such processes with massless quark, helicity is
conserved and therefore the hard gluon can not
produce sea quark polarization perturbatively.
This result is consistent with the HERMES data.
14
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15
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16
First moment
Our results
Experimental results(E-155 Collaboration)
It seems the results have good agreement with
experimental results.
17
Behavior of first moment of PPDFs in valon and
proton and study the orbital angular momentum
polarized Valence quark almost remain constant
with increasing Q
Gluon increase rapidly
Sea quark polarization consistent with zero
The first moment of PPDFs in the valon
18
The large gluon polarization in valon requires a
sizable negative orbital angular momentum and
the rule of this OAM is to cancel out the gluon
polarization completely.
The spin sum rule
19
But This cancellation in proton is partial
About 60 of the net spin of proton comes from
gluon and this is comparable With 50 momentum
contribution of gluon to the total momentum of
Proton
20
Future experiments on gluon polarization have
important rule to solve the spin crisis...
21
Conclusions until now
We calculate PPDF and polarized proton structure
functions in valon framework with using useful
initial input densities to solve the DGLAP
equations.
We calculate spin contribution of each type of
parton to the spin of proton.
Then calculate OAM versus Q2 from sum rule.
We find out that gluon have large contribution to
the spin of proton.
Our results have good agreement with experimental
data.
22
Many thanks for your attention
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